Subgroups — C₁₃×#61438 #15747777

Order 3328.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3475	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3369	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3344	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3314	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3312	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3266	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3172	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3108	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3107	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₁₃×#137	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#137	C₂²	1	2	yes	—
25	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
26	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#557	—	2	1	no	—
28	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#556	C₂²	1	1	yes	characteristic
30	C₁₃×#555	C₂²	1	1	yes	characteristic
31	C₁₃×#554	—	2	2	no	—
32	C₁₃×#554	—	2	1	no	—
33	C₁₃×#554	C₂²	1	1	yes	characteristic
34	C₁₃×#554	C₂²	1	2	yes	—
35	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#553	—	2	1	no	—
37	C₁₃×#552	—	2	1	no	—
38	C₁₃×#552	C₂²	1	2	yes	—
39	C₁₃×#551	—	2	2	no	—
40	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
41	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#547	C₂²	1	1	yes	characteristic
43	C₁₃×#546	C₂²	1	2	yes	—
44	C₁₃×#533	—	2	1	no	—
45	C₁₃×#533	—	2	2	no	—
46	C₁₃×#533	C₂²	1	1	yes	characteristic
47	C₁₃×#533	C₂²	1	1	yes	characteristic
48	C₁₃×#533	C₂²	1	2	yes	complemented
49	C₁₃×#529	—	2	2	no	—
50	C₁₃×#529	C₂²	1	2	yes	—
51	C₁₃×#525	—	2	1	no	—
52	C₄×C₁₃×#41	—	2	1	no	—
53	C₄×C₁₃×#41	C₂²	1	2	yes	—
54	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
55	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#117	—	2	1	no	—
59	C₁₃×#501	C₂²	1	2	yes	complemented
60	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#497	C₂²	1	2	yes	—
62	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#491	C₂²	1	2	yes	complemented
64	C₁₃×#489	C₂²	1	2	yes	—
65	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#485	C₂²	1	2	yes	complemented
68	C₁₃×#485	C₂²	1	2	yes	complemented
69	C₁₃×#484	C₂²	1	2	yes	—
70	C₁₃×#483	C₂²	1	2	yes	—
71	C₁₃×#483	C₂²	1	2	yes	complemented
72	C₁₃×#480	C₂²	1	2	yes	—
73	C₁₃×#479	C₂²	1	2	yes	complemented
74	C₁₃×#479	C₂²	1	2	yes	complemented
75	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#476	C₂²	1	1	yes	characteristic
78	C₁₃×#476	C₂²	1	1	yes	characteristic
79	C₁₃×#475	C₂²	1	2	yes	complemented
80	C₁₃×#474	C₂²	1	2	yes	—
81	C₁₃×#470	C₂²	1	2	yes	complemented
82	C₁₃×#470	C₂²	1	2	yes	complemented
83	C₁₃×#468	C₂²	1	2	yes	—
84	C₁₃×#468	C₂²	1	2	yes	—
85	C₁₃×#467	C₂²	1	2	yes	—
86	C₁₃×#467	C₂²	1	2	yes	—
87	C₁₃×#464	C₂²	1	2	yes	—
88	C₁₃×#464	C₂²	1	2	yes	—
89	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#462	C₂²	1	2	yes	complemented
91	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
92	C₁₃×#461	C₂²	1	2	yes	—
93	C₁₃×#461	C₂²	1	1	yes	characteristic
94	C₁₃×#461	C₂²	1	1	yes	characteristic
95	C₁₃×#452	C₂²	1	2	yes	—
96	C₁₃×#452	C₂²	1	2	yes	—
97	C₁₃×#451	C₂²	1	2	yes	—
98	C₁₃×#451	C₂²	1	2	yes	complemented
99	C₁₃×#450	C₂²	1	2	yes	—
100	C₁₃×#448	C₂²	1	2	yes	—
101	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
102	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
103	C₁₃×#441	C₂²	1	2	yes	complemented
104	C₁₃×#441	C₂²	1	2	yes	complemented
105	C₁₃×#440	C₂²	1	2	yes	—
106	C₁₃×#440	C₂²	1	2	yes	—
107	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
108	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
109	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
110	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
111	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
112	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
113	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
114	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
115	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
116	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
117	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
118	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
119	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
121	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
123	C₁₃×#435	C₂²	1	2	yes	—
124	C₁₃×#435	C₂²	1	2	yes	—
125	C₁₃×#431	C₂²	1	1	yes	characteristic
126	C₁₃×#431	C₂²	1	2	yes	complemented
127	C₁₃×#428	C₂²	1	2	yes	complemented
128	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
129	C₁₃×#419	C₂²	1	2	yes	complemented
130	C₁₃×#417	C₂²	1	2	yes	—
131	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
132	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
133	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
135	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
136	C₂×C₁₃×#41	C₂³	1	2	yes	—
137	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₁₃	—	2	1	no	—
141	C₁₃×#137	—	2	8	no	—
142	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
143	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
144	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
145	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
146	C₂×C₁₃×SD₁₆	—	2	4	no	—
147	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
151	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
154	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
155	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
157	C₁₃×C₄⋊Q₈	—	2	2	no	—
158	C₁₃×C₄⋊Q₈	—	2	1	no	—
159	C₁₃×C₄⋊Q₈	—	2	1	no	—
160	C₁₃×C₄⋊Q₈	—	2	2	no	—
161	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₁₃×#126	—	2	2	no	—
168	C₁₃×#126	—	2	2	no	—
169	C₁₃×#126	—	2	2	no	—
170	C₁₃×#125	—	2	2	no	—
171	C₁₃×#125	—	2	1	no	—
172	C₁₃×#125	—	2	2	no	—
173	C₁₃×#125	—	2	2	no	—
174	C₁₃×#125	—	2	1	no	—
175	C₁₃×#125	—	2	1	no	—
176	C₁₃×#125	—	2	1	no	—
177	C₁₃×#125	—	2	2	no	—
178	C₁₃×#125	C₂³	1	2	yes	—
179	C₁₃×#124	—	2	2	no	—
180	C₁₃×#124	C₂³	1	2	yes	—
181	C₁₃×#123	—	2	2	no	—
182	C₁₃×#123	—	2	2	no	—
183	C₁₃×#123	—	2	2	no	—
184	C₁₃×#123	—	2	2	no	—
185	C₁₃×C₂²⋊Q₈	—	2	1	no	—
186	C₁₃×C₂²⋊Q₈	—	2	1	no	—
187	C₁₃×C₂²⋊Q₈	—	2	1	no	—
188	C₁₃×C₂²⋊Q₈	—	2	1	no	—
189	C₁₃×C₂²⋊Q₈	—	2	2	no	—
190	C₁₃×C₂²⋊Q₈	—	2	2	no	—
191	C₁₃×C₂²⋊Q₈	—	2	2	no	—
192	C₁₃×C₂²⋊Q₈	—	2	2	no	—
193	C₁₃×C₂²⋊Q₈	—	2	2	no	—
194	C₁₃×C₂²⋊Q₈	—	2	2	no	—
195	C₁₃×C₂²⋊Q₈	—	2	2	no	—
196	C₁₃×C₂²⋊Q₈	—	2	2	no	—
197	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₁₃×#121	—	2	1	no	—
203	C₁₃×#121	—	2	1	no	—
204	C₁₃×#121	—	2	2	no	—
205	C₁₃×#121	C₂³	1	2	yes	—
206	C₁₃×#120	—	2	2	no	—
207	C₄×Q₈×C₁₃	—	2	1	no	—
208	C₄×Q₈×C₁₃	—	2	1	no	—
209	C₄×Q₈×C₁₃	—	2	1	no	—
210	C₄×Q₈×C₁₃	—	2	1	no	—
211	C₄×Q₈×C₁₃	—	2	2	no	—
212	C₄×Q₈×C₁₃	—	2	2	no	—
213	C₄×Q₈×C₁₃	—	2	1	no	—
214	C₄×Q₈×C₁₃	—	2	1	no	—
215	C₄×Q₈×C₁₃	—	2	2	no	—
216	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
217	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
220	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
223	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
224	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
225	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
226	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₁₃	—	2	2	no	—
228	C₄×D₄×C₁₃	—	2	1	no	—
229	C₄×D₄×C₁₃	—	2	2	no	—
230	C₄×D₄×C₁₃	—	2	1	no	—
231	C₄×D₄×C₁₃	—	2	2	no	—
232	C₄×D₄×C₁₃	—	2	2	no	—
233	C₄×D₄×C₁₃	—	2	2	no	—
234	C₄×D₄×C₁₃	—	2	1	no	—
235	C₄×D₄×C₁₃	—	2	1	no	—
236	C₄×D₄×C₁₃	D₄	1	2	yes	—
237	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
238	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₁₃	C₂³	1	2	yes	—
243	C₄×D₄×C₁₃	C₂³	1	2	yes	—
244	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
245	C₁₃×#117	—	2	1	no	—
246	C₁₃×#117	—	2	1	no	—
247	C₁₃×#117	—	2	2	no	—
248	C₁₃×#117	—	2	1	no	—
249	C₁₃×#117	—	2	1	no	—
250	C₁₃×#117	—	2	2	no	—
251	C₁₃×#117	—	2	2	no	—
252	C₁₃×#117	—	2	2	no	—
253	C₁₃×#117	D₄	1	1	yes	characteristic
254	C₁₃×#117	D₄	1	2	yes	—
255	C₁₃×#117	C₂³	1	2	yes	—
256	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
258	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
259	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
263	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²×C₁₃	—	2	1	no	—
266	C₂×C₄²×C₁₃	—	2	2	no	—
267	C₂×C₄²×C₁₃	—	2	2	no	—
268	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
270	C₁₃×#107	C₂³	1	2	yes	—
271	C₁₃×#107	C₂³	1	2	yes	—
272	C₁₃×#107	C₂³	1	2	yes	—
273	C₁₃×#107	C₂³	1	2	yes	—
274	C₁₃×#106	C₂³	1	1	yes	characteristic
275	C₁₃×#106	C₂³	1	1	yes	characteristic
276	C₁₃×#106	C₂³	1	1	yes	characteristic
277	C₁₃×#106	C₂³	1	1	yes	characteristic
278	C₁₃×#106	C₂³	1	2	yes	—
279	C₁₃×#106	C₂³	1	2	yes	—
280	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
283	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
284	C₁₃×#103	C₂³	1	1	yes	characteristic
285	C₁₃×#103	C₂³	1	1	yes	characteristic
286	C₁₃×#103	C₂³	1	1	yes	characteristic
287	C₁₃×#103	C₂³	1	1	yes	characteristic
288	C₁₃×#103	C₂³	1	2	yes	—
289	C₁₃×#103	C₂³	1	2	yes	—
290	C₁₃×#103	C₂³	1	2	yes	—
291	C₁₃×#103	C₂³	1	2	yes	—
292	C₁₃×#103	C₂³	1	2	yes	—
293	C₁₃×#103	C₂³	1	2	yes	—
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#103	C₂³	1	2	yes	—
296	C₁₃×#103	C₂³	1	2	yes	—
297	C₁₃×#103	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	1	yes	characteristic
299	C₁₃×#102	C₂³	1	1	yes	characteristic
300	C₁₃×#102	C₂³	1	1	yes	characteristic
301	C₁₃×#102	C₂³	1	1	yes	characteristic
302	C₁₃×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₁₃×#97	C₂³	1	2	yes	—
308	C₁₃×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₁₃	C₂³	1	2	yes	—
314	#61438	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂⁴×C₁₃	—	2	1	no	—
316	C₁₃×#41	—	2	4	no	—
317	C₁₃×#41	—	2	4	no	—
318	C₁₃×#41	—	4	2	no	—
319	C₂×Q₈×C₁₃	—	2	2	no	—
320	C₂×Q₈×C₁₃	—	2	1	no	—
321	C₂×Q₈×C₁₃	—	2	1	no	—
322	C₂×Q₈×C₁₃	—	2	2	no	—
323	C₂×Q₈×C₁₃	—	2	1	no	—
324	C₂×Q₈×C₁₃	—	2	2	no	—
325	C₂×Q₈×C₁₃	—	2	4	no	—
326	C₂×Q₈×C₁₃	—	4	1	no	—
327	C₂×Q₈×C₁₃	—	4	2	no	—
328	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₁₃	—	2	2	no	—
334	C₂×D₄×C₁₃	—	2	2	no	—
335	C₂×D₄×C₁₃	—	2	2	no	—
336	C₂×D₄×C₁₃	—	2	1	no	—
337	C₂×D₄×C₁₃	—	4	1	no	—
338	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
341	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₁₃	—	2	2	no	—
343	C₂²×C₄×C₁₃	—	2	1	no	—
344	C₂²×C₄×C₁₃	—	2	1	no	—
345	C₂²×C₄×C₁₃	—	2	2	no	—
346	C₂²×C₄×C₁₃	—	2	1	no	—
347	C₂²×C₄×C₁₃	—	2	2	no	—
348	C₂²×C₄×C₁₃	—	2	1	no	—
349	C₂²×C₄×C₁₃	—	2	1	no	—
350	C₂²×C₄×C₁₃	—	2	1	no	—
351	C₂²×C₄×C₁₃	—	2	1	no	—
352	C₂²×C₄×C₁₃	—	2	2	no	—
353	C₂²×C₄×C₁₃	—	4	4	no	—
354	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
355	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
357	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
360	C₁₃×Q₁₆	—	2	4	no	—
361	C₁₃×Q₁₆	—	2	4	no	—
362	C₁₃×Q₁₆	—	4	2	no	—
363	C₁₃×Q₁₆	—	4	2	no	—
364	C₁₃×SD₁₆	—	2	2	no	—
365	C₁₃×SD₁₆	—	2	2	no	—
366	C₁₃×SD₁₆	—	2	4	no	—
367	C₁₃×SD₁₆	—	2	2	no	—
368	C₁₃×SD₁₆	—	4	2	no	—
369	C₁₃×SD₁₆	#41	1	4	yes	complemented
370	C₁₃×M₁₆	—	2	4	no	—
371	C₁₃×M₁₆	—	4	2	no	—
372	C₂×C₈×C₁₃	—	2	2	no	—
373	C₂×C₈×C₁₃	—	4	1	no	—
374	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
378	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
379	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
380	C₁₃×C₄⋊C₄	—	2	1	no	—
381	C₁₃×C₄⋊C₄	—	2	1	no	—
382	C₁₃×C₄⋊C₄	—	2	1	no	—
383	C₁₃×C₄⋊C₄	—	2	2	no	—
384	C₁₃×C₄⋊C₄	—	2	2	no	—
385	C₁₃×C₄⋊C₄	—	2	2	no	—
386	C₁₃×C₄⋊C₄	—	2	1	no	—
387	C₁₃×C₄⋊C₄	—	2	1	no	—
388	C₁₃×C₄⋊C₄	—	2	2	no	—
389	C₁₃×C₄⋊C₄	—	2	2	no	—
390	C₁₃×C₄⋊C₄	—	2	1	no	—
391	C₁₃×C₄⋊C₄	—	2	1	no	—
392	C₁₃×C₄⋊C₄	—	2	2	no	—
393	C₁₃×C₄⋊C₄	—	2	1	no	—
394	C₁₃×C₄⋊C₄	—	2	2	no	—
395	C₁₃×C₄⋊C₄	—	2	1	no	—
396	C₁₃×C₄⋊C₄	—	2	2	no	—
397	C₁₃×C₄⋊C₄	—	2	1	no	—
398	C₁₃×C₄⋊C₄	—	2	2	no	—
399	C₁₃×C₄⋊C₄	—	2	2	no	—
400	C₁₃×C₄⋊C₄	—	2	2	no	—
401	C₁₃×C₄⋊C₄	—	2	2	no	—
402	C₁₃×C₄⋊C₄	—	2	2	no	—
403	C₁₃×C₄⋊C₄	—	2	1	no	—
404	C₁₃×C₄⋊C₄	—	2	2	no	—
405	C₁₃×C₄⋊C₄	—	2	2	no	—
406	C₁₃×C₄⋊C₄	—	2	2	no	—
407	C₁₃×C₄⋊C₄	—	2	1	no	—
408	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
409	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
410	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
411	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
412	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
413	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
414	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
415	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
416	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
417	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
418	C₁₃×C₂²⋊C₄	—	2	2	no	—
419	C₁₃×C₂²⋊C₄	—	2	2	no	—
420	C₁₃×C₂²⋊C₄	—	2	2	no	—
421	C₁₃×C₂²⋊C₄	—	2	2	no	—
422	C₁₃×C₂²⋊C₄	—	2	2	no	—
423	C₁₃×C₂²⋊C₄	—	2	2	no	—
424	C₁₃×C₂²⋊C₄	—	2	1	no	—
425	C₁₃×C₂²⋊C₄	—	2	2	no	—
426	C₁₃×C₂²⋊C₄	—	2	2	no	—
427	C₁₃×C₂²⋊C₄	—	2	1	no	—
428	C₁₃×C₂²⋊C₄	—	2	1	no	—
429	C₁₃×C₂²⋊C₄	—	2	1	no	—
430	C₁₃×C₂²⋊C₄	—	2	2	no	—
431	C₁₃×C₂²⋊C₄	—	2	2	no	—
432	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
433	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
434	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
435	C₄²×C₁₃	—	2	2	no	—
436	C₄²×C₁₃	—	2	2	no	—
437	C₄²×C₁₃	—	2	2	no	—
438	C₄²×C₁₃	—	2	1	no	—
439	C₄²×C₁₃	—	2	2	no	—
440	C₄²×C₁₃	—	2	1	no	—
441	C₄²×C₁₃	—	2	1	no	—
442	C₄²×C₁₃	—	2	2	no	—
443	C₄²×C₁₃	—	2	1	no	—
444	C₄²×C₁₃	—	2	2	no	—
445	C₄²×C₁₃	C₂×D₄	1	2	yes	—
446	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₁₃	C₂×D₄	1	2	yes	—
448	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
450	C₄²×C₁₃	C₂⁴	1	2	yes	—
451	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
452	Q₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
453	#3475	C₂×C₁₃	1	1	yes	characteristic
454	#3398	C₂×C₁₃	1	1	yes	characteristic, complemented
455	#3385	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#3372	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#3369	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#3357	C₂×C₁₃	1	1	yes	characteristic, complemented
459	#3344	C₂×C₁₃	1	2	yes	complemented
460	#3331	C₂×C₁₃	1	1	yes	characteristic, complemented
461	#3329	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3314	C₂×C₁₃	1	2	yes	complemented
463	#3312	C₂×C₁₃	1	2	yes	complemented
464	#3276	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3266	C₂×C₁₃	1	2	yes	complemented
466	#3172	C₂×C₁₃	1	2	yes	complemented
467	#3170	C₂×C₁₃	1	1	yes	characteristic, complemented
468	#3108	C₂×C₁₃	1	2	yes	complemented
469	#3107	C₂×C₁₃	1	2	yes	complemented
470	#3104	C₂×C₁₃	1	1	yes	characteristic, complemented
471	#3101	C₂×C₁₃	1	1	yes	characteristic, complemented
472	#2965	C₂×C₁₃	1	1	yes	characteristic, complemented
473	C₄×#137	C₂×C₁₃	1	2	yes	complemented
474	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
475	C₂³×C₁₃	—	2	1	no	—
476	C₂³×C₁₃	—	2	1	no	—
477	C₂³×C₁₃	—	4	2	no	—
478	C₂³×C₁₃	—	4	2	no	—
479	C₂³×C₁₃	—	8	1	no	—
480	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
481	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
482	Q₈×C₁₃	—	2	2	no	—
483	Q₈×C₁₃	—	2	1	no	—
484	Q₈×C₁₃	—	2	1	no	—
485	Q₈×C₁₃	—	2	2	no	—
486	Q₈×C₁₃	—	2	2	no	—
487	Q₈×C₁₃	—	2	2	no	—
488	Q₈×C₁₃	—	2	1	no	—
489	Q₈×C₁₃	—	2	2	no	—
490	Q₈×C₁₃	—	4	4	no	—
491	Q₈×C₁₃	—	4	2	no	—
492	Q₈×C₁₃	—	8	2	no	—
493	Q₈×C₁₃	—	8	1	no	—
494	Q₈×C₁₃	—	8	1	no	—
495	Q₈×C₁₃	C₂×#41	1	2	yes	—
496	D₄×C₁₃	—	2	4	no	—
497	D₄×C₁₃	—	2	2	no	—
498	D₄×C₁₃	—	2	1	no	—
499	D₄×C₁₃	—	2	1	no	—
500	D₄×C₁₃	—	2	1	no	—
501	D₄×C₁₃	—	4	2	no	—
502	D₄×C₁₃	—	4	4	no	—
503	D₄×C₁₃	—	8	2	no	—
504	D₄×C₁₃	C₂×#41	1	2	yes	—
505	C₂×C₄×C₁₃	—	2	1	no	—
506	C₂×C₄×C₁₃	—	2	4	no	—
507	C₂×C₄×C₁₃	—	2	1	no	—
508	C₂×C₄×C₁₃	—	2	2	no	—
509	C₂×C₄×C₁₃	—	2	1	no	—
510	C₂×C₄×C₁₃	—	2	2	no	—
511	C₂×C₄×C₁₃	—	2	1	no	—
512	C₂×C₄×C₁₃	—	2	1	no	—
513	C₂×C₄×C₁₃	—	2	2	no	—
514	C₂×C₄×C₁₃	—	2	2	no	—
515	C₂×C₄×C₁₃	—	2	1	no	—
516	C₂×C₄×C₁₃	—	2	2	no	—
517	C₂×C₄×C₁₃	—	2	2	no	—
518	C₂×C₄×C₁₃	—	2	1	no	—
519	C₂×C₄×C₁₃	—	2	1	no	—
520	C₂×C₄×C₁₃	—	4	2	no	—
521	C₂×C₄×C₁₃	—	4	1	no	—
522	C₂×C₄×C₁₃	—	4	2	no	—
523	C₂×C₄×C₁₃	—	4	4	no	—
524	C₂×C₄×C₁₃	—	4	4	no	—
525	C₂×C₄×C₁₃	—	4	2	no	—
526	C₂×C₄×C₁₃	—	4	2	no	—
527	C₂×C₄×C₁₃	—	4	2	no	—
528	C₂×C₄×C₁₃	—	4	2	no	—
529	C₂×C₄×C₁₃	—	4	2	no	—
530	C₂×C₄×C₁₃	—	8	2	no	—
531	C₂×C₄×C₁₃	—	8	1	no	—
532	C₂×C₄×C₁₃	—	8	2	no	—
533	C₂×C₄×C₁₃	#137	1	4	yes	complemented
534	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
543	C₈×C₁₃	—	2	1	no	—
544	C₈×C₁₃	—	2	2	no	—
545	C₈×C₁₃	—	2	1	no	—
546	C₈×C₁₃	—	2	1	no	—
547	C₈×C₁₃	—	2	2	no	—
548	C₈×C₁₃	C₂×#41	1	2	yes	—
549	C₂×#137	C₂²×C₁₃	1	2	yes	—
550	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
551	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
552	#557	—	2	1	no	—
553	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
554	#556	C₂²×C₁₃	1	1	yes	characteristic
555	#555	C₂²×C₁₃	1	1	yes	characteristic
556	#554	—	2	2	no	—
557	#554	—	2	1	no	—
558	#554	C₂²×C₁₃	1	1	yes	characteristic
559	#554	C₂²×C₁₃	1	2	yes	—
560	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
561	#553	—	2	1	no	—
562	#552	—	2	1	no	—
563	#552	C₂²×C₁₃	1	2	yes	—
564	#551	—	2	2	no	—
565	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
566	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
567	#547	C₂²×C₁₃	1	1	yes	characteristic
568	#546	C₂²×C₁₃	1	2	yes	—
569	#533	—	2	1	no	—
570	#533	—	2	2	no	—
571	#533	C₂²×C₁₃	1	1	yes	characteristic
572	#533	C₂²×C₁₃	1	1	yes	characteristic
573	#533	C₂²×C₁₃	1	2	yes	complemented
574	#529	—	2	2	no	—
575	#529	C₂²×C₁₃	1	2	yes	—
576	#525	—	2	1	no	—
577	C₄×#41	—	2	1	no	—
578	C₄×#41	C₂²×C₁₃	1	2	yes	—
579	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
580	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
581	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
582	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
583	C₂×#117	—	2	1	no	—
584	#501	C₂²×C₁₃	1	2	yes	complemented
585	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
586	#497	C₂²×C₁₃	1	2	yes	—
587	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
588	#491	C₂²×C₁₃	1	2	yes	complemented
589	#489	C₂²×C₁₃	1	2	yes	—
590	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
591	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
592	#485	C₂²×C₁₃	1	2	yes	complemented
593	#485	C₂²×C₁₃	1	2	yes	complemented
594	#484	C₂²×C₁₃	1	2	yes	—
595	#483	C₂²×C₁₃	1	2	yes	—
596	#483	C₂²×C₁₃	1	2	yes	complemented
597	#480	C₂²×C₁₃	1	2	yes	—
598	#479	C₂²×C₁₃	1	2	yes	complemented
599	#479	C₂²×C₁₃	1	2	yes	complemented
600	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
601	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
602	#476	C₂²×C₁₃	1	1	yes	characteristic
603	#476	C₂²×C₁₃	1	1	yes	characteristic
604	#475	C₂²×C₁₃	1	2	yes	complemented
605	#474	C₂²×C₁₃	1	2	yes	—
606	#470	C₂²×C₁₃	1	2	yes	complemented
607	#470	C₂²×C₁₃	1	2	yes	complemented
608	#468	C₂²×C₁₃	1	2	yes	—
609	#468	C₂²×C₁₃	1	2	yes	—
610	#467	C₂²×C₁₃	1	2	yes	—
611	#467	C₂²×C₁₃	1	2	yes	—
612	#464	C₂²×C₁₃	1	2	yes	—
613	#464	C₂²×C₁₃	1	2	yes	—
614	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
615	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
616	#462	C₂²×C₁₃	1	2	yes	complemented
617	#461	C₂²×C₁₃	1	1	yes	characteristic
618	#461	C₂²×C₁₃	1	1	yes	characteristic
619	#461	C₂²×C₁₃	1	2	yes	—
620	#452	C₂²×C₁₃	1	2	yes	—
621	#452	C₂²×C₁₃	1	2	yes	—
622	#451	C₂²×C₁₃	1	2	yes	—
623	#451	C₂²×C₁₃	1	2	yes	complemented
624	#450	C₂²×C₁₃	1	2	yes	—
625	#448	C₂²×C₁₃	1	2	yes	—
626	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
627	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
628	#441	C₂²×C₁₃	1	2	yes	complemented
629	#441	C₂²×C₁₃	1	2	yes	complemented
630	#440	C₂²×C₁₃	1	2	yes	—
631	#440	C₂²×C₁₃	1	2	yes	—
632	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
633	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
634	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
635	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
636	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
637	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
638	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
639	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
640	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
641	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
642	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
643	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
644	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
645	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
646	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
647	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
648	#435	C₂²×C₁₃	1	2	yes	—
649	#435	C₂²×C₁₃	1	2	yes	—
650	#431	C₂²×C₁₃	1	1	yes	characteristic
651	#431	C₂²×C₁₃	1	2	yes	complemented
652	#428	C₂²×C₁₃	1	2	yes	complemented
653	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
654	#419	C₂²×C₁₃	1	2	yes	complemented
655	#417	C₂²×C₁₃	1	2	yes	—
656	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
657	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
658	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
659	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
660	C₂²×C₁₃	—	2	1	no	—
661	C₂²×C₁₃	—	2	1	no	—
662	C₂²×C₁₃	—	2	2	no	—
663	C₂²×C₁₃	—	2	2	no	—
664	C₂²×C₁₃	—	2	2	no	—
665	C₂²×C₁₃	—	2	2	no	—
666	C₂²×C₁₃	—	4	1	no	—
667	C₂²×C₁₃	—	4	1	no	—
668	C₂²×C₁₃	—	4	1	no	—
669	C₂²×C₁₃	—	4	1	no	—
670	C₂²×C₁₃	—	4	1	no	—
671	C₂²×C₁₃	—	8	4	no	—
672	C₂²×C₁₃	C₂×#137	1	2	yes	—
673	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
674	C₄×C₁₃	—	2	1	no	—
675	C₄×C₁₃	—	2	2	no	—
676	C₄×C₁₃	—	2	1	no	—
677	C₄×C₁₃	—	2	2	no	—
678	C₄×C₁₃	—	2	1	no	—
679	C₄×C₁₃	—	2	2	no	—
680	C₄×C₁₃	—	2	2	no	—
681	C₄×C₁₃	—	4	1	no	—
682	C₄×C₁₃	—	4	2	no	—
683	C₄×C₁₃	—	4	1	no	—
684	C₄×C₁₃	—	4	2	no	—
685	C₄×C₁₃	—	4	2	no	—
686	C₄×C₁₃	—	4	1	no	—
687	C₄×C₁₃	—	4	2	no	—
688	C₄×C₁₃	—	4	1	no	—
689	C₄×C₁₃	—	4	1	no	—
690	C₄×C₁₃	C₂×#137	1	2	yes	—
691	C₄×C₁₃	C₂×#137	1	2	yes	—
692	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
693	C₄×C₁₃	#585	1	1	yes	characteristic
694	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
695	C₂×#41	C₂³×C₁₃	1	2	yes	—
696	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
697	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
698	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
699	C₂³×C₄	—	2	1	no	—
700	#137	—	2	8	no	—
701	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
702	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
703	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
704	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
705	C₂×SD₁₆	—	2	4	no	—
706	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
708	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
709	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
710	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
711	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
712	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
713	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
714	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
715	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
716	C₄⋊Q₈	—	2	2	no	—
717	C₄⋊Q₈	—	2	1	no	—
718	C₄⋊Q₈	—	2	1	no	—
719	C₄⋊Q₈	—	2	2	no	—
720	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
723	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#125	—	2	2	no	—
730	#125	—	2	1	no	—
731	#125	—	2	2	no	—
732	#125	—	2	2	no	—
733	#125	—	2	1	no	—
734	#125	—	2	1	no	—
735	#125	—	2	1	no	—
736	#125	—	2	2	no	—
737	#125	C₂³×C₁₃	1	2	yes	—
738	#124	—	2	2	no	—
739	#124	C₂³×C₁₃	1	2	yes	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
757	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
758	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
759	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
761	#121	—	2	1	no	—
762	#121	—	2	1	no	—
763	#121	—	2	2	no	—
764	#121	C₂³×C₁₃	1	2	yes	—
765	#120	—	2	2	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	1	no	—
770	C₄×Q₈	—	2	2	no	—
771	C₄×Q₈	—	2	2	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	2	no	—
775	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
776	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
778	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
781	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
782	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
783	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
784	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
785	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	D₄×C₁₃	1	2	yes	—
796	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
799	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
801	C₄×D₄	C₂³×C₁₃	1	2	yes	—
802	C₄×D₄	C₂³×C₁₃	1	2	yes	—
803	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
804	#117	—	2	1	no	—
805	#117	—	2	1	no	—
806	#117	—	2	2	no	—
807	#117	—	2	1	no	—
808	#117	—	2	1	no	—
809	#117	—	2	2	no	—
810	#117	—	2	2	no	—
811	#117	—	2	2	no	—
812	#117	D₄×C₁₃	1	1	yes	characteristic
813	#117	D₄×C₁₃	1	2	yes	—
814	#117	C₂³×C₁₃	1	2	yes	—
815	C₂×C₄⋊C₄	—	2	1	no	—
816	C₂×C₄⋊C₄	—	2	2	no	—
817	C₂×C₄⋊C₄	—	2	1	no	—
818	C₂×C₄⋊C₄	—	2	1	no	—
819	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
820	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
821	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
822	C₂×C₂²⋊C₄	—	2	1	no	—
823	C₂×C₂²⋊C₄	—	2	2	no	—
824	C₂×C₄²	—	2	1	no	—
825	C₂×C₄²	—	2	2	no	—
826	C₂×C₄²	—	2	2	no	—
827	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
828	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
829	#107	C₂³×C₁₃	1	2	yes	—
830	#107	C₂³×C₁₃	1	2	yes	—
831	#107	C₂³×C₁₃	1	2	yes	—
832	#107	C₂³×C₁₃	1	2	yes	—
833	#106	C₂³×C₁₃	1	1	yes	characteristic
834	#106	C₂³×C₁₃	1	1	yes	characteristic
835	#106	C₂³×C₁₃	1	1	yes	characteristic
836	#106	C₂³×C₁₃	1	1	yes	characteristic
837	#106	C₂³×C₁₃	1	2	yes	—
838	#106	C₂³×C₁₃	1	2	yes	—
839	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
840	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
841	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
842	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
843	#103	C₂³×C₁₃	1	1	yes	characteristic
844	#103	C₂³×C₁₃	1	1	yes	characteristic
845	#103	C₂³×C₁₃	1	1	yes	characteristic
846	#103	C₂³×C₁₃	1	1	yes	characteristic
847	#103	C₂³×C₁₃	1	2	yes	—
848	#103	C₂³×C₁₃	1	2	yes	—
849	#103	C₂³×C₁₃	1	2	yes	—
850	#103	C₂³×C₁₃	1	2	yes	—
851	#103	C₂³×C₁₃	1	2	yes	—
852	#103	C₂³×C₁₃	1	2	yes	—
853	#103	C₂³×C₁₃	1	2	yes	—
854	#103	C₂³×C₁₃	1	2	yes	—
855	#103	C₂³×C₁₃	1	2	yes	—
856	#103	C₂³×C₁₃	1	2	yes	—
857	#102	C₂³×C₁₃	1	1	yes	characteristic
858	#102	C₂³×C₁₃	1	1	yes	characteristic
859	#102	C₂³×C₁₃	1	1	yes	characteristic
860	#102	C₂³×C₁₃	1	1	yes	characteristic
861	#102	C₂³×C₁₃	1	2	yes	—
862	#102	C₂³×C₁₃	1	2	yes	—
863	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
864	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
866	#97	C₂³×C₁₃	1	2	yes	—
867	#97	C₂³×C₁₃	1	2	yes	—
868	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
869	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
870	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
871	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₁₃	1	2	yes	—
873	C₂×C₁₃	—	2	2	no	—
874	C₂×C₁₃	—	4	2	no	—
875	C₂×C₁₃	—	4	2	no	—
876	C₂×C₁₃	—	8	1	no	—
877	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
878	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
879	C₂×C₁₃	#3584	1	1	yes	characteristic
880	C₂⁴	—	2	1	no	—
881	#41	—	2	4	no	—
882	#41	—	2	4	no	—
883	#41	—	4	2	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	—	2	2	no	—
888	C₂×Q₈	—	2	1	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	—	2	4	no	—
891	C₂×Q₈	—	4	1	no	—
892	C₂×Q₈	—	4	2	no	—
893	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
894	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
895	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
897	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	4	1	no	—
903	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
904	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
905	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
906	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	4	4	no	—
919	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
920	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
921	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
922	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
924	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
925	Q₁₆	—	2	4	no	—
926	Q₁₆	—	2	4	no	—
927	Q₁₆	—	4	2	no	—
928	Q₁₆	—	4	2	no	—
929	SD₁₆	—	2	2	no	—
930	SD₁₆	—	2	2	no	—
931	SD₁₆	—	2	4	no	—
932	SD₁₆	—	2	2	no	—
933	SD₁₆	—	4	2	no	—
934	SD₁₆	C₁₃×#41	1	4	yes	complemented
935	M₁₆	—	2	4	no	—
936	M₁₆	—	4	2	no	—
937	C₂×C₈	—	2	2	no	—
938	C₂×C₈	—	4	1	no	—
939	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
940	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
941	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
942	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
943	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
944	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
974	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
975	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
976	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
979	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
998	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1011	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1012	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1013	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1014	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1015	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1016	C₄²	C₂⁴×C₁₃	1	2	yes	—
1017	C₁₃	#61438	1	1	yes	characteristic, direct product factor, Sylow
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	1	no	—
1020	C₂³	—	4	2	no	—
1021	C₂³	—	4	2	no	—
1022	C₂³	—	8	1	no	—
1023	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1024	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	2	no	—
1029	Q₈	—	2	2	no	—
1030	Q₈	—	2	2	no	—
1031	Q₈	—	2	1	no	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	4	4	no	—
1034	Q₈	—	4	2	no	—
1035	Q₈	—	8	2	no	—
1036	Q₈	—	8	1	no	—
1037	Q₈	—	8	1	no	—
1038	Q₈	C₂×C₁₃×#41	1	2	yes	—
1039	D₄	—	2	4	no	—
1040	D₄	—	2	2	no	—
1041	D₄	—	2	1	no	—
1042	D₄	—	2	1	no	—
1043	D₄	—	2	1	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	4	4	no	—
1046	D₄	—	8	2	no	—
1047	D₄	C₂×C₁₃×#41	1	2	yes	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	4	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	4	2	no	—
1064	C₂×C₄	—	4	1	no	—
1065	C₂×C₄	—	4	2	no	—
1066	C₂×C₄	—	4	4	no	—
1067	C₂×C₄	—	4	4	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	8	2	no	—
1074	C₂×C₄	—	8	1	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	C₁₃×#137	1	4	yes	complemented
1077	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1078	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1079	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1080	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1081	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1082	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1083	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1084	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1085	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1086	C₈	—	2	1	no	—
1087	C₈	—	2	2	no	—
1088	C₈	—	2	1	no	—
1089	C₈	—	2	1	no	—
1090	C₈	—	2	2	no	—
1091	C₈	C₂×C₁₃×#41	1	2	yes	—
1092	C₂²	—	2	1	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	2	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	4	1	no	—
1103	C₂²	—	8	4	no	—
1104	C₂²	C₂×C₁₃×#137	1	2	yes	—
1105	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1106	C₄	—	2	2	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	2	2	no	—
1111	C₄	—	2	1	no	—
1112	C₄	—	2	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	2	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	2	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	2	no	—
1122	C₄	C₂×C₁₃×#137	1	2	yes	—
1123	C₄	C₂×C₁₃×#137	1	2	yes	—
1124	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1125	C₄	C₁₃×#585	1	1	yes	characteristic
1126	C₂	—	2	2	no	—
1127	C₂	—	4	2	no	—
1128	C₂	—	4	2	no	—
1129	C₂	—	8	1	no	—
1130	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
1131	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
1132	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
prime radical	C₁₃×#3475	C₂
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. Q₈×C₁₃×#41	C₂	semidirect
3. C₁₃×#3398	C₂	semidirect
4. C₁₃×#3385	C₂	semidirect
5. C₁₃×#3372	C₂	semidirect
6. C₁₃×#3369	C₂	semidirect
7. C₁₃×#3357	C₂	semidirect
8. C₁₃×#3344	C₂	semidirect
9. C₁₃×#3331	C₂	semidirect
10. C₁₃×#3329	C₂	semidirect
11. C₁₃×#3314	C₂	semidirect
12. C₁₃×#3312	C₂	semidirect
13. C₁₃×#3276	C₂	semidirect
14. C₁₃×#3266	C₂	semidirect
15. C₁₃×#3172	C₂	semidirect
16. C₁₃×#3170	C₂	semidirect
17. C₁₃×#3108	C₂	semidirect
18. C₁₃×#3107	C₂	semidirect
19. C₁₃×#3104	C₂	semidirect
20. C₁₃×#3101	C₂	semidirect
21. C₁₃×#2965	C₂	semidirect
22. C₄×C₁₃×#137	C₂	semidirect
23. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
26. Q₈²×C₁₃	C₂²	semidirect
28. C₁₃×#557	C₂²	semidirect
35. C₁₃×#554	C₂²	semidirect
41. D₄×Q₈×C₁₃	C₂²	semidirect
48. C₁₃×#533	C₂²	semidirect
56. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
59. C₁₃×#501	C₂²	semidirect
60. C₁₃×#500	C₂²	semidirect
62. C₁₃×#494	C₂²	semidirect
63. C₁₃×#491	C₂²	semidirect
65. C₁₃×#487	C₂²	semidirect
66. C₁₃×#487	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
68. C₁₃×#485	C₂²	semidirect
71. C₁₃×#483	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
74. C₁₃×#479	C₂²	semidirect
75. C₁₃×#477	C₂²	semidirect
76. C₁₃×#477	C₂²	semidirect
79. C₁₃×#475	C₂²	semidirect
81. C₁₃×#470	C₂²	semidirect
82. C₁₃×#470	C₂²	semidirect
89. C₁₃×#462	C₂²	semidirect
90. C₁₃×#462	C₂²	semidirect
91. C₁₃×#462	C₂²	semidirect
98. C₁₃×#451	C₂²	semidirect
101. C₁₃×#446	C₂²	semidirect
102. C₁₃×#446	C₂²	semidirect
103. C₁₃×#441	C₂²	semidirect
104. C₁₃×#441	C₂²	semidirect
107. C₄×C₁₃×Q₁₆	C₂²	semidirect
108. C₄×C₁₃×Q₁₆	C₂²	semidirect
109. C₄×C₁₃×Q₁₆	C₂²	semidirect
110. C₄×C₁₃×Q₁₆	C₂²	semidirect
121. C₁₃×#436	C₂²	semidirect
122. C₁₃×#436	C₂²	semidirect
126. C₁₃×#431	C₂²	semidirect
127. C₁₃×#428	C₂²	semidirect
129. C₁₃×#419	C₂²	semidirect
133. C₄×C₁₃×M₁₆	C₂²	semidirect
314. #61438	C₁₃	direct (N × H)
369. C₁₃×SD₁₆	#41	semidirect
452. Q₈×#41	C₂×C₁₃	semidirect
454. #3398	C₂×C₁₃	semidirect
455. #3385	C₂×C₁₃	semidirect
456. #3372	C₂×C₁₃	semidirect
457. #3369	C₂×C₁₃	semidirect
458. #3357	C₂×C₁₃	semidirect
459. #3344	C₂×C₁₃	semidirect
460. #3331	C₂×C₁₃	semidirect
461. #3329	C₂×C₁₃	semidirect
462. #3314	C₂×C₁₃	semidirect
463. #3312	C₂×C₁₃	semidirect
464. #3276	C₂×C₁₃	semidirect
465. #3266	C₂×C₁₃	semidirect
466. #3172	C₂×C₁₃	semidirect
467. #3170	C₂×C₁₃	semidirect
468. #3108	C₂×C₁₃	semidirect
469. #3107	C₂×C₁₃	semidirect
470. #3104	C₂×C₁₃	semidirect
471. #3101	C₂×C₁₃	semidirect
472. #2965	C₂×C₁₃	semidirect
473. C₄×#137	C₂×C₁₃	semidirect
474. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
533. C₂×C₄×C₁₃	#137	semidirect
551. Q₈²	C₂²×C₁₃	semidirect
553. #557	C₂²×C₁₃	semidirect
560. #554	C₂²×C₁₃	semidirect
566. D₄×Q₈	C₂²×C₁₃	semidirect
573. #533	C₂²×C₁₃	semidirect
581. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
584. #501	C₂²×C₁₃	semidirect
585. #500	C₂²×C₁₃	semidirect
587. #494	C₂²×C₁₃	semidirect
588. #491	C₂²×C₁₃	semidirect
590. #487	C₂²×C₁₃	semidirect
591. #487	C₂²×C₁₃	semidirect
592. #485	C₂²×C₁₃	semidirect
593. #485	C₂²×C₁₃	semidirect
596. #483	C₂²×C₁₃	semidirect
598. #479	C₂²×C₁₃	semidirect
599. #479	C₂²×C₁₃	semidirect
600. #477	C₂²×C₁₃	semidirect
601. #477	C₂²×C₁₃	semidirect
604. #475	C₂²×C₁₃	semidirect
606. #470	C₂²×C₁₃	semidirect
607. #470	C₂²×C₁₃	semidirect
614. #462	C₂²×C₁₃	semidirect
615. #462	C₂²×C₁₃	semidirect
616. #462	C₂²×C₁₃	semidirect
623. #451	C₂²×C₁₃	semidirect
626. #446	C₂²×C₁₃	semidirect
627. #446	C₂²×C₁₃	semidirect
628. #441	C₂²×C₁₃	semidirect
629. #441	C₂²×C₁₃	semidirect
632. C₄×Q₁₆	C₂²×C₁₃	semidirect
633. C₄×Q₁₆	C₂²×C₁₃	semidirect
634. C₄×Q₁₆	C₂²×C₁₃	semidirect
635. C₄×Q₁₆	C₂²×C₁₃	semidirect
646. #436	C₂²×C₁₃	semidirect
647. #436	C₂²×C₁₃	semidirect
651. #431	C₂²×C₁₃	semidirect
652. #428	C₂²×C₁₃	semidirect
654. #419	C₂²×C₁₃	semidirect
658. C₄×M₁₆	C₂²×C₁₃	semidirect
934. SD₁₆	C₁₃×#41	semidirect
1017. C₁₃	#61438	direct (N × H)
1076. C₂×C₄	C₁₃×#137	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
Q₈×C₁₃×#41	2
C₁₃×#3475	2
C₁₃×#3398	2
C₁₃×#3385	2
C₁₃×#3372	2
C₁₃×#3369	2
C₁₃×#3357	2
C₁₃×#3344	2
C₁₃×#3331	2
C₁₃×#3329	2
C₁₃×#3314	2
C₁₃×#3312	2
C₁₃×#3276	2
C₁₃×#3266	2
C₁₃×#3172	2
C₁₃×#3170	2
C₁₃×#3108	2
C₁₃×#3107	2
C₁₃×#3104	2
C₁₃×#3101	2
C₁₃×#2965	2
C₄×C₁₃×#137	2
C₂×C₄×C₁₃×SD₁₆	2
#61438	13

Subgroups — C13×#61438 #15747777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61438 #15747777