Subgroups — C₁₃×#61258 #15747597

Order 3328.

1866 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3492	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3346	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3343	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3339	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3338	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3336	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3334	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3098	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3092	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3083	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3061	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#554	—	2	2	no	—
22	C₁₃×#554	C₂²	1	4	yes	—
23	C₁₃×#553	—	2	2	no	—
24	C₁₃×#553	C₂²	1	4	yes	—
25	C₁₃×#552	—	2	2	no	—
26	C₁₃×#552	C₂²	1	4	yes	—
27	C₁₃×#547	—	2	2	no	—
28	C₁₃×#547	C₂²	1	4	yes	—
29	C₁₃×#544	C₂²	1	2	yes	—
30	C₁₃×#539	—	2	4	no	—
31	C₁₃×#537	C₂²	1	2	yes	—
32	C₁₃×#525	—	2	4	no	—
33	C₁₃×#525	C₂²	1	2	yes	—
34	C₁₃×#525	C₂²	1	1	yes	characteristic
35	C₁₃×#520	C₂²	1	2	yes	—
36	C₁₃×#520	C₂²	1	2	yes	—
37	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
38	C₁₃×#501	C₂²	1	4	yes	complemented
39	C₁₃×#500	C₂²	1	2	yes	complemented
40	C₁₃×#499	C₂²	1	2	yes	complemented
41	C₁₃×#485	C₂²	1	4	yes	complemented
42	C₁₃×#484	C₂²	1	4	yes	—
43	C₁₃×#484	C₂²	1	4	yes	complemented
44	C₁₃×#483	C₂²	1	4	yes	—
45	C₁₃×#482	C₂²	1	4	yes	complemented
46	C₁₃×#481	C₂²	1	4	yes	—
47	C₁₃×#480	C₂²	1	4	yes	—
48	C₁₃×#480	C₂²	1	4	yes	complemented
49	C₁₃×#479	C₂²	1	4	yes	complemented
50	C₁₃×#478	C₂²	1	4	yes	complemented
51	C₁₃×#477	C₂²	1	4	yes	complemented
52	C₁₃×#474	C₂²	1	4	yes	complemented
53	C₁₃×#468	C₂²	1	4	yes	complemented
54	C₁₃×#467	C₂²	1	1	yes	characteristic
55	C₁₃×#467	C₂²	1	1	yes	characteristic
56	C₁₃×#467	C₂²	1	2	yes	complemented
57	C₁₃×#466	C₂²	1	1	yes	characteristic
58	C₁₃×#466	C₂²	1	1	yes	characteristic
59	C₁₃×#466	C₂²	1	2	yes	complemented
60	C₁₃×#465	C₂²	1	2	yes	—
61	C₁₃×#465	C₂²	1	2	yes	—
62	C₁₃×#440	C₂²	1	4	yes	complemented
63	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
64	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
65	C₁₃×#435	C₂²	1	2	yes	—
66	C₁₃×#435	C₂²	1	2	yes	—
67	C₈×D₄×C₁₃	C₂²	1	2	yes	—
68	C₈×D₄×C₁₃	C₂²	1	2	yes	—
69	C₁₃×#428	C₂²	1	2	yes	—
70	C₁₃×#428	C₂²	1	2	yes	—
71	C₁₃×#428	C₂²	1	4	yes	complemented
72	C₁₃×#427	C₂²	1	1	yes	characteristic
73	C₁₃×#427	C₂²	1	2	yes	complemented
74	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×#107	C₂²	1	2	yes	—
76	C₂×C₁₃×#107	C₂²	1	2	yes	—
77	C₂×C₁₃×#107	C₂²	1	2	yes	—
78	C₂×C₁₃×#107	C₂²	1	2	yes	—
79	C₂×C₁₃×#107	C₂²	1	2	yes	—
80	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
81	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
82	C₁₃×#424	C₂²	1	1	yes	characteristic
83	C₁₃×#417	C₂²	1	2	yes	—
84	C₁₃×#417	C₂²	1	2	yes	—
85	C₁₃×#416	C₂²	1	2	yes	—
86	C₁₃×#408	C₂²	1	1	yes	characteristic
87	C₁₃×#407	C₂²	1	1	yes	characteristic
88	C₁₃×#405	C₂²	1	1	yes	characteristic
89	C₂×C₁₃×#41	—	2	4	no	—
90	C₂×C₁₃×#41	C₂³	1	2	yes	—
91	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃	—	2	2	no	—
93	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₁₃×#135	—	2	4	no	—
95	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
97	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
98	C₁₃×#131	—	2	4	no	—
99	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
102	C₂²×C₈×C₁₃	—	2	4	no	—
103	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
109	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×C₄⋊Q₈	—	2	2	no	—
111	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
112	C₁₃×#126	—	2	4	no	—
113	C₁₃×#126	—	2	4	no	—
114	C₁₃×#125	—	2	4	no	—
115	C₁₃×#125	—	2	4	no	—
116	C₁₃×#125	—	2	2	no	—
117	C₁₃×#125	C₂³	1	4	yes	—
118	C₁₃×#123	—	2	4	no	—
119	C₁₃×#123	—	2	2	no	—
120	C₁₃×#123	—	2	4	no	—
121	C₁₃×#123	—	2	4	no	—
122	C₁₃×#123	—	2	4	no	—
123	C₁₃×#123	D₄	1	2	yes	—
124	C₁₃×C₂²⋊Q₈	—	2	2	no	—
125	C₁₃×C₂²⋊Q₈	—	2	4	no	—
126	C₁₃×C₂²⋊Q₈	—	2	4	no	—
127	C₁₃×C₂²⋊Q₈	—	2	4	no	—
128	C₁₃×C₂²⋊Q₈	—	2	4	no	—
129	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
130	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
131	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
132	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
133	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₁₃×#121	—	2	4	no	—
135	C₁₃×#121	—	2	4	no	—
136	C₁₃×#121	—	2	2	no	—
137	C₁₃×#121	D₄	1	1	yes	characteristic
138	C₁₃×#121	D₄	1	1	yes	characteristic
139	C₁₃×#121	C₂³	1	2	yes	—
140	C₁₃×#121	C₂³	1	2	yes	—
141	C₁₃×#121	C₂³	1	4	yes	—
142	C₁₃×#120	—	2	2	no	—
143	C₁₃×#120	D₄	1	2	yes	—
144	C₄×Q₈×C₁₃	—	2	2	no	—
145	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
146	C₄×D₄×C₁₃	—	2	4	no	—
147	C₄×D₄×C₁₃	—	2	2	no	—
148	C₄×D₄×C₁₃	—	2	4	no	—
149	C₄×D₄×C₁₃	—	2	2	no	—
150	C₄×D₄×C₁₃	—	2	2	no	—
151	C₄×D₄×C₁₃	—	2	4	no	—
152	C₄×D₄×C₁₃	—	2	4	no	—
153	C₄×D₄×C₁₃	C₂³	1	4	yes	—
154	C₄×D₄×C₁₃	C₂³	1	2	yes	—
155	C₄×D₄×C₁₃	C₂³	1	2	yes	—
156	C₁₃×#117	—	2	2	no	—
157	C₁₃×#117	—	2	4	no	—
158	C₁₃×#117	C₂³	1	2	yes	—
159	C₁₃×#117	C₂³	1	4	yes	—
160	C₁₃×#117	C₂³	1	1	yes	characteristic
161	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
170	C₁₃×#107	C₂³	1	2	yes	—
171	C₁₃×#107	C₂³	1	2	yes	—
172	C₁₃×#107	C₂³	1	2	yes	—
173	C₁₃×#107	C₂³	1	2	yes	—
174	C₁₃×#107	C₂³	1	4	yes	—
175	C₁₃×#107	C₂³	1	4	yes	—
176	C₁₃×#107	C₂³	1	1	yes	characteristic
177	C₁₃×#107	C₂³	1	4	yes	—
178	C₁₃×#107	C₂³	1	1	yes	characteristic
179	C₁₃×#107	C₂³	1	4	yes	—
180	C₁₃×#106	C₂³	1	2	yes	—
181	C₁₃×#106	C₂³	1	4	yes	—
182	C₁₃×#106	C₂³	1	4	yes	—
183	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
184	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
185	C₁₃×#103	C₂³	1	2	yes	—
186	C₁₃×#103	C₂³	1	2	yes	—
187	C₁₃×#103	C₂³	1	4	yes	—
188	C₁₃×#103	C₂³	1	4	yes	—
189	C₁₃×#102	C₂³	1	2	yes	—
190	C₁₃×#102	C₂³	1	2	yes	—
191	C₁₃×#102	C₂³	1	4	yes	—
192	C₁₃×#102	C₂³	1	4	yes	—
193	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
196	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
197	C₁₃×#97	C₂³	1	2	yes	—
198	C₄×C₈×C₁₃	C₂³	1	2	yes	—
199	#61258	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
201	C₁₃×#41	—	2	2	no	—
202	C₁₃×#41	—	2	2	no	—
203	C₁₃×#41	—	2	4	no	—
204	C₁₃×#41	—	2	4	no	—
205	C₁₃×#41	—	8	8	no	—
206	C₂×Q₈×C₁₃	—	2	4	no	—
207	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
209	C₂×D₄×C₁₃	—	2	2	no	—
210	C₂×D₄×C₁₃	—	2	2	no	—
211	C₂×D₄×C₁₃	—	2	2	no	—
212	C₂×D₄×C₁₃	—	2	4	no	—
213	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
214	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
215	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
216	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
217	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	2	no	—
220	C₂²×C₄×C₁₃	—	2	4	no	—
221	C₂²×C₄×C₁₃	—	2	2	no	—
222	C₂²×C₄×C₁₃	—	2	4	no	—
223	C₂²×C₄×C₁₃	—	2	2	no	—
224	C₂²×C₄×C₁₃	—	2	4	no	—
225	C₂²×C₄×C₁₃	—	2	2	no	—
226	C₂²×C₄×C₁₃	—	2	4	no	—
227	C₂²×C₄×C₁₃	—	8	4	no	—
228	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₁₃×Q₁₆	—	2	2	no	—
236	C₁₃×SD₁₆	—	2	4	no	—
237	C₁₃×D₈	—	2	2	no	—
238	C₁₃×M₁₆	—	2	2	no	—
239	C₁₃×M₁₆	—	2	2	no	—
240	C₁₃×M₁₆	—	2	4	no	—
241	C₂×C₈×C₁₃	—	2	2	no	—
242	C₂×C₈×C₁₃	—	2	2	no	—
243	C₂×C₈×C₁₃	—	2	2	no	—
244	C₂×C₈×C₁₃	—	2	2	no	—
245	C₂×C₈×C₁₃	—	2	2	no	—
246	C₂×C₈×C₁₃	—	2	4	no	—
247	C₂×C₈×C₁₃	#41	1	4	yes	complemented
248	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
249	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
250	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₁₃×C₄⋊C₄	—	2	2	no	—
255	C₁₃×C₄⋊C₄	—	2	2	no	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	—	2	4	no	—
258	C₁₃×C₄⋊C₄	—	2	4	no	—
259	C₁₃×C₄⋊C₄	—	2	4	no	—
260	C₁₃×C₄⋊C₄	—	2	4	no	—
261	C₁₃×C₄⋊C₄	—	2	4	no	—
262	C₁₃×C₄⋊C₄	—	2	2	no	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	2	2	no	—
266	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
267	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
268	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
269	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
270	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
271	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
272	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
273	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
274	C₁₃×C₂²⋊C₄	—	2	2	no	—
275	C₁₃×C₂²⋊C₄	—	2	2	no	—
276	C₁₃×C₂²⋊C₄	—	2	4	no	—
277	C₁₃×C₂²⋊C₄	—	2	2	no	—
278	C₁₃×C₂²⋊C₄	—	2	4	no	—
279	C₁₃×C₂²⋊C₄	—	2	4	no	—
280	C₁₃×C₂²⋊C₄	—	2	4	no	—
281	C₁₃×C₂²⋊C₄	—	2	2	no	—
282	C₁₃×C₂²⋊C₄	—	2	2	no	—
283	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
284	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
285	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
286	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
287	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
288	C₄²×C₁₃	—	2	4	no	—
289	C₄²×C₁₃	—	2	4	no	—
290	C₄²×C₁₃	—	2	2	no	—
291	C₄²×C₁₃	C₂⁴	1	2	yes	—
292	#3492	C₂×C₁₃	1	2	yes	complemented
293	#3346	C₂×C₁₃	1	4	yes	complemented
294	#3343	C₂×C₁₃	1	4	yes	complemented
295	#3339	C₂×C₁₃	1	2	yes	complemented
296	#3338	C₂×C₁₃	1	2	yes	complemented
297	#3336	C₂×C₁₃	1	2	yes	complemented
298	#3334	C₂×C₁₃	1	2	yes	complemented
299	#3164	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#3098	C₂×C₁₃	1	2	yes	complemented
301	#3092	C₂×C₁₃	1	2	yes	complemented
302	#3083	C₂×C₁₃	1	2	yes	complemented
303	#3061	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#3050	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#2951	C₂×C₁₃	1	1	yes	characteristic, complemented
306	#2929	C₂×C₁₃	1	1	yes	characteristic, complemented
307	#2913	C₂×C₁₃	1	1	yes	characteristic, complemented
308	C₂²×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
309	C₂³×C₁₃	—	2	2	no	—
310	C₂³×C₁₃	—	2	2	no	—
311	C₂³×C₁₃	—	2	2	no	—
312	C₂³×C₁₃	—	2	2	no	—
313	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
314	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
315	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
316	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
317	Q₈×C₁₃	—	2	2	no	—
318	Q₈×C₁₃	—	2	2	no	—
319	Q₈×C₁₃	—	2	2	no	—
320	Q₈×C₁₃	—	8	4	no	—
321	D₄×C₁₃	—	2	4	no	—
322	D₄×C₁₃	—	2	4	no	—
323	D₄×C₁₃	—	2	4	no	—
324	D₄×C₁₃	—	2	2	no	—
325	D₄×C₁₃	—	2	2	no	—
326	D₄×C₁₃	—	2	2	no	—
327	D₄×C₁₃	—	4	4	no	—
328	D₄×C₁₃	—	4	4	no	—
329	D₄×C₁₃	—	4	4	no	—
330	D₄×C₁₃	—	8	4	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	1	no	—
335	C₂×C₄×C₁₃	—	2	1	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	1	no	—
338	C₂×C₄×C₁₃	—	2	1	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	4	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	4	no	—
345	C₂×C₄×C₁₃	—	4	8	no	—
346	C₂×C₄×C₁₃	—	4	4	no	—
347	C₂×C₄×C₁₃	—	8	4	no	—
348	C₂×C₄×C₁₃	—	8	2	no	—
349	C₂×C₄×C₁₃	—	8	4	no	—
350	C₂×C₄×C₁₃	—	8	2	no	—
351	C₂×C₄×C₁₃	—	8	4	no	—
352	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
353	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
354	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
355	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
359	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
360	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
361	C₈×C₁₃	—	2	1	no	—
362	C₈×C₁₃	—	2	1	no	—
363	C₈×C₁₃	—	2	2	no	—
364	C₈×C₁₃	—	2	2	no	—
365	C₈×C₁₃	C₂×#41	1	2	yes	—
366	C₈×C₁₃	C₂×#41	1	2	yes	—
367	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
368	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
369	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
370	#554	—	2	2	no	—
371	#554	C₂²×C₁₃	1	4	yes	—
372	#553	—	2	2	no	—
373	#553	C₂²×C₁₃	1	4	yes	—
374	#552	—	2	2	no	—
375	#552	C₂²×C₁₃	1	4	yes	—
376	#547	—	2	2	no	—
377	#547	C₂²×C₁₃	1	4	yes	—
378	#544	C₂²×C₁₃	1	2	yes	—
379	#539	—	2	4	no	—
380	#537	C₂²×C₁₃	1	2	yes	—
381	#525	—	2	4	no	—
382	#525	C₂²×C₁₃	1	2	yes	—
383	#525	C₂²×C₁₃	1	1	yes	characteristic
384	#520	C₂²×C₁₃	1	2	yes	—
385	#520	C₂²×C₁₃	1	2	yes	—
386	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
387	#501	C₂²×C₁₃	1	4	yes	complemented
388	#500	C₂²×C₁₃	1	2	yes	complemented
389	#499	C₂²×C₁₃	1	2	yes	complemented
390	#485	C₂²×C₁₃	1	4	yes	complemented
391	#484	C₂²×C₁₃	1	4	yes	—
392	#484	C₂²×C₁₃	1	4	yes	complemented
393	#483	C₂²×C₁₃	1	4	yes	—
394	#482	C₂²×C₁₃	1	4	yes	complemented
395	#481	C₂²×C₁₃	1	4	yes	—
396	#480	C₂²×C₁₃	1	4	yes	—
397	#480	C₂²×C₁₃	1	4	yes	complemented
398	#479	C₂²×C₁₃	1	4	yes	complemented
399	#478	C₂²×C₁₃	1	4	yes	complemented
400	#477	C₂²×C₁₃	1	4	yes	complemented
401	#474	C₂²×C₁₃	1	4	yes	complemented
402	#468	C₂²×C₁₃	1	4	yes	complemented
403	#467	C₂²×C₁₃	1	1	yes	characteristic
404	#467	C₂²×C₁₃	1	1	yes	characteristic
405	#467	C₂²×C₁₃	1	2	yes	complemented
406	#466	C₂²×C₁₃	1	1	yes	characteristic
407	#466	C₂²×C₁₃	1	1	yes	characteristic
408	#466	C₂²×C₁₃	1	2	yes	complemented
409	#465	C₂²×C₁₃	1	2	yes	—
410	#465	C₂²×C₁₃	1	2	yes	—
411	#440	C₂²×C₁₃	1	4	yes	complemented
412	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
413	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
414	#435	C₂²×C₁₃	1	2	yes	—
415	#435	C₂²×C₁₃	1	2	yes	—
416	C₈×D₄	C₂²×C₁₃	1	2	yes	—
417	C₈×D₄	C₂²×C₁₃	1	2	yes	—
418	#428	C₂²×C₁₃	1	2	yes	—
419	#428	C₂²×C₁₃	1	2	yes	—
420	#428	C₂²×C₁₃	1	4	yes	complemented
421	#427	C₂²×C₁₃	1	1	yes	characteristic
422	#427	C₂²×C₁₃	1	2	yes	complemented
423	C₂×#107	C₂²×C₁₃	1	2	yes	—
424	C₂×#107	C₂²×C₁₃	1	2	yes	—
425	C₂×#107	C₂²×C₁₃	1	2	yes	—
426	C₂×#107	C₂²×C₁₃	1	2	yes	—
427	C₂×#107	C₂²×C₁₃	1	2	yes	—
428	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
429	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
431	#424	C₂²×C₁₃	1	1	yes	characteristic
432	#417	C₂²×C₁₃	1	2	yes	—
433	#417	C₂²×C₁₃	1	2	yes	—
434	#416	C₂²×C₁₃	1	2	yes	—
435	#408	C₂²×C₁₃	1	1	yes	characteristic
436	#407	C₂²×C₁₃	1	1	yes	characteristic
437	#405	C₂²×C₁₃	1	1	yes	characteristic
438	C₂²×C₁₃	—	2	8	no	—
439	C₂²×C₁₃	—	2	1	no	—
440	C₂²×C₁₃	—	2	1	no	—
441	C₂²×C₁₃	—	2	1	no	—
442	C₂²×C₁₃	—	2	1	no	—
443	C₂²×C₁₃	—	2	1	no	—
444	C₂²×C₁₃	—	2	1	no	—
445	C₂²×C₁₃	—	2	2	no	—
446	C₂²×C₁₃	—	2	2	no	—
447	C₂²×C₁₃	—	2	2	no	—
448	C₂²×C₁₃	—	4	2	no	—
449	C₂²×C₁₃	—	4	2	no	—
450	C₂²×C₁₃	—	4	2	no	—
451	C₂²×C₁₃	#547	1	2	yes	—
452	C₂²×C₁₃	#576	1	2	yes	—
453	C₂²×C₁₃	#578	1	2	yes	—
454	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
455	C₄×C₁₃	—	2	1	no	—
456	C₄×C₁₃	—	2	1	no	—
457	C₄×C₁₃	—	2	2	no	—
458	C₄×C₁₃	—	2	2	no	—
459	C₄×C₁₃	—	2	2	no	—
460	C₄×C₁₃	—	4	2	no	—
461	C₄×C₁₃	—	4	4	no	—
462	C₄×C₁₃	—	4	4	no	—
463	C₄×C₁₃	—	4	2	no	—
464	C₄×C₁₃	—	4	2	no	—
465	C₄×C₁₃	#547	1	2	yes	—
466	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
467	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
468	C₂×#41	—	2	4	no	—
469	C₂×#41	C₂³×C₁₃	1	2	yes	—
470	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
471	C₂³×C₄	—	2	2	no	—
472	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
473	#135	—	2	4	no	—
474	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
475	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
476	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
477	#131	—	2	4	no	—
478	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
479	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
480	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
481	C₂²×C₈	—	2	4	no	—
482	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
483	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
484	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
485	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
486	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
488	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
489	C₄⋊Q₈	—	2	2	no	—
490	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
491	#126	—	2	4	no	—
492	#126	—	2	4	no	—
493	#125	—	2	4	no	—
494	#125	—	2	4	no	—
495	#125	—	2	2	no	—
496	#125	C₂³×C₁₃	1	4	yes	—
497	#123	—	2	4	no	—
498	#123	—	2	2	no	—
499	#123	—	2	4	no	—
500	#123	—	2	4	no	—
501	#123	—	2	4	no	—
502	#123	D₄×C₁₃	1	2	yes	—
503	C₂²⋊Q₈	—	2	2	no	—
504	C₂²⋊Q₈	—	2	4	no	—
505	C₂²⋊Q₈	—	2	4	no	—
506	C₂²⋊Q₈	—	2	4	no	—
507	C₂²⋊Q₈	—	2	4	no	—
508	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
509	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
510	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
511	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
512	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
513	#121	—	2	4	no	—
514	#121	—	2	4	no	—
515	#121	—	2	2	no	—
516	#121	D₄×C₁₃	1	1	yes	characteristic
517	#121	D₄×C₁₃	1	1	yes	characteristic
518	#121	C₂³×C₁₃	1	2	yes	—
519	#121	C₂³×C₁₃	1	2	yes	—
520	#121	C₂³×C₁₃	1	4	yes	—
521	#120	—	2	2	no	—
522	#120	D₄×C₁₃	1	2	yes	—
523	C₄×Q₈	—	2	2	no	—
524	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	4	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	4	no	—
531	C₄×D₄	—	2	4	no	—
532	C₄×D₄	C₂³×C₁₃	1	4	yes	—
533	C₄×D₄	C₂³×C₁₃	1	2	yes	—
534	C₄×D₄	C₂³×C₁₃	1	2	yes	—
535	#117	—	2	2	no	—
536	#117	—	2	4	no	—
537	#117	C₂³×C₁₃	1	2	yes	—
538	#117	C₂³×C₁₃	1	4	yes	—
539	#117	C₂³×C₁₃	1	1	yes	characteristic
540	C₂×C₄⋊C₄	—	2	2	no	—
541	C₂×C₄⋊C₄	—	2	2	no	—
542	C₂×C₄⋊C₄	—	2	2	no	—
543	C₂×C₄⋊C₄	—	2	2	no	—
544	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
547	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
548	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
549	#107	C₂³×C₁₃	1	2	yes	—
550	#107	C₂³×C₁₃	1	2	yes	—
551	#107	C₂³×C₁₃	1	2	yes	—
552	#107	C₂³×C₁₃	1	2	yes	—
553	#107	C₂³×C₁₃	1	4	yes	—
554	#107	C₂³×C₁₃	1	4	yes	—
555	#107	C₂³×C₁₃	1	1	yes	characteristic
556	#107	C₂³×C₁₃	1	4	yes	—
557	#107	C₂³×C₁₃	1	1	yes	characteristic
558	#107	C₂³×C₁₃	1	4	yes	—
559	#106	C₂³×C₁₃	1	2	yes	—
560	#106	C₂³×C₁₃	1	4	yes	—
561	#106	C₂³×C₁₃	1	4	yes	—
562	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
563	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
564	#103	C₂³×C₁₃	1	2	yes	—
565	#103	C₂³×C₁₃	1	2	yes	—
566	#103	C₂³×C₁₃	1	4	yes	—
567	#103	C₂³×C₁₃	1	4	yes	—
568	#102	C₂³×C₁₃	1	2	yes	—
569	#102	C₂³×C₁₃	1	2	yes	—
570	#102	C₂³×C₁₃	1	4	yes	—
571	#102	C₂³×C₁₃	1	4	yes	—
572	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
573	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
574	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
575	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
576	#97	C₂³×C₁₃	1	2	yes	—
577	C₄×C₈	C₂³×C₁₃	1	2	yes	—
578	C₂×C₁₃	—	2	2	no	—
579	C₂×C₁₃	—	2	2	no	—
580	C₂×C₁₃	—	2	2	no	—
581	C₂×C₁₃	—	4	2	no	—
582	C₂×C₁₃	—	8	2	no	—
583	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
584	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
585	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
586	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
587	#41	—	2	2	no	—
588	#41	—	2	2	no	—
589	#41	—	2	4	no	—
590	#41	—	2	4	no	—
591	#41	—	8	8	no	—
592	C₂×Q₈	—	2	4	no	—
593	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
594	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
600	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
601	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
602	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
603	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	8	4	no	—
614	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
621	Q₁₆	—	2	2	no	—
622	SD₁₆	—	2	4	no	—
623	D₈	—	2	2	no	—
624	M₁₆	—	2	2	no	—
625	M₁₆	—	2	2	no	—
626	M₁₆	—	2	4	no	—
627	C₂×C₈	—	2	2	no	—
628	C₂×C₈	—	2	2	no	—
629	C₂×C₈	—	2	2	no	—
630	C₂×C₈	—	2	2	no	—
631	C₂×C₈	—	2	2	no	—
632	C₂×C₈	—	2	4	no	—
633	C₂×C₈	C₁₃×#41	1	4	yes	complemented
634	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
635	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
636	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
637	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
638	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
639	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
653	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
654	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
655	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
656	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
657	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
658	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
659	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	2	no	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
670	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
671	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
672	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
673	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
674	C₄²	—	2	4	no	—
675	C₄²	—	2	4	no	—
676	C₄²	—	2	2	no	—
677	C₄²	C₂⁴×C₁₃	1	2	yes	—
678	C₁₃	#61258	1	1	yes	characteristic, direct product factor, Sylow
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
684	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
685	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
686	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
687	Q₈	—	2	2	no	—
688	Q₈	—	2	2	no	—
689	Q₈	—	2	2	no	—
690	Q₈	—	8	4	no	—
691	D₄	—	2	4	no	—
692	D₄	—	2	4	no	—
693	D₄	—	2	4	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	2	no	—
697	D₄	—	4	4	no	—
698	D₄	—	4	4	no	—
699	D₄	—	4	4	no	—
700	D₄	—	8	4	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	4	8	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	8	4	no	—
718	C₂×C₄	—	8	2	no	—
719	C₂×C₄	—	8	4	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
723	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
724	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
725	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
726	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
727	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
728	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
729	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
730	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
731	C₈	—	2	1	no	—
732	C₈	—	2	1	no	—
733	C₈	—	2	2	no	—
734	C₈	—	2	2	no	—
735	C₈	C₂×C₁₃×#41	1	2	yes	—
736	C₈	C₂×C₁₃×#41	1	2	yes	—
737	C₂²	—	2	8	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	C₁₃×#547	1	2	yes	—
751	C₂²	C₁₃×#576	1	2	yes	—
752	C₂²	C₁₃×#578	1	2	yes	—
753	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	2	no	—
759	C₄	—	4	4	no	—
760	C₄	—	4	4	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	C₁₃×#547	1	2	yes	—
765	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
766	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
767	C₂	—	2	2	no	—
768	C₂	—	2	2	no	—
769	C₂	—	2	2	no	—
770	C₂	—	4	2	no	—
771	C₂	—	8	2	no	—
772	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
773	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
774	C₂	C₂×C₁₃×#578	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. C₁₃×#3492	C₂	semidirect
2. C₁₃×#3346	C₂	semidirect
3. C₁₃×#3343	C₂	semidirect
4. C₁₃×#3339	C₂	semidirect
5. C₁₃×#3338	C₂	semidirect
6. C₁₃×#3336	C₂	semidirect
7. C₁₃×#3334	C₂	semidirect
8. C₁₃×#3164	C₂	semidirect
9. C₁₃×#3098	C₂	semidirect
10. C₁₃×#3092	C₂	semidirect
11. C₁₃×#3083	C₂	semidirect
12. C₁₃×#3061	C₂	semidirect
13. C₁₃×#3050	C₂	semidirect
14. C₁₃×#2951	C₂	semidirect
15. C₁₃×#2929	C₂	semidirect
16. C₁₃×#2913	C₂	semidirect
17. C₂²×C₁₃×#107	C₂	semidirect
38. C₁₃×#501	C₂²	semidirect
39. C₁₃×#500	C₂²	semidirect
40. C₁₃×#499	C₂²	semidirect
41. C₁₃×#485	C₂²	semidirect
43. C₁₃×#484	C₂²	semidirect
45. C₁₃×#482	C₂²	semidirect
48. C₁₃×#480	C₂²	semidirect
49. C₁₃×#479	C₂²	semidirect
50. C₁₃×#478	C₂²	semidirect
51. C₁₃×#477	C₂²	semidirect
52. C₁₃×#474	C₂²	semidirect
53. C₁₃×#468	C₂²	semidirect
56. C₁₃×#467	C₂²	semidirect
59. C₁₃×#466	C₂²	semidirect
62. C₁₃×#440	C₂²	semidirect
63. C₄×C₁₃×Q₁₆	C₂²	semidirect
64. C₄×C₁₃×D₈	C₂²	semidirect
71. C₁₃×#428	C₂²	semidirect
73. C₁₃×#427	C₂²	semidirect
81. C₂×C₁₃×#107	C₂²	semidirect
199. #61258	C₁₃	direct (N × H)
247. C₂×C₈×C₁₃	#41	semidirect
292. #3492	C₂×C₁₃	semidirect
293. #3346	C₂×C₁₃	semidirect
294. #3343	C₂×C₁₃	semidirect
295. #3339	C₂×C₁₃	semidirect
296. #3338	C₂×C₁₃	semidirect
297. #3336	C₂×C₁₃	semidirect
298. #3334	C₂×C₁₃	semidirect
299. #3164	C₂×C₁₃	semidirect
300. #3098	C₂×C₁₃	semidirect
301. #3092	C₂×C₁₃	semidirect
302. #3083	C₂×C₁₃	semidirect
303. #3061	C₂×C₁₃	semidirect
304. #3050	C₂×C₁₃	semidirect
305. #2951	C₂×C₁₃	semidirect
306. #2929	C₂×C₁₃	semidirect
307. #2913	C₂×C₁₃	semidirect
308. C₂²×#107	C₂×C₁₃	semidirect
387. #501	C₂²×C₁₃	semidirect
388. #500	C₂²×C₁₃	semidirect
389. #499	C₂²×C₁₃	semidirect
390. #485	C₂²×C₁₃	semidirect
392. #484	C₂²×C₁₃	semidirect
394. #482	C₂²×C₁₃	semidirect
397. #480	C₂²×C₁₃	semidirect
398. #479	C₂²×C₁₃	semidirect
399. #478	C₂²×C₁₃	semidirect
400. #477	C₂²×C₁₃	semidirect
401. #474	C₂²×C₁₃	semidirect
402. #468	C₂²×C₁₃	semidirect
405. #467	C₂²×C₁₃	semidirect
408. #466	C₂²×C₁₃	semidirect
411. #440	C₂²×C₁₃	semidirect
412. C₄×Q₁₆	C₂²×C₁₃	semidirect
413. C₄×D₈	C₂²×C₁₃	semidirect
420. #428	C₂²×C₁₃	semidirect
422. #427	C₂²×C₁₃	semidirect
430. C₂×#107	C₂²×C₁₃	semidirect
633. C₂×C₈	C₁₃×#41	semidirect
678. C₁₃	#61258	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×#3492	2
C₁₃×#3346	2
C₁₃×#3343	2
C₁₃×#3339	2
C₁₃×#3338	2
C₁₃×#3336	2
C₁₃×#3334	2
C₁₃×#3164	2
C₁₃×#3098	2
C₁₃×#3092	2
C₁₃×#3083	2
C₁₃×#3061	2
C₁₃×#3050	2
C₁₃×#2951	2
C₁₃×#2929	2
C₁₃×#2913	2
C₂²×C₁₃×#107	2
#61258	13

Subgroups — C13×#61258 #15747597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61258 #15747597