Subgroups — C₁₃×#60764 #15747103

Order 3328.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3489	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3203	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3201	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3196	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3193	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3189	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3188	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3098	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3092	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3063	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3061	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3013	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#131	C₂²	1	2	yes	complemented
24	D₄×Q₈×C₁₃	—	2	1	no	—
25	C₁₃×#548	—	2	1	no	—
26	C₁₃×#547	—	2	2	no	—
27	C₁₃×#547	—	2	1	no	—
28	C₁₃×#546	—	2	2	no	—
29	C₁₃×#546	—	2	1	no	—
30	C₁₃×#537	—	2	2	no	—
31	C₁₃×#537	—	2	1	no	—
32	C₁₃×#537	—	2	1	no	—
33	C₁₃×#537	C₂²	1	2	yes	—
34	C₁₃×#537	C₂²	1	2	yes	—
35	C₁₃×#537	C₂²	1	4	yes	—
36	C₁₃×#537	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#537	C₂²	1	2	yes	complemented
38	C₁₃×#536	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#536	C₂²	1	2	yes	complemented
40	C₁₃×#525	C₂²	1	1	yes	characteristic
41	C₁₃×#525	C₂²	1	2	yes	—
42	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
43	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
45	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
46	C₂×C₁₃×#121	—	2	1	no	—
47	C₂×C₁₃×#121	—	2	2	no	—
48	C₂×C₁₃×#121	C₂²	1	2	yes	—
49	C₁₃×#520	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₁₃×#485	C₂²	1	4	yes	complemented
52	C₁₃×#484	C₂²	1	2	yes	—
53	C₁₃×#484	C₂²	1	2	yes	—
54	C₁₃×#484	C₂²	1	2	yes	—
55	C₁₃×#484	C₂²	1	4	yes	complemented
56	C₁₃×#484	C₂²	1	4	yes	complemented
57	C₁₃×#483	C₂²	1	2	yes	complemented
58	C₁₃×#482	C₂²	1	4	yes	complemented
59	C₁₃×#481	C₂²	1	2	yes	—
60	C₁₃×#480	C₂²	1	2	yes	complemented
61	C₁₃×#480	C₂²	1	4	yes	complemented
62	C₁₃×#470	C₂²	1	4	yes	complemented
63	C₁₃×#468	C₂²	1	4	yes	complemented
64	C₁₃×#468	C₂²	1	4	yes	complemented
65	C₁₃×#468	C₂²	1	4	yes	complemented
66	C₁₃×#467	C₂²	1	4	yes	complemented
67	C₁₃×#467	C₂²	1	4	yes	complemented
68	C₁₃×#466	C₂²	1	4	yes	complemented
69	C₁₃×#465	C₂²	1	4	yes	complemented
70	C₁₃×#452	C₂²	1	4	yes	complemented
71	C₁₃×#452	C₂²	1	4	yes	complemented
72	C₁₃×#452	C₂²	1	2	yes	complemented
73	C₁₃×#451	C₂²	1	2	yes	—
74	C₁₃×#451	C₂²	1	1	yes	characteristic
75	C₁₃×#451	C₂²	1	4	yes	complemented
76	C₁₃×#450	C₂²	1	2	yes	—
77	C₁₃×#450	C₂²	1	1	yes	characteristic
78	C₁₃×#449	C₂²	1	4	yes	complemented
79	C₁₃×#449	C₂²	1	2	yes	complemented
80	C₁₃×#448	C₂²	1	1	yes	characteristic
81	C₁₃×#448	C₂²	1	4	yes	complemented
82	C₁₃×#447	C₂²	1	1	yes	characteristic
83	C₁₃×#428	C₂²	1	2	yes	complemented
84	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
85	C₁₃×#417	C₂²	1	2	yes	complemented
86	C₁₃×#417	C₂²	1	2	yes	complemented
87	C₁₃×#416	C₂²	1	2	yes	complemented
88	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
89	C₁₃×#408	C₂²	1	2	yes	complemented
90	C₁₃×#408	C₂²	1	4	yes	complemented
91	C₁₃×#407	C₂²	1	1	yes	characteristic
92	C₁₃×#407	C₂²	1	2	yes	—
93	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
95	C₁₃×2₋¹⁺⁴	—	4	4	no	—
96	C₂×C₁₃×#41	—	2	1	no	—
97	C₂×C₁₃×#41	—	2	2	no	—
98	C₂×C₁₃×#41	—	2	1	no	—
99	C₂×C₁₃×#41	—	2	1	no	—
100	C₂×C₁₃×#41	—	4	4	no	—
101	C₂×C₁₃×#41	—	4	4	no	—
102	C₂×C₁₃×#41	D₄	1	2	yes	—
103	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
104	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
105	C₂×C₁₃×#41	C₂³	1	2	yes	—
106	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×#41	C₂³	1	2	yes	—
108	C₂×C₁₃×#41	C₂³	1	2	yes	—
109	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×#41	C₂³	1	2	yes	—
112	C₂²×Q₈×C₁₃	—	2	1	no	—
113	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
114	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
115	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
116	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
117	C₂²×D₄×C₁₃	—	2	1	no	—
118	C₂²×D₄×C₁₃	—	2	2	no	—
119	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
120	C₂²×D₄×C₁₃	D₄	1	2	yes	—
121	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃	—	2	1	no	—
123	C₂³×C₄×C₁₃	—	2	1	no	—
124	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
126	C₁₃×#137	—	4	4	no	—
127	C₁₃×#135	—	4	4	no	—
128	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
129	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
130	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
131	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
132	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
133	C₂×C₁₃×D₈	C₂³	1	2	yes	—
134	C₁₃×#131	—	4	4	no	—
135	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
136	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
137	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
138	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
139	C₁₃×C₄⋊Q₈	—	2	1	no	—
140	C₁₃×C₄⋊Q₈	—	2	2	no	—
141	C₁₃×#124	—	2	1	no	—
142	C₁₃×#124	—	2	2	no	—
143	C₁₃×#123	—	2	2	no	—
144	C₁₃×#123	—	2	2	no	—
145	C₁₃×#123	—	2	2	no	—
146	C₁₃×#123	—	2	1	no	—
147	C₁₃×#123	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	—	2	4	no	—
151	C₁₃×C₂²⋊Q₈	—	2	1	no	—
152	C₁₃×C₂²⋊Q₈	—	2	2	no	—
153	C₁₃×C₂²⋊Q₈	—	2	2	no	—
154	C₁₃×C₂²⋊Q₈	—	2	2	no	—
155	C₁₃×C₂²⋊Q₈	—	2	1	no	—
156	C₁₃×C₂²⋊Q₈	—	2	2	no	—
157	C₁₃×C₂²⋊Q₈	—	2	1	no	—
158	C₁₃×C₂²⋊Q₈	—	2	2	no	—
159	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
160	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
161	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
162	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
163	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
164	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
165	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
166	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
167	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
168	C₁₃×#121	—	2	2	no	—
169	C₁₃×#121	—	2	2	no	—
170	C₁₃×#121	—	2	4	no	—
171	C₁₃×#121	—	2	4	no	—
172	C₁₃×#121	—	2	4	no	—
173	C₁₃×#121	—	2	4	no	—
174	C₁₃×#121	—	2	4	no	—
175	C₁₃×#121	—	2	2	no	—
176	C₁₃×#121	—	2	2	no	—
177	C₁₃×#121	—	2	2	no	—
178	C₁₃×#121	—	2	1	no	—
179	C₁₃×#121	—	2	2	no	—
180	C₁₃×#121	—	2	2	no	—
181	C₁₃×#121	—	2	2	no	—
182	C₁₃×#121	C₂³	1	1	yes	characteristic
183	C₁₃×#121	C₂³	1	4	yes	—
184	C₁₃×#121	C₂³	1	1	yes	characteristic
185	C₁₃×#121	C₂³	1	4	yes	—
186	C₁₃×#121	C₂³	1	2	yes	—
187	C₁₃×#120	—	2	1	no	—
188	C₁₃×#120	—	2	2	no	—
189	C₄×Q₈×C₁₃	—	2	1	no	—
190	C₄×D₄×C₁₃	—	2	2	no	—
191	C₄×D₄×C₁₃	—	2	1	no	—
192	C₄×D₄×C₁₃	—	2	1	no	—
193	C₄×D₄×C₁₃	—	2	2	no	—
194	C₄×D₄×C₁₃	—	2	1	no	—
195	C₄×D₄×C₁₃	—	2	2	no	—
196	C₁₃×#117	C₂³	1	1	yes	characteristic
197	C₁₃×#117	C₂³	1	2	yes	—
198	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
202	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
208	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
210	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
211	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
212	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
213	C₁₃×#107	C₂³	1	4	yes	—
214	C₁₃×#107	C₂³	1	4	yes	—
215	C₁₃×#107	C₂³	1	4	yes	—
216	C₁₃×#106	C₂³	1	4	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#103	C₂³	1	2	yes	—
220	C₁₃×#103	C₂³	1	2	yes	—
221	C₁₃×#103	C₂³	1	4	yes	—
222	C₁₃×#103	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	2	yes	—
224	C₁₃×#102	C₂³	1	2	yes	—
225	C₁₃×#102	C₂³	1	4	yes	—
226	C₁₃×#102	C₂³	1	4	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
229	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
230	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
232	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
233	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
234	#60764	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂⁴×C₁₃	—	2	1	no	—
236	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
238	C₁₃×#41	—	2	4	no	—
239	C₁₃×#41	—	2	4	no	—
240	C₁₃×#41	—	2	4	no	—
241	C₁₃×#41	—	2	4	no	—
242	C₁₃×#41	—	2	4	no	—
243	C₁₃×#41	—	4	4	no	—
244	C₁₃×#41	—	4	4	no	—
245	C₁₃×#41	—	4	2	no	—
246	C₁₃×#41	—	4	2	no	—
247	C₁₃×#41	—	4	2	no	—
248	C₁₃×#41	—	4	2	no	—
249	C₁₃×#41	—	4	4	no	—
250	C₁₃×#41	—	4	4	no	—
251	C₁₃×#41	—	4	4	no	—
252	C₁₃×#41	—	4	8	no	—
253	C₁₃×#41	—	4	4	no	—
254	C₂×Q₈×C₁₃	—	2	1	no	—
255	C₂×Q₈×C₁₃	—	2	2	no	—
256	C₂×Q₈×C₁₃	—	2	1	no	—
257	C₂×Q₈×C₁₃	—	2	4	no	—
258	C₂×Q₈×C₁₃	—	4	2	no	—
259	C₂×Q₈×C₁₃	—	4	2	no	—
260	C₂×Q₈×C₁₃	—	4	4	no	—
261	C₂×Q₈×C₁₃	—	4	4	no	—
262	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
265	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
266	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
267	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
268	C₂×D₄×C₁₃	—	2	1	no	—
269	C₂×D₄×C₁₃	—	2	2	no	—
270	C₂×D₄×C₁₃	—	2	1	no	—
271	C₂×D₄×C₁₃	—	2	2	no	—
272	C₂×D₄×C₁₃	—	2	2	no	—
273	C₂×D₄×C₁₃	—	2	2	no	—
274	C₂×D₄×C₁₃	—	2	1	no	—
275	C₂×D₄×C₁₃	—	2	4	no	—
276	C₂×D₄×C₁₃	—	2	4	no	—
277	C₂×D₄×C₁₃	—	2	1	no	—
278	C₂×D₄×C₁₃	—	4	2	no	—
279	C₂×D₄×C₁₃	—	4	2	no	—
280	C₂×D₄×C₁₃	—	4	4	no	—
281	C₂×D₄×C₁₃	—	4	4	no	—
282	C₂×D₄×C₁₃	—	8	4	no	—
283	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
284	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
285	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
286	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
287	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
288	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
289	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
290	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₁₃	—	2	4	no	—
293	C₂²×C₄×C₁₃	—	2	2	no	—
294	C₂²×C₄×C₁₃	—	2	1	no	—
295	C₂²×C₄×C₁₃	—	2	2	no	—
296	C₂²×C₄×C₁₃	—	2	1	no	—
297	C₂²×C₄×C₁₃	—	2	2	no	—
298	C₂²×C₄×C₁₃	—	2	1	no	—
299	C₂²×C₄×C₁₃	—	2	2	no	—
300	C₂²×C₄×C₁₃	—	2	2	no	—
301	C₂²×C₄×C₁₃	—	2	2	no	—
302	C₂²×C₄×C₁₃	—	2	1	no	—
303	C₂²×C₄×C₁₃	—	2	2	no	—
304	C₂²×C₄×C₁₃	—	2	2	no	—
305	C₂²×C₄×C₁₃	—	4	4	no	—
306	C₂²×C₄×C₁₃	—	4	4	no	—
307	C₂²×C₄×C₁₃	—	8	2	no	—
308	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
312	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
313	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
314	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
319	C₁₃×Q₁₆	—	4	2	no	—
320	C₁₃×Q₁₆	—	4	4	no	—
321	C₁₃×SD₁₆	—	4	2	no	—
322	C₁₃×SD₁₆	—	4	2	no	—
323	C₁₃×SD₁₆	—	4	4	no	—
324	C₁₃×D₈	—	4	2	no	—
325	C₁₃×M₁₆	—	2	4	no	—
326	C₁₃×M₁₆	—	4	4	no	—
327	C₂×C₈×C₁₃	—	2	4	no	—
328	C₂×C₈×C₁₃	—	4	4	no	—
329	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
330	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
331	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
332	C₁₃×C₄⋊C₄	—	2	2	no	—
333	C₁₃×C₄⋊C₄	—	2	2	no	—
334	C₁₃×C₄⋊C₄	—	2	2	no	—
335	C₁₃×C₄⋊C₄	—	2	2	no	—
336	C₁₃×C₄⋊C₄	—	2	1	no	—
337	C₁₃×C₄⋊C₄	—	2	4	no	—
338	C₁₃×C₄⋊C₄	—	2	4	no	—
339	C₁₃×C₄⋊C₄	—	2	2	no	—
340	C₁₃×C₄⋊C₄	—	2	2	no	—
341	C₁₃×C₄⋊C₄	—	2	2	no	—
342	C₁₃×C₄⋊C₄	—	2	2	no	—
343	C₁₃×C₄⋊C₄	—	2	1	no	—
344	C₁₃×C₄⋊C₄	—	2	2	no	—
345	C₁₃×C₄⋊C₄	—	2	1	no	—
346	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
347	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
348	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
349	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
350	C₁₃×C₂²⋊C₄	—	2	2	no	—
351	C₁₃×C₂²⋊C₄	—	2	1	no	—
352	C₁₃×C₂²⋊C₄	—	2	4	no	—
353	C₁₃×C₂²⋊C₄	—	2	4	no	—
354	C₁₃×C₂²⋊C₄	—	2	2	no	—
355	C₁₃×C₂²⋊C₄	—	2	2	no	—
356	C₁₃×C₂²⋊C₄	—	2	2	no	—
357	C₁₃×C₂²⋊C₄	—	2	2	no	—
358	C₁₃×C₂²⋊C₄	—	2	1	no	—
359	C₁₃×C₂²⋊C₄	—	2	2	no	—
360	C₁₃×C₂²⋊C₄	—	2	1	no	—
361	C₁₃×C₂²⋊C₄	—	2	4	no	—
362	C₁₃×C₂²⋊C₄	—	2	4	no	—
363	C₁₃×C₂²⋊C₄	—	2	1	no	—
364	C₁₃×C₂²⋊C₄	—	2	2	no	—
365	C₁₃×C₂²⋊C₄	—	2	1	no	—
366	C₄²×C₁₃	—	2	2	no	—
367	C₄²×C₁₃	—	2	1	no	—
368	#3489	C₂×C₁₃	1	1	yes	characteristic, complemented
369	C₂×#537	C₂×C₁₃	1	1	yes	characteristic, complemented
370	#3203	C₂×C₁₃	1	4	yes	complemented
371	#3201	C₂×C₁₃	1	4	yes	complemented
372	#3196	C₂×C₁₃	1	2	yes	complemented
373	#3193	C₂×C₁₃	1	2	yes	complemented
374	#3189	C₂×C₁₃	1	2	yes	complemented
375	#3188	C₂×C₁₃	1	2	yes	complemented
376	#3098	C₂×C₁₃	1	2	yes	complemented
377	#3092	C₂×C₁₃	1	1	yes	characteristic, complemented
378	C₂×#484	C₂×C₁₃	1	1	yes	characteristic, complemented
379	#3063	C₂×C₁₃	1	2	yes	complemented
380	#3061	C₂×C₁₃	1	2	yes	complemented
381	#3013	C₂×C₁₃	1	2	yes	complemented
382	#3007	C₂×C₁₃	1	1	yes	characteristic, complemented
383	#3002	C₂×C₁₃	1	1	yes	characteristic, complemented
384	#2880	C₂×C₁₃	1	1	yes	characteristic, complemented
385	C₂³×C₁₃	—	2	2	no	—
386	C₂³×C₁₃	—	2	2	no	—
387	C₂³×C₁₃	—	2	4	no	—
388	C₂³×C₁₃	—	2	1	no	—
389	C₂³×C₁₃	—	2	2	no	—
390	C₂³×C₁₃	—	4	1	no	—
391	C₂³×C₁₃	—	4	2	no	—
392	C₂³×C₁₃	—	4	2	no	—
393	C₂³×C₁₃	—	4	2	no	—
394	C₂³×C₁₃	—	4	2	no	—
395	C₂³×C₁₃	—	4	2	no	—
396	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
397	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
398	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
399	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
400	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
401	Q₈×C₁₃	—	2	2	no	—
402	Q₈×C₁₃	—	2	2	no	—
403	Q₈×C₁₃	—	2	4	no	—
404	Q₈×C₁₃	—	2	2	no	—
405	Q₈×C₁₃	—	2	2	no	—
406	Q₈×C₁₃	—	2	2	no	—
407	Q₈×C₁₃	—	4	2	no	—
408	Q₈×C₁₃	—	4	4	no	—
409	Q₈×C₁₃	—	4	2	no	—
410	Q₈×C₁₃	—	4	2	no	—
411	D₄×C₁₃	—	2	4	no	—
412	D₄×C₁₃	—	2	4	no	—
413	D₄×C₁₃	—	2	2	no	—
414	D₄×C₁₃	—	2	2	no	—
415	D₄×C₁₃	—	2	2	no	—
416	D₄×C₁₃	—	2	2	no	—
417	D₄×C₁₃	—	2	2	no	—
418	D₄×C₁₃	—	4	2	no	—
419	D₄×C₁₃	—	4	2	no	—
420	D₄×C₁₃	—	4	2	no	—
421	D₄×C₁₃	—	4	2	no	—
422	D₄×C₁₃	—	4	4	no	—
423	D₄×C₁₃	—	4	4	no	—
424	D₄×C₁₃	—	4	4	no	—
425	D₄×C₁₃	—	4	2	no	—
426	D₄×C₁₃	—	4	2	no	—
427	D₄×C₁₃	—	8	1	no	—
428	D₄×C₁₃	—	8	2	no	—
429	D₄×C₁₃	—	8	4	no	—
430	D₄×C₁₃	—	8	4	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	2	2	no	—
434	C₂×C₄×C₁₃	—	2	4	no	—
435	C₂×C₄×C₁₃	—	2	2	no	—
436	C₂×C₄×C₁₃	—	2	2	no	—
437	C₂×C₄×C₁₃	—	2	4	no	—
438	C₂×C₄×C₁₃	—	2	1	no	—
439	C₂×C₄×C₁₃	—	2	2	no	—
440	C₂×C₄×C₁₃	—	2	1	no	—
441	C₂×C₄×C₁₃	—	2	4	no	—
442	C₂×C₄×C₁₃	—	2	2	no	—
443	C₂×C₄×C₁₃	—	2	2	no	—
444	C₂×C₄×C₁₃	—	2	1	no	—
445	C₂×C₄×C₁₃	—	4	2	no	—
446	C₂×C₄×C₁₃	—	4	2	no	—
447	C₂×C₄×C₁₃	—	4	2	no	—
448	C₂×C₄×C₁₃	—	4	4	no	—
449	C₂×C₄×C₁₃	—	4	4	no	—
450	C₂×C₄×C₁₃	—	4	2	no	—
451	C₂×C₄×C₁₃	—	4	4	no	—
452	C₂×C₄×C₁₃	—	4	4	no	—
453	C₂×C₄×C₁₃	—	4	2	no	—
454	C₂×C₄×C₁₃	—	4	4	no	—
455	C₂×C₄×C₁₃	—	4	2	no	—
456	C₂×C₄×C₁₃	—	8	1	no	—
457	C₂×C₄×C₁₃	—	8	2	no	—
458	C₂×C₄×C₁₃	—	8	2	no	—
459	C₂×C₄×C₁₃	—	8	2	no	—
460	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
461	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
466	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
467	C₈×C₁₃	—	2	2	no	—
468	C₈×C₁₃	—	2	2	no	—
469	C₈×C₁₃	—	2	4	no	—
470	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic, complemented
471	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
472	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
473	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
474	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
475	C₂×#131	C₂²×C₁₃	1	2	yes	complemented
476	D₄×Q₈	—	2	1	no	—
477	#548	—	2	1	no	—
478	#547	—	2	2	no	—
479	#547	—	2	1	no	—
480	#546	—	2	2	no	—
481	#546	—	2	1	no	—
482	#537	—	2	2	no	—
483	#537	—	2	1	no	—
484	#537	—	2	1	no	—
485	#537	C₂²×C₁₃	1	2	yes	—
486	#537	C₂²×C₁₃	1	4	yes	—
487	#537	C₂²×C₁₃	1	2	yes	—
488	#537	C₂²×C₁₃	1	2	yes	complemented
489	#537	C₂²×C₁₃	1	1	yes	characteristic, complemented
490	#536	C₂²×C₁₃	1	2	yes	complemented
491	#536	C₂²×C₁₃	1	1	yes	characteristic, complemented
492	#525	C₂²×C₁₃	1	1	yes	characteristic
493	#525	C₂²×C₁₃	1	2	yes	—
494	C₂×C₂²⋊Q₈	—	2	1	no	—
495	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
496	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
497	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
498	C₂×#121	—	2	1	no	—
499	C₂×#121	—	2	2	no	—
500	C₂×#121	C₂²×C₁₃	1	2	yes	—
501	#520	C₂²×C₁₃	1	1	yes	characteristic, complemented
502	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
503	#485	C₂²×C₁₃	1	4	yes	complemented
504	#484	C₂²×C₁₃	1	2	yes	—
505	#484	C₂²×C₁₃	1	2	yes	—
506	#484	C₂²×C₁₃	1	2	yes	—
507	#484	C₂²×C₁₃	1	4	yes	complemented
508	#484	C₂²×C₁₃	1	4	yes	complemented
509	#483	C₂²×C₁₃	1	2	yes	complemented
510	#482	C₂²×C₁₃	1	4	yes	complemented
511	#481	C₂²×C₁₃	1	2	yes	—
512	#480	C₂²×C₁₃	1	2	yes	complemented
513	#480	C₂²×C₁₃	1	4	yes	complemented
514	#470	C₂²×C₁₃	1	4	yes	complemented
515	#468	C₂²×C₁₃	1	4	yes	complemented
516	#468	C₂²×C₁₃	1	4	yes	complemented
517	#468	C₂²×C₁₃	1	4	yes	complemented
518	#467	C₂²×C₁₃	1	4	yes	complemented
519	#467	C₂²×C₁₃	1	4	yes	complemented
520	#466	C₂²×C₁₃	1	4	yes	complemented
521	#465	C₂²×C₁₃	1	4	yes	complemented
522	#452	C₂²×C₁₃	1	4	yes	complemented
523	#452	C₂²×C₁₃	1	2	yes	complemented
524	#452	C₂²×C₁₃	1	4	yes	complemented
525	#451	C₂²×C₁₃	1	1	yes	characteristic
526	#451	C₂²×C₁₃	1	2	yes	—
527	#451	C₂²×C₁₃	1	4	yes	complemented
528	#450	C₂²×C₁₃	1	2	yes	—
529	#450	C₂²×C₁₃	1	1	yes	characteristic
530	#449	C₂²×C₁₃	1	4	yes	complemented
531	#449	C₂²×C₁₃	1	2	yes	complemented
532	#448	C₂²×C₁₃	1	1	yes	characteristic
533	#448	C₂²×C₁₃	1	4	yes	complemented
534	#447	C₂²×C₁₃	1	1	yes	characteristic
535	#428	C₂²×C₁₃	1	2	yes	complemented
536	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
537	#417	C₂²×C₁₃	1	2	yes	complemented
538	#417	C₂²×C₁₃	1	2	yes	complemented
539	#416	C₂²×C₁₃	1	2	yes	complemented
540	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
541	#408	C₂²×C₁₃	1	2	yes	complemented
542	#408	C₂²×C₁₃	1	4	yes	complemented
543	#407	C₂²×C₁₃	1	1	yes	characteristic
544	#407	C₂²×C₁₃	1	2	yes	—
545	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
546	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
547	C₂²×C₁₃	—	2	1	no	—
548	C₂²×C₁₃	—	2	1	no	—
549	C₂²×C₁₃	—	2	1	no	—
550	C₂²×C₁₃	—	2	1	no	—
551	C₂²×C₁₃	—	2	1	no	—
552	C₂²×C₁₃	—	2	2	no	—
553	C₂²×C₁₃	—	2	2	no	—
554	C₂²×C₁₃	—	2	1	no	—
555	C₂²×C₁₃	—	2	2	no	—
556	C₂²×C₁₃	—	2	2	no	—
557	C₂²×C₁₃	—	2	1	no	—
558	C₂²×C₁₃	—	2	2	no	—
559	C₂²×C₁₃	—	2	2	no	—
560	C₂²×C₁₃	—	4	4	no	—
561	C₂²×C₁₃	—	4	2	no	—
562	C₂²×C₁₃	—	4	1	no	—
563	C₂²×C₁₃	—	4	1	no	—
564	C₂²×C₁₃	—	4	2	no	—
565	C₂²×C₁₃	—	4	1	no	—
566	C₂²×C₁₃	—	4	2	no	—
567	C₂²×C₁₃	—	8	4	no	—
568	C₂²×C₁₃	—	8	4	no	—
569	C₂²×C₁₃	#534	1	2	yes	—
570	C₂²×C₁₃	#578	1	2	yes	—
571	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
572	C₄×C₁₃	—	2	1	no	—
573	C₄×C₁₃	—	2	1	no	—
574	C₄×C₁₃	—	2	2	no	—
575	C₄×C₁₃	—	2	2	no	—
576	C₄×C₁₃	—	4	4	no	—
577	C₄×C₁₃	—	4	2	no	—
578	C₄×C₁₃	—	4	1	no	—
579	C₄×C₁₃	—	4	2	no	—
580	C₄×C₁₃	—	4	2	no	—
581	C₄×C₁₃	—	4	1	no	—
582	C₄×C₁₃	—	4	1	no	—
583	C₄×C₁₃	#534	1	2	yes	—
584	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
585	2₋¹⁺⁴	—	4	4	no	—
586	C₂×#41	—	2	1	no	—
587	C₂×#41	—	2	2	no	—
588	C₂×#41	—	2	1	no	—
589	C₂×#41	—	2	1	no	—
590	C₂×#41	—	4	4	no	—
591	C₂×#41	—	4	4	no	—
592	C₂×#41	D₄×C₁₃	1	2	yes	—
593	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
594	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
595	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
596	C₂×#41	C₂³×C₁₃	1	2	yes	—
597	C₂×#41	C₂³×C₁₃	1	2	yes	—
598	C₂×#41	C₂³×C₁₃	1	2	yes	—
599	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
600	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
601	C₂×#41	C₂³×C₁₃	1	2	yes	—
602	C₂²×Q₈	—	2	1	no	—
603	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
604	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
605	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
606	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
607	C₂²×D₄	—	2	1	no	—
608	C₂²×D₄	—	2	2	no	—
609	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
610	C₂²×D₄	D₄×C₁₃	1	2	yes	—
611	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
612	C₂³×C₄	—	2	1	no	—
613	C₂³×C₄	—	2	1	no	—
614	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
615	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
616	#137	—	4	4	no	—
617	#135	—	4	4	no	—
618	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
619	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
620	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
621	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
622	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
623	C₂×D₈	C₂³×C₁₃	1	2	yes	—
624	#131	—	4	4	no	—
625	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
626	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
627	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
628	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
629	C₄⋊Q₈	—	2	1	no	—
630	C₄⋊Q₈	—	2	2	no	—
631	#124	—	2	1	no	—
632	#124	—	2	2	no	—
633	#123	—	2	2	no	—
634	#123	—	2	2	no	—
635	#123	—	2	2	no	—
636	#123	—	2	1	no	—
637	#123	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	—	2	4	no	—
641	C₂²⋊Q₈	—	2	1	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	—	2	2	no	—
645	C₂²⋊Q₈	—	2	1	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	—	2	1	no	—
648	C₂²⋊Q₈	—	2	2	no	—
649	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
650	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
651	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
652	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
653	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
654	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
655	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
656	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
657	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
658	#121	—	2	2	no	—
659	#121	—	2	2	no	—
660	#121	—	2	4	no	—
661	#121	—	2	4	no	—
662	#121	—	2	4	no	—
663	#121	—	2	4	no	—
664	#121	—	2	4	no	—
665	#121	—	2	2	no	—
666	#121	—	2	2	no	—
667	#121	—	2	2	no	—
668	#121	—	2	1	no	—
669	#121	—	2	2	no	—
670	#121	—	2	2	no	—
671	#121	—	2	2	no	—
672	#121	C₂³×C₁₃	1	4	yes	—
673	#121	C₂³×C₁₃	1	4	yes	—
674	#121	C₂³×C₁₃	1	1	yes	characteristic
675	#121	C₂³×C₁₃	1	1	yes	characteristic
676	#121	C₂³×C₁₃	1	2	yes	—
677	#120	—	2	1	no	—
678	#120	—	2	2	no	—
679	C₄×Q₈	—	2	1	no	—
680	C₄×D₄	—	2	2	no	—
681	C₄×D₄	—	2	1	no	—
682	C₄×D₄	—	2	1	no	—
683	C₄×D₄	—	2	2	no	—
684	C₄×D₄	—	2	1	no	—
685	C₄×D₄	—	2	2	no	—
686	#117	C₂³×C₁₃	1	1	yes	characteristic
687	#117	C₂³×C₁₃	1	2	yes	—
688	C₂×C₄⋊C₄	—	2	1	no	—
689	C₂×C₄⋊C₄	—	2	1	no	—
690	C₂×C₄⋊C₄	—	2	1	no	—
691	C₂×C₄⋊C₄	—	2	2	no	—
692	C₂×C₄⋊C₄	—	2	1	no	—
693	C₂×C₄⋊C₄	—	2	2	no	—
694	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
695	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
699	C₂×C₂²⋊C₄	—	2	2	no	—
700	C₂×C₂²⋊C₄	—	2	1	no	—
701	C₂×C₂²⋊C₄	—	2	2	no	—
702	C₂×C₂²⋊C₄	—	2	2	no	—
703	#107	C₂³×C₁₃	1	4	yes	—
704	#107	C₂³×C₁₃	1	4	yes	—
705	#107	C₂³×C₁₃	1	4	yes	—
706	#106	C₂³×C₁₃	1	4	yes	—
707	#103	C₂³×C₁₃	1	4	yes	—
708	#103	C₂³×C₁₃	1	4	yes	—
709	#103	C₂³×C₁₃	1	2	yes	—
710	#103	C₂³×C₁₃	1	2	yes	—
711	#103	C₂³×C₁₃	1	4	yes	—
712	#103	C₂³×C₁₃	1	4	yes	—
713	#102	C₂³×C₁₃	1	2	yes	—
714	#102	C₂³×C₁₃	1	2	yes	—
715	#102	C₂³×C₁₃	1	4	yes	—
716	#102	C₂³×C₁₃	1	4	yes	—
717	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
718	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
719	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
720	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
721	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
722	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
723	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
724	C₂×C₁₃	—	2	2	no	—
725	C₂×C₁₃	—	2	2	no	—
726	C₂×C₁₃	—	4	1	no	—
727	C₂×C₁₃	—	4	2	no	—
728	C₂×C₁₃	—	4	2	no	—
729	C₂×C₁₃	—	8	1	no	—
730	C₂×C₁₃	—	8	2	no	—
731	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
732	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
733	C₂×C₁₃	#3585	1	1	yes	characteristic
734	C₂⁴	—	2	1	no	—
735	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
736	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
737	#41	—	2	4	no	—
738	#41	—	2	4	no	—
739	#41	—	2	4	no	—
740	#41	—	2	4	no	—
741	#41	—	2	4	no	—
742	#41	—	4	4	no	—
743	#41	—	4	4	no	—
744	#41	—	4	2	no	—
745	#41	—	4	2	no	—
746	#41	—	4	2	no	—
747	#41	—	4	2	no	—
748	#41	—	4	4	no	—
749	#41	—	4	4	no	—
750	#41	—	4	4	no	—
751	#41	—	4	8	no	—
752	#41	—	4	4	no	—
753	C₂×Q₈	—	2	1	no	—
754	C₂×Q₈	—	2	2	no	—
755	C₂×Q₈	—	2	1	no	—
756	C₂×Q₈	—	2	4	no	—
757	C₂×Q₈	—	4	2	no	—
758	C₂×Q₈	—	4	2	no	—
759	C₂×Q₈	—	4	4	no	—
760	C₂×Q₈	—	4	4	no	—
761	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
762	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
763	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
764	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
765	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
766	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
767	C₂×D₄	—	2	1	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	1	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	1	no	—
774	C₂×D₄	—	2	4	no	—
775	C₂×D₄	—	2	4	no	—
776	C₂×D₄	—	2	1	no	—
777	C₂×D₄	—	4	2	no	—
778	C₂×D₄	—	4	2	no	—
779	C₂×D₄	—	4	4	no	—
780	C₂×D₄	—	4	4	no	—
781	C₂×D₄	—	8	4	no	—
782	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
783	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
784	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
785	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
786	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
787	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
788	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
789	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
790	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
791	C₂²×C₄	—	2	4	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	1	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	1	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	1	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	1	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	4	4	no	—
805	C₂²×C₄	—	4	4	no	—
806	C₂²×C₄	—	8	2	no	—
807	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
808	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
809	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
810	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
811	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
812	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
813	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
814	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
815	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
816	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
817	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
818	Q₁₆	—	4	2	no	—
819	Q₁₆	—	4	4	no	—
820	SD₁₆	—	4	2	no	—
821	SD₁₆	—	4	2	no	—
822	SD₁₆	—	4	4	no	—
823	D₈	—	4	2	no	—
824	M₁₆	—	2	4	no	—
825	M₁₆	—	4	4	no	—
826	C₂×C₈	—	2	4	no	—
827	C₂×C₈	—	4	4	no	—
828	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
829	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
830	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	1	no	—
836	C₄⋊C₄	—	2	4	no	—
837	C₄⋊C₄	—	2	4	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	1	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	1	no	—
845	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
846	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
847	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
848	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	1	no	—
851	C₂²⋊C₄	—	2	4	no	—
852	C₂²⋊C₄	—	2	4	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	1	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	1	no	—
860	C₂²⋊C₄	—	2	4	no	—
861	C₂²⋊C₄	—	2	4	no	—
862	C₂²⋊C₄	—	2	1	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	1	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	1	no	—
867	C₁₃	#60764	1	1	yes	characteristic, direct product factor, Sylow
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	4	no	—
871	C₂³	—	2	1	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	4	1	no	—
874	C₂³	—	4	2	no	—
875	C₂³	—	4	2	no	—
876	C₂³	—	4	2	no	—
877	C₂³	—	4	2	no	—
878	C₂³	—	4	2	no	—
879	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
880	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
881	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
882	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
883	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
884	Q₈	—	2	2	no	—
885	Q₈	—	2	2	no	—
886	Q₈	—	2	4	no	—
887	Q₈	—	2	2	no	—
888	Q₈	—	2	2	no	—
889	Q₈	—	2	2	no	—
890	Q₈	—	4	2	no	—
891	Q₈	—	4	4	no	—
892	Q₈	—	4	2	no	—
893	Q₈	—	4	2	no	—
894	D₄	—	2	4	no	—
895	D₄	—	2	4	no	—
896	D₄	—	2	2	no	—
897	D₄	—	2	2	no	—
898	D₄	—	2	2	no	—
899	D₄	—	2	2	no	—
900	D₄	—	2	2	no	—
901	D₄	—	4	2	no	—
902	D₄	—	4	2	no	—
903	D₄	—	4	2	no	—
904	D₄	—	4	2	no	—
905	D₄	—	4	4	no	—
906	D₄	—	4	4	no	—
907	D₄	—	4	4	no	—
908	D₄	—	4	2	no	—
909	D₄	—	4	2	no	—
910	D₄	—	8	4	no	—
911	D₄	—	8	4	no	—
912	D₄	—	8	1	no	—
913	D₄	—	8	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	4	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	4	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	4	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	4	2	no	—
929	C₂×C₄	—	4	2	no	—
930	C₂×C₄	—	4	2	no	—
931	C₂×C₄	—	4	4	no	—
932	C₂×C₄	—	4	4	no	—
933	C₂×C₄	—	4	2	no	—
934	C₂×C₄	—	4	4	no	—
935	C₂×C₄	—	4	4	no	—
936	C₂×C₄	—	4	2	no	—
937	C₂×C₄	—	4	4	no	—
938	C₂×C₄	—	4	2	no	—
939	C₂×C₄	—	8	2	no	—
940	C₂×C₄	—	8	2	no	—
941	C₂×C₄	—	8	1	no	—
942	C₂×C₄	—	8	2	no	—
943	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
944	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
945	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
946	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
947	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
948	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
949	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
950	C₈	—	2	2	no	—
951	C₈	—	2	2	no	—
952	C₈	—	2	4	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	2	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	2	no	—
962	C₂²	—	2	2	no	—
963	C₂²	—	2	1	no	—
964	C₂²	—	2	2	no	—
965	C₂²	—	2	2	no	—
966	C₂²	—	4	4	no	—
967	C₂²	—	4	1	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	1	no	—
971	C₂²	—	4	1	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	8	4	no	—
974	C₂²	—	8	4	no	—
975	C₂²	C₁₃×#534	1	2	yes	—
976	C₂²	C₁₃×#578	1	2	yes	—
977	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
978	C₄	—	2	1	no	—
979	C₄	—	2	1	no	—
980	C₄	—	2	2	no	—
981	C₄	—	2	2	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	4	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	1	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	1	no	—
989	C₄	C₁₃×#534	1	2	yes	—
990	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
991	C₂	—	2	2	no	—
992	C₂	—	2	2	no	—
993	C₂	—	4	1	no	—
994	C₂	—	4	2	no	—
995	C₂	—	4	2	no	—
996	C₂	—	8	2	no	—
997	C₂	—	8	1	no	—
998	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
999	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
1000	C₂	C₁₃×#3585	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 ◁ C₂²×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3489	C₂	semidirect
2. C₂×C₁₃×#537	C₂	semidirect
3. C₁₃×#3203	C₂	semidirect
4. C₁₃×#3201	C₂	semidirect
5. C₁₃×#3196	C₂	semidirect
6. C₁₃×#3193	C₂	semidirect
7. C₁₃×#3189	C₂	semidirect
8. C₁₃×#3188	C₂	semidirect
9. C₁₃×#3098	C₂	semidirect
10. C₁₃×#3092	C₂	semidirect
11. C₂×C₁₃×#484	C₂	semidirect
12. C₁₃×#3063	C₂	semidirect
13. C₁₃×#3061	C₂	semidirect
14. C₁₃×#3013	C₂	semidirect
15. C₁₃×#3007	C₂	semidirect
16. C₁₃×#3002	C₂	semidirect
17. C₁₃×#2880	C₂	semidirect
18. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
21. C₂×C₁₃×#137	C₂²	semidirect
22. C₂×C₁₃×#135	C₂²	semidirect
23. C₂×C₁₃×#131	C₂²	semidirect
36. C₁₃×#537	C₂²	semidirect
37. C₁₃×#537	C₂²	semidirect
38. C₁₃×#536	C₂²	semidirect
39. C₁₃×#536	C₂²	semidirect
49. C₁₃×#520	C₂²	semidirect
51. C₁₃×#485	C₂²	semidirect
55. C₁₃×#484	C₂²	semidirect
56. C₁₃×#484	C₂²	semidirect
57. C₁₃×#483	C₂²	semidirect
58. C₁₃×#482	C₂²	semidirect
60. C₁₃×#480	C₂²	semidirect
61. C₁₃×#480	C₂²	semidirect
62. C₁₃×#470	C₂²	semidirect
63. C₁₃×#468	C₂²	semidirect
64. C₁₃×#468	C₂²	semidirect
65. C₁₃×#468	C₂²	semidirect
66. C₁₃×#467	C₂²	semidirect
67. C₁₃×#467	C₂²	semidirect
68. C₁₃×#466	C₂²	semidirect
69. C₁₃×#465	C₂²	semidirect
70. C₁₃×#452	C₂²	semidirect
71. C₁₃×#452	C₂²	semidirect
72. C₁₃×#452	C₂²	semidirect
75. C₁₃×#451	C₂²	semidirect
78. C₁₃×#449	C₂²	semidirect
79. C₁₃×#449	C₂²	semidirect
81. C₁₃×#448	C₂²	semidirect
83. C₁₃×#428	C₂²	semidirect
84. C₂×C₁₃×#107	C₂²	semidirect
85. C₁₃×#417	C₂²	semidirect
86. C₁₃×#417	C₂²	semidirect
87. C₁₃×#416	C₂²	semidirect
88. C₂×C₁₃×#103	C₂²	semidirect
89. C₁₃×#408	C₂²	semidirect
90. C₁₃×#408	C₂²	semidirect
234. #60764	C₁₃	direct (N × H)
368. #3489	C₂×C₁₃	semidirect
369. C₂×#537	C₂×C₁₃	semidirect
370. #3203	C₂×C₁₃	semidirect
371. #3201	C₂×C₁₃	semidirect
372. #3196	C₂×C₁₃	semidirect
373. #3193	C₂×C₁₃	semidirect
374. #3189	C₂×C₁₃	semidirect
375. #3188	C₂×C₁₃	semidirect
376. #3098	C₂×C₁₃	semidirect
377. #3092	C₂×C₁₃	semidirect
378. C₂×#484	C₂×C₁₃	semidirect
379. #3063	C₂×C₁₃	semidirect
380. #3061	C₂×C₁₃	semidirect
381. #3013	C₂×C₁₃	semidirect
382. #3007	C₂×C₁₃	semidirect
383. #3002	C₂×C₁₃	semidirect
384. #2880	C₂×C₁₃	semidirect
470. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
473. C₂×#137	C₂²×C₁₃	semidirect
474. C₂×#135	C₂²×C₁₃	semidirect
475. C₂×#131	C₂²×C₁₃	semidirect
488. #537	C₂²×C₁₃	semidirect
489. #537	C₂²×C₁₃	semidirect
490. #536	C₂²×C₁₃	semidirect
491. #536	C₂²×C₁₃	semidirect
501. #520	C₂²×C₁₃	semidirect
503. #485	C₂²×C₁₃	semidirect
507. #484	C₂²×C₁₃	semidirect
508. #484	C₂²×C₁₃	semidirect
509. #483	C₂²×C₁₃	semidirect
510. #482	C₂²×C₁₃	semidirect
512. #480	C₂²×C₁₃	semidirect
513. #480	C₂²×C₁₃	semidirect
514. #470	C₂²×C₁₃	semidirect
515. #468	C₂²×C₁₃	semidirect
516. #468	C₂²×C₁₃	semidirect
517. #468	C₂²×C₁₃	semidirect
518. #467	C₂²×C₁₃	semidirect
519. #467	C₂²×C₁₃	semidirect
520. #466	C₂²×C₁₃	semidirect
521. #465	C₂²×C₁₃	semidirect
522. #452	C₂²×C₁₃	semidirect
523. #452	C₂²×C₁₃	semidirect
524. #452	C₂²×C₁₃	semidirect
527. #451	C₂²×C₁₃	semidirect
530. #449	C₂²×C₁₃	semidirect
531. #449	C₂²×C₁₃	semidirect
533. #448	C₂²×C₁₃	semidirect
535. #428	C₂²×C₁₃	semidirect
536. C₂×#107	C₂²×C₁₃	semidirect
537. #417	C₂²×C₁₃	semidirect
538. #417	C₂²×C₁₃	semidirect
539. #416	C₂²×C₁₃	semidirect
540. C₂×#103	C₂²×C₁₃	semidirect
541. #408	C₂²×C₁₃	semidirect
542. #408	C₂²×C₁₃	semidirect
867. C₁₃	#60764	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×#3489	2
C₂×C₁₃×#537	2
C₁₃×#3203	2
C₁₃×#3201	2
C₁₃×#3196	2
C₁₃×#3193	2
C₁₃×#3189	2
C₁₃×#3188	2
C₁₃×#3098	2
C₁₃×#3092	2
C₂×C₁₃×#484	2
C₁₃×#3063	2
C₁₃×#3061	2
C₁₃×#3013	2
C₁₃×#3007	2
C₁₃×#3002	2
C₁₃×#2880	2
#60764	13

Subgroups — C13×#60764 #15747103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60764 #15747103