Subgroups — C₁₃×#61446 #15747785

Order 3328.

1830 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3482	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3402	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3390	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3377	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3352	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3343	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3327	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3312	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3308	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3277	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3270	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3172	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3108	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3104	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3102	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₁₃×#137	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×#137	C₂²	1	2	yes	—
21	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
22	C₁₃×#557	C₂²	1	2	yes	—
23	C₁₃×#556	—	2	2	no	—
24	C₁₃×#556	C₂²	1	2	yes	—
25	C₁₃×#552	—	2	2	no	—
26	C₁₃×#552	—	2	2	no	—
27	C₁₃×#552	C₂²	1	2	yes	—
28	C₁₃×#552	C₂²	1	2	yes	—
29	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
30	C₁₃×#548	C₂²	1	2	yes	—
31	C₁₃×#548	C₂²	1	2	yes	—
32	C₁₃×#547	—	2	2	no	—
33	C₁₃×#547	C₂²	1	2	yes	—
34	C₁₃×#533	—	2	2	no	—
35	C₁₃×#533	C₂²	1	2	yes	—
36	C₁₃×#529	—	2	2	no	—
37	C₁₃×#529	—	2	2	no	—
38	C₁₃×#529	C₂²	1	2	yes	—
39	C₁₃×#529	C₂²	1	2	yes	—
40	C₄×C₁₃×#41	—	2	2	no	—
41	C₄×C₁₃×#41	C₂²	1	2	yes	—
42	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
45	C₁₃×#501	C₂²	1	2	yes	—
46	C₁₃×#499	C₂²	1	1	yes	characteristic
47	C₁₃×#497	C₂²	1	2	yes	—
48	C₁₃×#495	C₂²	1	1	yes	characteristic
49	C₁₃×#491	C₂²	1	2	yes	—
50	C₁₃×#489	C₂²	1	2	yes	—
51	C₁₃×#488	C₂²	1	2	yes	—
52	C₁₃×#485	C₂²	1	2	yes	—
53	C₁₃×#484	C₂²	1	2	yes	—
54	C₁₃×#484	C₂²	1	2	yes	—
55	C₁₃×#483	C₂²	1	2	yes	—
56	C₁₃×#482	C₂²	1	2	yes	—
57	C₁₃×#480	C₂²	1	2	yes	—
58	C₁₃×#479	C₂²	1	2	yes	—
59	C₁₃×#479	C₂²	1	2	yes	—
60	C₁₃×#479	C₂²	1	2	yes	—
61	C₁₃×#478	C₂²	1	2	yes	—
62	C₁₃×#477	C₂²	1	2	yes	—
63	C₁₃×#477	C₂²	1	2	yes	—
64	C₁₃×#470	C₂²	1	2	yes	—
65	C₁₃×#470	C₂²	1	2	yes	—
66	C₁₃×#468	C₂²	1	2	yes	—
67	C₁₃×#468	C₂²	1	2	yes	—
68	C₁₃×#467	C₂²	1	1	yes	characteristic
69	C₁₃×#466	C₂²	1	1	yes	characteristic
70	C₁₃×#465	C₂²	1	2	yes	—
71	C₁₃×#464	C₂²	1	2	yes	—
72	C₁₃×#464	C₂²	1	2	yes	—
73	C₁₃×#464	C₂²	1	2	yes	—
74	C₁₃×#463	C₂²	1	2	yes	—
75	C₁₃×#462	C₂²	1	2	yes	—
76	C₁₃×#462	C₂²	1	2	yes	—
77	C₁₃×#452	C₂²	1	2	yes	—
78	C₁₃×#451	C₂²	1	2	yes	—
79	C₁₃×#451	C₂²	1	2	yes	—
80	C₁₃×#451	C₂²	1	2	yes	—
81	C₁₃×#449	C₂²	1	2	yes	—
82	C₁₃×#448	C₂²	1	2	yes	—
83	C₁₃×#446	C₂²	1	1	yes	characteristic
84	C₁₃×#446	C₂²	1	1	yes	characteristic
85	C₁₃×#441	C₂²	1	2	yes	—
86	C₁₃×#441	C₂²	1	2	yes	—
87	C₁₃×#440	C₂²	1	2	yes	—
88	C₁₃×#440	C₂²	1	2	yes	—
89	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
90	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
91	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
92	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
93	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
94	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
95	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
96	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
97	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
98	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
99	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
100	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
101	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
102	C₁₃×#436	C₂²	1	1	yes	characteristic
103	C₁₃×#436	C₂²	1	1	yes	characteristic
104	C₁₃×#435	C₂²	1	2	yes	—
105	C₁₃×#435	C₂²	1	2	yes	—
106	C₁₃×#431	C₂²	1	2	yes	—
107	C₁₃×#431	C₂²	1	1	yes	characteristic
108	C₁₃×#428	C₂²	1	2	yes	—
109	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
110	C₁₃×#419	C₂²	1	2	yes	—
111	C₁₃×#417	C₂²	1	2	yes	—
112	C₂×C₁₃×#103	C₂²	1	2	yes	—
113	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
114	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
115	C₂×C₁₃×#41	—	2	2	no	—
116	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
117	C₂×C₁₃×#41	C₂³	1	2	yes	—
118	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
119	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
120	C₁₃×#137	—	2	8	no	—
121	C₂×C₁₃×Q₁₆	—	2	4	no	—
122	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
123	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
124	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
126	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
128	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
129	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
130	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
131	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
132	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
133	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
134	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
136	C₁₃×C₄⋊Q₈	—	2	2	no	—
137	C₁₃×C₄⋊Q₈	—	2	2	no	—
138	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₁₃×#126	—	2	2	no	—
141	C₁₃×#126	—	2	2	no	—
142	C₁₃×#126	—	2	2	no	—
143	C₁₃×#126	—	2	2	no	—
144	C₁₃×#126	—	2	2	no	—
145	C₁₃×#126	—	2	2	no	—
146	C₁₃×#125	—	2	2	no	—
147	C₁₃×#125	—	2	2	no	—
148	C₁₃×#125	—	2	2	no	—
149	C₁₃×#125	—	2	2	no	—
150	C₁₃×#125	—	2	2	no	—
151	C₁₃×#125	C₂³	1	2	yes	—
152	C₁₃×#125	C₂³	1	2	yes	—
153	C₁₃×#124	—	2	2	no	—
154	C₁₃×#124	—	2	2	no	—
155	C₁₃×#124	C₂³	1	2	yes	—
156	C₁₃×#124	C₂³	1	2	yes	—
157	C₁₃×#123	—	2	2	no	—
158	C₁₃×#123	—	2	2	no	—
159	C₁₃×#123	—	2	2	no	—
160	C₁₃×#123	—	2	2	no	—
161	C₁₃×#123	—	2	2	no	—
162	C₁₃×#123	—	2	2	no	—
163	C₁₃×C₂²⋊Q₈	—	2	2	no	—
164	C₁₃×C₂²⋊Q₈	—	2	2	no	—
165	C₁₃×C₂²⋊Q₈	—	2	2	no	—
166	C₁₃×C₂²⋊Q₈	—	2	2	no	—
167	C₁₃×C₂²⋊Q₈	—	2	2	no	—
168	C₁₃×C₂²⋊Q₈	—	2	2	no	—
169	C₁₃×C₂²⋊Q₈	—	2	2	no	—
170	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
171	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
172	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
173	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
174	C₁₃×#121	—	2	2	no	—
175	C₁₃×#121	—	2	2	no	—
176	C₁₃×#121	C₂³	1	2	yes	—
177	C₁₃×#121	C₂³	1	2	yes	—
178	C₄×Q₈×C₁₃	—	2	2	no	—
179	C₄×Q₈×C₁₃	—	2	2	no	—
180	C₄×Q₈×C₁₃	—	2	2	no	—
181	C₄×Q₈×C₁₃	—	2	2	no	—
182	C₄×Q₈×C₁₃	—	2	2	no	—
183	C₄×Q₈×C₁₃	—	2	2	no	—
184	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
185	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
186	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
187	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
188	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
189	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
190	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
191	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
192	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
193	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
194	C₄×D₄×C₁₃	—	2	2	no	—
195	C₄×D₄×C₁₃	—	2	2	no	—
196	C₄×D₄×C₁₃	—	2	2	no	—
197	C₄×D₄×C₁₃	—	2	2	no	—
198	C₄×D₄×C₁₃	—	2	2	no	—
199	C₄×D₄×C₁₃	—	2	2	no	—
200	C₄×D₄×C₁₃	—	2	2	no	—
201	C₄×D₄×C₁₃	D₄	1	2	yes	—
202	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
203	C₄×D₄×C₁₃	C₂³	1	2	yes	—
204	C₄×D₄×C₁₃	C₂³	1	2	yes	—
205	C₄×D₄×C₁₃	C₂³	1	2	yes	—
206	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
207	C₁₃×#117	—	2	2	no	—
208	C₁₃×#117	—	2	2	no	—
209	C₁₃×#117	—	2	2	no	—
210	C₁₃×#117	—	2	2	no	—
211	C₁₃×#117	—	2	2	no	—
212	C₁₃×#117	—	2	2	no	—
213	C₁₃×#117	—	2	2	no	—
214	C₁₃×#117	D₄	1	1	yes	characteristic
215	C₁₃×#117	D₄	1	2	yes	—
216	C₁₃×#117	C₂³	1	2	yes	—
217	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
218	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
219	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
220	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
221	C₂×C₄²×C₁₃	—	2	2	no	—
222	C₂×C₄²×C₁₃	—	2	2	no	—
223	C₂×C₄²×C₁₃	—	2	2	no	—
224	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
226	C₁₃×#107	C₂³	1	1	yes	characteristic
227	C₁₃×#107	C₂³	1	1	yes	characteristic
228	C₁₃×#107	C₂³	1	2	yes	—
229	C₁₃×#107	C₂³	1	2	yes	—
230	C₁₃×#107	C₂³	1	1	yes	characteristic
231	C₁₃×#107	C₂³	1	1	yes	characteristic
232	C₁₃×#107	C₂³	1	2	yes	—
233	C₁₃×#106	C₂³	1	2	yes	—
234	C₁₃×#106	C₂³	1	2	yes	—
235	C₁₃×#106	C₂³	1	2	yes	—
236	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
237	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
238	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
239	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
240	C₁₃×#103	C₂³	1	2	yes	—
241	C₁₃×#103	C₂³	1	2	yes	—
242	C₁₃×#103	C₂³	1	2	yes	—
243	C₁₃×#103	C₂³	1	2	yes	—
244	C₁₃×#103	C₂³	1	2	yes	—
245	C₁₃×#103	C₂³	1	2	yes	—
246	C₁₃×#103	C₂³	1	2	yes	—
247	C₁₃×#103	C₂³	1	2	yes	—
248	C₁₃×#103	C₂³	1	2	yes	—
249	C₁₃×#103	C₂³	1	2	yes	—
250	C₁₃×#103	C₂³	1	2	yes	—
251	C₁₃×#103	C₂³	1	2	yes	—
252	C₁₃×#102	C₂³	1	2	yes	—
253	C₁₃×#102	C₂³	1	2	yes	—
254	C₁₃×#102	C₂³	1	2	yes	—
255	C₁₃×#102	C₂³	1	2	yes	—
256	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₁₃×#97	C₂³	1	2	yes	—
260	C₁₃×#97	C₂³	1	2	yes	—
261	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₁₃	C₂³	1	2	yes	—
266	#61446	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₁₃×#41	—	2	4	no	—
268	C₁₃×#41	—	4	2	no	—
269	C₁₃×#41	—	4	2	no	—
270	C₁₃×#41	—	4	8	no	—
271	C₂×Q₈×C₁₃	—	2	2	no	—
272	C₂×Q₈×C₁₃	—	2	2	no	—
273	C₂×Q₈×C₁₃	—	2	2	no	—
274	C₂×Q₈×C₁₃	—	2	4	no	—
275	C₂×Q₈×C₁₃	—	2	4	no	—
276	C₂×Q₈×C₁₃	—	4	2	no	—
277	C₂×Q₈×C₁₃	—	4	2	no	—
278	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
280	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
281	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
282	C₂×D₄×C₁₃	—	2	2	no	—
283	C₂×D₄×C₁₃	—	2	2	no	—
284	C₂×D₄×C₁₃	—	2	2	no	—
285	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
286	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
287	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₁₃	—	2	2	no	—
289	C₂²×C₄×C₁₃	—	2	2	no	—
290	C₂²×C₄×C₁₃	—	2	2	no	—
291	C₂²×C₄×C₁₃	—	2	2	no	—
292	C₂²×C₄×C₁₃	—	2	2	no	—
293	C₂²×C₄×C₁₃	—	2	2	no	—
294	C₂²×C₄×C₁₃	—	2	2	no	—
295	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
298	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
299	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
301	C₁₃×Q₁₆	—	2	4	no	—
302	C₁₃×Q₁₆	—	2	4	no	—
303	C₁₃×Q₁₆	—	2	2	no	—
304	C₁₃×Q₁₆	—	4	1	no	—
305	C₁₃×Q₁₆	—	4	2	no	—
306	C₁₃×Q₁₆	#41	1	4	yes	complemented
307	C₁₃×SD₁₆	—	2	4	no	—
308	C₁₃×SD₁₆	—	2	4	no	—
309	C₁₃×SD₁₆	—	4	2	no	—
310	C₁₃×D₈	—	4	1	no	—
311	C₁₃×M₁₆	—	2	4	no	—
312	C₁₃×M₁₆	—	4	2	no	—
313	C₂×C₈×C₁₃	—	2	2	no	—
314	C₂×C₈×C₁₃	—	4	1	no	—
315	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
316	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
317	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
318	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
319	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
320	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
321	C₁₃×C₄⋊C₄	—	2	2	no	—
322	C₁₃×C₄⋊C₄	—	2	2	no	—
323	C₁₃×C₄⋊C₄	—	2	2	no	—
324	C₁₃×C₄⋊C₄	—	2	2	no	—
325	C₁₃×C₄⋊C₄	—	2	2	no	—
326	C₁₃×C₄⋊C₄	—	2	2	no	—
327	C₁₃×C₄⋊C₄	—	2	2	no	—
328	C₁₃×C₄⋊C₄	—	2	2	no	—
329	C₁₃×C₄⋊C₄	—	2	2	no	—
330	C₁₃×C₄⋊C₄	—	2	2	no	—
331	C₁₃×C₄⋊C₄	—	2	2	no	—
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	2	no	—
337	C₁₃×C₄⋊C₄	—	2	2	no	—
338	C₁₃×C₄⋊C₄	—	2	2	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	C₂×D₄	1	2	yes	—
343	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
344	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
345	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
346	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
347	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
348	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
349	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
350	C₁₃×C₂²⋊C₄	—	2	2	no	—
351	C₁₃×C₂²⋊C₄	—	2	2	no	—
352	C₁₃×C₂²⋊C₄	—	2	2	no	—
353	C₁₃×C₂²⋊C₄	—	2	2	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	2	no	—
359	C₁₃×C₂²⋊C₄	—	2	2	no	—
360	C₁₃×C₂²⋊C₄	—	2	2	no	—
361	C₁₃×C₂²⋊C₄	—	2	2	no	—
362	C₁₃×C₂²⋊C₄	—	2	2	no	—
363	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
364	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
365	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
366	C₄²×C₁₃	—	2	2	no	—
367	C₄²×C₁₃	—	2	2	no	—
368	C₄²×C₁₃	—	2	2	no	—
369	C₄²×C₁₃	—	2	2	no	—
370	C₄²×C₁₃	—	2	2	no	—
371	C₄²×C₁₃	—	2	2	no	—
372	C₄²×C₁₃	—	2	2	no	—
373	C₄²×C₁₃	—	2	2	no	—
374	C₄²×C₁₃	—	2	2	no	—
375	C₄²×C₁₃	C₂×D₄	1	2	yes	—
376	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₁₃	C₂×D₄	1	2	yes	—
378	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
379	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
380	C₄²×C₁₃	C₂⁴	1	2	yes	—
381	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
382	#3482	C₂×C₁₃	1	2	yes	complemented
383	#3402	C₂×C₁₃	1	1	yes	characteristic, complemented
384	#3390	C₂×C₁₃	1	1	yes	characteristic, complemented
385	#3377	C₂×C₁₃	1	2	yes	complemented
386	#3352	C₂×C₁₃	1	1	yes	characteristic, complemented
387	#3343	C₂×C₁₃	1	2	yes	complemented
388	#3327	C₂×C₁₃	1	2	yes	complemented
389	#3312	C₂×C₁₃	1	2	yes	complemented
390	#3308	C₂×C₁₃	1	2	yes	complemented
391	#3277	C₂×C₁₃	1	1	yes	characteristic, complemented
392	#3270	C₂×C₁₃	1	2	yes	complemented
393	#3172	C₂×C₁₃	1	2	yes	complemented
394	#3168	C₂×C₁₃	1	1	yes	characteristic, complemented
395	#3108	C₂×C₁₃	1	2	yes	complemented
396	#3104	C₂×C₁₃	1	2	yes	complemented
397	#3102	C₂×C₁₃	1	2	yes	complemented
398	#2965	C₂×C₁₃	1	1	yes	characteristic, complemented
399	C₄×#137	C₂×C₁₃	1	2	yes	complemented
400	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
401	C₂³×C₁₃	—	2	2	no	—
402	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
403	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
404	Q₈×C₁₃	—	2	2	no	—
405	Q₈×C₁₃	—	2	2	no	—
406	Q₈×C₁₃	—	2	2	no	—
407	Q₈×C₁₃	—	2	2	no	—
408	Q₈×C₁₃	—	2	2	no	—
409	Q₈×C₁₃	—	4	1	no	—
410	Q₈×C₁₃	—	4	4	no	—
411	Q₈×C₁₃	—	4	4	no	—
412	Q₈×C₁₃	—	4	4	no	—
413	Q₈×C₁₃	C₂×#41	1	4	yes	—
414	D₄×C₁₃	—	2	4	no	—
415	D₄×C₁₃	—	2	2	no	—
416	D₄×C₁₃	—	2	2	no	—
417	D₄×C₁₃	—	4	1	no	—
418	D₄×C₁₃	—	4	4	no	—
419	D₄×C₁₃	—	4	4	no	—
420	D₄×C₁₃	—	4	4	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	2	4	no	—
425	C₂×C₄×C₁₃	—	2	1	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	1	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	2	2	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	2	no	—
435	C₂×C₄×C₁₃	—	4	2	no	—
436	C₂×C₄×C₁₃	—	4	4	no	—
437	C₂×C₄×C₁₃	—	4	4	no	—
438	C₂×C₄×C₁₃	—	4	4	no	—
439	C₂×C₄×C₁₃	—	4	4	no	—
440	C₂×C₄×C₁₃	—	4	4	no	—
441	C₂×C₄×C₁₃	—	4	4	no	—
442	C₂×C₄×C₁₃	—	4	4	no	—
443	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
446	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
447	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
452	C₈×C₁₃	—	2	1	no	—
453	C₈×C₁₃	—	2	2	no	—
454	C₈×C₁₃	—	2	1	no	—
455	C₈×C₁₃	—	2	1	no	—
456	C₈×C₁₃	—	2	2	no	—
457	C₈×C₁₃	C₂×#41	1	2	yes	—
458	C₂×#137	C₂²×C₁₃	1	2	yes	—
459	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
460	#557	C₂²×C₁₃	1	2	yes	—
461	#556	—	2	2	no	—
462	#556	C₂²×C₁₃	1	2	yes	—
463	#552	—	2	2	no	—
464	#552	—	2	2	no	—
465	#552	C₂²×C₁₃	1	2	yes	—
466	#552	C₂²×C₁₃	1	2	yes	—
467	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
468	#548	C₂²×C₁₃	1	2	yes	—
469	#548	C₂²×C₁₃	1	2	yes	—
470	#547	—	2	2	no	—
471	#547	C₂²×C₁₃	1	2	yes	—
472	#533	—	2	2	no	—
473	#533	C₂²×C₁₃	1	2	yes	—
474	#529	—	2	2	no	—
475	#529	—	2	2	no	—
476	#529	C₂²×C₁₃	1	2	yes	—
477	#529	C₂²×C₁₃	1	2	yes	—
478	C₄×#41	—	2	2	no	—
479	C₄×#41	C₂²×C₁₃	1	2	yes	—
480	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
481	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
482	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
483	#501	C₂²×C₁₃	1	2	yes	—
484	#499	C₂²×C₁₃	1	1	yes	characteristic
485	#497	C₂²×C₁₃	1	2	yes	—
486	#495	C₂²×C₁₃	1	1	yes	characteristic
487	#491	C₂²×C₁₃	1	2	yes	—
488	#489	C₂²×C₁₃	1	2	yes	—
489	#488	C₂²×C₁₃	1	2	yes	—
490	#485	C₂²×C₁₃	1	2	yes	—
491	#484	C₂²×C₁₃	1	2	yes	—
492	#484	C₂²×C₁₃	1	2	yes	—
493	#483	C₂²×C₁₃	1	2	yes	—
494	#482	C₂²×C₁₃	1	2	yes	—
495	#480	C₂²×C₁₃	1	2	yes	—
496	#479	C₂²×C₁₃	1	2	yes	—
497	#479	C₂²×C₁₃	1	2	yes	—
498	#479	C₂²×C₁₃	1	2	yes	—
499	#478	C₂²×C₁₃	1	2	yes	—
500	#477	C₂²×C₁₃	1	2	yes	—
501	#477	C₂²×C₁₃	1	2	yes	—
502	#470	C₂²×C₁₃	1	2	yes	—
503	#470	C₂²×C₁₃	1	2	yes	—
504	#468	C₂²×C₁₃	1	2	yes	—
505	#468	C₂²×C₁₃	1	2	yes	—
506	#467	C₂²×C₁₃	1	1	yes	characteristic
507	#466	C₂²×C₁₃	1	1	yes	characteristic
508	#465	C₂²×C₁₃	1	2	yes	—
509	#464	C₂²×C₁₃	1	2	yes	—
510	#464	C₂²×C₁₃	1	2	yes	—
511	#464	C₂²×C₁₃	1	2	yes	—
512	#463	C₂²×C₁₃	1	2	yes	—
513	#462	C₂²×C₁₃	1	2	yes	—
514	#462	C₂²×C₁₃	1	2	yes	—
515	#452	C₂²×C₁₃	1	2	yes	—
516	#451	C₂²×C₁₃	1	2	yes	—
517	#451	C₂²×C₁₃	1	2	yes	—
518	#451	C₂²×C₁₃	1	2	yes	—
519	#449	C₂²×C₁₃	1	2	yes	—
520	#448	C₂²×C₁₃	1	2	yes	—
521	#446	C₂²×C₁₃	1	1	yes	characteristic
522	#446	C₂²×C₁₃	1	1	yes	characteristic
523	#441	C₂²×C₁₃	1	2	yes	—
524	#441	C₂²×C₁₃	1	2	yes	—
525	#440	C₂²×C₁₃	1	2	yes	—
526	#440	C₂²×C₁₃	1	2	yes	—
527	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
528	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
529	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
530	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
531	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
532	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
533	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
534	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
535	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
536	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
537	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
538	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
539	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
540	#436	C₂²×C₁₃	1	1	yes	characteristic
541	#436	C₂²×C₁₃	1	1	yes	characteristic
542	#435	C₂²×C₁₃	1	2	yes	—
543	#435	C₂²×C₁₃	1	2	yes	—
544	#431	C₂²×C₁₃	1	2	yes	—
545	#431	C₂²×C₁₃	1	1	yes	characteristic
546	#428	C₂²×C₁₃	1	2	yes	—
547	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
548	#419	C₂²×C₁₃	1	2	yes	—
549	#417	C₂²×C₁₃	1	2	yes	—
550	C₂×#103	C₂²×C₁₃	1	2	yes	—
551	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
552	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
553	C₂²×C₁₃	—	2	1	no	—
554	C₂²×C₁₃	—	2	1	no	—
555	C₂²×C₁₃	—	2	2	no	—
556	C₂²×C₁₃	—	2	2	no	—
557	C₂²×C₁₃	—	2	2	no	—
558	C₂²×C₁₃	—	4	2	no	—
559	C₂²×C₁₃	—	4	2	no	—
560	C₂²×C₁₃	—	4	2	no	—
561	C₂²×C₁₃	#575	1	2	yes	—
562	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
563	C₄×C₁₃	—	2	2	no	—
564	C₄×C₁₃	—	2	1	no	—
565	C₄×C₁₃	—	2	4	no	—
566	C₄×C₁₃	—	2	1	no	—
567	C₄×C₁₃	—	2	1	no	—
568	C₄×C₁₃	—	2	2	no	—
569	C₄×C₁₃	—	2	1	no	—
570	C₄×C₁₃	—	2	2	no	—
571	C₄×C₁₃	—	4	2	no	—
572	C₄×C₁₃	—	4	2	no	—
573	C₄×C₁₃	—	4	2	no	—
574	C₄×C₁₃	—	4	2	no	—
575	C₄×C₁₃	—	4	2	no	—
576	C₄×C₁₃	—	4	2	no	—
577	C₄×C₁₃	#578	1	2	yes	—
578	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
579	C₄×C₁₃	#585	1	1	yes	characteristic
580	C₂×#41	—	2	2	no	—
581	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
582	C₂×#41	C₂³×C₁₃	1	2	yes	—
583	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
584	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
585	#137	—	2	8	no	—
586	C₂×Q₁₆	—	2	4	no	—
587	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
588	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
589	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
590	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
591	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
592	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
593	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
594	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
595	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
596	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
597	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
598	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
599	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
600	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
601	C₄⋊Q₈	—	2	2	no	—
602	C₄⋊Q₈	—	2	2	no	—
603	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
604	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
605	#126	—	2	2	no	—
606	#126	—	2	2	no	—
607	#126	—	2	2	no	—
608	#126	—	2	2	no	—
609	#126	—	2	2	no	—
610	#126	—	2	2	no	—
611	#125	—	2	2	no	—
612	#125	—	2	2	no	—
613	#125	—	2	2	no	—
614	#125	—	2	2	no	—
615	#125	—	2	2	no	—
616	#125	C₂³×C₁₃	1	2	yes	—
617	#125	C₂³×C₁₃	1	2	yes	—
618	#124	—	2	2	no	—
619	#124	—	2	2	no	—
620	#124	C₂³×C₁₃	1	2	yes	—
621	#124	C₂³×C₁₃	1	2	yes	—
622	#123	—	2	2	no	—
623	#123	—	2	2	no	—
624	#123	—	2	2	no	—
625	#123	—	2	2	no	—
626	#123	—	2	2	no	—
627	#123	—	2	2	no	—
628	C₂²⋊Q₈	—	2	2	no	—
629	C₂²⋊Q₈	—	2	2	no	—
630	C₂²⋊Q₈	—	2	2	no	—
631	C₂²⋊Q₈	—	2	2	no	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
636	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
637	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
638	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
639	#121	—	2	2	no	—
640	#121	—	2	2	no	—
641	#121	C₂³×C₁₃	1	2	yes	—
642	#121	C₂³×C₁₃	1	2	yes	—
643	C₄×Q₈	—	2	2	no	—
644	C₄×Q₈	—	2	2	no	—
645	C₄×Q₈	—	2	2	no	—
646	C₄×Q₈	—	2	2	no	—
647	C₄×Q₈	—	2	2	no	—
648	C₄×Q₈	—	2	2	no	—
649	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
650	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
651	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
652	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
653	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
654	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
655	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
656	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
657	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
658	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
659	C₄×D₄	—	2	2	no	—
660	C₄×D₄	—	2	2	no	—
661	C₄×D₄	—	2	2	no	—
662	C₄×D₄	—	2	2	no	—
663	C₄×D₄	—	2	2	no	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	D₄×C₁₃	1	2	yes	—
667	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
668	C₄×D₄	C₂³×C₁₃	1	2	yes	—
669	C₄×D₄	C₂³×C₁₃	1	2	yes	—
670	C₄×D₄	C₂³×C₁₃	1	2	yes	—
671	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
672	#117	—	2	2	no	—
673	#117	—	2	2	no	—
674	#117	—	2	2	no	—
675	#117	—	2	2	no	—
676	#117	—	2	2	no	—
677	#117	—	2	2	no	—
678	#117	—	2	2	no	—
679	#117	D₄×C₁₃	1	1	yes	characteristic
680	#117	D₄×C₁₃	1	2	yes	—
681	#117	C₂³×C₁₃	1	2	yes	—
682	C₂×C₄⋊C₄	—	2	2	no	—
683	C₂×C₄⋊C₄	—	2	2	no	—
684	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
685	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
686	C₂×C₄²	—	2	2	no	—
687	C₂×C₄²	—	2	2	no	—
688	C₂×C₄²	—	2	2	no	—
689	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
691	#107	C₂³×C₁₃	1	1	yes	characteristic
692	#107	C₂³×C₁₃	1	1	yes	characteristic
693	#107	C₂³×C₁₃	1	2	yes	—
694	#107	C₂³×C₁₃	1	2	yes	—
695	#107	C₂³×C₁₃	1	1	yes	characteristic
696	#107	C₂³×C₁₃	1	1	yes	characteristic
697	#107	C₂³×C₁₃	1	2	yes	—
698	#106	C₂³×C₁₃	1	2	yes	—
699	#106	C₂³×C₁₃	1	2	yes	—
700	#106	C₂³×C₁₃	1	2	yes	—
701	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
702	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
703	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
704	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
705	#103	C₂³×C₁₃	1	2	yes	—
706	#103	C₂³×C₁₃	1	2	yes	—
707	#103	C₂³×C₁₃	1	2	yes	—
708	#103	C₂³×C₁₃	1	2	yes	—
709	#103	C₂³×C₁₃	1	2	yes	—
710	#103	C₂³×C₁₃	1	2	yes	—
711	#103	C₂³×C₁₃	1	2	yes	—
712	#103	C₂³×C₁₃	1	2	yes	—
713	#103	C₂³×C₁₃	1	2	yes	—
714	#103	C₂³×C₁₃	1	2	yes	—
715	#103	C₂³×C₁₃	1	2	yes	—
716	#103	C₂³×C₁₃	1	2	yes	—
717	#102	C₂³×C₁₃	1	2	yes	—
718	#102	C₂³×C₁₃	1	2	yes	—
719	#102	C₂³×C₁₃	1	2	yes	—
720	#102	C₂³×C₁₃	1	2	yes	—
721	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
722	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
723	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
724	#97	C₂³×C₁₃	1	2	yes	—
725	#97	C₂³×C₁₃	1	2	yes	—
726	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
727	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
728	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
729	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
730	C₄×C₈	C₂³×C₁₃	1	2	yes	—
731	C₂×C₁₃	—	2	2	no	—
732	C₂×C₁₃	—	4	2	no	—
733	C₂×C₁₃	—	8	2	no	—
734	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
735	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
736	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
737	#41	—	2	4	no	—
738	#41	—	4	2	no	—
739	#41	—	4	2	no	—
740	#41	—	4	8	no	—
741	C₂×Q₈	—	2	2	no	—
742	C₂×Q₈	—	2	2	no	—
743	C₂×Q₈	—	2	2	no	—
744	C₂×Q₈	—	2	4	no	—
745	C₂×Q₈	—	2	4	no	—
746	C₂×Q₈	—	4	2	no	—
747	C₂×Q₈	—	4	2	no	—
748	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
749	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
750	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
751	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
756	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
757	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
766	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
767	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
768	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
771	Q₁₆	—	2	4	no	—
772	Q₁₆	—	2	4	no	—
773	Q₁₆	—	2	2	no	—
774	Q₁₆	—	4	1	no	—
775	Q₁₆	—	4	2	no	—
776	Q₁₆	C₁₃×#41	1	4	yes	complemented
777	SD₁₆	—	2	4	no	—
778	SD₁₆	—	2	4	no	—
779	SD₁₆	—	4	2	no	—
780	D₈	—	4	1	no	—
781	M₁₆	—	2	4	no	—
782	M₁₆	—	4	2	no	—
783	C₂×C₈	—	2	2	no	—
784	C₂×C₈	—	4	1	no	—
785	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
786	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
787	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
788	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
789	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
790	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
813	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
814	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
815	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
816	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
817	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
818	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
819	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
834	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
835	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	2	no	—
842	C₄²	—	2	2	no	—
843	C₄²	—	2	2	no	—
844	C₄²	—	2	2	no	—
845	C₄²	C₂×D₄×C₁₃	1	2	yes	—
846	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
847	C₄²	C₂×D₄×C₁₃	1	2	yes	—
848	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
849	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
850	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
851	C₄²	C₂⁴×C₁₃	1	2	yes	—
852	C₁₃	#61446	1	1	yes	characteristic, direct product factor, Sylow
853	C₂³	—	2	2	no	—
854	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
855	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
856	Q₈	—	2	2	no	—
857	Q₈	—	2	2	no	—
858	Q₈	—	2	2	no	—
859	Q₈	—	2	2	no	—
860	Q₈	—	2	2	no	—
861	Q₈	—	4	1	no	—
862	Q₈	—	4	4	no	—
863	Q₈	—	4	4	no	—
864	Q₈	—	4	4	no	—
865	Q₈	C₂×C₁₃×#41	1	4	yes	—
866	D₄	—	2	4	no	—
867	D₄	—	2	2	no	—
868	D₄	—	2	2	no	—
869	D₄	—	4	1	no	—
870	D₄	—	4	4	no	—
871	D₄	—	4	4	no	—
872	D₄	—	4	4	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	4	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	4	2	no	—
888	C₂×C₄	—	4	4	no	—
889	C₂×C₄	—	4	4	no	—
890	C₂×C₄	—	4	4	no	—
891	C₂×C₄	—	4	4	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
896	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
897	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
898	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
899	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
901	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
903	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
904	C₈	—	2	1	no	—
905	C₈	—	2	2	no	—
906	C₈	—	2	1	no	—
907	C₈	—	2	1	no	—
908	C₈	—	2	2	no	—
909	C₈	C₂×C₁₃×#41	1	2	yes	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	2	no	—
917	C₂²	—	4	2	no	—
918	C₂²	C₁₃×#575	1	2	yes	—
919	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	2	no	—
925	C₄	—	2	2	no	—
926	C₄	—	2	1	no	—
927	C₄	—	2	4	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	2	no	—
934	C₄	C₁₃×#578	1	2	yes	—
935	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
936	C₄	C₁₃×#585	1	1	yes	characteristic
937	C₂	—	2	2	no	—
938	C₂	—	4	2	no	—
939	C₂	—	8	2	no	—
940	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
941	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
942	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3482	C₂	semidirect
2. C₁₃×#3402	C₂	semidirect
3. C₁₃×#3390	C₂	semidirect
4. C₁₃×#3377	C₂	semidirect
5. C₁₃×#3352	C₂	semidirect
6. C₁₃×#3343	C₂	semidirect
7. C₁₃×#3327	C₂	semidirect
8. C₁₃×#3312	C₂	semidirect
9. C₁₃×#3308	C₂	semidirect
10. C₁₃×#3277	C₂	semidirect
11. C₁₃×#3270	C₂	semidirect
12. C₁₃×#3172	C₂	semidirect
13. C₁₃×#3168	C₂	semidirect
14. C₁₃×#3108	C₂	semidirect
15. C₁₃×#3104	C₂	semidirect
16. C₁₃×#3102	C₂	semidirect
17. C₁₃×#2965	C₂	semidirect
18. C₄×C₁₃×#137	C₂	semidirect
19. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
266. #61446	C₁₃	direct (N × H)
306. C₁₃×Q₁₆	#41	semidirect
382. #3482	C₂×C₁₃	semidirect
383. #3402	C₂×C₁₃	semidirect
384. #3390	C₂×C₁₃	semidirect
385. #3377	C₂×C₁₃	semidirect
386. #3352	C₂×C₁₃	semidirect
387. #3343	C₂×C₁₃	semidirect
388. #3327	C₂×C₁₃	semidirect
389. #3312	C₂×C₁₃	semidirect
390. #3308	C₂×C₁₃	semidirect
391. #3277	C₂×C₁₃	semidirect
392. #3270	C₂×C₁₃	semidirect
393. #3172	C₂×C₁₃	semidirect
394. #3168	C₂×C₁₃	semidirect
395. #3108	C₂×C₁₃	semidirect
396. #3104	C₂×C₁₃	semidirect
397. #3102	C₂×C₁₃	semidirect
398. #2965	C₂×C₁₃	semidirect
399. C₄×#137	C₂×C₁₃	semidirect
400. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
776. Q₁₆	C₁₃×#41	semidirect
852. C₁₃	#61446	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×#3482	2
C₁₃×#3402	2
C₁₃×#3390	2
C₁₃×#3377	2
C₁₃×#3352	2
C₁₃×#3343	2
C₁₃×#3327	2
C₁₃×#3312	2
C₁₃×#3308	2
C₁₃×#3277	2
C₁₃×#3270	2
C₁₃×#3172	2
C₁₃×#3168	2
C₁₃×#3108	2
C₁₃×#3104	2
C₁₃×#3102	2
C₁₃×#2965	2
C₄×C₁₃×#137	2
C₂×C₄×C₁₃×Q₁₆	2
#61446	13

Subgroups — C13×#61446 #15747785

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61446 #15747785