Subgroups — C₁₃×#61076 #15747415

Order 3328.

2672 conjugacy classes of subgroups.

The subgroup lattice has 1382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3486	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₁₃×Q₁₆	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3282	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3277	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3276	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3270	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3270	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3269	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3266	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3056	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3046	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3011	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₁₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
27	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#578	—	2	8	no	—
29	C₂×C₁₃×#137	—	2	8	no	—
30	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#137	C₂²	1	2	yes	—
33	C₂×C₁₃×#137	C₂²	1	2	yes	—
34	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
37	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
38	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
42	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
43	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
44	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
47	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
48	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
49	D₄×Q₈×C₁₃	—	2	1	no	—
50	D₄×Q₈×C₁₃	—	2	1	no	—
51	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
52	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
53	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
54	C₁₃×#548	—	2	1	no	—
55	C₁₃×#548	—	2	1	no	—
56	C₁₃×#548	C₂²	1	2	yes	—
57	C₁₃×#548	C₂²	1	2	yes	—
58	C₁₃×#548	C₂²	1	2	yes	complemented
59	C₁₃×#547	—	2	2	no	—
60	C₁₃×#547	C₂²	1	2	yes	—
61	C₁₃×#546	—	2	2	no	—
62	C₁₃×#546	C₂²	1	2	yes	—
63	C₁₃×#537	—	2	1	no	—
64	C₁₃×#537	C₂²	1	1	yes	characteristic
65	C₁₃×#536	—	2	2	no	—
66	C₁₃×#536	—	2	1	no	—
67	C₁₃×#536	C₂²	1	1	yes	characteristic
68	C₁₃×#536	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#536	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#525	—	2	1	no	—
71	C₁₃×#525	—	2	2	no	—
72	C₁₃×#525	C₂²	1	1	yes	characteristic
73	C₁₃×#525	C₂²	1	1	yes	characteristic
74	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
75	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
76	C₁₃×#520	C₂²	1	1	yes	characteristic
77	C₁₃×#519	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#497	C₂²	1	2	yes	complemented
79	C₁₃×#497	C₂²	1	2	yes	complemented
80	C₁₃×#495	C₂²	1	2	yes	complemented
81	C₁₃×#494	C₂²	1	2	yes	complemented
82	C₁₃×#470	C₂²	1	2	yes	complemented
83	C₁₃×#470	C₂²	1	2	yes	complemented
84	C₁₃×#468	C₂²	1	2	yes	complemented
85	C₁₃×#468	C₂²	1	2	yes	complemented
86	C₁₃×#467	C₂²	1	2	yes	—
87	C₁₃×#467	C₂²	1	2	yes	complemented
88	C₁₃×#465	C₂²	1	2	yes	—
89	C₁₃×#465	C₂²	1	2	yes	complemented
90	C₁₃×#464	C₂²	1	2	yes	complemented
91	C₁₃×#464	C₂²	1	2	yes	complemented
92	C₁₃×#464	C₂²	1	2	yes	complemented
93	C₁₃×#463	C₂²	1	2	yes	complemented
94	C₁₃×#462	C₂²	1	2	yes	complemented
95	C₁₃×#462	C₂²	1	2	yes	complemented
96	C₁₃×#462	C₂²	1	2	yes	complemented
97	C₁₃×#461	C₂²	1	2	yes	complemented
98	C₁₃×#452	C₂²	1	1	yes	characteristic
99	C₁₃×#452	C₂²	1	1	yes	characteristic
100	C₁₃×#452	C₂²	1	2	yes	complemented
101	C₁₃×#452	C₂²	1	2	yes	complemented
102	C₁₃×#452	C₂²	1	2	yes	complemented
103	C₁₃×#451	C₂²	1	2	yes	—
104	C₁₃×#451	C₂²	1	2	yes	—
105	C₁₃×#451	C₂²	1	1	yes	characteristic
106	C₁₃×#451	C₂²	1	2	yes	complemented
107	C₁₃×#451	C₂²	1	2	yes	complemented
108	C₁₃×#451	C₂²	1	2	yes	complemented
109	C₁₃×#451	C₂²	1	2	yes	complemented
110	C₁₃×#451	C₂²	1	2	yes	complemented
111	C₁₃×#450	C₂²	1	1	yes	characteristic
112	C₁₃×#449	C₂²	1	1	yes	characteristic
113	C₁₃×#449	C₂²	1	1	yes	characteristic
114	C₁₃×#449	C₂²	1	2	yes	complemented
115	C₁₃×#448	C₂²	1	1	yes	characteristic
116	C₁₃×#448	C₂²	1	2	yes	complemented
117	C₁₃×#447	C₂²	1	1	yes	characteristic
118	C₁₃×#441	C₂²	1	2	yes	complemented
119	C₁₃×#440	C₂²	1	2	yes	complemented
120	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
121	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
122	C₁₃×#436	C₂²	1	2	yes	complemented
123	C₁₃×#435	C₂²	1	2	yes	—
124	C₁₃×#435	C₂²	1	2	yes	complemented
125	C₈×D₄×C₁₃	C₂²	1	2	yes	—
126	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
127	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
128	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
129	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
130	C₁₃×#416	C₂²	1	1	yes	characteristic
131	C₁₃×#416	C₂²	1	1	yes	characteristic
132	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
134	C₁₃×#408	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
136	C₁₃×#405	C₂²	1	1	yes	characteristic, complemented
137	C₁₃×2₋¹⁺⁴	—	2	4	no	—
138	C₁₃×2₋¹⁺⁴	—	2	4	no	—
139	C₁₃×2₋¹⁺⁴	—	4	2	no	—
140	C₁₃×2₋¹⁺⁴	—	4	2	no	—
141	C₂×C₁₃×#41	—	2	2	no	—
142	C₂×C₁₃×#41	—	2	1	no	—
143	C₂×C₁₃×#41	—	2	2	no	—
144	C₂×C₁₃×#41	—	2	1	no	—
145	C₂×C₁₃×#41	—	2	1	no	—
146	C₂×C₁₃×#41	—	2	1	no	—
147	C₂×C₁₃×#41	—	2	4	no	—
148	C₂×C₁₃×#41	—	4	2	no	—
149	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×#41	C₂³	1	2	yes	—
154	C₂×C₁₃×#41	C₂³	1	2	yes	—
155	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
157	C₂²×Q₈×C₁₃	—	2	1	no	—
158	C₂²×Q₈×C₁₃	—	2	1	no	—
159	C₂²×Q₈×C₁₃	—	2	1	no	—
160	C₂²×Q₈×C₁₃	—	2	1	no	—
161	C₂²×Q₈×C₁₃	—	2	1	no	—
162	C₂²×Q₈×C₁₃	—	2	4	no	—
163	C₂²×Q₈×C₁₃	—	4	2	no	—
164	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
165	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
166	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
167	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
168	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
170	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
171	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
172	C₂²×D₄×C₁₃	—	2	1	no	—
173	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
174	C₂³×C₄×C₁₃	—	2	1	no	—
175	C₂³×C₄×C₁₃	—	2	1	no	—
176	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
177	C₁₃×#137	—	2	4	no	—
178	C₁₃×#137	—	2	4	no	—
179	C₁₃×#137	—	2	8	no	—
180	C₁₃×#137	—	2	8	no	—
181	C₁₃×#137	—	2	8	no	—
182	C₁₃×#137	—	2	8	no	—
183	C₁₃×#137	—	2	4	no	—
184	C₁₃×#137	—	2	4	no	—
185	C₁₃×#137	D₄	1	8	yes	complemented
186	C₁₃×#135	—	2	4	no	—
187	C₁₃×#135	—	2	8	no	—
188	C₁₃×#135	—	4	2	no	—
189	C₂×C₁₃×Q₁₆	—	2	4	no	—
190	C₂×C₁₃×Q₁₆	—	2	8	no	—
191	C₂×C₁₃×Q₁₆	—	2	8	no	—
192	C₂×C₁₃×Q₁₆	—	4	2	no	—
193	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
194	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
195	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
196	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
197	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
198	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
199	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
200	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
201	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
202	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
203	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
204	C₂×C₁₃×SD₁₆	—	2	8	no	—
205	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
206	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
207	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
208	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
209	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
210	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
211	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
212	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
213	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
214	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
215	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
216	C₁₃×#131	—	2	4	no	—
217	C₂×C₁₃×M₁₆	—	2	4	no	—
218	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
219	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
220	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
221	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
222	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
223	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
224	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
225	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
226	C₁₃×C₄⋊Q₈	—	2	1	no	—
227	C₁₃×C₄⋊Q₈	—	2	2	no	—
228	C₁₃×C₄⋊Q₈	—	2	2	no	—
229	C₁₃×C₄⋊Q₈	—	2	2	no	—
230	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
231	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
232	C₁₃×#124	—	2	1	no	—
233	C₁₃×#124	—	2	2	no	—
234	C₁₃×#124	—	2	2	no	—
235	C₁₃×#124	—	2	2	no	—
236	C₁₃×#124	C₂³	1	2	yes	—
237	C₁₃×#124	C₂³	1	2	yes	—
238	C₁₃×#123	—	2	2	no	—
239	C₁₃×#123	—	2	1	no	—
240	C₁₃×#123	—	2	2	no	—
241	C₁₃×#123	—	2	2	no	—
242	C₁₃×#123	—	2	2	no	—
243	C₁₃×#123	—	2	2	no	—
244	C₁₃×#123	—	2	2	no	—
245	C₁₃×#123	D₄	1	2	yes	—
246	C₁₃×C₂²⋊Q₈	—	2	1	no	—
247	C₁₃×C₂²⋊Q₈	—	2	1	no	—
248	C₁₃×C₂²⋊Q₈	—	2	1	no	—
249	C₁₃×C₂²⋊Q₈	—	2	1	no	—
250	C₁₃×C₂²⋊Q₈	—	2	2	no	—
251	C₁₃×C₂²⋊Q₈	—	2	1	no	—
252	C₁₃×C₂²⋊Q₈	—	2	2	no	—
253	C₁₃×C₂²⋊Q₈	—	2	2	no	—
254	C₁₃×C₂²⋊Q₈	—	2	1	no	—
255	C₁₃×C₂²⋊Q₈	—	2	1	no	—
256	C₁₃×C₂²⋊Q₈	—	2	2	no	—
257	C₁₃×C₂²⋊Q₈	—	2	2	no	—
258	C₁₃×C₂²⋊Q₈	—	2	2	no	—
259	C₁₃×C₂²⋊Q₈	—	2	2	no	—
260	C₁₃×C₂²⋊Q₈	—	2	2	no	—
261	C₁₃×C₂²⋊Q₈	—	2	2	no	—
262	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
263	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
264	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
265	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
266	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
267	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
268	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
269	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
270	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
271	C₁₃×#121	—	2	1	no	—
272	C₁₃×#121	—	2	2	no	—
273	C₁₃×#121	—	2	2	no	—
274	C₁₃×#121	—	2	2	no	—
275	C₁₃×#121	—	2	2	no	—
276	C₁₃×#121	—	2	2	no	—
277	C₁₃×#121	—	2	2	no	—
278	C₁₃×#121	D₄	1	1	yes	characteristic
279	C₁₃×#121	D₄	1	1	yes	characteristic
280	C₁₃×#121	C₂³	1	1	yes	characteristic
281	C₁₃×#121	C₂³	1	2	yes	—
282	C₁₃×#121	C₂³	1	1	yes	characteristic
283	C₁₃×#120	—	2	1	no	—
284	C₁₃×#120	—	2	2	no	—
285	C₁₃×#120	D₄	1	2	yes	—
286	C₄×Q₈×C₁₃	—	2	1	no	—
287	C₄×Q₈×C₁₃	—	2	1	no	—
288	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
289	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
290	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
291	C₄×D₄×C₁₃	—	2	2	no	—
292	C₄×D₄×C₁₃	—	2	2	no	—
293	C₄×D₄×C₁₃	—	2	2	no	—
294	C₄×D₄×C₁₃	—	2	1	no	—
295	C₄×D₄×C₁₃	—	2	1	no	—
296	C₄×D₄×C₁₃	—	2	2	no	—
297	C₄×D₄×C₁₃	—	2	2	no	—
298	C₄×D₄×C₁₃	—	2	2	no	—
299	C₄×D₄×C₁₃	—	2	2	no	—
300	C₄×D₄×C₁₃	C₂³	1	2	yes	—
301	C₄×D₄×C₁₃	C₂³	1	2	yes	—
302	C₄×D₄×C₁₃	C₂³	1	2	yes	—
303	C₁₃×#117	—	2	1	no	—
304	C₁₃×#117	—	2	2	no	—
305	C₁₃×#117	C₂³	1	1	yes	characteristic
306	C₁₃×#117	C₂³	1	1	yes	characteristic
307	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
308	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
309	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
310	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
311	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
313	C₁₃×#107	C₂³	1	2	yes	—
314	C₁₃×#106	C₂³	1	2	yes	—
315	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
316	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
317	C₁₃×#103	C₂³	1	2	yes	—
318	C₁₃×#103	C₂³	1	2	yes	—
319	C₁₃×#103	C₂³	1	2	yes	—
320	C₁₃×#103	C₂³	1	2	yes	—
321	C₁₃×#103	C₂³	1	1	yes	characteristic
322	C₁₃×#103	C₂³	1	1	yes	characteristic
323	C₁₃×#103	C₂³	1	1	yes	characteristic
324	C₁₃×#103	C₂³	1	1	yes	characteristic
325	C₁₃×#103	C₂³	1	2	yes	—
326	C₁₃×#103	C₂³	1	2	yes	—
327	C₁₃×#103	C₂³	1	2	yes	—
328	C₁₃×#102	C₂³	1	1	yes	characteristic
329	C₁₃×#102	C₂³	1	1	yes	characteristic
330	C₁₃×#102	C₂³	1	1	yes	characteristic
331	C₁₃×#102	C₂³	1	1	yes	characteristic
332	C₁₃×#102	C₂³	1	2	yes	—
333	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
334	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
335	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
336	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
337	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
339	C₁₃×#97	C₂³	1	2	yes	—
340	C₄×C₈×C₁₃	C₂³	1	2	yes	—
341	#61076	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
342	C₂⁴×C₁₃	—	2	1	no	—
343	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
344	C₁₃×#41	—	2	2	no	—
345	C₁₃×#41	—	2	2	no	—
346	C₁₃×#41	—	2	2	no	—
347	C₁₃×#41	—	2	4	no	—
348	C₁₃×#41	—	2	2	no	—
349	C₁₃×#41	—	2	4	no	—
350	C₁₃×#41	—	2	2	no	—
351	C₁₃×#41	—	2	2	no	—
352	C₁₃×#41	—	2	2	no	—
353	C₁₃×#41	—	2	2	no	—
354	C₁₃×#41	—	2	2	no	—
355	C₁₃×#41	—	4	4	no	—
356	C₁₃×#41	—	4	1	no	—
357	C₁₃×#41	—	4	1	no	—
358	C₁₃×#41	—	4	2	no	—
359	C₁₃×#41	—	4	2	no	—
360	C₁₃×#41	—	4	4	no	—
361	C₁₃×#41	—	4	8	no	—
362	C₁₃×#41	—	4	4	no	—
363	C₁₃×#41	—	4	8	no	—
364	C₁₃×#41	—	4	4	no	—
365	C₁₃×#41	C₂×D₄	1	4	yes	—
366	C₂×Q₈×C₁₃	—	2	1	no	—
367	C₂×Q₈×C₁₃	—	2	1	no	—
368	C₂×Q₈×C₁₃	—	2	2	no	—
369	C₂×Q₈×C₁₃	—	2	2	no	—
370	C₂×Q₈×C₁₃	—	2	1	no	—
371	C₂×Q₈×C₁₃	—	2	2	no	—
372	C₂×Q₈×C₁₃	—	2	2	no	—
373	C₂×Q₈×C₁₃	—	2	1	no	—
374	C₂×Q₈×C₁₃	—	2	2	no	—
375	C₂×Q₈×C₁₃	—	2	4	no	—
376	C₂×Q₈×C₁₃	—	2	2	no	—
377	C₂×Q₈×C₁₃	—	2	4	no	—
378	C₂×Q₈×C₁₃	—	2	4	no	—
379	C₂×Q₈×C₁₃	—	2	4	no	—
380	C₂×Q₈×C₁₃	—	2	2	no	—
381	C₂×Q₈×C₁₃	—	2	2	no	—
382	C₂×Q₈×C₁₃	—	2	2	no	—
383	C₂×Q₈×C₁₃	—	2	2	no	—
384	C₂×Q₈×C₁₃	—	4	4	no	—
385	C₂×Q₈×C₁₃	—	4	2	no	—
386	C₂×Q₈×C₁₃	—	4	2	no	—
387	C₂×Q₈×C₁₃	—	4	1	no	—
388	C₂×Q₈×C₁₃	—	4	2	no	—
389	C₂×Q₈×C₁₃	—	4	2	no	—
390	C₂×Q₈×C₁₃	—	4	4	no	—
391	C₂×Q₈×C₁₃	—	4	4	no	—
392	C₂×Q₈×C₁₃	—	4	4	no	—
393	C₂×Q₈×C₁₃	—	4	4	no	—
394	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
395	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
396	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
397	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
398	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
399	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
400	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
401	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
402	C₂×D₄×C₁₃	—	2	1	no	—
403	C₂×D₄×C₁₃	—	2	2	no	—
404	C₂×D₄×C₁₃	—	2	1	no	—
405	C₂×D₄×C₁₃	—	2	1	no	—
406	C₂×D₄×C₁₃	—	2	2	no	—
407	C₂×D₄×C₁₃	—	2	1	no	—
408	C₂×D₄×C₁₃	—	2	1	no	—
409	C₂×D₄×C₁₃	—	2	1	no	—
410	C₂×D₄×C₁₃	—	2	1	no	—
411	C₂×D₄×C₁₃	—	2	2	no	—
412	C₂×D₄×C₁₃	—	2	2	no	—
413	C₂×D₄×C₁₃	—	2	1	no	—
414	C₂×D₄×C₁₃	—	4	1	no	—
415	C₂×D₄×C₁₃	—	4	4	no	—
416	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
417	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
418	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
419	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
420	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
421	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
422	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
423	C₂²×C₄×C₁₃	—	2	1	no	—
424	C₂²×C₄×C₁₃	—	2	1	no	—
425	C₂²×C₄×C₁₃	—	2	2	no	—
426	C₂²×C₄×C₁₃	—	2	2	no	—
427	C₂²×C₄×C₁₃	—	2	1	no	—
428	C₂²×C₄×C₁₃	—	2	2	no	—
429	C₂²×C₄×C₁₃	—	2	2	no	—
430	C₂²×C₄×C₁₃	—	2	2	no	—
431	C₂²×C₄×C₁₃	—	2	1	no	—
432	C₂²×C₄×C₁₃	—	2	2	no	—
433	C₂²×C₄×C₁₃	—	2	1	no	—
434	C₂²×C₄×C₁₃	—	2	1	no	—
435	C₂²×C₄×C₁₃	—	2	2	no	—
436	C₂²×C₄×C₁₃	—	2	1	no	—
437	C₂²×C₄×C₁₃	—	2	1	no	—
438	C₂²×C₄×C₁₃	—	2	2	no	—
439	C₂²×C₄×C₁₃	—	2	1	no	—
440	C₂²×C₄×C₁₃	—	2	1	no	—
441	C₂²×C₄×C₁₃	—	2	2	no	—
442	C₂²×C₄×C₁₃	—	4	4	no	—
443	C₂²×C₄×C₁₃	—	4	4	no	—
444	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
445	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
446	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
447	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
448	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
449	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
451	C₁₃×Q₁₆	—	2	4	no	—
452	C₁₃×Q₁₆	—	2	2	no	—
453	C₁₃×Q₁₆	—	2	4	no	—
454	C₁₃×Q₁₆	—	2	4	no	—
455	C₁₃×Q₁₆	—	2	4	no	—
456	C₁₃×Q₁₆	—	2	4	no	—
457	C₁₃×Q₁₆	—	2	4	no	—
458	C₁₃×Q₁₆	—	4	2	no	—
459	C₁₃×Q₁₆	—	4	2	no	—
460	C₁₃×Q₁₆	—	4	1	no	—
461	C₁₃×Q₁₆	C₂×D₄	1	8	yes	—
462	C₁₃×SD₁₆	—	2	4	no	—
463	C₁₃×SD₁₆	—	2	2	no	—
464	C₁₃×SD₁₆	—	2	4	no	—
465	C₁₃×SD₁₆	—	2	2	no	—
466	C₁₃×SD₁₆	—	2	4	no	—
467	C₁₃×SD₁₆	—	2	4	no	—
468	C₁₃×SD₁₆	—	4	1	no	—
469	C₁₃×SD₁₆	—	4	1	no	—
470	C₁₃×SD₁₆	C₂×D₄	1	8	yes	—
471	C₁₃×D₈	—	2	2	no	—
472	C₁₃×D₈	—	4	1	no	—
473	C₁₃×M₁₆	—	2	2	no	—
474	C₁₃×M₁₆	—	2	4	no	—
475	C₁₃×M₁₆	—	2	4	no	—
476	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
477	C₂×C₈×C₁₃	—	2	2	no	—
478	C₂×C₈×C₁₃	—	2	2	no	—
479	C₂×C₈×C₁₃	—	2	4	no	—
480	C₂×C₈×C₁₃	—	2	4	no	—
481	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
482	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
483	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
484	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
485	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
486	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
487	C₁₃×C₄⋊C₄	—	2	2	no	—
488	C₁₃×C₄⋊C₄	—	2	1	no	—
489	C₁₃×C₄⋊C₄	—	2	2	no	—
490	C₁₃×C₄⋊C₄	—	2	2	no	—
491	C₁₃×C₄⋊C₄	—	2	2	no	—
492	C₁₃×C₄⋊C₄	—	2	2	no	—
493	C₁₃×C₄⋊C₄	—	2	2	no	—
494	C₁₃×C₄⋊C₄	—	2	2	no	—
495	C₁₃×C₄⋊C₄	—	2	2	no	—
496	C₁₃×C₄⋊C₄	—	2	2	no	—
497	C₁₃×C₄⋊C₄	—	2	2	no	—
498	C₁₃×C₄⋊C₄	—	2	2	no	—
499	C₁₃×C₄⋊C₄	—	2	1	no	—
500	C₁₃×C₄⋊C₄	—	2	1	no	—
501	C₁₃×C₄⋊C₄	—	2	2	no	—
502	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
503	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
504	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
505	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
506	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
507	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
508	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
509	C₁₃×C₂²⋊C₄	—	2	2	no	—
510	C₁₃×C₂²⋊C₄	—	2	2	no	—
511	C₁₃×C₂²⋊C₄	—	2	1	no	—
512	C₁₃×C₂²⋊C₄	—	2	1	no	—
513	C₁₃×C₂²⋊C₄	—	2	1	no	—
514	C₁₃×C₂²⋊C₄	—	2	2	no	—
515	C₁₃×C₂²⋊C₄	—	2	2	no	—
516	C₁₃×C₂²⋊C₄	—	2	2	no	—
517	C₁₃×C₂²⋊C₄	—	2	2	no	—
518	C₁₃×C₂²⋊C₄	—	2	2	no	—
519	C₁₃×C₂²⋊C₄	—	2	2	no	—
520	C₁₃×C₂²⋊C₄	—	2	2	no	—
521	C₁₃×C₂²⋊C₄	—	2	2	no	—
522	C₁₃×C₂²⋊C₄	—	2	2	no	—
523	C₁₃×C₂²⋊C₄	—	2	1	no	—
524	C₁₃×C₂²⋊C₄	—	2	1	no	—
525	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
526	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
527	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
528	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
529	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
530	C₄²×C₁₃	—	2	2	no	—
531	C₄²×C₁₃	—	2	2	no	—
532	C₄²×C₁₃	—	2	2	no	—
533	C₄²×C₁₃	—	2	1	no	—
534	C₄²×C₁₃	C₂⁴	1	2	yes	—
535	C₂×#578	C₂×C₁₃	1	1	yes	characteristic, complemented
536	C₂²×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
537	#3489	C₂×C₁₃	1	1	yes	characteristic, complemented
538	#3486	C₂×C₁₃	1	1	yes	characteristic, complemented
539	D₄×Q₁₆	C₂×C₁₃	1	2	yes	complemented
540	#3282	C₂×C₁₃	1	2	yes	complemented
541	#3277	C₂×C₁₃	1	2	yes	complemented
542	#3276	C₂×C₁₃	1	2	yes	complemented
543	#3270	C₂×C₁₃	1	2	yes	complemented
544	#3270	C₂×C₁₃	1	2	yes	complemented
545	#3269	C₂×C₁₃	1	2	yes	complemented
546	#3266	C₂×C₁₃	1	2	yes	complemented
547	#3156	C₂×C₁₃	1	1	yes	characteristic, complemented
548	#3063	C₂×C₁₃	1	1	yes	characteristic, complemented
549	#3056	C₂×C₁₃	1	1	yes	characteristic, complemented
550	#3046	C₂×C₁₃	1	1	yes	characteristic, complemented
551	#3044	C₂×C₁₃	1	1	yes	characteristic, complemented
552	#3013	C₂×C₁₃	1	1	yes	characteristic, complemented
553	#3011	C₂×C₁₃	1	1	yes	characteristic, complemented
554	#3002	C₂×C₁₃	1	1	yes	characteristic, complemented
555	C₂×#451	C₂×C₁₃	1	1	yes	characteristic, complemented
556	#2947	C₂×C₁₃	1	1	yes	characteristic, complemented
557	#2933	C₂×C₁₃	1	1	yes	characteristic, complemented
558	C₂³×C₁₃	—	2	2	no	—
559	C₂³×C₁₃	—	2	2	no	—
560	C₂³×C₁₃	—	2	1	no	—
561	C₂³×C₁₃	—	2	1	no	—
562	C₂³×C₁₃	—	2	1	no	—
563	C₂³×C₁₃	—	4	1	no	—
564	C₂³×C₁₃	—	4	2	no	—
565	C₂³×C₁₃	—	4	2	no	—
566	C₂³×C₁₃	—	8	1	no	—
567	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
568	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
569	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
570	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
571	Q₈×C₁₃	—	2	4	no	—
572	Q₈×C₁₃	—	2	2	no	—
573	Q₈×C₁₃	—	2	2	no	—
574	Q₈×C₁₃	—	2	1	no	—
575	Q₈×C₁₃	—	2	2	no	—
576	Q₈×C₁₃	—	2	1	no	—
577	Q₈×C₁₃	—	2	2	no	—
578	Q₈×C₁₃	—	2	1	no	—
579	Q₈×C₁₃	—	2	1	no	—
580	Q₈×C₁₃	—	2	1	no	—
581	Q₈×C₁₃	—	2	2	no	—
582	Q₈×C₁₃	—	2	2	no	—
583	Q₈×C₁₃	—	4	4	no	—
584	Q₈×C₁₃	—	4	4	no	—
585	Q₈×C₁₃	—	4	4	no	—
586	Q₈×C₁₃	—	4	4	no	—
587	Q₈×C₁₃	—	4	2	no	—
588	Q₈×C₁₃	—	4	2	no	—
589	Q₈×C₁₃	—	4	2	no	—
590	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
591	Q₈×C₁₃	C₂²×D₄	1	2	yes	—
592	D₄×C₁₃	—	2	4	no	—
593	D₄×C₁₃	—	2	4	no	—
594	D₄×C₁₃	—	2	4	no	—
595	D₄×C₁₃	—	2	2	no	—
596	D₄×C₁₃	—	2	1	no	—
597	D₄×C₁₃	—	2	1	no	—
598	D₄×C₁₃	—	2	1	no	—
599	D₄×C₁₃	—	2	1	no	—
600	D₄×C₁₃	—	2	1	no	—
601	D₄×C₁₃	—	4	2	no	—
602	D₄×C₁₃	—	4	2	no	—
603	D₄×C₁₃	—	4	2	no	—
604	D₄×C₁₃	—	4	4	no	—
605	D₄×C₁₃	—	4	2	no	—
606	D₄×C₁₃	—	4	4	no	—
607	D₄×C₁₃	—	4	2	no	—
608	D₄×C₁₃	—	4	2	no	—
609	D₄×C₁₃	—	4	2	no	—
610	D₄×C₁₃	—	4	2	no	—
611	D₄×C₁₃	—	8	2	no	—
612	D₄×C₁₃	C₂²×D₄	1	2	yes	—
613	C₂×C₄×C₁₃	—	2	2	no	—
614	C₂×C₄×C₁₃	—	2	4	no	—
615	C₂×C₄×C₁₃	—	2	1	no	—
616	C₂×C₄×C₁₃	—	2	2	no	—
617	C₂×C₄×C₁₃	—	2	2	no	—
618	C₂×C₄×C₁₃	—	2	2	no	—
619	C₂×C₄×C₁₃	—	2	4	no	—
620	C₂×C₄×C₁₃	—	2	1	no	—
621	C₂×C₄×C₁₃	—	2	2	no	—
622	C₂×C₄×C₁₃	—	2	1	no	—
623	C₂×C₄×C₁₃	—	2	1	no	—
624	C₂×C₄×C₁₃	—	2	1	no	—
625	C₂×C₄×C₁₃	—	2	2	no	—
626	C₂×C₄×C₁₃	—	2	1	no	—
627	C₂×C₄×C₁₃	—	2	1	no	—
628	C₂×C₄×C₁₃	—	2	2	no	—
629	C₂×C₄×C₁₃	—	2	2	no	—
630	C₂×C₄×C₁₃	—	2	2	no	—
631	C₂×C₄×C₁₃	—	2	1	no	—
632	C₂×C₄×C₁₃	—	2	1	no	—
633	C₂×C₄×C₁₃	—	4	2	no	—
634	C₂×C₄×C₁₃	—	4	4	no	—
635	C₂×C₄×C₁₃	—	4	2	no	—
636	C₂×C₄×C₁₃	—	4	4	no	—
637	C₂×C₄×C₁₃	—	4	4	no	—
638	C₂×C₄×C₁₃	—	4	2	no	—
639	C₂×C₄×C₁₃	—	4	4	no	—
640	C₂×C₄×C₁₃	—	4	4	no	—
641	C₂×C₄×C₁₃	—	4	4	no	—
642	C₂×C₄×C₁₃	—	4	2	no	—
643	C₂×C₄×C₁₃	—	4	2	no	—
644	C₂×C₄×C₁₃	—	4	2	no	—
645	C₂×C₄×C₁₃	—	4	2	no	—
646	C₂×C₄×C₁₃	—	8	2	no	—
647	C₂×C₄×C₁₃	—	8	1	no	—
648	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
649	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
650	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
651	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
652	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
653	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
654	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
655	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
656	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
657	C₈×C₁₃	—	2	1	no	—
658	C₈×C₁₃	—	2	1	no	—
659	C₈×C₁₃	—	2	2	no	—
660	C₈×C₁₃	—	2	1	no	—
661	C₈×C₁₃	—	2	1	no	—
662	C₈×C₁₃	C₂²×D₄	1	4	yes	—
663	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
664	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic, complemented
665	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
666	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
667	#578	—	2	8	no	—
668	C₂×#137	—	2	8	no	—
669	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
670	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
671	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
672	C₂×#137	C₂²×C₁₃	1	2	yes	—
673	C₂×#137	C₂²×C₁₃	1	2	yes	—
674	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
675	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic, complemented
676	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
677	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
678	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
679	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
680	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
681	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
682	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
683	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
684	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
685	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
686	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
687	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
688	D₄×Q₈	—	2	1	no	—
689	D₄×Q₈	—	2	1	no	—
690	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
691	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
692	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
693	#548	—	2	1	no	—
694	#548	—	2	1	no	—
695	#548	C₂²×C₁₃	1	2	yes	—
696	#548	C₂²×C₁₃	1	2	yes	—
697	#548	C₂²×C₁₃	1	2	yes	complemented
698	#547	—	2	2	no	—
699	#547	C₂²×C₁₃	1	2	yes	—
700	#546	—	2	2	no	—
701	#546	C₂²×C₁₃	1	2	yes	—
702	#537	—	2	1	no	—
703	#537	C₂²×C₁₃	1	1	yes	characteristic
704	#536	—	2	2	no	—
705	#536	—	2	1	no	—
706	#536	C₂²×C₁₃	1	1	yes	characteristic
707	#536	C₂²×C₁₃	1	1	yes	characteristic, complemented
708	#536	C₂²×C₁₃	1	1	yes	characteristic, complemented
709	#525	—	2	1	no	—
710	#525	—	2	2	no	—
711	#525	C₂²×C₁₃	1	1	yes	characteristic
712	#525	C₂²×C₁₃	1	1	yes	characteristic
713	C₂×C₂²⋊Q₈	—	2	1	no	—
714	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
715	#520	C₂²×C₁₃	1	1	yes	characteristic
716	#519	C₂²×C₁₃	1	1	yes	characteristic, complemented
717	#497	C₂²×C₁₃	1	2	yes	complemented
718	#497	C₂²×C₁₃	1	2	yes	complemented
719	#495	C₂²×C₁₃	1	2	yes	complemented
720	#494	C₂²×C₁₃	1	2	yes	complemented
721	#470	C₂²×C₁₃	1	2	yes	complemented
722	#470	C₂²×C₁₃	1	2	yes	complemented
723	#468	C₂²×C₁₃	1	2	yes	complemented
724	#468	C₂²×C₁₃	1	2	yes	complemented
725	#467	C₂²×C₁₃	1	2	yes	—
726	#467	C₂²×C₁₃	1	2	yes	complemented
727	#465	C₂²×C₁₃	1	2	yes	—
728	#465	C₂²×C₁₃	1	2	yes	complemented
729	#464	C₂²×C₁₃	1	2	yes	complemented
730	#464	C₂²×C₁₃	1	2	yes	complemented
731	#464	C₂²×C₁₃	1	2	yes	complemented
732	#463	C₂²×C₁₃	1	2	yes	complemented
733	#462	C₂²×C₁₃	1	2	yes	complemented
734	#462	C₂²×C₁₃	1	2	yes	complemented
735	#462	C₂²×C₁₃	1	2	yes	complemented
736	#461	C₂²×C₁₃	1	2	yes	complemented
737	#452	C₂²×C₁₃	1	1	yes	characteristic
738	#452	C₂²×C₁₃	1	1	yes	characteristic
739	#452	C₂²×C₁₃	1	2	yes	complemented
740	#452	C₂²×C₁₃	1	2	yes	complemented
741	#452	C₂²×C₁₃	1	2	yes	complemented
742	#451	C₂²×C₁₃	1	2	yes	—
743	#451	C₂²×C₁₃	1	2	yes	—
744	#451	C₂²×C₁₃	1	1	yes	characteristic
745	#451	C₂²×C₁₃	1	2	yes	complemented
746	#451	C₂²×C₁₃	1	2	yes	complemented
747	#451	C₂²×C₁₃	1	2	yes	complemented
748	#451	C₂²×C₁₃	1	2	yes	complemented
749	#451	C₂²×C₁₃	1	2	yes	complemented
750	#450	C₂²×C₁₃	1	1	yes	characteristic
751	#449	C₂²×C₁₃	1	1	yes	characteristic
752	#449	C₂²×C₁₃	1	1	yes	characteristic
753	#449	C₂²×C₁₃	1	2	yes	complemented
754	#448	C₂²×C₁₃	1	1	yes	characteristic
755	#448	C₂²×C₁₃	1	2	yes	complemented
756	#447	C₂²×C₁₃	1	1	yes	characteristic
757	#441	C₂²×C₁₃	1	2	yes	complemented
758	#440	C₂²×C₁₃	1	2	yes	complemented
759	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
760	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
761	#436	C₂²×C₁₃	1	2	yes	complemented
762	#435	C₂²×C₁₃	1	2	yes	—
763	#435	C₂²×C₁₃	1	2	yes	complemented
764	C₈×D₄	C₂²×C₁₃	1	2	yes	—
765	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
766	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
767	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
768	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
769	#416	C₂²×C₁₃	1	1	yes	characteristic
770	#416	C₂²×C₁₃	1	1	yes	characteristic
771	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
772	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
773	#408	C₂²×C₁₃	1	1	yes	characteristic, complemented
774	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
775	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
776	C₂²×C₁₃	—	2	1	no	—
777	C₂²×C₁₃	—	2	1	no	—
778	C₂²×C₁₃	—	2	1	no	—
779	C₂²×C₁₃	—	2	1	no	—
780	C₂²×C₁₃	—	2	1	no	—
781	C₂²×C₁₃	—	2	2	no	—
782	C₂²×C₁₃	—	2	1	no	—
783	C₂²×C₁₃	—	2	2	no	—
784	C₂²×C₁₃	—	2	2	no	—
785	C₂²×C₁₃	—	2	2	no	—
786	C₂²×C₁₃	—	2	1	no	—
787	C₂²×C₁₃	—	4	4	no	—
788	C₂²×C₁₃	—	4	1	no	—
789	C₂²×C₁₃	—	4	1	no	—
790	C₂²×C₁₃	—	4	1	no	—
791	C₂²×C₁₃	—	4	1	no	—
792	C₂²×C₁₃	—	4	1	no	—
793	C₂²×C₁₃	—	4	1	no	—
794	C₂²×C₁₃	—	4	1	no	—
795	C₂²×C₁₃	—	4	1	no	—
796	C₂²×C₁₃	—	8	4	no	—
797	C₂²×C₁₃	D₄²	1	2	yes	—
798	C₂²×C₁₃	#578	1	2	yes	complemented
799	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
800	C₄×C₁₃	—	2	2	no	—
801	C₄×C₁₃	—	2	1	no	—
802	C₄×C₁₃	—	2	1	no	—
803	C₄×C₁₃	—	2	2	no	—
804	C₄×C₁₃	—	2	4	no	—
805	C₄×C₁₃	—	2	2	no	—
806	C₄×C₁₃	—	2	2	no	—
807	C₄×C₁₃	—	4	2	no	—
808	C₄×C₁₃	—	4	1	no	—
809	C₄×C₁₃	—	4	1	no	—
810	C₄×C₁₃	—	4	2	no	—
811	C₄×C₁₃	—	4	1	no	—
812	C₄×C₁₃	—	4	2	no	—
813	C₄×C₁₃	—	4	1	no	—
814	C₄×C₁₃	D₄²	1	2	yes	—
815	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
816	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
817	2₋¹⁺⁴	—	2	4	no	—
818	2₋¹⁺⁴	—	2	4	no	—
819	2₋¹⁺⁴	—	4	2	no	—
820	2₋¹⁺⁴	—	4	2	no	—
821	C₂×#41	—	2	2	no	—
822	C₂×#41	—	2	1	no	—
823	C₂×#41	—	2	2	no	—
824	C₂×#41	—	2	1	no	—
825	C₂×#41	—	2	1	no	—
826	C₂×#41	—	2	1	no	—
827	C₂×#41	—	2	4	no	—
828	C₂×#41	—	4	2	no	—
829	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
830	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
831	C₂×#41	C₂³×C₁₃	1	2	yes	—
832	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
833	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
834	C₂×#41	C₂³×C₁₃	1	2	yes	—
835	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
836	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
837	C₂²×Q₈	—	2	1	no	—
838	C₂²×Q₈	—	2	1	no	—
839	C₂²×Q₈	—	2	1	no	—
840	C₂²×Q₈	—	2	1	no	—
841	C₂²×Q₈	—	2	1	no	—
842	C₂²×Q₈	—	2	4	no	—
843	C₂²×Q₈	—	4	2	no	—
844	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
845	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
846	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
847	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
848	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
849	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
850	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
851	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
852	C₂²×D₄	—	2	1	no	—
853	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
854	C₂³×C₄	—	2	1	no	—
855	C₂³×C₄	—	2	1	no	—
856	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
857	#137	—	2	4	no	—
858	#137	—	2	4	no	—
859	#137	—	2	8	no	—
860	#137	—	2	8	no	—
861	#137	—	2	8	no	—
862	#137	—	2	8	no	—
863	#137	—	2	4	no	—
864	#137	—	2	4	no	—
865	#137	D₄×C₁₃	1	8	yes	complemented
866	#135	—	2	4	no	—
867	#135	—	2	8	no	—
868	#135	—	4	2	no	—
869	C₂×Q₁₆	—	2	4	no	—
870	C₂×Q₁₆	—	2	8	no	—
871	C₂×Q₁₆	—	2	8	no	—
872	C₂×Q₁₆	—	4	2	no	—
873	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
874	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
875	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
876	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
877	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
878	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
879	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
880	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
881	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
882	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
883	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
884	C₂×SD₁₆	—	2	8	no	—
885	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
886	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
887	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
888	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
889	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
890	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
891	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
892	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
893	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
894	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
895	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
896	#131	—	2	4	no	—
897	C₂×M₁₆	—	2	4	no	—
898	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
899	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
900	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
901	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
902	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
903	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
904	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
905	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
906	C₄⋊Q₈	—	2	1	no	—
907	C₄⋊Q₈	—	2	2	no	—
908	C₄⋊Q₈	—	2	2	no	—
909	C₄⋊Q₈	—	2	2	no	—
910	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
911	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
912	#124	—	2	1	no	—
913	#124	—	2	2	no	—
914	#124	—	2	2	no	—
915	#124	—	2	2	no	—
916	#124	C₂³×C₁₃	1	2	yes	—
917	#124	C₂³×C₁₃	1	2	yes	—
918	#123	—	2	2	no	—
919	#123	—	2	1	no	—
920	#123	—	2	2	no	—
921	#123	—	2	2	no	—
922	#123	—	2	2	no	—
923	#123	—	2	2	no	—
924	#123	—	2	2	no	—
925	#123	D₄×C₁₃	1	2	yes	—
926	C₂²⋊Q₈	—	2	1	no	—
927	C₂²⋊Q₈	—	2	1	no	—
928	C₂²⋊Q₈	—	2	1	no	—
929	C₂²⋊Q₈	—	2	1	no	—
930	C₂²⋊Q₈	—	2	2	no	—
931	C₂²⋊Q₈	—	2	1	no	—
932	C₂²⋊Q₈	—	2	2	no	—
933	C₂²⋊Q₈	—	2	2	no	—
934	C₂²⋊Q₈	—	2	1	no	—
935	C₂²⋊Q₈	—	2	1	no	—
936	C₂²⋊Q₈	—	2	2	no	—
937	C₂²⋊Q₈	—	2	2	no	—
938	C₂²⋊Q₈	—	2	2	no	—
939	C₂²⋊Q₈	—	2	2	no	—
940	C₂²⋊Q₈	—	2	2	no	—
941	C₂²⋊Q₈	—	2	2	no	—
942	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
943	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
944	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
945	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
946	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
947	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
948	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
949	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
950	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
951	#121	—	2	1	no	—
952	#121	—	2	2	no	—
953	#121	—	2	2	no	—
954	#121	—	2	2	no	—
955	#121	—	2	2	no	—
956	#121	—	2	2	no	—
957	#121	—	2	2	no	—
958	#121	D₄×C₁₃	1	1	yes	characteristic
959	#121	D₄×C₁₃	1	1	yes	characteristic
960	#121	C₂³×C₁₃	1	1	yes	characteristic
961	#121	C₂³×C₁₃	1	1	yes	characteristic
962	#121	C₂³×C₁₃	1	2	yes	—
963	#120	—	2	1	no	—
964	#120	—	2	2	no	—
965	#120	D₄×C₁₃	1	2	yes	—
966	C₄×Q₈	—	2	1	no	—
967	C₄×Q₈	—	2	1	no	—
968	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
969	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
970	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
971	C₄×D₄	—	2	2	no	—
972	C₄×D₄	—	2	2	no	—
973	C₄×D₄	—	2	2	no	—
974	C₄×D₄	—	2	1	no	—
975	C₄×D₄	—	2	1	no	—
976	C₄×D₄	—	2	2	no	—
977	C₄×D₄	—	2	2	no	—
978	C₄×D₄	—	2	2	no	—
979	C₄×D₄	—	2	2	no	—
980	C₄×D₄	C₂³×C₁₃	1	2	yes	—
981	C₄×D₄	C₂³×C₁₃	1	2	yes	—
982	C₄×D₄	C₂³×C₁₃	1	2	yes	—
983	#117	—	2	1	no	—
984	#117	—	2	2	no	—
985	#117	C₂³×C₁₃	1	1	yes	characteristic
986	#117	C₂³×C₁₃	1	1	yes	characteristic
987	C₂×C₄⋊C₄	—	2	1	no	—
988	C₂×C₄⋊C₄	—	2	1	no	—
989	C₂×C₄⋊C₄	—	2	2	no	—
990	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
991	C₂×C₂²⋊C₄	—	2	1	no	—
992	C₂×C₂²⋊C₄	—	2	2	no	—
993	#107	C₂³×C₁₃	1	2	yes	—
994	#106	C₂³×C₁₃	1	2	yes	—
995	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
996	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
997	#103	C₂³×C₁₃	1	2	yes	—
998	#103	C₂³×C₁₃	1	2	yes	—
999	#103	C₂³×C₁₃	1	2	yes	—
1000	#103	C₂³×C₁₃	1	2	yes	—
1001	#103	C₂³×C₁₃	1	1	yes	characteristic
1002	#103	C₂³×C₁₃	1	1	yes	characteristic
1003	#103	C₂³×C₁₃	1	1	yes	characteristic
1004	#103	C₂³×C₁₃	1	1	yes	characteristic
1005	#103	C₂³×C₁₃	1	2	yes	—
1006	#103	C₂³×C₁₃	1	2	yes	—
1007	#103	C₂³×C₁₃	1	2	yes	—
1008	#102	C₂³×C₁₃	1	1	yes	characteristic
1009	#102	C₂³×C₁₃	1	1	yes	characteristic
1010	#102	C₂³×C₁₃	1	1	yes	characteristic
1011	#102	C₂³×C₁₃	1	1	yes	characteristic
1012	#102	C₂³×C₁₃	1	2	yes	—
1013	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
1014	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
1015	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
1016	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
1017	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
1018	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
1019	#97	C₂³×C₁₃	1	2	yes	—
1020	C₄×C₈	C₂³×C₁₃	1	2	yes	—
1021	C₂×C₁₃	—	2	2	no	—
1022	C₂×C₁₃	—	2	2	no	—
1023	C₂×C₁₃	—	4	2	no	—
1024	C₂×C₁₃	—	4	1	no	—
1025	C₂×C₁₃	—	4	2	no	—
1026	C₂×C₁₃	—	8	1	no	—
1027	C₂×C₁₃	—	8	1	no	—
1028	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
1029	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
1030	C₂×C₁₃	#3586	1	1	yes	characteristic
1031	C₂⁴	—	2	1	no	—
1032	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
1033	#41	—	2	2	no	—
1034	#41	—	2	2	no	—
1035	#41	—	2	2	no	—
1036	#41	—	2	4	no	—
1037	#41	—	2	2	no	—
1038	#41	—	2	4	no	—
1039	#41	—	2	2	no	—
1040	#41	—	2	2	no	—
1041	#41	—	2	2	no	—
1042	#41	—	2	2	no	—
1043	#41	—	2	2	no	—
1044	#41	—	4	4	no	—
1045	#41	—	4	1	no	—
1046	#41	—	4	1	no	—
1047	#41	—	4	2	no	—
1048	#41	—	4	2	no	—
1049	#41	—	4	4	no	—
1050	#41	—	4	8	no	—
1051	#41	—	4	4	no	—
1052	#41	—	4	8	no	—
1053	#41	—	4	4	no	—
1054	#41	C₂×D₄×C₁₃	1	4	yes	—
1055	C₂×Q₈	—	2	1	no	—
1056	C₂×Q₈	—	2	1	no	—
1057	C₂×Q₈	—	2	2	no	—
1058	C₂×Q₈	—	2	2	no	—
1059	C₂×Q₈	—	2	1	no	—
1060	C₂×Q₈	—	2	2	no	—
1061	C₂×Q₈	—	2	2	no	—
1062	C₂×Q₈	—	2	1	no	—
1063	C₂×Q₈	—	2	2	no	—
1064	C₂×Q₈	—	2	4	no	—
1065	C₂×Q₈	—	2	2	no	—
1066	C₂×Q₈	—	2	4	no	—
1067	C₂×Q₈	—	2	4	no	—
1068	C₂×Q₈	—	2	4	no	—
1069	C₂×Q₈	—	2	2	no	—
1070	C₂×Q₈	—	2	2	no	—
1071	C₂×Q₈	—	2	2	no	—
1072	C₂×Q₈	—	2	2	no	—
1073	C₂×Q₈	—	4	4	no	—
1074	C₂×Q₈	—	4	2	no	—
1075	C₂×Q₈	—	4	2	no	—
1076	C₂×Q₈	—	4	1	no	—
1077	C₂×Q₈	—	4	2	no	—
1078	C₂×Q₈	—	4	2	no	—
1079	C₂×Q₈	—	4	4	no	—
1080	C₂×Q₈	—	4	4	no	—
1081	C₂×Q₈	—	4	4	no	—
1082	C₂×Q₈	—	4	4	no	—
1083	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
1084	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
1085	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
1086	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
1087	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
1088	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
1089	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
1090	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
1091	C₂×D₄	—	2	1	no	—
1092	C₂×D₄	—	2	2	no	—
1093	C₂×D₄	—	2	1	no	—
1094	C₂×D₄	—	2	1	no	—
1095	C₂×D₄	—	2	2	no	—
1096	C₂×D₄	—	2	1	no	—
1097	C₂×D₄	—	2	1	no	—
1098	C₂×D₄	—	2	1	no	—
1099	C₂×D₄	—	2	1	no	—
1100	C₂×D₄	—	2	2	no	—
1101	C₂×D₄	—	2	2	no	—
1102	C₂×D₄	—	2	1	no	—
1103	C₂×D₄	—	4	1	no	—
1104	C₂×D₄	—	4	4	no	—
1105	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1106	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1107	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1108	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1109	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1110	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1111	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1112	C₂²×C₄	—	2	1	no	—
1113	C₂²×C₄	—	2	1	no	—
1114	C₂²×C₄	—	2	2	no	—
1115	C₂²×C₄	—	2	2	no	—
1116	C₂²×C₄	—	2	1	no	—
1117	C₂²×C₄	—	2	2	no	—
1118	C₂²×C₄	—	2	2	no	—
1119	C₂²×C₄	—	2	2	no	—
1120	C₂²×C₄	—	2	1	no	—
1121	C₂²×C₄	—	2	2	no	—
1122	C₂²×C₄	—	2	1	no	—
1123	C₂²×C₄	—	2	1	no	—
1124	C₂²×C₄	—	2	2	no	—
1125	C₂²×C₄	—	2	1	no	—
1126	C₂²×C₄	—	2	1	no	—
1127	C₂²×C₄	—	2	2	no	—
1128	C₂²×C₄	—	2	1	no	—
1129	C₂²×C₄	—	2	1	no	—
1130	C₂²×C₄	—	2	2	no	—
1131	C₂²×C₄	—	4	4	no	—
1132	C₂²×C₄	—	4	4	no	—
1133	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1134	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1135	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1136	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1137	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1138	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1139	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1140	Q₁₆	—	2	4	no	—
1141	Q₁₆	—	2	2	no	—
1142	Q₁₆	—	2	4	no	—
1143	Q₁₆	—	2	4	no	—
1144	Q₁₆	—	2	4	no	—
1145	Q₁₆	—	2	4	no	—
1146	Q₁₆	—	2	4	no	—
1147	Q₁₆	—	4	2	no	—
1148	Q₁₆	—	4	2	no	—
1149	Q₁₆	—	4	1	no	—
1150	Q₁₆	C₂×D₄×C₁₃	1	8	yes	—
1151	SD₁₆	—	2	4	no	—
1152	SD₁₆	—	2	2	no	—
1153	SD₁₆	—	2	4	no	—
1154	SD₁₆	—	2	2	no	—
1155	SD₁₆	—	2	4	no	—
1156	SD₁₆	—	2	4	no	—
1157	SD₁₆	—	4	1	no	—
1158	SD₁₆	—	4	1	no	—
1159	SD₁₆	C₂×D₄×C₁₃	1	8	yes	—
1160	D₈	—	2	2	no	—
1161	D₈	—	4	1	no	—
1162	M₁₆	—	2	2	no	—
1163	M₁₆	—	2	4	no	—
1164	M₁₆	—	2	4	no	—
1165	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
1166	C₂×C₈	—	2	2	no	—
1167	C₂×C₈	—	2	2	no	—
1168	C₂×C₈	—	2	4	no	—
1169	C₂×C₈	—	2	4	no	—
1170	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1171	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1172	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1173	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1174	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1175	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1176	C₄⋊C₄	—	2	2	no	—
1177	C₄⋊C₄	—	2	1	no	—
1178	C₄⋊C₄	—	2	2	no	—
1179	C₄⋊C₄	—	2	2	no	—
1180	C₄⋊C₄	—	2	2	no	—
1181	C₄⋊C₄	—	2	2	no	—
1182	C₄⋊C₄	—	2	2	no	—
1183	C₄⋊C₄	—	2	2	no	—
1184	C₄⋊C₄	—	2	2	no	—
1185	C₄⋊C₄	—	2	2	no	—
1186	C₄⋊C₄	—	2	2	no	—
1187	C₄⋊C₄	—	2	2	no	—
1188	C₄⋊C₄	—	2	1	no	—
1189	C₄⋊C₄	—	2	1	no	—
1190	C₄⋊C₄	—	2	2	no	—
1191	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1192	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1193	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1194	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1195	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1196	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1197	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1198	C₂²⋊C₄	—	2	2	no	—
1199	C₂²⋊C₄	—	2	2	no	—
1200	C₂²⋊C₄	—	2	1	no	—
1201	C₂²⋊C₄	—	2	1	no	—
1202	C₂²⋊C₄	—	2	1	no	—
1203	C₂²⋊C₄	—	2	2	no	—
1204	C₂²⋊C₄	—	2	2	no	—
1205	C₂²⋊C₄	—	2	2	no	—
1206	C₂²⋊C₄	—	2	2	no	—
1207	C₂²⋊C₄	—	2	2	no	—
1208	C₂²⋊C₄	—	2	2	no	—
1209	C₂²⋊C₄	—	2	2	no	—
1210	C₂²⋊C₄	—	2	2	no	—
1211	C₂²⋊C₄	—	2	2	no	—
1212	C₂²⋊C₄	—	2	1	no	—
1213	C₂²⋊C₄	—	2	1	no	—
1214	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1215	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1216	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1217	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1218	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1219	C₄²	—	2	2	no	—
1220	C₄²	—	2	2	no	—
1221	C₄²	—	2	2	no	—
1222	C₄²	—	2	1	no	—
1223	C₄²	C₂⁴×C₁₃	1	2	yes	—
1224	C₁₃	#61076	1	1	yes	characteristic, direct product factor, Sylow
1225	C₂³	—	2	2	no	—
1226	C₂³	—	2	2	no	—
1227	C₂³	—	2	1	no	—
1228	C₂³	—	2	1	no	—
1229	C₂³	—	2	1	no	—
1230	C₂³	—	4	1	no	—
1231	C₂³	—	4	2	no	—
1232	C₂³	—	4	2	no	—
1233	C₂³	—	8	1	no	—
1234	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1235	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1236	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1237	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1238	Q₈	—	2	4	no	—
1239	Q₈	—	2	2	no	—
1240	Q₈	—	2	2	no	—
1241	Q₈	—	2	1	no	—
1242	Q₈	—	2	2	no	—
1243	Q₈	—	2	1	no	—
1244	Q₈	—	2	2	no	—
1245	Q₈	—	2	1	no	—
1246	Q₈	—	2	1	no	—
1247	Q₈	—	2	1	no	—
1248	Q₈	—	2	2	no	—
1249	Q₈	—	2	2	no	—
1250	Q₈	—	4	4	no	—
1251	Q₈	—	4	4	no	—
1252	Q₈	—	4	4	no	—
1253	Q₈	—	4	4	no	—
1254	Q₈	—	4	2	no	—
1255	Q₈	—	4	2	no	—
1256	Q₈	—	4	2	no	—
1257	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
1258	Q₈	C₂²×D₄×C₁₃	1	2	yes	—
1259	D₄	—	2	4	no	—
1260	D₄	—	2	4	no	—
1261	D₄	—	2	4	no	—
1262	D₄	—	2	2	no	—
1263	D₄	—	2	1	no	—
1264	D₄	—	2	1	no	—
1265	D₄	—	2	1	no	—
1266	D₄	—	2	1	no	—
1267	D₄	—	2	1	no	—
1268	D₄	—	4	2	no	—
1269	D₄	—	4	2	no	—
1270	D₄	—	4	2	no	—
1271	D₄	—	4	4	no	—
1272	D₄	—	4	2	no	—
1273	D₄	—	4	4	no	—
1274	D₄	—	4	2	no	—
1275	D₄	—	4	2	no	—
1276	D₄	—	4	2	no	—
1277	D₄	—	4	2	no	—
1278	D₄	—	8	2	no	—
1279	D₄	C₂²×D₄×C₁₃	1	2	yes	—
1280	C₂×C₄	—	2	2	no	—
1281	C₂×C₄	—	2	4	no	—
1282	C₂×C₄	—	2	1	no	—
1283	C₂×C₄	—	2	2	no	—
1284	C₂×C₄	—	2	2	no	—
1285	C₂×C₄	—	2	2	no	—
1286	C₂×C₄	—	2	4	no	—
1287	C₂×C₄	—	2	1	no	—
1288	C₂×C₄	—	2	2	no	—
1289	C₂×C₄	—	2	1	no	—
1290	C₂×C₄	—	2	1	no	—
1291	C₂×C₄	—	2	1	no	—
1292	C₂×C₄	—	2	2	no	—
1293	C₂×C₄	—	2	1	no	—
1294	C₂×C₄	—	2	1	no	—
1295	C₂×C₄	—	2	2	no	—
1296	C₂×C₄	—	2	2	no	—
1297	C₂×C₄	—	2	2	no	—
1298	C₂×C₄	—	2	1	no	—
1299	C₂×C₄	—	2	1	no	—
1300	C₂×C₄	—	4	2	no	—
1301	C₂×C₄	—	4	4	no	—
1302	C₂×C₄	—	4	2	no	—
1303	C₂×C₄	—	4	4	no	—
1304	C₂×C₄	—	4	4	no	—
1305	C₂×C₄	—	4	2	no	—
1306	C₂×C₄	—	4	4	no	—
1307	C₂×C₄	—	4	4	no	—
1308	C₂×C₄	—	4	4	no	—
1309	C₂×C₄	—	4	2	no	—
1310	C₂×C₄	—	4	2	no	—
1311	C₂×C₄	—	4	2	no	—
1312	C₂×C₄	—	4	2	no	—
1313	C₂×C₄	—	8	2	no	—
1314	C₂×C₄	—	8	1	no	—
1315	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1316	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1317	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1318	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1319	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1320	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1321	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1322	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1323	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1324	C₈	—	2	1	no	—
1325	C₈	—	2	1	no	—
1326	C₈	—	2	2	no	—
1327	C₈	—	2	1	no	—
1328	C₈	—	2	1	no	—
1329	C₈	C₂²×D₄×C₁₃	1	4	yes	—
1330	C₂²	—	2	1	no	—
1331	C₂²	—	2	1	no	—
1332	C₂²	—	2	1	no	—
1333	C₂²	—	2	1	no	—
1334	C₂²	—	2	2	no	—
1335	C₂²	—	2	1	no	—
1336	C₂²	—	2	1	no	—
1337	C₂²	—	2	2	no	—
1338	C₂²	—	2	1	no	—
1339	C₂²	—	2	2	no	—
1340	C₂²	—	2	2	no	—
1341	C₂²	—	4	4	no	—
1342	C₂²	—	4	1	no	—
1343	C₂²	—	4	1	no	—
1344	C₂²	—	4	1	no	—
1345	C₂²	—	4	1	no	—
1346	C₂²	—	4	1	no	—
1347	C₂²	—	4	1	no	—
1348	C₂²	—	4	1	no	—
1349	C₂²	—	4	1	no	—
1350	C₂²	—	8	4	no	—
1351	C₂²	D₄²×C₁₃	1	2	yes	—
1352	C₂²	C₁₃×#578	1	2	yes	complemented
1353	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1354	C₄	—	2	2	no	—
1355	C₄	—	2	2	no	—
1356	C₄	—	2	1	no	—
1357	C₄	—	2	1	no	—
1358	C₄	—	2	2	no	—
1359	C₄	—	2	4	no	—
1360	C₄	—	2	2	no	—
1361	C₄	—	4	1	no	—
1362	C₄	—	4	2	no	—
1363	C₄	—	4	1	no	—
1364	C₄	—	4	1	no	—
1365	C₄	—	4	2	no	—
1366	C₄	—	4	1	no	—
1367	C₄	—	4	2	no	—
1368	C₄	D₄²×C₁₃	1	2	yes	—
1369	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
1370	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1371	C₂	—	2	2	no	—
1372	C₂	—	2	2	no	—
1373	C₂	—	4	1	no	—
1374	C₂	—	4	2	no	—
1375	C₂	—	4	2	no	—
1376	C₂	—	8	1	no	—
1377	C₂	—	8	1	no	—
1378	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
1379	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
1380	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#525 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₁₃×#578	C₂	semidirect
2. C₂²×C₁₃×#137	C₂	semidirect
3. C₁₃×#3489	C₂	semidirect
4. C₁₃×#3486	C₂	semidirect
5. D₄×C₁₃×Q₁₆	C₂	semidirect
6. C₁₃×#3282	C₂	semidirect
7. C₁₃×#3277	C₂	semidirect
8. C₁₃×#3276	C₂	semidirect
9. C₁₃×#3270	C₂	semidirect
10. C₁₃×#3270	C₂	semidirect
11. C₁₃×#3269	C₂	semidirect
12. C₁₃×#3266	C₂	semidirect
13. C₁₃×#3156	C₂	semidirect
14. C₁₃×#3063	C₂	semidirect
15. C₁₃×#3056	C₂	semidirect
16. C₁₃×#3046	C₂	semidirect
17. C₁₃×#3044	C₂	semidirect
18. C₁₃×#3013	C₂	semidirect
19. C₁₃×#3011	C₂	semidirect
20. C₁₃×#3002	C₂	semidirect
21. C₂×C₁₃×#451	C₂	semidirect
22. C₁₃×#2947	C₂	semidirect
23. C₁₃×#2933	C₂	semidirect
25. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
36. C₂×C₁₃×#137	C₂²	semidirect
37. C₂×C₁₃×#137	C₂²	semidirect
38. C₂×C₁₃×#137	C₂²	semidirect
41. C₂×C₁₃×#135	C₂²	semidirect
43. C₂²×C₁₃×Q₁₆	C₂²	semidirect
44. C₂²×C₁₃×Q₁₆	C₂²	semidirect
45. C₂²×C₁₃×Q₁₆	C₂²	semidirect
47. C₂×C₁₃×#131	C₂²	semidirect
53. D₄×Q₈×C₁₃	C₂²	semidirect
58. C₁₃×#548	C₂²	semidirect
68. C₁₃×#536	C₂²	semidirect
69. C₁₃×#536	C₂²	semidirect
77. C₁₃×#519	C₂²	semidirect
78. C₁₃×#497	C₂²	semidirect
79. C₁₃×#497	C₂²	semidirect
80. C₁₃×#495	C₂²	semidirect
81. C₁₃×#494	C₂²	semidirect
82. C₁₃×#470	C₂²	semidirect
83. C₁₃×#470	C₂²	semidirect
84. C₁₃×#468	C₂²	semidirect
85. C₁₃×#468	C₂²	semidirect
87. C₁₃×#467	C₂²	semidirect
89. C₁₃×#465	C₂²	semidirect
90. C₁₃×#464	C₂²	semidirect
91. C₁₃×#464	C₂²	semidirect
92. C₁₃×#464	C₂²	semidirect
93. C₁₃×#463	C₂²	semidirect
94. C₁₃×#462	C₂²	semidirect
95. C₁₃×#462	C₂²	semidirect
96. C₁₃×#462	C₂²	semidirect
97. C₁₃×#461	C₂²	semidirect
100. C₁₃×#452	C₂²	semidirect
101. C₁₃×#452	C₂²	semidirect
102. C₁₃×#452	C₂²	semidirect
106. C₁₃×#451	C₂²	semidirect
107. C₁₃×#451	C₂²	semidirect
108. C₁₃×#451	C₂²	semidirect
109. C₁₃×#451	C₂²	semidirect
110. C₁₃×#451	C₂²	semidirect
114. C₁₃×#449	C₂²	semidirect
116. C₁₃×#448	C₂²	semidirect
118. C₁₃×#441	C₂²	semidirect
119. C₁₃×#440	C₂²	semidirect
120. C₄×C₁₃×Q₁₆	C₂²	semidirect
121. C₄×C₁₃×SD₁₆	C₂²	semidirect
122. C₁₃×#436	C₂²	semidirect
124. C₁₃×#435	C₂²	semidirect
126. C₁₃×#428	C₂²	semidirect
127. C₁₃×#424	C₂²	semidirect
128. C₁₃×#419	C₂²	semidirect
129. C₁₃×#417	C₂²	semidirect
132. C₂×C₁₃×#103	C₂²	semidirect
133. C₂×C₁₃×#103	C₂²	semidirect
134. C₁₃×#408	C₂²	semidirect
136. C₁₃×#405	C₂²	semidirect
185. C₁₃×#137	D₄	semidirect
341. #61076	C₁₃	direct (N × H)
535. C₂×#578	C₂×C₁₃	semidirect
536. C₂²×#137	C₂×C₁₃	semidirect
537. #3489	C₂×C₁₃	semidirect
538. #3486	C₂×C₁₃	semidirect
539. D₄×Q₁₆	C₂×C₁₃	semidirect
540. #3282	C₂×C₁₃	semidirect
541. #3277	C₂×C₁₃	semidirect
542. #3276	C₂×C₁₃	semidirect
543. #3270	C₂×C₁₃	semidirect
544. #3270	C₂×C₁₃	semidirect
545. #3269	C₂×C₁₃	semidirect
546. #3266	C₂×C₁₃	semidirect
547. #3156	C₂×C₁₃	semidirect
548. #3063	C₂×C₁₃	semidirect
549. #3056	C₂×C₁₃	semidirect
550. #3046	C₂×C₁₃	semidirect
551. #3044	C₂×C₁₃	semidirect
552. #3013	C₂×C₁₃	semidirect
553. #3011	C₂×C₁₃	semidirect
554. #3002	C₂×C₁₃	semidirect
555. C₂×#451	C₂×C₁₃	semidirect
556. #2947	C₂×C₁₃	semidirect
557. #2933	C₂×C₁₃	semidirect
664. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
675. C₂×#137	C₂²×C₁₃	semidirect
676. C₂×#137	C₂²×C₁₃	semidirect
677. C₂×#137	C₂²×C₁₃	semidirect
680. C₂×#135	C₂²×C₁₃	semidirect
682. C₂²×Q₁₆	C₂²×C₁₃	semidirect
683. C₂²×Q₁₆	C₂²×C₁₃	semidirect
684. C₂²×Q₁₆	C₂²×C₁₃	semidirect
686. C₂×#131	C₂²×C₁₃	semidirect
692. D₄×Q₈	C₂²×C₁₃	semidirect
697. #548	C₂²×C₁₃	semidirect
707. #536	C₂²×C₁₃	semidirect
708. #536	C₂²×C₁₃	semidirect
716. #519	C₂²×C₁₃	semidirect
717. #497	C₂²×C₁₃	semidirect
718. #497	C₂²×C₁₃	semidirect
719. #495	C₂²×C₁₃	semidirect
720. #494	C₂²×C₁₃	semidirect
721. #470	C₂²×C₁₃	semidirect
722. #470	C₂²×C₁₃	semidirect
723. #468	C₂²×C₁₃	semidirect
724. #468	C₂²×C₁₃	semidirect
726. #467	C₂²×C₁₃	semidirect
728. #465	C₂²×C₁₃	semidirect
729. #464	C₂²×C₁₃	semidirect
730. #464	C₂²×C₁₃	semidirect
731. #464	C₂²×C₁₃	semidirect
732. #463	C₂²×C₁₃	semidirect
733. #462	C₂²×C₁₃	semidirect
734. #462	C₂²×C₁₃	semidirect
735. #462	C₂²×C₁₃	semidirect
736. #461	C₂²×C₁₃	semidirect
739. #452	C₂²×C₁₃	semidirect
740. #452	C₂²×C₁₃	semidirect
741. #452	C₂²×C₁₃	semidirect
745. #451	C₂²×C₁₃	semidirect
746. #451	C₂²×C₁₃	semidirect
747. #451	C₂²×C₁₃	semidirect
748. #451	C₂²×C₁₃	semidirect
749. #451	C₂²×C₁₃	semidirect
753. #449	C₂²×C₁₃	semidirect
755. #448	C₂²×C₁₃	semidirect
757. #441	C₂²×C₁₃	semidirect
758. #440	C₂²×C₁₃	semidirect
759. C₄×Q₁₆	C₂²×C₁₃	semidirect
760. C₄×SD₁₆	C₂²×C₁₃	semidirect
761. #436	C₂²×C₁₃	semidirect
763. #435	C₂²×C₁₃	semidirect
765. #428	C₂²×C₁₃	semidirect
766. #424	C₂²×C₁₃	semidirect
767. #419	C₂²×C₁₃	semidirect
768. #417	C₂²×C₁₃	semidirect
771. C₂×#103	C₂²×C₁₃	semidirect
772. C₂×#103	C₂²×C₁₃	semidirect
773. #408	C₂²×C₁₃	semidirect
775. #405	C₂²×C₁₃	semidirect
798. C₂²×C₁₃	#578	semidirect
865. #137	D₄×C₁₃	semidirect
1224. C₁₃	#61076	direct (N × H)
1352. C₂²	C₁₃×#578	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#578	2
C₂²×C₁₃×#137	2
C₁₃×#3489	2
C₁₃×#3486	2
D₄×C₁₃×Q₁₆	2
C₁₃×#3282	2
C₁₃×#3277	2
C₁₃×#3276	2
C₁₃×#3270	2
C₁₃×#3269	2
C₁₃×#3266	2
C₁₃×#3156	2
C₁₃×#3063	2
C₁₃×#3056	2
C₁₃×#3046	2
C₁₃×#3044	2
C₁₃×#3013	2
C₁₃×#3011	2
C₁₃×#3002	2
C₂×C₁₃×#451	2
C₁₃×#2947	2
C₁₃×#2933	2
#61076	13

Subgroups — C13×#61076 #15747415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61076 #15747415