Subgroups — C₁₃×#61442 #15747781

Order 3328.

1868 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3475	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3402	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3376	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3352	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3348	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3323	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3319	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3315	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3273	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3267	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×#3107	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3105	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×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
19	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
22	C₁₃×#556	C₂²	1	2	yes	complemented
23	C₁₃×#555	C₂²	1	2	yes	—
24	C₁₃×#554	C₂²	1	2	yes	complemented
25	C₁₃×#553	—	2	2	no	—
26	C₁₃×#552	—	2	2	no	—
27	C₁₃×#552	C₂²	1	2	yes	—
28	C₁₃×#552	C₂²	1	2	yes	complemented
29	C₁₃×#551	—	2	2	no	—
30	C₁₃×#551	—	2	2	no	—
31	C₁₃×#547	C₂²	1	2	yes	—
32	C₁₃×#546	C₂²	1	2	yes	—
33	C₁₃×#546	C₂²	1	2	yes	complemented
34	C₁₃×#533	C₂²	1	2	yes	complemented
35	C₁₃×#529	—	2	2	no	—
36	C₁₃×#529	—	2	2	no	—
37	C₁₃×#529	C₂²	1	2	yes	—
38	C₁₃×#529	C₂²	1	2	yes	complemented
39	C₁₃×#525	—	2	2	no	—
40	C₄×C₁₃×#41	C₂²	1	2	yes	—
41	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
42	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
43	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
44	C₂×C₁₃×#117	—	2	2	no	—
45	C₁₃×#501	C₂²	1	2	yes	complemented
46	C₁₃×#499	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#497	C₂²	1	2	yes	complemented
48	C₁₃×#495	C₂²	1	1	yes	characteristic
49	C₁₃×#491	C₂²	1	2	yes	complemented
50	C₁₃×#489	C₂²	1	2	yes	complemented
51	C₁₃×#488	C₂²	1	2	yes	complemented
52	C₁₃×#485	C₂²	1	2	yes	complemented
53	C₁₃×#485	C₂²	1	2	yes	complemented
54	C₁₃×#485	C₂²	1	2	yes	complemented
55	C₁₃×#484	C₂²	1	2	yes	complemented
56	C₁₃×#482	C₂²	1	2	yes	complemented
57	C₁₃×#481	C₂²	1	2	yes	—
58	C₁₃×#479	C₂²	1	2	yes	complemented
59	C₁₃×#478	C₂²	1	2	yes	complemented
60	C₁₃×#478	C₂²	1	2	yes	complemented
61	C₁₃×#478	C₂²	1	2	yes	complemented
62	C₁₃×#475	C₂²	1	2	yes	complemented
63	C₁₃×#474	C₂²	1	2	yes	complemented
64	C₁₃×#470	C₂²	1	2	yes	complemented
65	C₁₃×#470	C₂²	1	2	yes	complemented
66	C₁₃×#468	C₂²	1	2	yes	—
67	C₁₃×#468	C₂²	1	2	yes	—
68	C₁₃×#467	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#466	C₂²	1	1	yes	characteristic
70	C₁₃×#465	C₂²	1	2	yes	complemented
71	C₁₃×#464	C₂²	1	2	yes	complemented
72	C₁₃×#463	C₂²	1	2	yes	—
73	C₁₃×#463	C₂²	1	2	yes	—
74	C₁₃×#463	C₂²	1	2	yes	—
75	C₁₃×#462	C₂²	1	2	yes	complemented
76	C₁₃×#461	C₂²	1	2	yes	complemented
77	C₁₃×#452	C₂²	1	2	yes	—
78	C₁₃×#452	C₂²	1	2	yes	—
79	C₁₃×#452	C₂²	1	2	yes	complemented
80	C₁₃×#450	C₂²	1	2	yes	complemented
81	C₁₃×#449	C₂²	1	2	yes	—
82	C₁₃×#447	C₂²	1	2	yes	—
83	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
84	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
85	C₁₃×#442	C₂²	1	2	yes	—
86	C₁₃×#442	C₂²	1	2	yes	—
87	C₁₃×#440	C₂²	1	2	yes	complemented
88	C₁₃×#440	C₂²	1	2	yes	complemented
89	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
90	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
91	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
92	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
94	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
95	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
96	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
97	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
98	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
99	C₄×C₁₃×D₈	C₂²	1	2	yes	—
100	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
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	complemented
105	C₁₃×#435	C₂²	1	2	yes	complemented
106	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
107	C₁₃×#431	C₂²	1	2	yes	complemented
108	C₁₃×#428	C₂²	1	2	yes	complemented
109	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
110	C₁₃×#418	C₂²	1	2	yes	complemented
111	C₁₃×#417	C₂²	1	2	yes	—
112	C₁₃×#416	C₂²	1	2	yes	complemented
113	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
114	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
116	C₂×C₁₃×#41	C₂³	1	2	yes	—
117	C₂×C₁₃×#41	C₂³	1	2	yes	—
118	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₁₃	—	2	2	no	—
120	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
121	C₁₃×#135	—	2	4	no	—
122	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
123	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
124	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
126	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
128	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
129	C₂×C₁₃×D₈	C₂³	1	2	yes	—
130	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
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	C₂³	1	2	yes	—
137	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₁₃×#126	—	2	2	no	—
139	C₁₃×#126	—	2	2	no	—
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×#125	—	2	2	no	—
145	C₁₃×#125	—	2	2	no	—
146	C₁₃×#125	—	2	2	no	—
147	C₁₃×#125	C₂³	1	2	yes	—
148	C₁₃×#125	C₂³	1	2	yes	—
149	C₁₃×#124	—	2	2	no	—
150	C₁₃×#124	—	2	2	no	—
151	C₁₃×#124	C₂³	1	2	yes	—
152	C₁₃×#124	C₂³	1	2	yes	—
153	C₁₃×#123	—	2	2	no	—
154	C₁₃×#123	—	2	2	no	—
155	C₁₃×#123	—	2	2	no	—
156	C₁₃×#123	—	2	2	no	—
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×C₂²⋊Q₈	—	2	2	no	—
162	C₁₃×C₂²⋊Q₈	—	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	C₂³	1	2	yes	—
167	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
168	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
169	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
170	C₁₃×#121	—	2	2	no	—
171	C₁₃×#121	—	2	2	no	—
172	C₁₃×#121	—	2	2	no	—
173	C₁₃×#121	—	2	2	no	—
174	C₁₃×#121	C₂³	1	2	yes	—
175	C₁₃×#121	C₂³	1	2	yes	—
176	C₁₃×#120	—	2	2	no	—
177	C₁₃×#120	—	2	2	no	—
178	C₄×Q₈×C₁₃	—	2	2	no	—
179	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
180	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
181	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
182	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
183	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
184	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₁₃	—	2	2	no	—
186	C₄×D₄×C₁₃	—	2	2	no	—
187	C₄×D₄×C₁₃	—	2	2	no	—
188	C₄×D₄×C₁₃	—	2	2	no	—
189	C₄×D₄×C₁₃	—	2	2	no	—
190	C₄×D₄×C₁₃	—	2	2	no	—
191	C₄×D₄×C₁₃	—	2	2	no	—
192	C₄×D₄×C₁₃	—	2	2	no	—
193	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
194	C₄×D₄×C₁₃	D₄	1	2	yes	—
195	C₄×D₄×C₁₃	C₂³	1	2	yes	—
196	C₄×D₄×C₁₃	C₂³	1	2	yes	—
197	C₄×D₄×C₁₃	C₂³	1	2	yes	—
198	C₄×D₄×C₁₃	C₂³	1	2	yes	—
199	C₄×D₄×C₁₃	C₂³	1	2	yes	—
200	C₄×D₄×C₁₃	C₂³	1	2	yes	—
201	C₄×D₄×C₁₃	C₂³	1	2	yes	—
202	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
203	C₁₃×#117	—	2	2	no	—
204	C₁₃×#117	—	2	2	no	—
205	C₁₃×#117	—	2	2	no	—
206	C₁₃×#117	—	2	2	no	—
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	D₄	1	2	yes	—
213	C₁₃×#117	D₄	1	1	yes	characteristic
214	C₁₃×#117	C₂³	1	2	yes	—
215	C₁₃×#117	C₂³	1	2	yes	—
216	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
217	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
218	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
219	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
220	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
221	C₂×C₁₃×C₂²⋊C₄	—	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	1	yes	characteristic
230	C₁₃×#107	C₂³	1	1	yes	characteristic
231	C₁₃×#107	C₂³	1	2	yes	—
232	C₁₃×#106	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×#102	C₂³	1	2	yes	—
249	C₁₃×#102	C₂³	1	2	yes	—
250	C₁₃×#102	C₂³	1	2	yes	—
251	C₁₃×#102	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	#61442	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂⁴×C₁₃	—	2	2	no	—
268	C₁₃×#41	—	2	4	no	—
269	C₁₃×#41	—	2	4	no	—
270	C₁₃×#41	—	4	2	no	—
271	C₁₃×#41	—	4	2	no	—
272	C₁₃×#41	—	4	2	no	—
273	C₂×Q₈×C₁₃	—	2	2	no	—
274	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
276	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
277	C₂×D₄×C₁₃	—	2	4	no	—
278	C₂×D₄×C₁₃	—	2	2	no	—
279	C₂×D₄×C₁₃	—	2	2	no	—
280	C₂×D₄×C₁₃	—	2	2	no	—
281	C₂×D₄×C₁₃	—	2	2	no	—
282	C₂×D₄×C₁₃	—	2	2	no	—
283	C₂×D₄×C₁₃	—	4	2	no	—
284	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
285	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
286	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
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	—	2	2	no	—
296	C₂²×C₄×C₁₃	—	2	2	no	—
297	C₂²×C₄×C₁₃	—	4	8	no	—
298	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
299	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
301	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
304	C₁₃×Q₁₆	—	2	2	no	—
305	C₁₃×Q₁₆	—	4	1	no	—
306	C₁₃×Q₁₆	—	4	2	no	—
307	C₁₃×SD₁₆	—	2	4	no	—
308	C₁₃×SD₁₆	—	2	4	no	—
309	C₁₃×SD₁₆	—	2	4	no	—
310	C₁₃×SD₁₆	—	4	2	no	—
311	C₁₃×D₈	—	2	4	no	—
312	C₁₃×D₈	—	4	1	no	—
313	C₁₃×D₈	#41	1	4	yes	complemented
314	C₁₃×M₁₆	—	2	4	no	—
315	C₁₃×M₁₆	—	4	2	no	—
316	C₂×C₈×C₁₃	—	2	2	no	—
317	C₂×C₈×C₁₃	—	4	1	no	—
318	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
319	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
320	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
321	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
322	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
323	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
341	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
342	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
343	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
344	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
345	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
346	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
347	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
348	C₁₃×C₂²⋊C₄	—	2	2	no	—
349	C₁₃×C₂²⋊C₄	—	2	2	no	—
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	—	2	2	no	—
364	C₁₃×C₂²⋊C₄	—	2	2	no	—
365	C₁₃×C₂²⋊C₄	—	2	2	no	—
366	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
367	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
368	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
376	C₄²×C₁₃	C₂×D₄	1	2	yes	—
377	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
378	C₄²×C₁₃	C₂×D₄	1	2	yes	—
379	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
380	C₄²×C₁₃	C₂⁴	1	2	yes	—
381	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
382	#3475	C₂×C₁₃	1	2	yes	complemented
383	#3402	C₂×C₁₃	1	1	yes	characteristic, complemented
384	#3389	C₂×C₁₃	1	1	yes	characteristic, complemented
385	#3376	C₂×C₁₃	1	2	yes	complemented
386	#3352	C₂×C₁₃	1	1	yes	characteristic, complemented
387	#3348	C₂×C₁₃	1	2	yes	complemented
388	#3323	C₂×C₁₃	1	2	yes	complemented
389	#3319	C₂×C₁₃	1	2	yes	complemented
390	#3315	C₂×C₁₃	1	2	yes	complemented
391	#3273	C₂×C₁₃	1	1	yes	characteristic, complemented
392	#3267	C₂×C₁₃	1	2	yes	complemented
393	#3172	C₂×C₁₃	1	2	yes	complemented
394	#3168	C₂×C₁₃	1	1	yes	characteristic, complemented
395	#3107	C₂×C₁₃	1	2	yes	complemented
396	#3105	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×AGL(1,ℤ/8)	C₂×C₁₃	1	2	yes	complemented
400	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
401	C₂³×C₁₃	—	2	2	no	—
402	C₂³×C₁₃	—	2	2	no	—
403	C₂³×C₁₃	—	4	4	no	—
404	C₂³×C₁₃	—	4	4	no	—
405	C₂³×C₁₃	—	8	2	no	—
406	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
407	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	Q₈×C₁₃	—	2	2	no	—
409	Q₈×C₁₃	—	2	2	no	—
410	Q₈×C₁₃	—	2	2	no	—
411	Q₈×C₁₃	—	2	2	no	—
412	Q₈×C₁₃	—	4	1	no	—
413	Q₈×C₁₃	—	8	2	no	—
414	D₄×C₁₃	—	2	2	no	—
415	D₄×C₁₃	—	2	2	no	—
416	D₄×C₁₃	—	2	2	no	—
417	D₄×C₁₃	—	4	2	no	—
418	D₄×C₁₃	—	4	1	no	—
419	D₄×C₁₃	—	4	4	no	—
420	D₄×C₁₃	—	4	4	no	—
421	D₄×C₁₃	—	4	4	no	—
422	D₄×C₁₃	—	8	2	no	—
423	D₄×C₁₃	—	8	2	no	—
424	D₄×C₁₃	C₂×#41	1	4	yes	—
425	C₂×C₄×C₁₃	—	2	4	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	1	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	—	2	2	no	—
436	C₂×C₄×C₁₃	—	2	2	no	—
437	C₂×C₄×C₁₃	—	4	1	no	—
438	C₂×C₄×C₁₃	—	4	2	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	—	4	4	no	—
444	C₂×C₄×C₁₃	—	4	4	no	—
445	C₂×C₄×C₁₃	—	4	4	no	—
446	C₂×C₄×C₁₃	—	8	2	no	—
447	C₂×C₄×C₁₃	—	8	2	no	—
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	2	yes	—
451	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
455	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
457	C₈×C₁₃	—	2	1	no	—
458	C₈×C₁₃	—	2	2	no	—
459	C₈×C₁₃	—	2	1	no	—
460	C₈×C₁₃	—	2	1	no	—
461	C₈×C₁₃	—	2	2	no	—
462	C₈×C₁₃	C₂×#41	1	2	yes	—
463	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
464	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
465	#556	C₂²×C₁₃	1	2	yes	complemented
466	#555	C₂²×C₁₃	1	2	yes	—
467	#554	C₂²×C₁₃	1	2	yes	complemented
468	#553	—	2	2	no	—
469	#552	—	2	2	no	—
470	#552	C₂²×C₁₃	1	2	yes	—
471	#552	C₂²×C₁₃	1	2	yes	complemented
472	#551	—	2	2	no	—
473	#551	—	2	2	no	—
474	#547	C₂²×C₁₃	1	2	yes	—
475	#546	C₂²×C₁₃	1	2	yes	—
476	#546	C₂²×C₁₃	1	2	yes	complemented
477	#533	C₂²×C₁₃	1	2	yes	complemented
478	#529	—	2	2	no	—
479	#529	—	2	2	no	—
480	#529	C₂²×C₁₃	1	2	yes	—
481	#529	C₂²×C₁₃	1	2	yes	complemented
482	#525	—	2	2	no	—
483	C₄×#41	C₂²×C₁₃	1	2	yes	—
484	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
485	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
486	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
487	C₂×#117	—	2	2	no	—
488	#501	C₂²×C₁₃	1	2	yes	complemented
489	#499	C₂²×C₁₃	1	1	yes	characteristic, complemented
490	#497	C₂²×C₁₃	1	2	yes	complemented
491	#495	C₂²×C₁₃	1	1	yes	characteristic
492	#491	C₂²×C₁₃	1	2	yes	complemented
493	#489	C₂²×C₁₃	1	2	yes	complemented
494	#488	C₂²×C₁₃	1	2	yes	complemented
495	#485	C₂²×C₁₃	1	2	yes	complemented
496	#485	C₂²×C₁₃	1	2	yes	complemented
497	#485	C₂²×C₁₃	1	2	yes	complemented
498	#484	C₂²×C₁₃	1	2	yes	complemented
499	#482	C₂²×C₁₃	1	2	yes	complemented
500	#481	C₂²×C₁₃	1	2	yes	—
501	#479	C₂²×C₁₃	1	2	yes	complemented
502	#478	C₂²×C₁₃	1	2	yes	complemented
503	#478	C₂²×C₁₃	1	2	yes	complemented
504	#478	C₂²×C₁₃	1	2	yes	complemented
505	#475	C₂²×C₁₃	1	2	yes	complemented
506	#474	C₂²×C₁₃	1	2	yes	complemented
507	#470	C₂²×C₁₃	1	2	yes	complemented
508	#470	C₂²×C₁₃	1	2	yes	complemented
509	#468	C₂²×C₁₃	1	2	yes	—
510	#468	C₂²×C₁₃	1	2	yes	—
511	#467	C₂²×C₁₃	1	1	yes	characteristic, complemented
512	#466	C₂²×C₁₃	1	1	yes	characteristic
513	#465	C₂²×C₁₃	1	2	yes	complemented
514	#464	C₂²×C₁₃	1	2	yes	complemented
515	#463	C₂²×C₁₃	1	2	yes	—
516	#463	C₂²×C₁₃	1	2	yes	—
517	#463	C₂²×C₁₃	1	2	yes	—
518	#462	C₂²×C₁₃	1	2	yes	complemented
519	#461	C₂²×C₁₃	1	2	yes	complemented
520	#452	C₂²×C₁₃	1	2	yes	—
521	#452	C₂²×C₁₃	1	2	yes	—
522	#452	C₂²×C₁₃	1	2	yes	complemented
523	#450	C₂²×C₁₃	1	2	yes	complemented
524	#449	C₂²×C₁₃	1	2	yes	—
525	#447	C₂²×C₁₃	1	2	yes	—
526	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
527	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
528	#442	C₂²×C₁₃	1	2	yes	—
529	#442	C₂²×C₁₃	1	2	yes	—
530	#440	C₂²×C₁₃	1	2	yes	complemented
531	#440	C₂²×C₁₃	1	2	yes	complemented
532	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
533	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
534	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
535	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
536	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
537	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
538	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
539	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
540	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
541	C₄×D₈	C₂²×C₁₃	1	2	yes	—
542	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
543	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
544	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
545	#436	C₂²×C₁₃	1	1	yes	characteristic
546	#436	C₂²×C₁₃	1	1	yes	characteristic
547	#435	C₂²×C₁₃	1	2	yes	complemented
548	#435	C₂²×C₁₃	1	2	yes	complemented
549	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
550	#431	C₂²×C₁₃	1	2	yes	complemented
551	#428	C₂²×C₁₃	1	2	yes	complemented
552	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
553	#418	C₂²×C₁₃	1	2	yes	complemented
554	#417	C₂²×C₁₃	1	2	yes	—
555	#416	C₂²×C₁₃	1	2	yes	complemented
556	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
557	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
558	C₂²×C₁₃	—	2	1	no	—
559	C₂²×C₁₃	—	2	2	no	—
560	C₂²×C₁₃	—	2	1	no	—
561	C₂²×C₁₃	—	2	2	no	—
562	C₂²×C₁₃	—	2	4	no	—
563	C₂²×C₁₃	—	2	2	no	—
564	C₂²×C₁₃	—	2	1	no	—
565	C₂²×C₁₃	—	4	2	no	—
566	C₂²×C₁₃	—	4	2	no	—
567	C₂²×C₁₃	—	4	2	no	—
568	C₂²×C₁₃	—	4	2	no	—
569	C₂²×C₁₃	—	4	2	no	—
570	C₂²×C₁₃	—	8	8	no	—
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	1	no	—
576	C₄×C₁₃	—	2	2	no	—
577	C₄×C₁₃	—	2	2	no	—
578	C₄×C₁₃	—	2	1	no	—
579	C₄×C₁₃	—	4	2	no	—
580	C₄×C₁₃	—	4	2	no	—
581	C₄×C₁₃	—	4	2	no	—
582	C₄×C₁₃	—	4	2	no	—
583	C₄×C₁₃	—	4	2	no	—
584	C₄×C₁₃	—	4	2	no	—
585	C₄×C₁₃	#575	1	2	yes	—
586	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
587	C₄×C₁₃	#585	1	1	yes	characteristic
588	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
589	C₂×#41	C₂³×C₁₃	1	2	yes	—
590	C₂×#41	C₂³×C₁₃	1	2	yes	—
591	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
592	C₂³×C₄	—	2	2	no	—
593	AGL(1,ℤ/8)	—	2	8	no	—
594	#135	—	2	4	no	—
595	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
596	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
597	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
598	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
599	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
600	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
601	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
602	C₂×D₈	C₂³×C₁₃	1	2	yes	—
603	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
604	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
605	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
606	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
607	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
608	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
609	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
610	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
611	#126	—	2	2	no	—
612	#126	—	2	2	no	—
613	#126	—	2	2	no	—
614	#126	—	2	2	no	—
615	#126	—	2	2	no	—
616	#126	—	2	2	no	—
617	#125	—	2	2	no	—
618	#125	—	2	2	no	—
619	#125	—	2	2	no	—
620	#125	C₂³×C₁₃	1	2	yes	—
621	#125	C₂³×C₁₃	1	2	yes	—
622	#124	—	2	2	no	—
623	#124	—	2	2	no	—
624	#124	C₂³×C₁₃	1	2	yes	—
625	#124	C₂³×C₁₃	1	2	yes	—
626	#123	—	2	2	no	—
627	#123	—	2	2	no	—
628	#123	—	2	2	no	—
629	#123	—	2	2	no	—
630	#123	—	2	2	no	—
631	#123	—	2	2	no	—
632	#123	—	2	2	no	—
633	#123	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
640	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
641	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
642	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
643	#121	—	2	2	no	—
644	#121	—	2	2	no	—
645	#121	—	2	2	no	—
646	#121	—	2	2	no	—
647	#121	C₂³×C₁₃	1	2	yes	—
648	#121	C₂³×C₁₃	1	2	yes	—
649	#120	—	2	2	no	—
650	#120	—	2	2	no	—
651	C₄×Q₈	—	2	2	no	—
652	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
658	C₄×D₄	—	2	2	no	—
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	1	yes	characteristic
667	C₄×D₄	D₄×C₁₃	1	2	yes	—
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	2	yes	—
672	C₄×D₄	C₂³×C₁₃	1	2	yes	—
673	C₄×D₄	C₂³×C₁₃	1	2	yes	—
674	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
675	C₄×D₄	C₂³×C₁₃	1	2	yes	—
676	#117	—	2	2	no	—
677	#117	—	2	2	no	—
678	#117	—	2	2	no	—
679	#117	—	2	2	no	—
680	#117	—	2	2	no	—
681	#117	—	2	2	no	—
682	#117	—	2	2	no	—
683	#117	—	2	2	no	—
684	#117	—	2	2	no	—
685	#117	D₄×C₁₃	1	2	yes	—
686	#117	D₄×C₁₃	1	1	yes	characteristic
687	#117	C₂³×C₁₃	1	2	yes	—
688	#117	C₂³×C₁₃	1	2	yes	—
689	C₂×C₄⋊C₄	—	2	2	no	—
690	C₂×C₄⋊C₄	—	2	2	no	—
691	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
692	C₂×C₂²⋊C₄	—	2	2	no	—
693	C₂×C₂²⋊C₄	—	2	2	no	—
694	C₂×C₂²⋊C₄	—	2	2	no	—
695	C₂×C₄²	—	2	2	no	—
696	C₂×C₄²	—	2	2	no	—
697	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
698	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
699	#107	C₂³×C₁₃	1	1	yes	characteristic
700	#107	C₂³×C₁₃	1	1	yes	characteristic
701	#107	C₂³×C₁₃	1	2	yes	—
702	#107	C₂³×C₁₃	1	1	yes	characteristic
703	#107	C₂³×C₁₃	1	1	yes	characteristic
704	#107	C₂³×C₁₃	1	2	yes	—
705	#106	C₂³×C₁₃	1	2	yes	—
706	#106	C₂³×C₁₃	1	2	yes	—
707	#106	C₂³×C₁₃	1	2	yes	—
708	#106	C₂³×C₁₃	1	2	yes	—
709	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
710	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
711	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
712	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
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	#103	C₂³×C₁₃	1	2	yes	—
718	#103	C₂³×C₁₃	1	2	yes	—
719	#103	C₂³×C₁₃	1	2	yes	—
720	#103	C₂³×C₁₃	1	2	yes	—
721	#102	C₂³×C₁₃	1	2	yes	—
722	#102	C₂³×C₁₃	1	2	yes	—
723	#102	C₂³×C₁₃	1	2	yes	—
724	#102	C₂³×C₁₃	1	2	yes	—
725	#102	C₂³×C₁₃	1	2	yes	—
726	#102	C₂³×C₁₃	1	2	yes	—
727	#102	C₂³×C₁₃	1	2	yes	—
728	#102	C₂³×C₁₃	1	2	yes	—
729	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
730	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
731	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
732	#97	C₂³×C₁₃	1	2	yes	—
733	#97	C₂³×C₁₃	1	2	yes	—
734	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
735	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
736	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
737	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
738	C₄×C₈	C₂³×C₁₃	1	2	yes	—
739	C₂×C₁₃	—	4	1	no	—
740	C₂×C₁₃	—	4	2	no	—
741	C₂×C₁₃	—	4	4	no	—
742	C₂×C₁₃	—	8	2	no	—
743	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
744	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
745	C₂×C₁₃	#3584	1	1	yes	characteristic
746	C₂⁴	—	2	2	no	—
747	#41	—	2	4	no	—
748	#41	—	2	4	no	—
749	#41	—	4	2	no	—
750	#41	—	4	2	no	—
751	#41	—	4	2	no	—
752	C₂×Q₈	—	2	2	no	—
753	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
754	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
755	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
756	C₂×D₄	—	2	4	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	4	2	no	—
763	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
764	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
765	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
766	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	4	8	no	—
777	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
778	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
779	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
780	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
783	Q₁₆	—	2	2	no	—
784	Q₁₆	—	4	1	no	—
785	Q₁₆	—	4	2	no	—
786	SD₁₆	—	2	4	no	—
787	SD₁₆	—	2	4	no	—
788	SD₁₆	—	2	4	no	—
789	SD₁₆	—	4	2	no	—
790	D₈	—	2	4	no	—
791	D₈	—	4	1	no	—
792	D₈	C₁₃×#41	1	4	yes	complemented
793	M₁₆	—	2	4	no	—
794	M₁₆	—	4	2	no	—
795	C₂×C₈	—	2	2	no	—
796	C₂×C₈	—	4	1	no	—
797	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
798	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
799	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
800	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
801	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
802	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
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	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
820	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
821	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
822	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
823	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
824	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
825	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
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	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
846	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
847	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
855	C₄²	C₂×D₄×C₁₃	1	2	yes	—
856	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
857	C₄²	C₂×D₄×C₁₃	1	2	yes	—
858	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
859	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
860	C₄²	C₂⁴×C₁₃	1	2	yes	—
861	C₁₃	#61442	1	1	yes	characteristic, direct product factor, Sylow
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	4	4	no	—
865	C₂³	—	4	4	no	—
866	C₂³	—	8	2	no	—
867	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
868	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
869	Q₈	—	2	2	no	—
870	Q₈	—	2	2	no	—
871	Q₈	—	2	2	no	—
872	Q₈	—	2	2	no	—
873	Q₈	—	4	1	no	—
874	Q₈	—	8	2	no	—
875	D₄	—	2	2	no	—
876	D₄	—	2	2	no	—
877	D₄	—	2	2	no	—
878	D₄	—	4	2	no	—
879	D₄	—	4	1	no	—
880	D₄	—	4	4	no	—
881	D₄	—	4	4	no	—
882	D₄	—	4	4	no	—
883	D₄	—	8	2	no	—
884	D₄	—	8	2	no	—
885	D₄	C₂×C₁₃×#41	1	4	yes	—
886	C₂×C₄	—	2	4	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	4	1	no	—
899	C₂×C₄	—	4	2	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	4	4	no	—
903	C₂×C₄	—	4	4	no	—
904	C₂×C₄	—	4	4	no	—
905	C₂×C₄	—	4	4	no	—
906	C₂×C₄	—	4	4	no	—
907	C₂×C₄	—	8	2	no	—
908	C₂×C₄	—	8	2	no	—
909	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
910	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
911	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
912	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
913	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
914	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
915	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
916	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
917	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
918	C₈	—	2	1	no	—
919	C₈	—	2	2	no	—
920	C₈	—	2	1	no	—
921	C₈	—	2	1	no	—
922	C₈	—	2	2	no	—
923	C₈	C₂×C₁₃×#41	1	2	yes	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	4	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	8	8	no	—
937	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
938	C₄	—	2	2	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	1	no	—
944	C₄	—	2	2	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	2	no	—
951	C₄	C₁₃×#575	1	2	yes	—
952	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
953	C₄	C₁₃×#585	1	1	yes	characteristic
954	C₂	—	4	2	no	—
955	C₂	—	4	1	no	—
956	C₂	—	4	4	no	—
957	C₂	—	8	2	no	—
958	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
959	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
960	C₂	C₁₃×#3584	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×#3475	C₂	semidirect
2. C₁₃×#3402	C₂	semidirect
3. C₁₃×#3389	C₂	semidirect
4. C₁₃×#3376	C₂	semidirect
5. C₁₃×#3352	C₂	semidirect
6. C₁₃×#3348	C₂	semidirect
7. C₁₃×#3323	C₂	semidirect
8. C₁₃×#3319	C₂	semidirect
9. C₁₃×#3315	C₂	semidirect
10. C₁₃×#3273	C₂	semidirect
11. C₁₃×#3267	C₂	semidirect
12. C₁₃×#3172	C₂	semidirect
13. C₁₃×#3168	C₂	semidirect
14. C₁₃×#3107	C₂	semidirect
15. C₁₃×#3105	C₂	semidirect
16. C₁₃×#3102	C₂	semidirect
17. C₁₃×#2965	C₂	semidirect
18. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
19. C₄×C₁₃×#135	C₂	semidirect
22. C₁₃×#556	C₂²	semidirect
24. C₁₃×#554	C₂²	semidirect
28. C₁₃×#552	C₂²	semidirect
33. C₁₃×#546	C₂²	semidirect
34. C₁₃×#533	C₂²	semidirect
38. C₁₃×#529	C₂²	semidirect
42. C₄×C₁₃×#41	C₂²	semidirect
43. C₂×C₄×D₄×C₁₃	C₂²	semidirect
45. C₁₃×#501	C₂²	semidirect
46. C₁₃×#499	C₂²	semidirect
47. C₁₃×#497	C₂²	semidirect
49. C₁₃×#491	C₂²	semidirect
50. C₁₃×#489	C₂²	semidirect
51. C₁₃×#488	C₂²	semidirect
52. C₁₃×#485	C₂²	semidirect
53. C₁₃×#485	C₂²	semidirect
54. C₁₃×#485	C₂²	semidirect
55. C₁₃×#484	C₂²	semidirect
56. C₁₃×#482	C₂²	semidirect
58. C₁₃×#479	C₂²	semidirect
59. C₁₃×#478	C₂²	semidirect
60. C₁₃×#478	C₂²	semidirect
61. C₁₃×#478	C₂²	semidirect
62. C₁₃×#475	C₂²	semidirect
63. C₁₃×#474	C₂²	semidirect
64. C₁₃×#470	C₂²	semidirect
65. C₁₃×#470	C₂²	semidirect
68. C₁₃×#467	C₂²	semidirect
70. C₁₃×#465	C₂²	semidirect
71. C₁₃×#464	C₂²	semidirect
75. C₁₃×#462	C₂²	semidirect
76. C₁₃×#461	C₂²	semidirect
79. C₁₃×#452	C₂²	semidirect
80. C₁₃×#450	C₂²	semidirect
83. C₁₃×#446	C₂²	semidirect
84. C₁₃×#446	C₂²	semidirect
87. C₁₃×#440	C₂²	semidirect
88. C₁₃×#440	C₂²	semidirect
89. C₄×C₁₃×Q₁₆	C₂²	semidirect
90. C₄×C₁₃×Q₁₆	C₂²	semidirect
91. C₄×C₁₃×Q₁₆	C₂²	semidirect
92. C₄×C₁₃×Q₁₆	C₂²	semidirect
93. C₄×C₁₃×SD₁₆	C₂²	semidirect
94. C₄×C₁₃×SD₁₆	C₂²	semidirect
95. C₄×C₁₃×SD₁₆	C₂²	semidirect
96. C₄×C₁₃×SD₁₆	C₂²	semidirect
97. C₄×C₁₃×SD₁₆	C₂²	semidirect
104. C₁₃×#435	C₂²	semidirect
105. C₁₃×#435	C₂²	semidirect
106. C₁₃×#431	C₂²	semidirect
107. C₁₃×#431	C₂²	semidirect
108. C₁₃×#428	C₂²	semidirect
109. C₁₃×#427	C₂²	semidirect
110. C₁₃×#418	C₂²	semidirect
112. C₁₃×#416	C₂²	semidirect
113. C₄×C₁₃×M₁₆	C₂²	semidirect
114. C₂×C₄×C₈×C₁₃	C₂²	semidirect
266. #61442	C₁₃	direct (N × H)
313. C₁₃×D₈	#41	semidirect
382. #3475	C₂×C₁₃	semidirect
383. #3402	C₂×C₁₃	semidirect
384. #3389	C₂×C₁₃	semidirect
385. #3376	C₂×C₁₃	semidirect
386. #3352	C₂×C₁₃	semidirect
387. #3348	C₂×C₁₃	semidirect
388. #3323	C₂×C₁₃	semidirect
389. #3319	C₂×C₁₃	semidirect
390. #3315	C₂×C₁₃	semidirect
391. #3273	C₂×C₁₃	semidirect
392. #3267	C₂×C₁₃	semidirect
393. #3172	C₂×C₁₃	semidirect
394. #3168	C₂×C₁₃	semidirect
395. #3107	C₂×C₁₃	semidirect
396. #3105	C₂×C₁₃	semidirect
397. #3102	C₂×C₁₃	semidirect
398. #2965	C₂×C₁₃	semidirect
399. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
400. C₄×#135	C₂×C₁₃	semidirect
465. #556	C₂²×C₁₃	semidirect
467. #554	C₂²×C₁₃	semidirect
471. #552	C₂²×C₁₃	semidirect
476. #546	C₂²×C₁₃	semidirect
477. #533	C₂²×C₁₃	semidirect
481. #529	C₂²×C₁₃	semidirect
485. C₄×#41	C₂²×C₁₃	semidirect
486. C₂×C₄×D₄	C₂²×C₁₃	semidirect
488. #501	C₂²×C₁₃	semidirect
489. #499	C₂²×C₁₃	semidirect
490. #497	C₂²×C₁₃	semidirect
492. #491	C₂²×C₁₃	semidirect
493. #489	C₂²×C₁₃	semidirect
494. #488	C₂²×C₁₃	semidirect
495. #485	C₂²×C₁₃	semidirect
496. #485	C₂²×C₁₃	semidirect
497. #485	C₂²×C₁₃	semidirect
498. #484	C₂²×C₁₃	semidirect
499. #482	C₂²×C₁₃	semidirect
501. #479	C₂²×C₁₃	semidirect
502. #478	C₂²×C₁₃	semidirect
503. #478	C₂²×C₁₃	semidirect
504. #478	C₂²×C₁₃	semidirect
505. #475	C₂²×C₁₃	semidirect
506. #474	C₂²×C₁₃	semidirect
507. #470	C₂²×C₁₃	semidirect
508. #470	C₂²×C₁₃	semidirect
511. #467	C₂²×C₁₃	semidirect
513. #465	C₂²×C₁₃	semidirect
514. #464	C₂²×C₁₃	semidirect
518. #462	C₂²×C₁₃	semidirect
519. #461	C₂²×C₁₃	semidirect
522. #452	C₂²×C₁₃	semidirect
523. #450	C₂²×C₁₃	semidirect
526. #446	C₂²×C₁₃	semidirect
527. #446	C₂²×C₁₃	semidirect
530. #440	C₂²×C₁₃	semidirect
531. #440	C₂²×C₁₃	semidirect
532. C₄×Q₁₆	C₂²×C₁₃	semidirect
533. C₄×Q₁₆	C₂²×C₁₃	semidirect
534. C₄×Q₁₆	C₂²×C₁₃	semidirect
535. C₄×Q₁₆	C₂²×C₁₃	semidirect
536. C₄×SD₁₆	C₂²×C₁₃	semidirect
537. C₄×SD₁₆	C₂²×C₁₃	semidirect
538. C₄×SD₁₆	C₂²×C₁₃	semidirect
539. C₄×SD₁₆	C₂²×C₁₃	semidirect
540. C₄×SD₁₆	C₂²×C₁₃	semidirect
547. #435	C₂²×C₁₃	semidirect
548. #435	C₂²×C₁₃	semidirect
549. #431	C₂²×C₁₃	semidirect
550. #431	C₂²×C₁₃	semidirect
551. #428	C₂²×C₁₃	semidirect
552. #427	C₂²×C₁₃	semidirect
553. #418	C₂²×C₁₃	semidirect
555. #416	C₂²×C₁₃	semidirect
556. C₄×M₁₆	C₂²×C₁₃	semidirect
557. C₂×C₄×C₈	C₂²×C₁₃	semidirect
792. D₈	C₁₃×#41	semidirect
861. C₁₃	#61442	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×#3475	2
C₁₃×#3402	2
C₁₃×#3389	2
C₁₃×#3376	2
C₁₃×#3352	2
C₁₃×#3348	2
C₁₃×#3323	2
C₁₃×#3319	2
C₁₃×#3315	2
C₁₃×#3273	2
C₁₃×#3267	2
C₁₃×#3172	2
C₁₃×#3168	2
C₁₃×#3107	2
C₁₃×#3105	2
C₁₃×#3102	2
C₁₃×#2965	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₄×C₁₃×#135	2
#61442	13

Subgroups — C13×#61442 #15747781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61442 #15747781