Subgroups — C₁₃×#61173 #15747512

Order 3328.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3489	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3315	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3314	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3313	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3312	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3302	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3300	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3299	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3296	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3095	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3083	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3011	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#556	C₂²	1	2	yes	complemented
32	C₁₃×#554	C₂²	1	2	yes	—
33	C₁₃×#552	—	2	2	no	—
34	C₁₃×#552	C₂²	1	2	yes	—
35	C₁₃×#552	C₂²	1	2	yes	complemented
36	C₁₃×#551	—	2	2	no	—
37	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
38	C₁₃×#548	C₂²	1	2	yes	—
39	C₁₃×#547	—	2	2	no	—
40	C₁₃×#547	C₂²	1	2	yes	—
41	C₁₃×#546	—	2	2	no	—
42	C₁₃×#546	C₂²	1	2	yes	—
43	C₁₃×#544	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#542	—	2	1	no	—
45	C₁₃×#541	—	2	1	no	—
46	C₁₃×#537	—	2	1	no	—
47	C₁₃×#537	C₂²	1	1	yes	characteristic
48	C₁₃×#536	—	2	1	no	—
49	C₁₃×#536	C₂²	1	1	yes	characteristic
50	C₁₃×#536	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#533	—	2	1	no	—
52	C₁₃×#529	—	2	1	no	—
53	C₁₃×#525	—	2	1	no	—
54	C₁₃×#525	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
56	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₁₃×#520	C₂²	1	1	yes	characteristic
59	C₁₃×#520	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#519	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
62	C₁₃×#491	C₂²	1	2	yes	complemented
63	C₁₃×#489	C₂²	1	2	yes	complemented
64	C₁₃×#488	C₂²	1	2	yes	complemented
65	C₁₃×#487	C₂²	1	2	yes	complemented
66	C₁₃×#485	C₂²	1	2	yes	complemented
67	C₁₃×#485	C₂²	1	2	yes	complemented
68	C₁₃×#485	C₂²	1	2	yes	complemented
69	C₁₃×#484	C₂²	1	2	yes	—
70	C₁₃×#484	C₂²	1	2	yes	complemented
71	C₁₃×#483	C₂²	1	2	yes	—
72	C₁₃×#482	C₂²	1	2	yes	complemented
73	C₁₃×#480	C₂²	1	2	yes	complemented
74	C₁₃×#479	C₂²	1	2	yes	complemented
75	C₁₃×#478	C₂²	1	2	yes	complemented
76	C₁₃×#477	C₂²	1	2	yes	complemented
77	C₁₃×#474	C₂²	1	2	yes	complemented
78	C₁₃×#470	C₂²	1	2	yes	complemented
79	C₁₃×#468	C₂²	1	2	yes	complemented
80	C₁₃×#467	C₂²	1	2	yes	—
81	C₁₃×#467	C₂²	1	2	yes	—
82	C₁₃×#467	C₂²	1	2	yes	complemented
83	C₁₃×#467	C₂²	1	2	yes	complemented
84	C₁₃×#467	C₂²	1	2	yes	complemented
85	C₁₃×#465	C₂²	1	2	yes	complemented
86	C₁₃×#464	C₂²	1	2	yes	complemented
87	C₁₃×#464	C₂²	1	2	yes	complemented
88	C₁₃×#462	C₂²	1	2	yes	complemented
89	C₁₃×#462	C₂²	1	2	yes	complemented
90	C₁₃×#452	C₂²	1	2	yes	—
91	C₁₃×#452	C₂²	1	2	yes	—
92	C₁₃×#452	C₂²	1	2	yes	complemented
93	C₁₃×#452	C₂²	1	2	yes	complemented
94	C₁₃×#451	C₂²	1	2	yes	—
95	C₁₃×#451	C₂²	1	2	yes	complemented
96	C₁₃×#451	C₂²	1	2	yes	complemented
97	C₁₃×#450	C₂²	1	2	yes	—
98	C₁₃×#441	C₂²	1	2	yes	complemented
99	C₁₃×#440	C₂²	1	2	yes	complemented
100	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
101	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
102	C₁₃×#435	C₂²	1	2	yes	—
103	C₁₃×#435	C₂²	1	2	yes	complemented
104	C₈×D₄×C₁₃	C₂²	1	2	yes	—
105	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
106	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
107	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
109	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
110	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
111	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
112	C₁₃×#419	C₂²	1	2	yes	complemented
113	C₁₃×#417	C₂²	1	1	yes	characteristic
114	C₁₃×#417	C₂²	1	1	yes	characteristic
115	C₁₃×#417	C₂²	1	2	yes	complemented
116	C₁₃×#416	C₂²	1	1	yes	characteristic
117	C₁₃×#416	C₂²	1	1	yes	characteristic
118	C₁₃×#416	C₂²	1	1	yes	characteristic
119	C₁₃×#416	C₂²	1	1	yes	characteristic
120	C₁₃×#416	C₂²	1	1	yes	characteristic
121	C₁₃×#416	C₂²	1	1	yes	characteristic
122	C₁₃×#416	C₂²	1	1	yes	characteristic
123	C₁₃×#416	C₂²	1	1	yes	characteristic
124	C₁₃×#416	C₂²	1	2	yes	complemented
125	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
126	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
127	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
128	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
131	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
132	C₁₃×#408	C₂²	1	1	yes	characteristic, complemented
133	C₁₃×#407	C₂²	1	1	yes	characteristic
134	C₁₃×#405	C₂²	1	1	yes	characteristic, complemented
135	C₁₃×2₋¹⁺⁴	—	2	4	no	—
136	C₁₃×2₋¹⁺⁴	—	4	2	no	—
137	C₂×C₁₃×#41	—	2	1	no	—
138	C₂×C₁₃×#41	—	2	2	no	—
139	C₂×C₁₃×#41	—	2	1	no	—
140	C₂×C₁₃×#41	—	2	1	no	—
141	C₂×C₁₃×#41	—	2	4	no	—
142	C₂×C₁₃×#41	—	4	2	no	—
143	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×#41	C₂³	1	2	yes	—
147	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₁₃	—	2	1	no	—
150	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
151	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
152	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
153	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
154	C₂²×D₄×C₁₃	—	2	1	no	—
155	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₁₃	—	2	1	no	—
157	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
158	C₁₃×#137	—	2	4	no	—
159	C₁₃×#137	—	4	2	no	—
160	C₂×C₁₃×Q₁₆	—	4	2	no	—
161	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
162	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
163	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
164	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
165	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
166	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
167	C₁₃×#131	—	4	2	no	—
168	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
171	C₂²×C₈×C₁₃	—	4	2	no	—
172	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
173	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
174	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
177	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
179	C₁₃×C₄⋊Q₈	—	2	1	no	—
180	C₁₃×C₄⋊Q₈	—	2	1	no	—
181	C₁₃×C₄⋊Q₈	—	2	2	no	—
182	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
183	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
184	C₁₃×#126	—	2	2	no	—
185	C₁₃×#126	—	2	2	no	—
186	C₁₃×#126	—	2	2	no	—
187	C₁₃×#126	—	2	2	no	—
188	C₁₃×#125	—	2	1	no	—
189	C₁₃×#125	—	2	2	no	—
190	C₁₃×#125	—	2	2	no	—
191	C₁₃×#125	—	2	2	no	—
192	C₁₃×#125	C₂³	1	2	yes	—
193	C₁₃×#124	—	2	1	no	—
194	C₁₃×#124	—	2	2	no	—
195	C₁₃×#124	—	2	2	no	—
196	C₁₃×#124	C₂³	1	2	yes	—
197	C₁₃×#123	—	2	2	no	—
198	C₁₃×#123	—	2	2	no	—
199	C₁₃×#123	—	2	2	no	—
200	C₁₃×#123	—	2	2	no	—
201	C₁₃×#123	—	2	2	no	—
202	C₁₃×#123	—	2	2	no	—
203	C₁₃×#123	—	2	2	no	—
204	C₁₃×#123	D₄	1	2	yes	—
205	C₁₃×C₂²⋊Q₈	—	2	1	no	—
206	C₁₃×C₂²⋊Q₈	—	2	1	no	—
207	C₁₃×C₂²⋊Q₈	—	2	1	no	—
208	C₁₃×C₂²⋊Q₈	—	2	1	no	—
209	C₁₃×C₂²⋊Q₈	—	2	1	no	—
210	C₁₃×C₂²⋊Q₈	—	2	1	no	—
211	C₁₃×C₂²⋊Q₈	—	2	2	no	—
212	C₁₃×C₂²⋊Q₈	—	2	1	no	—
213	C₁₃×C₂²⋊Q₈	—	2	2	no	—
214	C₁₃×C₂²⋊Q₈	—	2	2	no	—
215	C₁₃×C₂²⋊Q₈	—	2	2	no	—
216	C₁₃×C₂²⋊Q₈	—	2	2	no	—
217	C₁₃×C₂²⋊Q₈	—	2	2	no	—
218	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
219	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
220	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
226	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
227	C₁₃×#121	—	2	1	no	—
228	C₁₃×#121	—	2	2	no	—
229	C₁₃×#121	—	2	2	no	—
230	C₁₃×#121	—	2	2	no	—
231	C₁₃×#121	—	2	2	no	—
232	C₁₃×#121	D₄	1	1	yes	characteristic
233	C₁₃×#121	D₄	1	1	yes	characteristic
234	C₁₃×#121	C₂³	1	2	yes	—
235	C₁₃×#120	—	2	2	no	—
236	C₁₃×#120	D₄	1	2	yes	—
237	C₄×Q₈×C₁₃	—	2	1	no	—
238	C₄×Q₈×C₁₃	—	2	1	no	—
239	C₄×Q₈×C₁₃	—	2	1	no	—
240	C₄×Q₈×C₁₃	—	2	2	no	—
241	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
242	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
243	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
244	C₄×D₄×C₁₃	—	2	1	no	—
245	C₄×D₄×C₁₃	—	2	2	no	—
246	C₄×D₄×C₁₃	—	2	2	no	—
247	C₄×D₄×C₁₃	—	2	2	no	—
248	C₄×D₄×C₁₃	—	2	2	no	—
249	C₄×D₄×C₁₃	—	2	2	no	—
250	C₄×D₄×C₁₃	C₂³	1	2	yes	—
251	C₄×D₄×C₁₃	C₂³	1	2	yes	—
252	C₄×D₄×C₁₃	C₂³	1	2	yes	—
253	C₁₃×#117	—	2	1	no	—
254	C₁₃×#117	—	2	1	no	—
255	C₁₃×#117	—	2	1	no	—
256	C₁₃×#117	—	2	2	no	—
257	C₁₃×#117	—	2	2	no	—
258	C₁₃×#117	—	2	2	no	—
259	C₁₃×#117	C₂³	1	1	yes	characteristic
260	C₁₃×#117	C₂³	1	1	yes	characteristic
261	C₁₃×#117	C₂³	1	1	yes	characteristic
262	C₁₃×#117	C₂³	1	1	yes	characteristic
263	C₁₃×#117	C₂³	1	2	yes	—
264	C₁₃×#117	C₂³	1	1	yes	characteristic
265	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
267	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
268	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
269	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
273	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₄²×C₁₃	—	2	1	no	—
279	C₁₃×#107	C₂³	1	2	yes	—
280	C₁₃×#107	C₂³	1	2	yes	—
281	C₁₃×#107	C₂³	1	2	yes	—
282	C₁₃×#107	C₂³	1	2	yes	—
283	C₁₃×#106	C₂³	1	2	yes	—
284	C₁₃×#106	C₂³	1	2	yes	—
285	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
286	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
287	C₁₃×#103	C₂³	1	1	yes	characteristic
288	C₁₃×#103	C₂³	1	1	yes	characteristic
289	C₁₃×#103	C₂³	1	1	yes	characteristic
290	C₁₃×#103	C₂³	1	1	yes	characteristic
291	C₁₃×#103	C₂³	1	1	yes	characteristic
292	C₁₃×#103	C₂³	1	1	yes	characteristic
293	C₁₃×#103	C₂³	1	1	yes	characteristic
294	C₁₃×#103	C₂³	1	1	yes	characteristic
295	C₁₃×#103	C₂³	1	2	yes	—
296	C₁₃×#103	C₂³	1	2	yes	—
297	C₁₃×#103	C₂³	1	2	yes	—
298	C₁₃×#103	C₂³	1	2	yes	—
299	C₁₃×#103	C₂³	1	2	yes	—
300	C₁₃×#103	C₂³	1	2	yes	—
301	C₁₃×#103	C₂³	1	2	yes	—
302	C₁₃×#103	C₂³	1	2	yes	—
303	C₁₃×#103	C₂³	1	2	yes	—
304	C₁₃×#103	C₂³	1	2	yes	—
305	C₁₃×#102	C₂³	1	1	yes	characteristic
306	C₁₃×#102	C₂³	1	1	yes	characteristic
307	C₁₃×#102	C₂³	1	1	yes	characteristic
308	C₁₃×#102	C₂³	1	1	yes	characteristic
309	C₁₃×#102	C₂³	1	1	yes	characteristic
310	C₁₃×#102	C₂³	1	1	yes	characteristic
311	C₁₃×#102	C₂³	1	1	yes	characteristic
312	C₁₃×#102	C₂³	1	1	yes	characteristic
313	C₁₃×#102	C₂³	1	2	yes	—
314	C₁₃×#102	C₂³	1	2	yes	—
315	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
316	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₁₃×#97	C₂³	1	2	yes	—
320	C₄×C₈×C₁₃	C₂³	1	2	yes	—
321	#61173	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂⁴×C₁₃	—	2	1	no	—
323	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
324	C₁₃×#41	—	2	2	no	—
325	C₁₃×#41	—	2	2	no	—
326	C₁₃×#41	—	2	2	no	—
327	C₁₃×#41	—	2	2	no	—
328	C₁₃×#41	—	2	2	no	—
329	C₁₃×#41	—	2	4	no	—
330	C₁₃×#41	—	2	2	no	—
331	C₁₃×#41	—	2	2	no	—
332	C₁₃×#41	—	4	4	no	—
333	C₁₃×#41	—	4	1	no	—
334	C₁₃×#41	—	4	1	no	—
335	C₁₃×#41	—	4	2	no	—
336	C₁₃×#41	—	4	4	no	—
337	C₁₃×#41	—	4	4	no	—
338	C₁₃×#41	—	4	8	no	—
339	C₁₃×#41	#41	1	4	yes	—
340	C₂×Q₈×C₁₃	—	2	1	no	—
341	C₂×Q₈×C₁₃	—	2	1	no	—
342	C₂×Q₈×C₁₃	—	2	2	no	—
343	C₂×Q₈×C₁₃	—	2	1	no	—
344	C₂×Q₈×C₁₃	—	2	2	no	—
345	C₂×Q₈×C₁₃	—	2	2	no	—
346	C₂×Q₈×C₁₃	—	2	4	no	—
347	C₂×Q₈×C₁₃	—	2	2	no	—
348	C₂×Q₈×C₁₃	—	2	2	no	—
349	C₂×Q₈×C₁₃	—	2	2	no	—
350	C₂×Q₈×C₁₃	—	2	2	no	—
351	C₂×Q₈×C₁₃	—	4	1	no	—
352	C₂×Q₈×C₁₃	—	4	2	no	—
353	C₂×Q₈×C₁₃	—	4	4	no	—
354	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
355	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
356	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
357	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
358	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
359	C₂×D₄×C₁₃	—	2	1	no	—
360	C₂×D₄×C₁₃	—	2	2	no	—
361	C₂×D₄×C₁₃	—	2	2	no	—
362	C₂×D₄×C₁₃	—	2	1	no	—
363	C₂×D₄×C₁₃	—	2	1	no	—
364	C₂×D₄×C₁₃	—	2	1	no	—
365	C₂×D₄×C₁₃	—	2	2	no	—
366	C₂×D₄×C₁₃	—	2	1	no	—
367	C₂×D₄×C₁₃	—	4	1	no	—
368	C₂×D₄×C₁₃	—	4	4	no	—
369	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
371	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
372	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
373	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
374	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₁₃	—	2	1	no	—
376	C₂²×C₄×C₁₃	—	2	2	no	—
377	C₂²×C₄×C₁₃	—	2	2	no	—
378	C₂²×C₄×C₁₃	—	2	1	no	—
379	C₂²×C₄×C₁₃	—	2	1	no	—
380	C₂²×C₄×C₁₃	—	2	1	no	—
381	C₂²×C₄×C₁₃	—	2	2	no	—
382	C₂²×C₄×C₁₃	—	2	1	no	—
383	C₂²×C₄×C₁₃	—	2	1	no	—
384	C₂²×C₄×C₁₃	—	2	1	no	—
385	C₂²×C₄×C₁₃	—	2	1	no	—
386	C₂²×C₄×C₁₃	—	2	2	no	—
387	C₂²×C₄×C₁₃	—	2	2	no	—
388	C₂²×C₄×C₁₃	—	2	1	no	—
389	C₂²×C₄×C₁₃	—	2	1	no	—
390	C₂²×C₄×C₁₃	—	2	1	no	—
391	C₂²×C₄×C₁₃	—	2	2	no	—
392	C₂²×C₄×C₁₃	—	4	4	no	—
393	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
398	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
400	C₁₃×Q₁₆	—	2	4	no	—
401	C₁₃×Q₁₆	—	4	2	no	—
402	C₁₃×Q₁₆	—	4	2	no	—
403	C₁₃×Q₁₆	—	4	2	no	—
404	C₁₃×SD₁₆	—	2	4	no	—
405	C₁₃×SD₁₆	—	4	2	no	—
406	C₁₃×M₁₆	—	2	2	no	—
407	C₁₃×M₁₆	—	2	2	no	—
408	C₁₃×M₁₆	—	4	2	no	—
409	C₂×C₈×C₁₃	—	2	2	no	—
410	C₂×C₈×C₁₃	—	2	2	no	—
411	C₂×C₈×C₁₃	—	4	1	no	—
412	C₂×C₈×C₁₃	—	4	1	no	—
413	C₂×C₈×C₁₃	—	4	1	no	—
414	C₂×C₈×C₁₃	—	4	1	no	—
415	C₂×C₈×C₁₃	—	4	2	no	—
416	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
417	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
418	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
419	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
420	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
421	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
422	C₁₃×C₄⋊C₄	—	2	2	no	—
423	C₁₃×C₄⋊C₄	—	2	1	no	—
424	C₁₃×C₄⋊C₄	—	2	2	no	—
425	C₁₃×C₄⋊C₄	—	2	2	no	—
426	C₁₃×C₄⋊C₄	—	2	2	no	—
427	C₁₃×C₄⋊C₄	—	2	2	no	—
428	C₁₃×C₄⋊C₄	—	2	2	no	—
429	C₁₃×C₄⋊C₄	—	2	2	no	—
430	C₁₃×C₄⋊C₄	—	2	1	no	—
431	C₁₃×C₄⋊C₄	—	2	1	no	—
432	C₁₃×C₄⋊C₄	—	2	1	no	—
433	C₁₃×C₄⋊C₄	—	2	2	no	—
434	C₁₃×C₄⋊C₄	—	2	2	no	—
435	C₁₃×C₄⋊C₄	—	2	2	no	—
436	C₁₃×C₄⋊C₄	—	2	2	no	—
437	C₁₃×C₄⋊C₄	—	2	2	no	—
438	C₁₃×C₄⋊C₄	—	2	2	no	—
439	C₁₃×C₄⋊C₄	—	2	2	no	—
440	C₁₃×C₄⋊C₄	—	2	2	no	—
441	C₁₃×C₄⋊C₄	—	2	2	no	—
442	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
443	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
444	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
445	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
446	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
447	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
448	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
449	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
450	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
451	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
452	C₁₃×C₂²⋊C₄	—	2	2	no	—
453	C₁₃×C₂²⋊C₄	—	2	1	no	—
454	C₁₃×C₂²⋊C₄	—	2	1	no	—
455	C₁₃×C₂²⋊C₄	—	2	1	no	—
456	C₁₃×C₂²⋊C₄	—	2	1	no	—
457	C₁₃×C₂²⋊C₄	—	2	2	no	—
458	C₁₃×C₂²⋊C₄	—	2	2	no	—
459	C₁₃×C₂²⋊C₄	—	2	2	no	—
460	C₁₃×C₂²⋊C₄	—	2	2	no	—
461	C₁₃×C₂²⋊C₄	—	2	2	no	—
462	C₁₃×C₂²⋊C₄	—	2	2	no	—
463	C₁₃×C₂²⋊C₄	—	2	2	no	—
464	C₁₃×C₂²⋊C₄	—	2	2	no	—
465	C₁₃×C₂²⋊C₄	—	2	2	no	—
466	C₁₃×C₂²⋊C₄	—	2	2	no	—
467	C₁₃×C₂²⋊C₄	—	2	2	no	—
468	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
469	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
470	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
471	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
472	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
473	C₄²×C₁₃	—	2	1	no	—
474	C₄²×C₁₃	—	2	1	no	—
475	C₄²×C₁₃	—	2	1	no	—
476	C₄²×C₁₃	—	2	1	no	—
477	C₄²×C₁₃	—	2	2	no	—
478	C₄²×C₁₃	—	2	2	no	—
479	C₄²×C₁₃	—	2	2	no	—
480	C₄²×C₁₃	—	2	2	no	—
481	C₄²×C₁₃	C₂⁴	1	2	yes	—
482	#3495	C₂×C₁₃	1	1	yes	characteristic, complemented
483	#3489	C₂×C₁₃	1	1	yes	characteristic
484	#3315	C₂×C₁₃	1	2	yes	complemented
485	#3314	C₂×C₁₃	1	2	yes	complemented
486	#3313	C₂×C₁₃	1	2	yes	complemented
487	#3312	C₂×C₁₃	1	2	yes	complemented
488	#3302	C₂×C₁₃	1	2	yes	complemented
489	#3300	C₂×C₁₃	1	2	yes	complemented
490	#3299	C₂×C₁₃	1	2	yes	complemented
491	#3296	C₂×C₁₃	1	2	yes	complemented
492	#3137	C₂×C₁₃	1	1	yes	characteristic, complemented
493	#3098	C₂×C₁₃	1	1	yes	characteristic, complemented
494	#3095	C₂×C₁₃	1	1	yes	characteristic, complemented
495	#3083	C₂×C₁₃	1	1	yes	characteristic, complemented
496	#3063	C₂×C₁₃	1	1	yes	characteristic, complemented
497	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
498	#3044	C₂×C₁₃	1	1	yes	characteristic, complemented
499	#3011	C₂×C₁₃	1	1	yes	characteristic, complemented
500	#3007	C₂×C₁₃	1	1	yes	characteristic, complemented
501	#2947	C₂×C₁₃	1	1	yes	characteristic, complemented
502	#2929	C₂×C₁₃	1	1	yes	characteristic, complemented
503	#2898	C₂×C₁₃	1	1	yes	characteristic, complemented
504	C₂×#416	C₂×C₁₃	1	1	yes	characteristic, complemented
505	C₂³×C₁₃	—	2	2	no	—
506	C₂³×C₁₃	—	2	2	no	—
507	C₂³×C₁₃	—	2	1	no	—
508	C₂³×C₁₃	—	2	1	no	—
509	C₂³×C₁₃	—	4	1	no	—
510	C₂³×C₁₃	—	4	2	no	—
511	C₂³×C₁₃	—	4	2	no	—
512	C₂³×C₁₃	—	8	1	no	—
513	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
514	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
515	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
516	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
517	Q₈×C₁₃	—	2	2	no	—
518	Q₈×C₁₃	—	2	1	no	—
519	Q₈×C₁₃	—	2	2	no	—
520	Q₈×C₁₃	—	2	2	no	—
521	Q₈×C₁₃	—	2	1	no	—
522	Q₈×C₁₃	—	2	2	no	—
523	Q₈×C₁₃	—	2	2	no	—
524	Q₈×C₁₃	—	2	1	no	—
525	Q₈×C₁₃	—	4	4	no	—
526	Q₈×C₁₃	—	4	2	no	—
527	Q₈×C₁₃	—	4	2	no	—
528	Q₈×C₁₃	—	4	2	no	—
529	Q₈×C₁₃	—	8	2	no	—
530	Q₈×C₁₃	C₂×#41	1	2	yes	—
531	D₄×C₁₃	—	2	4	no	—
532	D₄×C₁₃	—	2	4	no	—
533	D₄×C₁₃	—	2	4	no	—
534	D₄×C₁₃	—	2	2	no	—
535	D₄×C₁₃	—	2	1	no	—
536	D₄×C₁₃	—	2	1	no	—
537	D₄×C₁₃	—	2	1	no	—
538	D₄×C₁₃	—	4	2	no	—
539	D₄×C₁₃	—	4	2	no	—
540	D₄×C₁₃	—	4	2	no	—
541	D₄×C₁₃	—	4	2	no	—
542	D₄×C₁₃	—	4	4	no	—
543	D₄×C₁₃	—	4	2	no	—
544	D₄×C₁₃	—	8	2	no	—
545	D₄×C₁₃	C₂×#41	1	2	yes	—
546	C₂×C₄×C₁₃	—	2	2	no	—
547	C₂×C₄×C₁₃	—	2	1	no	—
548	C₂×C₄×C₁₃	—	2	2	no	—
549	C₂×C₄×C₁₃	—	2	2	no	—
550	C₂×C₄×C₁₃	—	2	4	no	—
551	C₂×C₄×C₁₃	—	2	1	no	—
552	C₂×C₄×C₁₃	—	2	1	no	—
553	C₂×C₄×C₁₃	—	2	2	no	—
554	C₂×C₄×C₁₃	—	2	1	no	—
555	C₂×C₄×C₁₃	—	2	1	no	—
556	C₂×C₄×C₁₃	—	2	2	no	—
557	C₂×C₄×C₁₃	—	2	1	no	—
558	C₂×C₄×C₁₃	—	2	1	no	—
559	C₂×C₄×C₁₃	—	2	1	no	—
560	C₂×C₄×C₁₃	—	2	2	no	—
561	C₂×C₄×C₁₃	—	2	1	no	—
562	C₂×C₄×C₁₃	—	2	2	no	—
563	C₂×C₄×C₁₃	—	2	2	no	—
564	C₂×C₄×C₁₃	—	2	2	no	—
565	C₂×C₄×C₁₃	—	2	1	no	—
566	C₂×C₄×C₁₃	—	4	2	no	—
567	C₂×C₄×C₁₃	—	4	2	no	—
568	C₂×C₄×C₁₃	—	4	2	no	—
569	C₂×C₄×C₁₃	—	4	4	no	—
570	C₂×C₄×C₁₃	—	4	4	no	—
571	C₂×C₄×C₁₃	—	4	2	no	—
572	C₂×C₄×C₁₃	—	4	2	no	—
573	C₂×C₄×C₁₃	—	4	2	no	—
574	C₂×C₄×C₁₃	—	4	2	no	—
575	C₂×C₄×C₁₃	—	8	2	no	—
576	C₂×C₄×C₁₃	—	8	2	no	—
577	C₂×C₄×C₁₃	—	8	1	no	—
578	C₂×C₄×C₁₃	—	8	1	no	—
579	C₂×C₄×C₁₃	—	8	1	no	—
580	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
581	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
583	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
584	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
586	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
587	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
588	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
589	C₈×C₁₃	—	2	2	no	—
590	C₈×C₁₃	—	2	1	no	—
591	C₈×C₁₃	—	2	1	no	—
592	C₈×C₁₃	—	2	1	no	—
593	C₈×C₁₃	—	2	1	no	—
594	C₈×C₁₃	—	2	2	no	—
595	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
596	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
597	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
598	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
599	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
600	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
601	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
602	#556	C₂²×C₁₃	1	2	yes	complemented
603	#554	C₂²×C₁₃	1	2	yes	—
604	#552	—	2	2	no	—
605	#552	C₂²×C₁₃	1	2	yes	—
606	#552	C₂²×C₁₃	1	2	yes	complemented
607	#551	—	2	2	no	—
608	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
609	#548	C₂²×C₁₃	1	2	yes	—
610	#547	—	2	2	no	—
611	#547	C₂²×C₁₃	1	2	yes	—
612	#546	—	2	2	no	—
613	#546	C₂²×C₁₃	1	2	yes	—
614	#544	C₂²×C₁₃	1	1	yes	characteristic, complemented
615	#542	—	2	1	no	—
616	#541	—	2	1	no	—
617	#537	—	2	1	no	—
618	#537	C₂²×C₁₃	1	1	yes	characteristic
619	#536	—	2	1	no	—
620	#536	C₂²×C₁₃	1	1	yes	characteristic
621	#536	C₂²×C₁₃	1	1	yes	characteristic, complemented
622	#533	—	2	1	no	—
623	#529	—	2	1	no	—
624	#525	—	2	1	no	—
625	#525	C₂²×C₁₃	1	1	yes	characteristic
626	C₂×C₂²⋊Q₈	—	2	1	no	—
627	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
628	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
629	#520	C₂²×C₁₃	1	1	yes	characteristic
630	#520	C₂²×C₁₃	1	1	yes	characteristic, complemented
631	#519	C₂²×C₁₃	1	1	yes	characteristic, complemented
632	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
633	#491	C₂²×C₁₃	1	2	yes	complemented
634	#489	C₂²×C₁₃	1	2	yes	complemented
635	#488	C₂²×C₁₃	1	2	yes	complemented
636	#487	C₂²×C₁₃	1	2	yes	complemented
637	#485	C₂²×C₁₃	1	2	yes	complemented
638	#485	C₂²×C₁₃	1	2	yes	complemented
639	#485	C₂²×C₁₃	1	2	yes	complemented
640	#484	C₂²×C₁₃	1	2	yes	—
641	#484	C₂²×C₁₃	1	2	yes	complemented
642	#483	C₂²×C₁₃	1	2	yes	—
643	#482	C₂²×C₁₃	1	2	yes	complemented
644	#480	C₂²×C₁₃	1	2	yes	complemented
645	#479	C₂²×C₁₃	1	2	yes	complemented
646	#478	C₂²×C₁₃	1	2	yes	complemented
647	#477	C₂²×C₁₃	1	2	yes	complemented
648	#474	C₂²×C₁₃	1	2	yes	complemented
649	#470	C₂²×C₁₃	1	2	yes	complemented
650	#468	C₂²×C₁₃	1	2	yes	complemented
651	#467	C₂²×C₁₃	1	2	yes	—
652	#467	C₂²×C₁₃	1	2	yes	—
653	#467	C₂²×C₁₃	1	2	yes	complemented
654	#467	C₂²×C₁₃	1	2	yes	complemented
655	#467	C₂²×C₁₃	1	2	yes	complemented
656	#465	C₂²×C₁₃	1	2	yes	complemented
657	#464	C₂²×C₁₃	1	2	yes	complemented
658	#464	C₂²×C₁₃	1	2	yes	complemented
659	#462	C₂²×C₁₃	1	2	yes	complemented
660	#462	C₂²×C₁₃	1	2	yes	complemented
661	#452	C₂²×C₁₃	1	2	yes	—
662	#452	C₂²×C₁₃	1	2	yes	—
663	#452	C₂²×C₁₃	1	2	yes	complemented
664	#452	C₂²×C₁₃	1	2	yes	complemented
665	#451	C₂²×C₁₃	1	2	yes	—
666	#451	C₂²×C₁₃	1	2	yes	complemented
667	#451	C₂²×C₁₃	1	2	yes	complemented
668	#450	C₂²×C₁₃	1	2	yes	—
669	#441	C₂²×C₁₃	1	2	yes	complemented
670	#440	C₂²×C₁₃	1	2	yes	complemented
671	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
672	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
673	#435	C₂²×C₁₃	1	2	yes	—
674	#435	C₂²×C₁₃	1	2	yes	complemented
675	C₈×D₄	C₂²×C₁₃	1	2	yes	—
676	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
677	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
678	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
679	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
680	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
681	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
682	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
683	#419	C₂²×C₁₃	1	2	yes	complemented
684	#417	C₂²×C₁₃	1	1	yes	characteristic
685	#417	C₂²×C₁₃	1	1	yes	characteristic
686	#417	C₂²×C₁₃	1	2	yes	complemented
687	#416	C₂²×C₁₃	1	1	yes	characteristic
688	#416	C₂²×C₁₃	1	1	yes	characteristic
689	#416	C₂²×C₁₃	1	1	yes	characteristic
690	#416	C₂²×C₁₃	1	1	yes	characteristic
691	#416	C₂²×C₁₃	1	1	yes	characteristic
692	#416	C₂²×C₁₃	1	1	yes	characteristic
693	#416	C₂²×C₁₃	1	1	yes	characteristic
694	#416	C₂²×C₁₃	1	1	yes	characteristic
695	#416	C₂²×C₁₃	1	2	yes	complemented
696	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
697	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
698	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
699	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
700	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
701	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
702	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
703	#408	C₂²×C₁₃	1	1	yes	characteristic, complemented
704	#407	C₂²×C₁₃	1	1	yes	characteristic
705	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
706	C₂²×C₁₃	—	2	1	no	—
707	C₂²×C₁₃	—	2	1	no	—
708	C₂²×C₁₃	—	2	1	no	—
709	C₂²×C₁₃	—	2	1	no	—
710	C₂²×C₁₃	—	2	2	no	—
711	C₂²×C₁₃	—	2	1	no	—
712	C₂²×C₁₃	—	2	1	no	—
713	C₂²×C₁₃	—	2	2	no	—
714	C₂²×C₁₃	—	2	2	no	—
715	C₂²×C₁₃	—	2	2	no	—
716	C₂²×C₁₃	—	2	1	no	—
717	C₂²×C₁₃	—	4	4	no	—
718	C₂²×C₁₃	—	4	1	no	—
719	C₂²×C₁₃	—	4	1	no	—
720	C₂²×C₁₃	—	4	1	no	—
721	C₂²×C₁₃	—	4	1	no	—
722	C₂²×C₁₃	—	4	1	no	—
723	C₂²×C₁₃	—	8	4	no	—
724	C₂²×C₁₃	#546	1	2	yes	—
725	C₂²×C₁₃	#578	1	2	yes	—
726	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
727	C₄×C₁₃	—	2	2	no	—
728	C₄×C₁₃	—	2	1	no	—
729	C₄×C₁₃	—	2	1	no	—
730	C₄×C₁₃	—	2	2	no	—
731	C₄×C₁₃	—	2	2	no	—
732	C₄×C₁₃	—	2	2	no	—
733	C₄×C₁₃	—	4	1	no	—
734	C₄×C₁₃	—	4	2	no	—
735	C₄×C₁₃	—	4	2	no	—
736	C₄×C₁₃	—	4	1	no	—
737	C₄×C₁₃	—	4	1	no	—
738	C₄×C₁₃	—	4	2	no	—
739	C₄×C₁₃	—	4	2	no	—
740	C₄×C₁₃	—	4	1	no	—
741	C₄×C₁₃	—	4	1	no	—
742	C₄×C₁₃	#546	1	2	yes	—
743	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
744	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
745	2₋¹⁺⁴	—	2	4	no	—
746	2₋¹⁺⁴	—	4	2	no	—
747	C₂×#41	—	2	1	no	—
748	C₂×#41	—	2	2	no	—
749	C₂×#41	—	2	1	no	—
750	C₂×#41	—	2	1	no	—
751	C₂×#41	—	2	4	no	—
752	C₂×#41	—	4	2	no	—
753	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
754	C₂×#41	C₂³×C₁₃	1	2	yes	—
755	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
756	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
757	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
758	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
759	C₂²×Q₈	—	2	1	no	—
760	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
761	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
762	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
763	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
764	C₂²×D₄	—	2	1	no	—
765	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
766	C₂³×C₄	—	2	1	no	—
767	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
768	#137	—	2	4	no	—
769	#137	—	4	2	no	—
770	C₂×Q₁₆	—	4	2	no	—
771	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
772	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
773	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
774	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
776	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
777	#131	—	4	2	no	—
778	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
779	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
780	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
781	C₂²×C₈	—	4	2	no	—
782	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
783	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
784	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
785	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
786	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
787	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
788	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
789	C₄⋊Q₈	—	2	1	no	—
790	C₄⋊Q₈	—	2	1	no	—
791	C₄⋊Q₈	—	2	2	no	—
792	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
793	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
794	#126	—	2	2	no	—
795	#126	—	2	2	no	—
796	#126	—	2	2	no	—
797	#126	—	2	2	no	—
798	#125	—	2	1	no	—
799	#125	—	2	2	no	—
800	#125	—	2	2	no	—
801	#125	—	2	2	no	—
802	#125	C₂³×C₁₃	1	2	yes	—
803	#124	—	2	1	no	—
804	#124	—	2	2	no	—
805	#124	—	2	2	no	—
806	#124	C₂³×C₁₃	1	2	yes	—
807	#123	—	2	2	no	—
808	#123	—	2	2	no	—
809	#123	—	2	2	no	—
810	#123	—	2	2	no	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	#123	D₄×C₁₃	1	2	yes	—
815	C₂²⋊Q₈	—	2	1	no	—
816	C₂²⋊Q₈	—	2	1	no	—
817	C₂²⋊Q₈	—	2	1	no	—
818	C₂²⋊Q₈	—	2	1	no	—
819	C₂²⋊Q₈	—	2	1	no	—
820	C₂²⋊Q₈	—	2	1	no	—
821	C₂²⋊Q₈	—	2	2	no	—
822	C₂²⋊Q₈	—	2	1	no	—
823	C₂²⋊Q₈	—	2	2	no	—
824	C₂²⋊Q₈	—	2	2	no	—
825	C₂²⋊Q₈	—	2	2	no	—
826	C₂²⋊Q₈	—	2	2	no	—
827	C₂²⋊Q₈	—	2	2	no	—
828	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
829	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
830	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
831	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
832	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
833	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
834	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
835	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
836	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
837	#121	—	2	1	no	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	—	2	2	no	—
841	#121	—	2	2	no	—
842	#121	D₄×C₁₃	1	1	yes	characteristic
843	#121	D₄×C₁₃	1	1	yes	characteristic
844	#121	C₂³×C₁₃	1	2	yes	—
845	#120	—	2	2	no	—
846	#120	D₄×C₁₃	1	2	yes	—
847	C₄×Q₈	—	2	1	no	—
848	C₄×Q₈	—	2	1	no	—
849	C₄×Q₈	—	2	1	no	—
850	C₄×Q₈	—	2	2	no	—
851	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
852	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
853	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	—	2	2	no	—
856	C₄×D₄	—	2	2	no	—
857	C₄×D₄	—	2	2	no	—
858	C₄×D₄	—	2	2	no	—
859	C₄×D₄	—	2	2	no	—
860	C₄×D₄	C₂³×C₁₃	1	2	yes	—
861	C₄×D₄	C₂³×C₁₃	1	2	yes	—
862	C₄×D₄	C₂³×C₁₃	1	2	yes	—
863	#117	—	2	1	no	—
864	#117	—	2	1	no	—
865	#117	—	2	1	no	—
866	#117	—	2	2	no	—
867	#117	—	2	2	no	—
868	#117	—	2	2	no	—
869	#117	C₂³×C₁₃	1	1	yes	characteristic
870	#117	C₂³×C₁₃	1	1	yes	characteristic
871	#117	C₂³×C₁₃	1	1	yes	characteristic
872	#117	C₂³×C₁₃	1	1	yes	characteristic
873	#117	C₂³×C₁₃	1	2	yes	—
874	#117	C₂³×C₁₃	1	1	yes	characteristic
875	C₂×C₄⋊C₄	—	2	1	no	—
876	C₂×C₄⋊C₄	—	2	1	no	—
877	C₂×C₄⋊C₄	—	2	1	no	—
878	C₂×C₄⋊C₄	—	2	2	no	—
879	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
880	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
881	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
882	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
883	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
884	C₂×C₂²⋊C₄	—	2	1	no	—
885	C₂×C₂²⋊C₄	—	2	1	no	—
886	C₂×C₂²⋊C₄	—	2	1	no	—
887	C₂×C₂²⋊C₄	—	2	2	no	—
888	C₂×C₄²	—	2	1	no	—
889	#107	C₂³×C₁₃	1	2	yes	—
890	#107	C₂³×C₁₃	1	2	yes	—
891	#107	C₂³×C₁₃	1	2	yes	—
892	#107	C₂³×C₁₃	1	2	yes	—
893	#106	C₂³×C₁₃	1	2	yes	—
894	#106	C₂³×C₁₃	1	2	yes	—
895	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
896	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
897	#103	C₂³×C₁₃	1	1	yes	characteristic
898	#103	C₂³×C₁₃	1	1	yes	characteristic
899	#103	C₂³×C₁₃	1	1	yes	characteristic
900	#103	C₂³×C₁₃	1	1	yes	characteristic
901	#103	C₂³×C₁₃	1	1	yes	characteristic
902	#103	C₂³×C₁₃	1	1	yes	characteristic
903	#103	C₂³×C₁₃	1	1	yes	characteristic
904	#103	C₂³×C₁₃	1	1	yes	characteristic
905	#103	C₂³×C₁₃	1	2	yes	—
906	#103	C₂³×C₁₃	1	2	yes	—
907	#103	C₂³×C₁₃	1	2	yes	—
908	#103	C₂³×C₁₃	1	2	yes	—
909	#103	C₂³×C₁₃	1	2	yes	—
910	#103	C₂³×C₁₃	1	2	yes	—
911	#103	C₂³×C₁₃	1	2	yes	—
912	#103	C₂³×C₁₃	1	2	yes	—
913	#103	C₂³×C₁₃	1	2	yes	—
914	#103	C₂³×C₁₃	1	2	yes	—
915	#102	C₂³×C₁₃	1	1	yes	characteristic
916	#102	C₂³×C₁₃	1	1	yes	characteristic
917	#102	C₂³×C₁₃	1	1	yes	characteristic
918	#102	C₂³×C₁₃	1	1	yes	characteristic
919	#102	C₂³×C₁₃	1	1	yes	characteristic
920	#102	C₂³×C₁₃	1	1	yes	characteristic
921	#102	C₂³×C₁₃	1	1	yes	characteristic
922	#102	C₂³×C₁₃	1	1	yes	characteristic
923	#102	C₂³×C₁₃	1	2	yes	—
924	#102	C₂³×C₁₃	1	2	yes	—
925	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
926	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
927	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
928	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
929	#97	C₂³×C₁₃	1	2	yes	—
930	C₄×C₈	C₂³×C₁₃	1	2	yes	—
931	C₂×C₁₃	—	2	2	no	—
932	C₂×C₁₃	—	2	2	no	—
933	C₂×C₁₃	—	4	2	no	—
934	C₂×C₁₃	—	4	1	no	—
935	C₂×C₁₃	—	4	2	no	—
936	C₂×C₁₃	—	8	1	no	—
937	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
938	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
939	C₂×C₁₃	#3584	1	1	yes	characteristic
940	C₂⁴	—	2	1	no	—
941	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
942	#41	—	2	2	no	—
943	#41	—	2	2	no	—
944	#41	—	2	2	no	—
945	#41	—	2	2	no	—
946	#41	—	2	2	no	—
947	#41	—	2	4	no	—
948	#41	—	2	2	no	—
949	#41	—	2	2	no	—
950	#41	—	4	4	no	—
951	#41	—	4	1	no	—
952	#41	—	4	1	no	—
953	#41	—	4	2	no	—
954	#41	—	4	4	no	—
955	#41	—	4	4	no	—
956	#41	—	4	8	no	—
957	#41	C₁₃×#41	1	4	yes	—
958	C₂×Q₈	—	2	1	no	—
959	C₂×Q₈	—	2	1	no	—
960	C₂×Q₈	—	2	2	no	—
961	C₂×Q₈	—	2	1	no	—
962	C₂×Q₈	—	2	2	no	—
963	C₂×Q₈	—	2	2	no	—
964	C₂×Q₈	—	2	4	no	—
965	C₂×Q₈	—	2	2	no	—
966	C₂×Q₈	—	2	2	no	—
967	C₂×Q₈	—	2	2	no	—
968	C₂×Q₈	—	2	2	no	—
969	C₂×Q₈	—	4	1	no	—
970	C₂×Q₈	—	4	2	no	—
971	C₂×Q₈	—	4	4	no	—
972	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
973	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
974	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
975	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
976	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
977	C₂×D₄	—	2	1	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	2	no	—
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	1	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	4	1	no	—
986	C₂×D₄	—	4	4	no	—
987	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
988	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
989	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
990	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
991	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
992	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	—	2	2	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	2	no	—
1010	C₂²×C₄	—	4	4	no	—
1011	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1012	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1013	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1014	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1015	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1016	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1017	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1018	Q₁₆	—	2	4	no	—
1019	Q₁₆	—	4	2	no	—
1020	Q₁₆	—	4	2	no	—
1021	Q₁₆	—	4	2	no	—
1022	SD₁₆	—	2	4	no	—
1023	SD₁₆	—	4	2	no	—
1024	M₁₆	—	2	2	no	—
1025	M₁₆	—	2	2	no	—
1026	M₁₆	—	4	2	no	—
1027	C₂×C₈	—	2	2	no	—
1028	C₂×C₈	—	2	2	no	—
1029	C₂×C₈	—	4	1	no	—
1030	C₂×C₈	—	4	1	no	—
1031	C₂×C₈	—	4	1	no	—
1032	C₂×C₈	—	4	1	no	—
1033	C₂×C₈	—	4	2	no	—
1034	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1035	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1036	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1037	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1038	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1039	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1061	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1062	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1063	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1064	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1065	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1067	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1068	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1069	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	1	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	2	no	—
1079	C₂²⋊C₄	—	2	2	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1087	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1088	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1089	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1090	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1091	C₄²	—	2	1	no	—
1092	C₄²	—	2	1	no	—
1093	C₄²	—	2	1	no	—
1094	C₄²	—	2	1	no	—
1095	C₄²	—	2	2	no	—
1096	C₄²	—	2	2	no	—
1097	C₄²	—	2	2	no	—
1098	C₄²	—	2	2	no	—
1099	C₄²	C₂⁴×C₁₃	1	2	yes	—
1100	C₁₃	#61173	1	1	yes	characteristic, direct product factor, Sylow
1101	C₂³	—	2	2	no	—
1102	C₂³	—	2	2	no	—
1103	C₂³	—	2	1	no	—
1104	C₂³	—	2	1	no	—
1105	C₂³	—	4	1	no	—
1106	C₂³	—	4	2	no	—
1107	C₂³	—	4	2	no	—
1108	C₂³	—	8	1	no	—
1109	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1110	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1111	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1112	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1113	Q₈	—	2	2	no	—
1114	Q₈	—	2	1	no	—
1115	Q₈	—	2	2	no	—
1116	Q₈	—	2	2	no	—
1117	Q₈	—	2	1	no	—
1118	Q₈	—	2	2	no	—
1119	Q₈	—	2	2	no	—
1120	Q₈	—	2	1	no	—
1121	Q₈	—	4	4	no	—
1122	Q₈	—	4	2	no	—
1123	Q₈	—	4	2	no	—
1124	Q₈	—	4	2	no	—
1125	Q₈	—	8	2	no	—
1126	Q₈	C₂×C₁₃×#41	1	2	yes	—
1127	D₄	—	2	4	no	—
1128	D₄	—	2	4	no	—
1129	D₄	—	2	4	no	—
1130	D₄	—	2	2	no	—
1131	D₄	—	2	1	no	—
1132	D₄	—	2	1	no	—
1133	D₄	—	2	1	no	—
1134	D₄	—	4	2	no	—
1135	D₄	—	4	2	no	—
1136	D₄	—	4	2	no	—
1137	D₄	—	4	2	no	—
1138	D₄	—	4	4	no	—
1139	D₄	—	4	2	no	—
1140	D₄	—	8	2	no	—
1141	D₄	C₂×C₁₃×#41	1	2	yes	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	4	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	2	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	4	2	no	—
1163	C₂×C₄	—	4	2	no	—
1164	C₂×C₄	—	4	2	no	—
1165	C₂×C₄	—	4	4	no	—
1166	C₂×C₄	—	4	4	no	—
1167	C₂×C₄	—	4	2	no	—
1168	C₂×C₄	—	4	2	no	—
1169	C₂×C₄	—	4	2	no	—
1170	C₂×C₄	—	4	2	no	—
1171	C₂×C₄	—	8	2	no	—
1172	C₂×C₄	—	8	2	no	—
1173	C₂×C₄	—	8	1	no	—
1174	C₂×C₄	—	8	1	no	—
1175	C₂×C₄	—	8	1	no	—
1176	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1177	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1178	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1179	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1180	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1181	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1182	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1183	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1184	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1185	C₈	—	2	2	no	—
1186	C₈	—	2	1	no	—
1187	C₈	—	2	1	no	—
1188	C₈	—	2	1	no	—
1189	C₈	—	2	1	no	—
1190	C₈	—	2	2	no	—
1191	C₂²	—	2	1	no	—
1192	C₂²	—	2	1	no	—
1193	C₂²	—	2	1	no	—
1194	C₂²	—	2	1	no	—
1195	C₂²	—	2	2	no	—
1196	C₂²	—	2	1	no	—
1197	C₂²	—	2	2	no	—
1198	C₂²	—	2	1	no	—
1199	C₂²	—	2	1	no	—
1200	C₂²	—	2	2	no	—
1201	C₂²	—	2	2	no	—
1202	C₂²	—	4	4	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	1	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	8	4	no	—
1209	C₂²	C₁₃×#546	1	2	yes	—
1210	C₂²	C₁₃×#578	1	2	yes	—
1211	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1212	C₄	—	2	2	no	—
1213	C₄	—	2	2	no	—
1214	C₄	—	2	1	no	—
1215	C₄	—	2	1	no	—
1216	C₄	—	2	2	no	—
1217	C₄	—	2	2	no	—
1218	C₄	—	4	1	no	—
1219	C₄	—	4	1	no	—
1220	C₄	—	4	1	no	—
1221	C₄	—	4	2	no	—
1222	C₄	—	4	2	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	4	2	no	—
1226	C₄	—	4	2	no	—
1227	C₄	C₁₃×#546	1	2	yes	—
1228	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1229	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1230	C₂	—	2	2	no	—
1231	C₂	—	2	2	no	—
1232	C₂	—	4	1	no	—
1233	C₂	—	4	2	no	—
1234	C₂	—	4	2	no	—
1235	C₂	—	8	1	no	—
1236	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
1237	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
1238	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3489	C₂
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. C₁₃×#3495	C₂	semidirect
3. C₁₃×#3315	C₂	semidirect
4. C₁₃×#3314	C₂	semidirect
5. C₁₃×#3313	C₂	semidirect
6. C₁₃×#3312	C₂	semidirect
7. C₁₃×#3302	C₂	semidirect
8. C₁₃×#3300	C₂	semidirect
9. C₁₃×#3299	C₂	semidirect
10. C₁₃×#3296	C₂	semidirect
11. C₁₃×#3137	C₂	semidirect
12. C₁₃×#3098	C₂	semidirect
13. C₁₃×#3095	C₂	semidirect
14. C₁₃×#3083	C₂	semidirect
15. C₁₃×#3063	C₂	semidirect
16. C₂×C₁₃×#467	C₂	semidirect
17. C₁₃×#3044	C₂	semidirect
18. C₁₃×#3011	C₂	semidirect
19. C₁₃×#3007	C₂	semidirect
20. C₁₃×#2947	C₂	semidirect
21. C₁₃×#2929	C₂	semidirect
22. C₁₃×#2898	C₂	semidirect
23. C₂×C₁₃×#416	C₂	semidirect
28. C₂²×C₁₃×Q₁₆	C₂²	semidirect
29. C₂×C₁₃×#131	C₂²	semidirect
31. C₁₃×#556	C₂²	semidirect
35. C₁₃×#552	C₂²	semidirect
43. C₁₃×#544	C₂²	semidirect
50. C₁₃×#536	C₂²	semidirect
59. C₁₃×#520	C₂²	semidirect
60. C₁₃×#519	C₂²	semidirect
62. C₁₃×#491	C₂²	semidirect
63. C₁₃×#489	C₂²	semidirect
64. C₁₃×#488	C₂²	semidirect
65. C₁₃×#487	C₂²	semidirect
66. C₁₃×#485	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
68. C₁₃×#485	C₂²	semidirect
70. C₁₃×#484	C₂²	semidirect
72. C₁₃×#482	C₂²	semidirect
73. C₁₃×#480	C₂²	semidirect
74. C₁₃×#479	C₂²	semidirect
75. C₁₃×#478	C₂²	semidirect
76. C₁₃×#477	C₂²	semidirect
77. C₁₃×#474	C₂²	semidirect
78. C₁₃×#470	C₂²	semidirect
79. C₁₃×#468	C₂²	semidirect
82. C₁₃×#467	C₂²	semidirect
83. C₁₃×#467	C₂²	semidirect
84. C₁₃×#467	C₂²	semidirect
85. C₁₃×#465	C₂²	semidirect
86. C₁₃×#464	C₂²	semidirect
87. C₁₃×#464	C₂²	semidirect
88. C₁₃×#462	C₂²	semidirect
89. C₁₃×#462	C₂²	semidirect
92. C₁₃×#452	C₂²	semidirect
93. C₁₃×#452	C₂²	semidirect
95. C₁₃×#451	C₂²	semidirect
96. C₁₃×#451	C₂²	semidirect
98. C₁₃×#441	C₂²	semidirect
99. C₁₃×#440	C₂²	semidirect
100. C₄×C₁₃×Q₁₆	C₂²	semidirect
101. C₄×C₁₃×SD₁₆	C₂²	semidirect
103. C₁₃×#435	C₂²	semidirect
105. C₈×D₄×C₁₃	C₂²	semidirect
106. C₁₃×#428	C₂²	semidirect
107. C₁₃×#428	C₂²	semidirect
108. C₂×C₁₃×#107	C₂²	semidirect
109. C₁₃×#424	C₂²	semidirect
110. C₁₃×#419	C₂²	semidirect
111. C₁₃×#419	C₂²	semidirect
112. C₁₃×#419	C₂²	semidirect
115. C₁₃×#417	C₂²	semidirect
124. C₁₃×#416	C₂²	semidirect
127. C₂×C₁₃×#103	C₂²	semidirect
128. C₂×C₁₃×#103	C₂²	semidirect
129. C₂×C₁₃×#103	C₂²	semidirect
132. C₁₃×#408	C₂²	semidirect
134. C₁₃×#405	C₂²	semidirect
321. #61173	C₁₃	direct (N × H)
482. #3495	C₂×C₁₃	semidirect
484. #3315	C₂×C₁₃	semidirect
485. #3314	C₂×C₁₃	semidirect
486. #3313	C₂×C₁₃	semidirect
487. #3312	C₂×C₁₃	semidirect
488. #3302	C₂×C₁₃	semidirect
489. #3300	C₂×C₁₃	semidirect
490. #3299	C₂×C₁₃	semidirect
491. #3296	C₂×C₁₃	semidirect
492. #3137	C₂×C₁₃	semidirect
493. #3098	C₂×C₁₃	semidirect
494. #3095	C₂×C₁₃	semidirect
495. #3083	C₂×C₁₃	semidirect
496. #3063	C₂×C₁₃	semidirect
497. C₂×#467	C₂×C₁₃	semidirect
498. #3044	C₂×C₁₃	semidirect
499. #3011	C₂×C₁₃	semidirect
500. #3007	C₂×C₁₃	semidirect
501. #2947	C₂×C₁₃	semidirect
502. #2929	C₂×C₁₃	semidirect
503. #2898	C₂×C₁₃	semidirect
504. C₂×#416	C₂×C₁₃	semidirect
599. C₂²×Q₁₆	C₂²×C₁₃	semidirect
600. C₂×#131	C₂²×C₁₃	semidirect
602. #556	C₂²×C₁₃	semidirect
606. #552	C₂²×C₁₃	semidirect
614. #544	C₂²×C₁₃	semidirect
621. #536	C₂²×C₁₃	semidirect
630. #520	C₂²×C₁₃	semidirect
631. #519	C₂²×C₁₃	semidirect
633. #491	C₂²×C₁₃	semidirect
634. #489	C₂²×C₁₃	semidirect
635. #488	C₂²×C₁₃	semidirect
636. #487	C₂²×C₁₃	semidirect
637. #485	C₂²×C₁₃	semidirect
638. #485	C₂²×C₁₃	semidirect
639. #485	C₂²×C₁₃	semidirect
641. #484	C₂²×C₁₃	semidirect
643. #482	C₂²×C₁₃	semidirect
644. #480	C₂²×C₁₃	semidirect
645. #479	C₂²×C₁₃	semidirect
646. #478	C₂²×C₁₃	semidirect
647. #477	C₂²×C₁₃	semidirect
648. #474	C₂²×C₁₃	semidirect
649. #470	C₂²×C₁₃	semidirect
650. #468	C₂²×C₁₃	semidirect
653. #467	C₂²×C₁₃	semidirect
654. #467	C₂²×C₁₃	semidirect
655. #467	C₂²×C₁₃	semidirect
656. #465	C₂²×C₁₃	semidirect
657. #464	C₂²×C₁₃	semidirect
658. #464	C₂²×C₁₃	semidirect
659. #462	C₂²×C₁₃	semidirect
660. #462	C₂²×C₁₃	semidirect
663. #452	C₂²×C₁₃	semidirect
664. #452	C₂²×C₁₃	semidirect
666. #451	C₂²×C₁₃	semidirect
667. #451	C₂²×C₁₃	semidirect
669. #441	C₂²×C₁₃	semidirect
670. #440	C₂²×C₁₃	semidirect
671. C₄×Q₁₆	C₂²×C₁₃	semidirect
672. C₄×SD₁₆	C₂²×C₁₃	semidirect
674. #435	C₂²×C₁₃	semidirect
676. C₈×D₄	C₂²×C₁₃	semidirect
677. #428	C₂²×C₁₃	semidirect
678. #428	C₂²×C₁₃	semidirect
679. C₂×#107	C₂²×C₁₃	semidirect
680. #424	C₂²×C₁₃	semidirect
681. #419	C₂²×C₁₃	semidirect
682. #419	C₂²×C₁₃	semidirect
683. #419	C₂²×C₁₃	semidirect
686. #417	C₂²×C₁₃	semidirect
695. #416	C₂²×C₁₃	semidirect
698. C₂×#103	C₂²×C₁₃	semidirect
699. C₂×#103	C₂²×C₁₃	semidirect
700. C₂×#103	C₂²×C₁₃	semidirect
703. #408	C₂²×C₁₃	semidirect
705. #405	C₂²×C₁₃	semidirect
1100. C₁₃	#61173	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3495	2
C₁₃×#3489	2
C₁₃×#3315	2
C₁₃×#3314	2
C₁₃×#3313	2
C₁₃×#3312	2
C₁₃×#3302	2
C₁₃×#3300	2
C₁₃×#3299	2
C₁₃×#3296	2
C₁₃×#3137	2
C₁₃×#3098	2
C₁₃×#3095	2
C₁₃×#3083	2
C₁₃×#3063	2
C₂×C₁₃×#467	2
C₁₃×#3044	2
C₁₃×#3011	2
C₁₃×#3007	2
C₁₃×#2947	2
C₁₃×#2929	2
C₁₃×#2898	2
C₂×C₁₃×#416	2
#61173	13

Subgroups — C13×#61173 #15747512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61173 #15747512