Subgroups — C₁₃×#62109 #15748448

Order 3328.

1974 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3386	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3368	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3353	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3343	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3324	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3310	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3254	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3235	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3110	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3077	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	—	2	1	no	—
19	C₁₃×#557	—	2	1	no	—
20	C₁₃×#557	C₂²	1	2	yes	complemented
21	C₁₃×#556	—	2	1	no	—
22	C₁₃×#556	C₂²	1	2	yes	complemented
23	C₁₃×#552	—	2	2	no	—
24	C₁₃×#552	C₂²	1	4	yes	complemented
25	C₁₃×#550	C₂²	1	1	yes	characteristic
26	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#548	—	2	1	no	—
28	C₁₃×#547	C₂²	1	2	yes	—
29	C₁₃×#547	C₂²	1	1	yes	characteristic
30	C₁₃×#546	—	2	2	no	—
31	C₁₃×#546	—	2	1	no	—
32	D₄²×C₁₃	C₂²	1	2	yes	—
33	D₄²×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#541	—	2	2	no	—
35	C₁₃×#536	—	2	1	no	—
36	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#533	C₂²	1	2	yes	complemented
38	C₁₃×#533	C₂²	1	2	yes	complemented
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₁₃×#532	C₂²	1	2	yes	—
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#525	—	2	1	no	—
43	C₁₃×#525	—	2	2	no	—
44	C₁₃×#519	—	2	1	no	—
45	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
48	C₁₃×#501	C₂²	1	4	yes	complemented
49	C₁₃×#500	C₂²	1	2	yes	complemented
50	C₁₃×#490	C₂²	1	4	yes	complemented
51	C₁₃×#486	C₂²	1	2	yes	complemented
52	C₁₃×#484	C₂²	1	4	yes	complemented
53	C₁₃×#483	C₂²	1	2	yes	complemented
54	C₁₃×#482	C₂²	1	4	yes	complemented
55	C₁₃×#482	C₂²	1	4	yes	complemented
56	C₁₃×#480	C₂²	1	4	yes	complemented
57	C₁₃×#478	C₂²	1	4	yes	—
58	C₁₃×#478	C₂²	1	4	yes	complemented
59	C₁₃×#477	C₂²	1	4	yes	complemented
60	C₁₃×#476	C₂²	1	1	yes	characteristic
61	C₁₃×#476	C₂²	1	2	yes	complemented
62	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#475	C₂²	1	2	yes	complemented
64	C₁₃×#474	C₂²	1	2	yes	—
65	C₁₃×#474	C₂²	1	2	yes	—
66	C₁₃×#474	C₂²	1	2	yes	complemented
67	C₁₃×#474	C₂²	1	2	yes	complemented
68	C₁₃×#474	C₂²	1	2	yes	complemented
69	C₁₃×#474	C₂²	1	2	yes	complemented
70	C₁₃×#468	C₂²	1	4	yes	complemented
71	C₁₃×#468	C₂²	1	4	yes	complemented
72	C₁₃×#465	C₂²	1	4	yes	complemented
73	C₁₃×#461	C₂²	1	1	yes	characteristic
74	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#461	C₂²	1	2	yes	complemented
76	C₁₃×#460	C₂²	1	4	yes	complemented
77	C₁₃×#460	C₂²	1	2	yes	complemented
78	C₁₃×#450	C₂²	1	2	yes	—
79	C₁₃×#450	C₂²	1	4	yes	—
80	C₁₃×#446	C₂²	1	2	yes	complemented
81	C₁₃×#440	C₂²	1	4	yes	—
82	C₁₃×#440	C₂²	1	4	yes	complemented
83	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
84	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
85	C₁₃×#436	C₂²	1	2	yes	complemented
86	C₁₃×#435	C₂²	1	4	yes	complemented
87	C₁₃×#432	C₂²	1	2	yes	complemented
88	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#428	C₂²	1	4	yes	complemented
90	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
91	C₁₃×#423	C₂²	1	2	yes	complemented
92	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#418	C₂²	1	4	yes	—
94	C₂×C₁₃×#102	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	—	2	1	no	—
98	C₂×C₁₃×#41	—	2	2	no	—
99	C₂×C₁₃×#41	—	2	1	no	—
100	C₂×C₁₃×#41	—	4	8	no	—
101	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
102	C₂²×Q₈×C₁₃	—	2	1	no	—
103	C₂²×Q₈×C₁₃	—	2	1	no	—
104	C₂²×D₄×C₁₃	—	2	2	no	—
105	C₂²×D₄×C₁₃	—	2	1	no	—
106	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
108	C₂³×C₄×C₁₃	—	2	2	no	—
109	C₂³×C₄×C₁₃	—	2	1	no	—
110	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
111	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
112	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
113	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
114	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
115	C₁₃×C₄⋊Q₈	—	2	2	no	—
116	C₁₃×C₄⋊Q₈	—	2	1	no	—
117	C₁₃×C₄⋊Q₈	—	2	1	no	—
118	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
122	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
124	C₁₃×#127	C₂³	1	1	yes	characteristic
125	C₁₃×#127	C₂³	1	2	yes	—
126	C₁₃×#126	—	2	4	no	—
127	C₁₃×#126	—	2	4	no	—
128	C₁₃×#125	—	2	4	no	—
129	C₁₃×#125	—	2	4	no	—
130	C₁₃×#125	—	2	1	no	—
131	C₁₃×#125	—	2	2	no	—
132	C₁₃×#125	C₂³	1	4	yes	—
133	C₁₃×#124	—	2	2	no	—
134	C₁₃×#124	—	2	2	no	—
135	C₁₃×#124	—	2	1	no	—
136	C₁₃×#123	—	2	4	no	—
137	C₁₃×#123	—	2	2	no	—
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	—	2	2	no	—
141	C₁₃×C₂²⋊Q₈	—	2	2	no	—
142	C₁₃×C₂²⋊Q₈	—	2	1	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	1	no	—
145	C₁₃×C₂²⋊Q₈	—	2	2	no	—
146	C₁₃×C₂²⋊Q₈	—	2	1	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
150	C₁₃×#121	—	2	1	no	—
151	C₁₃×#121	—	2	2	no	—
152	C₁₃×#121	—	2	1	no	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	1	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	C₂³	1	2	yes	—
157	C₁₃×#121	C₂³	1	2	yes	—
158	C₁₃×#121	C₂³	1	2	yes	—
159	C₁₃×#120	—	2	2	no	—
160	C₁₃×#120	—	2	2	no	—
161	C₁₃×#120	—	2	2	no	—
162	C₄×Q₈×C₁₃	—	2	2	no	—
163	C₄×Q₈×C₁₃	—	2	2	no	—
164	C₄×Q₈×C₁₃	—	2	2	no	—
165	C₄×Q₈×C₁₃	—	2	2	no	—
166	C₄×Q₈×C₁₃	—	2	2	no	—
167	C₄×Q₈×C₁₃	—	2	1	no	—
168	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
169	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
171	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₁₃	—	2	2	no	—
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	—	2	2	no	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	D₄	1	2	yes	—
179	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
180	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₁₃	C₂³	1	2	yes	—
183	C₄×D₄×C₁₃	C₂³	1	2	yes	—
184	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₁₃	C₂³	1	2	yes	—
187	C₄×D₄×C₁₃	C₂³	1	2	yes	—
188	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
189	C₁₃×#117	—	2	1	no	—
190	C₁₃×#117	—	2	2	no	—
191	C₁₃×#117	—	2	4	no	—
192	C₁₃×#117	D₄	1	1	yes	characteristic
193	C₁₃×#117	D₄	1	2	yes	—
194	C₁₃×#117	C₂³	1	4	yes	—
195	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
200	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
203	C₁₃×#107	C₂³	1	4	yes	—
204	C₁₃×#107	C₂³	1	4	yes	—
205	C₁₃×#107	C₂³	1	4	yes	—
206	C₁₃×#107	C₂³	1	4	yes	—
207	C₁₃×#106	C₂³	1	2	yes	—
208	C₁₃×#106	C₂³	1	4	yes	—
209	C₁₃×#106	C₂³	1	2	yes	—
210	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
213	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
214	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₁₃×#103	C₂³	1	2	yes	—
216	C₁₃×#103	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#102	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	2	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	2	yes	—
224	C₁₃×#102	C₂³	1	4	yes	—
225	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₁₃×#97	C₂³	1	4	yes	—
228	C₄×C₈×C₁₃	C₂³	1	2	yes	—
229	#62109	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂⁴×C₁₃	—	2	2	no	—
231	C₂⁴×C₁₃	—	2	1	no	—
232	C₁₃×#41	—	2	4	no	—
233	C₁₃×#41	—	4	8	no	—
234	C₁₃×#41	—	4	8	no	—
235	C₁₃×#41	—	4	4	no	—
236	C₁₃×#41	—	4	4	no	—
237	C₁₃×#41	—	4	4	no	—
238	C₂×Q₈×C₁₃	—	2	1	no	—
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	2	1	no	—
243	C₂×Q₈×C₁₃	—	4	4	no	—
244	C₂×Q₈×C₁₃	—	4	4	no	—
245	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	2	4	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	1	no	—
254	C₂×D₄×C₁₃	—	2	2	no	—
255	C₂×D₄×C₁₃	—	2	1	no	—
256	C₂×D₄×C₁₃	—	2	2	no	—
257	C₂×D₄×C₁₃	—	2	1	no	—
258	C₂×D₄×C₁₃	—	4	1	no	—
259	C₂×D₄×C₁₃	—	4	2	no	—
260	C₂×D₄×C₁₃	—	4	8	no	—
261	C₂×D₄×C₁₃	—	4	4	no	—
262	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
263	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
266	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	—	2	2	no	—
268	C₂²×C₄×C₁₃	—	2	1	no	—
269	C₂²×C₄×C₁₃	—	2	2	no	—
270	C₂²×C₄×C₁₃	—	2	1	no	—
271	C₂²×C₄×C₁₃	—	2	2	no	—
272	C₂²×C₄×C₁₃	—	2	1	no	—
273	C₂²×C₄×C₁₃	—	2	2	no	—
274	C₂²×C₄×C₁₃	—	2	1	no	—
275	C₂²×C₄×C₁₃	—	2	2	no	—
276	C₂²×C₄×C₁₃	—	2	1	no	—
277	C₂²×C₄×C₁₃	—	4	8	no	—
278	C₂²×C₄×C₁₃	—	4	4	no	—
279	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
280	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
282	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
285	C₁₃×SD₁₆	—	2	4	no	—
286	C₁₃×SD₁₆	—	4	4	no	—
287	C₁₃×SD₁₆	—	4	2	no	—
288	C₁₃×M₁₆	—	4	4	no	—
289	C₂×C₈×C₁₃	—	4	2	no	—
290	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
291	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
292	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	1	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	1	no	—
299	C₁₃×C₄⋊C₄	—	2	1	no	—
300	C₁₃×C₄⋊C₄	—	2	1	no	—
301	C₁₃×C₄⋊C₄	—	2	4	no	—
302	C₁₃×C₄⋊C₄	—	2	4	no	—
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	—	2	1	no	—
305	C₁₃×C₄⋊C₄	—	2	4	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	—	2	4	no	—
308	C₁₃×C₄⋊C₄	—	2	2	no	—
309	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
310	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
311	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
312	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
313	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
314	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
316	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
317	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	4	no	—
320	C₁₃×C₂²⋊C₄	—	2	4	no	—
321	C₁₃×C₂²⋊C₄	—	2	1	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	—	2	1	no	—
324	C₁₃×C₂²⋊C₄	—	2	2	no	—
325	C₁₃×C₂²⋊C₄	—	2	1	no	—
326	C₁₃×C₂²⋊C₄	—	2	1	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	—	2	2	no	—
330	C₁₃×C₂²⋊C₄	—	2	2	no	—
331	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
332	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
333	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
334	C₄²×C₁₃	—	2	4	no	—
335	C₄²×C₁₃	—	2	4	no	—
336	C₄²×C₁₃	—	2	2	no	—
337	C₄²×C₁₃	C₂×D₄	1	2	yes	—
338	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₁₃	C₂×D₄	1	2	yes	—
340	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
342	C₄²×C₁₃	C₂⁴	1	2	yes	—
343	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
344	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
345	D₄×#41	C₂×C₁₃	1	1	yes	characteristic
346	#3386	C₂×C₁₃	1	2	yes	complemented
347	#3368	C₂×C₁₃	1	2	yes	complemented
348	#3353	C₂×C₁₃	1	2	yes	complemented
349	#3343	C₂×C₁₃	1	4	yes	complemented
350	#3324	C₂×C₁₃	1	2	yes	complemented
351	#3310	C₂×C₁₃	1	4	yes	complemented
352	#3254	C₂×C₁₃	1	2	yes	complemented
353	#3246	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#3235	C₂×C₁₃	1	2	yes	complemented
355	#3226	C₂×C₁₃	1	1	yes	characteristic, complemented
356	#3110	C₂×C₁₃	1	2	yes	complemented
357	#3101	C₂×C₁₃	1	1	yes	characteristic, complemented
358	#3077	C₂×C₁₃	1	2	yes	complemented
359	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#2989	C₂×C₁₃	1	1	yes	characteristic, complemented
361	C₂³×C₁₃	—	2	1	no	—
362	C₂³×C₁₃	—	2	2	no	—
363	C₂³×C₁₃	—	2	1	no	—
364	C₂³×C₁₃	—	4	2	no	—
365	C₂³×C₁₃	—	4	4	no	—
366	C₂³×C₁₃	—	4	4	no	—
367	C₂³×C₁₃	—	4	2	no	—
368	C₂³×C₁₃	—	8	1	no	—
369	C₂³×C₁₃	—	8	2	no	—
370	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
371	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
372	Q₈×C₁₃	—	2	2	no	—
373	Q₈×C₁₃	—	2	2	no	—
374	Q₈×C₁₃	—	2	2	no	—
375	Q₈×C₁₃	—	4	2	no	—
376	Q₈×C₁₃	—	4	4	no	—
377	Q₈×C₁₃	—	4	4	no	—
378	Q₈×C₁₃	—	4	4	no	—
379	Q₈×C₁₃	—	4	2	no	—
380	D₄×C₁₃	—	2	4	no	—
381	D₄×C₁₃	—	2	2	no	—
382	D₄×C₁₃	—	2	1	no	—
383	D₄×C₁₃	—	2	2	no	—
384	D₄×C₁₃	—	2	1	no	—
385	D₄×C₁₃	—	2	2	no	—
386	D₄×C₁₃	—	2	1	no	—
387	D₄×C₁₃	—	4	2	no	—
388	D₄×C₁₃	—	4	4	no	—
389	D₄×C₁₃	—	4	4	no	—
390	D₄×C₁₃	—	4	4	no	—
391	D₄×C₁₃	—	4	4	no	—
392	D₄×C₁₃	—	4	4	no	—
393	D₄×C₁₃	—	4	2	no	—
394	D₄×C₁₃	—	8	2	no	—
395	D₄×C₁₃	—	8	1	no	—
396	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
397	C₂×C₄×C₁₃	—	2	4	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	4	no	—
405	C₂×C₄×C₁₃	—	2	1	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	1	no	—
408	C₂×C₄×C₁₃	—	4	1	no	—
409	C₂×C₄×C₁₃	—	4	2	no	—
410	C₂×C₄×C₁₃	—	4	4	no	—
411	C₂×C₄×C₁₃	—	4	4	no	—
412	C₂×C₄×C₁₃	—	4	4	no	—
413	C₂×C₄×C₁₃	—	4	2	no	—
414	C₂×C₄×C₁₃	—	4	4	no	—
415	C₂×C₄×C₁₃	—	4	2	no	—
416	C₂×C₄×C₁₃	—	4	2	no	—
417	C₂×C₄×C₁₃	—	4	2	no	—
418	C₂×C₄×C₁₃	—	4	4	no	—
419	C₂×C₄×C₁₃	—	4	2	no	—
420	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
421	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
423	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
427	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
430	C₈×C₁₃	—	2	2	no	—
431	C₈×C₁₃	—	2	4	no	—
432	C₈×C₁₃	—	2	2	no	—
433	C₂²×#41	—	2	1	no	—
434	#557	—	2	1	no	—
435	#557	C₂²×C₁₃	1	2	yes	complemented
436	#556	—	2	1	no	—
437	#556	C₂²×C₁₃	1	2	yes	complemented
438	#552	—	2	2	no	—
439	#552	C₂²×C₁₃	1	4	yes	complemented
440	#550	C₂²×C₁₃	1	1	yes	characteristic
441	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
442	#548	—	2	1	no	—
443	#547	C₂²×C₁₃	1	2	yes	—
444	#547	C₂²×C₁₃	1	1	yes	characteristic
445	#546	—	2	2	no	—
446	#546	—	2	1	no	—
447	D₄²	C₂²×C₁₃	1	2	yes	—
448	D₄²	C₂²×C₁₃	1	1	yes	characteristic
449	#541	—	2	2	no	—
450	#536	—	2	1	no	—
451	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
452	#533	C₂²×C₁₃	1	2	yes	complemented
453	#533	C₂²×C₁₃	1	2	yes	complemented
454	#532	C₂²×C₁₃	1	1	yes	characteristic
455	#532	C₂²×C₁₃	1	2	yes	—
456	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
457	#525	—	2	1	no	—
458	#525	—	2	2	no	—
459	#519	—	2	1	no	—
460	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
461	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
462	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
463	#501	C₂²×C₁₃	1	4	yes	complemented
464	#500	C₂²×C₁₃	1	2	yes	complemented
465	#490	C₂²×C₁₃	1	4	yes	complemented
466	#486	C₂²×C₁₃	1	2	yes	complemented
467	#484	C₂²×C₁₃	1	4	yes	complemented
468	#483	C₂²×C₁₃	1	2	yes	complemented
469	#482	C₂²×C₁₃	1	4	yes	complemented
470	#482	C₂²×C₁₃	1	4	yes	complemented
471	#480	C₂²×C₁₃	1	4	yes	complemented
472	#478	C₂²×C₁₃	1	4	yes	—
473	#478	C₂²×C₁₃	1	4	yes	complemented
474	#477	C₂²×C₁₃	1	4	yes	complemented
475	#476	C₂²×C₁₃	1	1	yes	characteristic
476	#476	C₂²×C₁₃	1	2	yes	complemented
477	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
478	#475	C₂²×C₁₃	1	2	yes	complemented
479	#474	C₂²×C₁₃	1	2	yes	—
480	#474	C₂²×C₁₃	1	2	yes	—
481	#474	C₂²×C₁₃	1	2	yes	complemented
482	#474	C₂²×C₁₃	1	2	yes	complemented
483	#474	C₂²×C₁₃	1	2	yes	complemented
484	#474	C₂²×C₁₃	1	2	yes	complemented
485	#468	C₂²×C₁₃	1	4	yes	complemented
486	#468	C₂²×C₁₃	1	4	yes	complemented
487	#465	C₂²×C₁₃	1	4	yes	complemented
488	#461	C₂²×C₁₃	1	1	yes	characteristic
489	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
490	#461	C₂²×C₁₃	1	2	yes	complemented
491	#460	C₂²×C₁₃	1	2	yes	complemented
492	#460	C₂²×C₁₃	1	4	yes	complemented
493	#450	C₂²×C₁₃	1	2	yes	—
494	#450	C₂²×C₁₃	1	4	yes	—
495	#446	C₂²×C₁₃	1	2	yes	complemented
496	#440	C₂²×C₁₃	1	4	yes	—
497	#440	C₂²×C₁₃	1	4	yes	complemented
498	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
499	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
500	#436	C₂²×C₁₃	1	2	yes	complemented
501	#435	C₂²×C₁₃	1	4	yes	complemented
502	#432	C₂²×C₁₃	1	2	yes	complemented
503	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
504	#428	C₂²×C₁₃	1	4	yes	complemented
505	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
506	#423	C₂²×C₁₃	1	2	yes	complemented
507	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
508	#418	C₂²×C₁₃	1	4	yes	—
509	C₂×#102	C₂²×C₁₃	1	2	yes	—
510	C₂²×C₁₃	—	2	1	no	—
511	C₂²×C₁₃	—	2	1	no	—
512	C₂²×C₁₃	—	2	2	no	—
513	C₂²×C₁₃	—	2	2	no	—
514	C₂²×C₁₃	—	2	2	no	—
515	C₂²×C₁₃	—	2	2	no	—
516	C₂²×C₁₃	—	4	1	no	—
517	C₂²×C₁₃	—	4	1	no	—
518	C₂²×C₁₃	—	4	1	no	—
519	C₂²×C₁₃	—	4	2	no	—
520	C₂²×C₁₃	—	4	1	no	—
521	C₂²×C₁₃	—	4	2	no	—
522	C₂²×C₁₃	—	4	2	no	—
523	C₂²×C₁₃	—	4	1	no	—
524	C₂²×C₁₃	—	8	4	no	—
525	C₂²×C₁₃	—	8	8	no	—
526	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
527	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
528	C₄×C₁₃	—	2	1	no	—
529	C₄×C₁₃	—	2	2	no	—
530	C₄×C₁₃	—	2	1	no	—
531	C₄×C₁₃	—	2	1	no	—
532	C₄×C₁₃	—	2	2	no	—
533	C₄×C₁₃	—	2	2	no	—
534	C₄×C₁₃	—	4	2	no	—
535	C₄×C₁₃	—	4	2	no	—
536	C₄×C₁₃	—	4	1	no	—
537	C₄×C₁₃	—	4	2	no	—
538	C₄×C₁₃	—	4	1	no	—
539	C₄×C₁₃	—	4	4	no	—
540	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
541	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
542	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
543	C₄×C₁₃	#585	1	1	yes	characteristic
544	C₂×#41	—	2	1	no	—
545	C₂×#41	—	2	2	no	—
546	C₂×#41	—	2	1	no	—
547	C₂×#41	—	2	2	no	—
548	C₂×#41	—	2	1	no	—
549	C₂×#41	—	4	8	no	—
550	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
551	C₂²×Q₈	—	2	1	no	—
552	C₂²×Q₈	—	2	1	no	—
553	C₂²×D₄	—	2	2	no	—
554	C₂²×D₄	—	2	1	no	—
555	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
556	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
557	C₂³×C₄	—	2	2	no	—
558	C₂³×C₄	—	2	1	no	—
559	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
560	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
561	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
562	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
563	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
564	C₄⋊Q₈	—	2	2	no	—
565	C₄⋊Q₈	—	2	1	no	—
566	C₄⋊Q₈	—	2	1	no	—
567	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
568	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
569	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
570	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
571	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
572	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
573	#127	C₂³×C₁₃	1	1	yes	characteristic
574	#127	C₂³×C₁₃	1	2	yes	—
575	#126	—	2	4	no	—
576	#126	—	2	4	no	—
577	#125	—	2	4	no	—
578	#125	—	2	4	no	—
579	#125	—	2	1	no	—
580	#125	—	2	2	no	—
581	#125	C₂³×C₁₃	1	4	yes	—
582	#124	—	2	2	no	—
583	#124	—	2	2	no	—
584	#124	—	2	1	no	—
585	#123	—	2	4	no	—
586	#123	—	2	2	no	—
587	#123	—	2	2	no	—
588	#123	—	2	2	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	—	2	1	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	C₂²⋊Q₈	—	2	1	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	2	1	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
598	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
599	#121	—	2	1	no	—
600	#121	—	2	2	no	—
601	#121	—	2	1	no	—
602	#121	—	2	2	no	—
603	#121	—	2	1	no	—
604	#121	—	2	2	no	—
605	#121	C₂³×C₁₃	1	2	yes	—
606	#121	C₂³×C₁₃	1	2	yes	—
607	#121	C₂³×C₁₃	1	2	yes	—
608	#120	—	2	2	no	—
609	#120	—	2	2	no	—
610	#120	—	2	2	no	—
611	C₄×Q₈	—	2	2	no	—
612	C₄×Q₈	—	2	2	no	—
613	C₄×Q₈	—	2	2	no	—
614	C₄×Q₈	—	2	2	no	—
615	C₄×Q₈	—	2	2	no	—
616	C₄×Q₈	—	2	1	no	—
617	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
618	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
619	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
620	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	D₄×C₁₃	1	2	yes	—
628	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
629	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
630	C₄×D₄	C₂³×C₁₃	1	2	yes	—
631	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
632	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
633	C₄×D₄	C₂³×C₁₃	1	2	yes	—
634	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
635	C₄×D₄	C₂³×C₁₃	1	2	yes	—
636	C₄×D₄	C₂³×C₁₃	1	2	yes	—
637	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
638	#117	—	2	1	no	—
639	#117	—	2	2	no	—
640	#117	—	2	4	no	—
641	#117	D₄×C₁₃	1	1	yes	characteristic
642	#117	D₄×C₁₃	1	2	yes	—
643	#117	C₂³×C₁₃	1	4	yes	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
648	C₂×C₂²⋊C₄	—	2	1	no	—
649	C₂×C₂²⋊C₄	—	2	2	no	—
650	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
652	#107	C₂³×C₁₃	1	4	yes	—
653	#107	C₂³×C₁₃	1	4	yes	—
654	#107	C₂³×C₁₃	1	4	yes	—
655	#107	C₂³×C₁₃	1	4	yes	—
656	#106	C₂³×C₁₃	1	2	yes	—
657	#106	C₂³×C₁₃	1	4	yes	—
658	#106	C₂³×C₁₃	1	2	yes	—
659	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
660	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
661	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
662	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
663	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
664	#103	C₂³×C₁₃	1	2	yes	—
665	#103	C₂³×C₁₃	1	2	yes	—
666	#103	C₂³×C₁₃	1	4	yes	—
667	#102	C₂³×C₁₃	1	4	yes	—
668	#102	C₂³×C₁₃	1	4	yes	—
669	#102	C₂³×C₁₃	1	2	yes	—
670	#102	C₂³×C₁₃	1	4	yes	—
671	#102	C₂³×C₁₃	1	4	yes	—
672	#102	C₂³×C₁₃	1	2	yes	—
673	#102	C₂³×C₁₃	1	4	yes	—
674	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
675	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
676	#97	C₂³×C₁₃	1	4	yes	—
677	C₄×C₈	C₂³×C₁₃	1	2	yes	—
678	C₂×C₁₃	—	2	2	no	—
679	C₂×C₁₃	—	4	2	no	—
680	C₂×C₁₃	—	4	2	no	—
681	C₂×C₁₃	—	8	1	no	—
682	C₂×C₁₃	—	8	2	no	—
683	C₂×C₁₃	#3489	1	1	yes	characteristic
684	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
685	C₂×C₁₃	#3586	1	1	yes	characteristic
686	C₂⁴	—	2	2	no	—
687	C₂⁴	—	2	1	no	—
688	#41	—	2	4	no	—
689	#41	—	4	8	no	—
690	#41	—	4	8	no	—
691	#41	—	4	4	no	—
692	#41	—	4	4	no	—
693	#41	—	4	4	no	—
694	C₂×Q₈	—	2	1	no	—
695	C₂×Q₈	—	2	2	no	—
696	C₂×Q₈	—	2	2	no	—
697	C₂×Q₈	—	2	2	no	—
698	C₂×Q₈	—	2	1	no	—
699	C₂×Q₈	—	4	4	no	—
700	C₂×Q₈	—	4	4	no	—
701	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
702	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	4	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	4	1	no	—
715	C₂×D₄	—	4	2	no	—
716	C₂×D₄	—	4	8	no	—
717	C₂×D₄	—	4	4	no	—
718	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
719	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
720	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
721	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
722	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	4	8	no	—
734	C₂²×C₄	—	4	4	no	—
735	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
736	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
737	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
738	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
741	SD₁₆	—	2	4	no	—
742	SD₁₆	—	4	4	no	—
743	SD₁₆	—	4	2	no	—
744	M₁₆	—	4	4	no	—
745	C₂×C₈	—	4	2	no	—
746	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
747	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
748	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
766	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
767	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
768	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
769	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
770	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
771	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
772	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
773	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	1	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	1	no	—
782	C₂²⋊C₄	—	2	1	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
788	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
789	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
790	C₄²	—	2	4	no	—
791	C₄²	—	2	4	no	—
792	C₄²	—	2	2	no	—
793	C₄²	C₂×D₄×C₁₃	1	2	yes	—
794	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
795	C₄²	C₂×D₄×C₁₃	1	2	yes	—
796	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
797	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
798	C₄²	C₂⁴×C₁₃	1	2	yes	—
799	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
800	C₁₃	#62109	1	1	yes	characteristic, direct product factor, Sylow
801	C₂³	—	2	1	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	4	2	no	—
805	C₂³	—	4	4	no	—
806	C₂³	—	4	4	no	—
807	C₂³	—	4	2	no	—
808	C₂³	—	8	1	no	—
809	C₂³	—	8	2	no	—
810	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
811	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
812	Q₈	—	2	2	no	—
813	Q₈	—	2	2	no	—
814	Q₈	—	2	2	no	—
815	Q₈	—	4	4	no	—
816	Q₈	—	4	2	no	—
817	Q₈	—	4	2	no	—
818	Q₈	—	4	4	no	—
819	Q₈	—	4	4	no	—
820	D₄	—	2	4	no	—
821	D₄	—	2	2	no	—
822	D₄	—	2	1	no	—
823	D₄	—	2	2	no	—
824	D₄	—	2	1	no	—
825	D₄	—	2	2	no	—
826	D₄	—	2	1	no	—
827	D₄	—	4	2	no	—
828	D₄	—	4	4	no	—
829	D₄	—	4	4	no	—
830	D₄	—	4	4	no	—
831	D₄	—	4	4	no	—
832	D₄	—	4	4	no	—
833	D₄	—	4	2	no	—
834	D₄	—	8	2	no	—
835	D₄	—	8	1	no	—
836	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
837	C₂×C₄	—	2	4	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	4	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	4	1	no	—
849	C₂×C₄	—	4	2	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	—	4	4	no	—
852	C₂×C₄	—	4	4	no	—
853	C₂×C₄	—	4	2	no	—
854	C₂×C₄	—	4	4	no	—
855	C₂×C₄	—	4	2	no	—
856	C₂×C₄	—	4	2	no	—
857	C₂×C₄	—	4	2	no	—
858	C₂×C₄	—	4	4	no	—
859	C₂×C₄	—	4	2	no	—
860	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
861	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
862	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
863	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
864	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
865	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
866	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
867	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
868	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
869	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
870	C₈	—	2	2	no	—
871	C₈	—	2	4	no	—
872	C₈	—	2	2	no	—
873	C₂²	—	2	1	no	—
874	C₂²	—	2	1	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	2	2	no	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	1	no	—
883	C₂²	—	4	1	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	1	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	8	4	no	—
888	C₂²	—	8	8	no	—
889	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
890	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
891	C₄	—	2	2	no	—
892	C₄	—	2	1	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	2	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	4	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
904	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
905	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
906	C₄	C₁₃×#585	1	1	yes	characteristic
907	C₂	—	2	2	no	—
908	C₂	—	4	2	no	—
909	C₂	—	4	2	no	—
910	C₂	—	8	1	no	—
911	C₂	—	8	2	no	—
912	C₂	C₁₃×#3489	1	1	yes	characteristic
913	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
914	C₂	C₁₃×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3509	C₂	semidirect
3. C₁₃×#3386	C₂	semidirect
4. C₁₃×#3368	C₂	semidirect
5. C₁₃×#3353	C₂	semidirect
6. C₁₃×#3343	C₂	semidirect
7. C₁₃×#3324	C₂	semidirect
8. C₁₃×#3310	C₂	semidirect
9. C₁₃×#3254	C₂	semidirect
10. C₁₃×#3246	C₂	semidirect
11. C₁₃×#3235	C₂	semidirect
12. C₁₃×#3226	C₂	semidirect
13. C₁₃×#3110	C₂	semidirect
14. C₁₃×#3101	C₂	semidirect
15. C₁₃×#3077	C₂	semidirect
16. C₂×C₁₃×#474	C₂	semidirect
17. C₁₃×#2989	C₂	semidirect
20. C₁₃×#557	C₂²	semidirect
22. C₁₃×#556	C₂²	semidirect
24. C₁₃×#552	C₂²	semidirect
36. C₁₃×#533	C₂²	semidirect
37. C₁₃×#533	C₂²	semidirect
38. C₁₃×#533	C₂²	semidirect
41. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
48. C₁₃×#501	C₂²	semidirect
49. C₁₃×#500	C₂²	semidirect
50. C₁₃×#490	C₂²	semidirect
51. C₁₃×#486	C₂²	semidirect
52. C₁₃×#484	C₂²	semidirect
53. C₁₃×#483	C₂²	semidirect
54. C₁₃×#482	C₂²	semidirect
55. C₁₃×#482	C₂²	semidirect
56. C₁₃×#480	C₂²	semidirect
58. C₁₃×#478	C₂²	semidirect
59. C₁₃×#477	C₂²	semidirect
61. C₁₃×#476	C₂²	semidirect
62. C₁₃×#476	C₂²	semidirect
63. C₁₃×#475	C₂²	semidirect
66. C₁₃×#474	C₂²	semidirect
67. C₁₃×#474	C₂²	semidirect
68. C₁₃×#474	C₂²	semidirect
69. C₁₃×#474	C₂²	semidirect
70. C₁₃×#468	C₂²	semidirect
71. C₁₃×#468	C₂²	semidirect
72. C₁₃×#465	C₂²	semidirect
74. C₁₃×#461	C₂²	semidirect
75. C₁₃×#461	C₂²	semidirect
76. C₁₃×#460	C₂²	semidirect
77. C₁₃×#460	C₂²	semidirect
80. C₁₃×#446	C₂²	semidirect
82. C₁₃×#440	C₂²	semidirect
84. C₄×C₁₃×SD₁₆	C₂²	semidirect
85. C₁₃×#436	C₂²	semidirect
86. C₁₃×#435	C₂²	semidirect
87. C₁₃×#432	C₂²	semidirect
88. C₁₃×#431	C₂²	semidirect
89. C₁₃×#428	C₂²	semidirect
90. C₂×C₁₃×#107	C₂²	semidirect
91. C₁₃×#423	C₂²	semidirect
92. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
229. #62109	C₁₃	direct (N × H)
344. #3509	C₂×C₁₃	semidirect
346. #3386	C₂×C₁₃	semidirect
347. #3368	C₂×C₁₃	semidirect
348. #3353	C₂×C₁₃	semidirect
349. #3343	C₂×C₁₃	semidirect
350. #3324	C₂×C₁₃	semidirect
351. #3310	C₂×C₁₃	semidirect
352. #3254	C₂×C₁₃	semidirect
353. #3246	C₂×C₁₃	semidirect
354. #3235	C₂×C₁₃	semidirect
355. #3226	C₂×C₁₃	semidirect
356. #3110	C₂×C₁₃	semidirect
357. #3101	C₂×C₁₃	semidirect
358. #3077	C₂×C₁₃	semidirect
359. C₂×#474	C₂×C₁₃	semidirect
360. #2989	C₂×C₁₃	semidirect
435. #557	C₂²×C₁₃	semidirect
437. #556	C₂²×C₁₃	semidirect
439. #552	C₂²×C₁₃	semidirect
451. #533	C₂²×C₁₃	semidirect
452. #533	C₂²×C₁₃	semidirect
453. #533	C₂²×C₁₃	semidirect
456. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
463. #501	C₂²×C₁₃	semidirect
464. #500	C₂²×C₁₃	semidirect
465. #490	C₂²×C₁₃	semidirect
466. #486	C₂²×C₁₃	semidirect
467. #484	C₂²×C₁₃	semidirect
468. #483	C₂²×C₁₃	semidirect
469. #482	C₂²×C₁₃	semidirect
470. #482	C₂²×C₁₃	semidirect
471. #480	C₂²×C₁₃	semidirect
473. #478	C₂²×C₁₃	semidirect
474. #477	C₂²×C₁₃	semidirect
476. #476	C₂²×C₁₃	semidirect
477. #476	C₂²×C₁₃	semidirect
478. #475	C₂²×C₁₃	semidirect
481. #474	C₂²×C₁₃	semidirect
482. #474	C₂²×C₁₃	semidirect
483. #474	C₂²×C₁₃	semidirect
484. #474	C₂²×C₁₃	semidirect
485. #468	C₂²×C₁₃	semidirect
486. #468	C₂²×C₁₃	semidirect
487. #465	C₂²×C₁₃	semidirect
489. #461	C₂²×C₁₃	semidirect
490. #461	C₂²×C₁₃	semidirect
491. #460	C₂²×C₁₃	semidirect
492. #460	C₂²×C₁₃	semidirect
495. #446	C₂²×C₁₃	semidirect
497. #440	C₂²×C₁₃	semidirect
499. C₄×SD₁₆	C₂²×C₁₃	semidirect
500. #436	C₂²×C₁₃	semidirect
501. #435	C₂²×C₁₃	semidirect
502. #432	C₂²×C₁₃	semidirect
503. #431	C₂²×C₁₃	semidirect
504. #428	C₂²×C₁₃	semidirect
505. C₂×#107	C₂²×C₁₃	semidirect
506. #423	C₂²×C₁₃	semidirect
507. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
800. C₁₃	#62109	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×#3509	2
D₄×C₁₃×#41	2
C₁₃×#3386	2
C₁₃×#3368	2
C₁₃×#3353	2
C₁₃×#3343	2
C₁₃×#3324	2
C₁₃×#3310	2
C₁₃×#3254	2
C₁₃×#3246	2
C₁₃×#3235	2
C₁₃×#3226	2
C₁₃×#3110	2
C₁₃×#3101	2
C₁₃×#3077	2
C₂×C₁₃×#474	2
C₁₃×#2989	2
#62109	13

Subgroups — C13×#62109 #15748448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62109 #15748448