Subgroups — C₁₃×#62122 #15748461

Order 3328.

1780 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3350	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3347	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3319	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3311	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3256	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3240	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3114	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3077	C₂	1	2	yes	maximal, complemented
22	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#559	C₂²	1	1	yes	characteristic
25	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#556	—	2	1	no	—
27	C₁₃×#556	—	2	2	no	—
28	C₁₃×#556	C₂²	1	1	yes	characteristic
29	C₁₃×#556	C₂²	1	2	yes	complemented
30	C₁₃×#555	C₂²	1	1	yes	characteristic
31	C₁₃×#555	C₂²	1	2	yes	complemented
32	C₁₃×#554	C₂²	1	1	yes	characteristic
33	C₁₃×#554	C₂²	1	1	yes	characteristic
34	C₁₃×#553	—	2	1	no	—
35	C₁₃×#553	C₂²	1	2	yes	—
36	C₁₃×#551	—	2	2	no	—
37	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#548	—	2	1	no	—
39	C₁₃×#546	—	2	1	no	—
40	C₁₃×#546	C₂²	1	2	yes	—
41	D₄²×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#542	—	2	1	no	—
43	C₁₃×#542	—	2	2	no	—
44	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#533	C₂²	1	2	yes	complemented
46	C₁₃×#532	C₂²	1	1	yes	characteristic
47	C₁₃×#529	—	2	1	no	—
48	C₁₃×#529	C₂²	1	2	yes	—
49	C₁₃×#529	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#529	C₂²	1	2	yes	complemented
51	C₁₃×#525	—	2	2	no	—
52	C₁₃×#519	—	2	1	no	—
53	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
54	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₁₃	—	2	1	no	—
56	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
57	C₁₃×#501	C₂²	1	2	yes	complemented
58	C₁₃×#501	C₂²	1	2	yes	complemented
59	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#489	C₂²	1	2	yes	complemented
62	C₁₃×#489	C₂²	1	2	yes	complemented
63	C₁₃×#486	C₂²	1	1	yes	characteristic
64	C₁₃×#486	C₂²	1	1	yes	characteristic
65	C₁₃×#485	C₂²	1	2	yes	complemented
66	C₁₃×#485	C₂²	1	2	yes	complemented
67	C₁₃×#485	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#483	C₂²	1	2	yes	complemented
69	C₁₃×#482	C₂²	1	2	yes	—
70	C₁₃×#482	C₂²	1	2	yes	—
71	C₁₃×#482	C₂²	1	2	yes	complemented
72	C₁₃×#482	C₂²	1	2	yes	complemented
73	C₁₃×#482	C₂²	1	1	yes	characteristic, complemented
74	C₁₃×#480	C₂²	1	2	yes	complemented
75	C₁₃×#479	C₂²	1	2	yes	complemented
76	C₁₃×#479	C₂²	1	2	yes	complemented
77	C₁₃×#479	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#478	C₂²	1	2	yes	—
79	C₁₃×#478	C₂²	1	1	yes	characteristic
80	C₁₃×#478	C₂²	1	2	yes	complemented
81	C₁₃×#478	C₂²	1	2	yes	complemented
82	C₁₃×#478	C₂²	1	2	yes	complemented
83	C₁₃×#478	C₂²	1	2	yes	complemented
84	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
85	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
86	C₁₃×#476	C₂²	1	2	yes	—
87	C₁₃×#476	C₂²	1	1	yes	characteristic
88	C₁₃×#476	C₂²	1	2	yes	complemented
89	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#474	C₂²	1	2	yes	—
92	C₁₃×#474	C₂²	1	1	yes	characteristic
93	C₁₃×#474	C₂²	1	2	yes	complemented
94	C₁₃×#470	C₂²	1	2	yes	complemented
95	C₁₃×#469	C₂²	1	2	yes	—
96	C₁₃×#468	C₂²	1	2	yes	—
97	C₁₃×#468	C₂²	1	2	yes	complemented
98	C₁₃×#466	C₂²	1	2	yes	complemented
99	C₁₃×#465	C₂²	1	2	yes	complemented
100	C₁₃×#464	C₂²	1	2	yes	complemented
101	C₁₃×#464	C₂²	1	1	yes	characteristic, complemented
102	C₁₃×#463	C₂²	1	1	yes	characteristic
103	C₁₃×#463	C₂²	1	2	yes	complemented
104	C₁₃×#463	C₂²	1	2	yes	complemented
105	C₁₃×#460	C₂²	1	1	yes	characteristic
106	C₁₃×#459	C₂²	1	1	yes	characteristic
107	C₁₃×#452	C₂²	1	1	yes	characteristic
108	C₁₃×#450	C₂²	1	2	yes	—
109	C₁₃×#449	C₂²	1	1	yes	characteristic
110	C₁₃×#447	C₂²	1	2	yes	—
111	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
112	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
113	C₁₃×#442	C₂²	1	2	yes	—
114	C₁₃×#442	C₂²	1	2	yes	complemented
115	C₁₃×#440	C₂²	1	2	yes	—
116	C₁₃×#440	C₂²	1	2	yes	complemented
117	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
119	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
121	C₁₃×#436	C₂²	1	1	yes	characteristic
122	C₁₃×#436	C₂²	1	1	yes	characteristic
123	C₁₃×#435	C₂²	1	2	yes	complemented
124	C₁₃×#435	C₂²	1	2	yes	complemented
125	C₁₃×#432	C₂²	1	2	yes	complemented
126	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
127	C₁₃×#428	C₂²	1	2	yes	complemented
128	C₁₃×#428	C₂²	1	2	yes	complemented
129	C₁₃×#427	C₂²	1	2	yes	complemented
130	C₁₃×#423	C₂²	1	2	yes	complemented
131	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	C₁₃×#418	C₂²	1	2	yes	—
133	C₁₃×#418	C₂²	1	2	yes	—
134	C₁₃×#416	C₂²	1	2	yes	—
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
137	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₁₃	—	2	1	no	—
139	C₂²×D₄×C₁₃	—	2	1	no	—
140	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
141	C₂³×C₄×C₁₃	—	2	2	no	—
142	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
146	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×D₈	C₂³	1	2	yes	—
148	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
149	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
150	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
151	C₁₃×C₄⋊Q₈	—	2	1	no	—
152	C₁₃×C₄⋊Q₈	—	2	2	no	—
153	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
154	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₁₃×#127	C₂³	1	1	yes	characteristic
159	C₁₃×#126	—	2	2	no	—
160	C₁₃×#126	—	2	2	no	—
161	C₁₃×#126	—	2	2	no	—
162	C₁₃×#126	—	2	2	no	—
163	C₁₃×#126	—	2	2	no	—
164	C₁₃×#126	—	2	1	no	—
165	C₁₃×#126	—	2	2	no	—
166	C₁₃×#125	—	2	1	no	—
167	C₁₃×#125	C₂³	1	2	yes	—
168	C₁₃×#125	C₂³	1	1	yes	characteristic
169	C₁₃×#125	C₂³	1	2	yes	—
170	C₁₃×#124	—	2	1	no	—
171	C₁₃×#124	—	2	1	no	—
172	C₁₃×#124	—	2	2	no	—
173	C₁₃×#124	—	2	2	no	—
174	C₁₃×#124	—	2	2	no	—
175	C₁₃×#124	—	2	2	no	—
176	C₁₃×#124	—	2	1	no	—
177	C₁₃×#124	C₂³	1	1	yes	characteristic
178	C₁₃×#124	C₂³	1	2	yes	—
179	C₁₃×#123	—	2	2	no	—
180	C₁₃×#123	—	2	2	no	—
181	C₁₃×#123	—	2	1	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	2	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	1	no	—
192	C₁₃×C₂²⋊Q₈	—	2	2	no	—
193	C₁₃×C₂²⋊Q₈	—	2	2	no	—
194	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
196	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₁₃×#121	—	2	2	no	—
198	C₁₃×#121	—	2	1	no	—
199	C₁₃×#121	—	2	2	no	—
200	C₁₃×#121	—	2	1	no	—
201	C₁₃×#121	—	2	1	no	—
202	C₁₃×#121	—	2	2	no	—
203	C₁₃×#121	C₂³	1	2	yes	—
204	C₁₃×#121	C₂³	1	1	yes	characteristic
205	C₁₃×#121	C₂³	1	2	yes	—
206	C₁₃×#121	C₂³	1	2	yes	—
207	C₁₃×#120	—	2	2	no	—
208	C₁₃×#120	—	2	2	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	1	no	—
213	C₄×Q₈×C₁₃	—	2	2	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×D₄×C₁₃	—	2	1	no	—
223	C₄×D₄×C₁₃	—	2	2	no	—
224	C₄×D₄×C₁₃	—	2	1	no	—
225	C₄×D₄×C₁₃	—	2	1	no	—
226	C₄×D₄×C₁₃	—	2	1	no	—
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	D₄	1	1	yes	characteristic
234	C₄×D₄×C₁₃	D₄	1	2	yes	—
235	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₁₃	C₂³	1	2	yes	—
238	C₄×D₄×C₁₃	C₂³	1	2	yes	—
239	C₄×D₄×C₁₃	C₂³	1	2	yes	—
240	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₁₃	C₂³	1	2	yes	—
242	C₄×D₄×C₁₃	C₂³	1	2	yes	—
243	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
244	C₁₃×#117	—	2	1	no	—
245	C₁₃×#117	—	2	2	no	—
246	C₁₃×#117	—	2	1	no	—
247	C₁₃×#117	—	2	1	no	—
248	C₁₃×#117	—	2	2	no	—
249	C₁₃×#117	—	2	2	no	—
250	C₁₃×#117	D₄	1	2	yes	—
251	C₁₃×#117	D₄	1	1	yes	characteristic
252	C₁₃×#117	C₂³	1	2	yes	—
253	C₁₃×#117	C₂³	1	2	yes	—
254	C₁₃×#117	C₂³	1	2	yes	—
255	C₁₃×#117	C₂³	1	1	yes	characteristic
256	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
258	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₄²×C₁₃	—	2	1	no	—
261	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
263	C₁₃×#107	C₂³	1	2	yes	—
264	C₁₃×#107	C₂³	1	2	yes	—
265	C₁₃×#107	C₂³	1	1	yes	characteristic
266	C₁₃×#107	C₂³	1	2	yes	—
267	C₁₃×#107	C₂³	1	2	yes	—
268	C₁₃×#107	C₂³	1	1	yes	characteristic
269	C₁₃×#107	C₂³	1	2	yes	—
270	C₁₃×#106	C₂³	1	2	yes	—
271	C₁₃×#106	C₂³	1	2	yes	—
272	C₁₃×#106	C₂³	1	1	yes	characteristic
273	C₁₃×#106	C₂³	1	2	yes	—
274	C₁₃×#106	C₂³	1	2	yes	—
275	C₁₃×#106	C₂³	1	1	yes	characteristic
276	C₁₃×#106	C₂³	1	2	yes	—
277	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
278	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
283	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₁₃×#103	C₂³	1	2	yes	—
285	C₁₃×#103	C₂³	1	2	yes	—
286	C₁₃×#103	C₂³	1	1	yes	characteristic
287	C₁₃×#103	C₂³	1	1	yes	characteristic
288	C₁₃×#103	C₂³	1	1	yes	characteristic
289	C₁₃×#103	C₂³	1	1	yes	characteristic
290	C₁₃×#103	C₂³	1	2	yes	—
291	C₁₃×#102	C₂³	1	2	yes	—
292	C₁₃×#102	C₂³	1	2	yes	—
293	C₁₃×#102	C₂³	1	1	yes	characteristic
294	C₁₃×#102	C₂³	1	1	yes	characteristic
295	C₁₃×#102	C₂³	1	2	yes	—
296	C₁₃×#102	C₂³	1	2	yes	—
297	C₁₃×#102	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	2	yes	—
299	C₁₃×#102	C₂³	1	1	yes	characteristic
300	C₁₃×#102	C₂³	1	1	yes	characteristic
301	C₁₃×#102	C₂³	1	2	yes	—
302	C₁₃×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₁₃×#97	C₂³	1	2	yes	—
309	C₁₃×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
312	#62122	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₂⁴×C₁₃	—	2	2	no	—
314	C₁₃×#41	—	2	2	no	—
315	C₁₃×#41	—	4	2	no	—
316	C₁₃×#41	—	4	1	no	—
317	C₁₃×#41	—	8	2	no	—
318	C₂×Q₈×C₁₃	—	2	2	no	—
319	C₂×Q₈×C₁₃	—	2	1	no	—
320	C₂×Q₈×C₁₃	—	2	2	no	—
321	C₂×Q₈×C₁₃	—	2	1	no	—
322	C₂×Q₈×C₁₃	—	2	1	no	—
323	C₂×Q₈×C₁₃	—	4	4	no	—
324	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₁₃	—	2	4	no	—
328	C₂×D₄×C₁₃	—	2	1	no	—
329	C₂×D₄×C₁₃	—	2	2	no	—
330	C₂×D₄×C₁₃	—	2	2	no	—
331	C₂×D₄×C₁₃	—	2	1	no	—
332	C₂×D₄×C₁₃	—	2	2	no	—
333	C₂×D₄×C₁₃	—	2	2	no	—
334	C₂×D₄×C₁₃	—	2	1	no	—
335	C₂×D₄×C₁₃	—	2	1	no	—
336	C₂×D₄×C₁₃	—	4	2	no	—
337	C₂×D₄×C₁₃	—	4	4	no	—
338	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
339	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
340	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
341	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
342	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₁₃	—	2	2	no	—
344	C₂²×C₄×C₁₃	—	2	1	no	—
345	C₂²×C₄×C₁₃	—	2	1	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	2	no	—
350	C₂²×C₄×C₁₃	—	2	2	no	—
351	C₂²×C₄×C₁₃	—	2	2	no	—
352	C₂²×C₄×C₁₃	—	8	4	no	—
353	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
355	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
356	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
358	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
359	C₁₃×Q₁₆	—	4	1	no	—
360	C₁₃×SD₁₆	—	2	2	no	—
361	C₁₃×SD₁₆	—	4	2	no	—
362	C₁₃×SD₁₆	—	4	1	no	—
363	C₁₃×D₈	—	2	2	no	—
364	C₁₃×D₈	—	4	2	no	—
365	C₁₃×M₁₆	—	4	2	no	—
366	C₁₃×M₁₆	—	4	2	no	—
367	C₂×C₈×C₁₃	—	4	2	no	—
368	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
373	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
374	C₁₃×C₄⋊C₄	—	2	1	no	—
375	C₁₃×C₄⋊C₄	—	2	2	no	—
376	C₁₃×C₄⋊C₄	—	2	2	no	—
377	C₁₃×C₄⋊C₄	—	2	1	no	—
378	C₁₃×C₄⋊C₄	—	2	1	no	—
379	C₁₃×C₄⋊C₄	—	2	2	no	—
380	C₁₃×C₄⋊C₄	—	2	1	no	—
381	C₁₃×C₄⋊C₄	—	2	1	no	—
382	C₁₃×C₄⋊C₄	—	2	2	no	—
383	C₁₃×C₄⋊C₄	—	2	1	no	—
384	C₁₃×C₄⋊C₄	—	2	2	no	—
385	C₁₃×C₄⋊C₄	—	2	2	no	—
386	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
392	C₁₃×C₄⋊C₄	—	2	1	no	—
393	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
394	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
395	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
396	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
397	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
398	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
399	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
400	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
401	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
402	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
403	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₁₃×C₂²⋊C₄	—	2	2	no	—
405	C₁₃×C₂²⋊C₄	—	2	1	no	—
406	C₁₃×C₂²⋊C₄	—	2	2	no	—
407	C₁₃×C₂²⋊C₄	—	2	2	no	—
408	C₁₃×C₂²⋊C₄	—	2	2	no	—
409	C₁₃×C₂²⋊C₄	—	2	2	no	—
410	C₁₃×C₂²⋊C₄	—	2	1	no	—
411	C₁₃×C₂²⋊C₄	—	2	1	no	—
412	C₁₃×C₂²⋊C₄	—	2	2	no	—
413	C₁₃×C₂²⋊C₄	—	2	2	no	—
414	C₁₃×C₂²⋊C₄	—	2	2	no	—
415	C₁₃×C₂²⋊C₄	—	2	2	no	—
416	C₁₃×C₂²⋊C₄	—	2	2	no	—
417	C₁₃×C₂²⋊C₄	—	2	1	no	—
418	C₁₃×C₂²⋊C₄	—	2	2	no	—
419	C₁₃×C₂²⋊C₄	—	2	1	no	—
420	C₁₃×C₂²⋊C₄	—	2	1	no	—
421	C₁₃×C₂²⋊C₄	—	2	2	no	—
422	C₁₃×C₂²⋊C₄	—	2	2	no	—
423	C₁₃×C₂²⋊C₄	—	2	1	no	—
424	C₁₃×C₂²⋊C₄	—	2	2	no	—
425	C₁₃×C₂²⋊C₄	—	2	1	no	—
426	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
427	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
428	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
429	C₄²×C₁₃	—	2	1	no	—
430	C₄²×C₁₃	—	2	1	no	—
431	C₄²×C₁₃	—	2	1	no	—
432	C₄²×C₁₃	—	2	2	no	—
433	C₄²×C₁₃	—	2	2	no	—
434	C₄²×C₁₃	—	2	2	no	—
435	C₄²×C₁₃	—	2	2	no	—
436	C₄²×C₁₃	—	2	1	no	—
437	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₁₃	C₂×D₄	1	2	yes	—
439	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₁₃	C₂×D₄	1	2	yes	—
441	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
442	C₄²×C₁₃	C₂⁴	1	2	yes	—
443	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
444	#3518	C₂×C₁₃	1	1	yes	characteristic, complemented
445	#3481	C₂×C₁₃	1	1	yes	characteristic, complemented
446	#3385	C₂×C₁₃	1	1	yes	characteristic, complemented
447	#3384	C₂×C₁₃	1	1	yes	characteristic, complemented
448	#3375	C₂×C₁₃	1	1	yes	characteristic, complemented
449	#3373	C₂×C₁₃	1	1	yes	characteristic, complemented
450	#3357	C₂×C₁₃	1	1	yes	characteristic, complemented
451	#3356	C₂×C₁₃	1	1	yes	characteristic, complemented
452	#3350	C₂×C₁₃	1	2	yes	complemented
453	#3347	C₂×C₁₃	1	2	yes	complemented
454	#3325	C₂×C₁₃	1	1	yes	characteristic, complemented
455	#3324	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#3319	C₂×C₁₃	1	2	yes	complemented
457	#3311	C₂×C₁₃	1	2	yes	complemented
458	#3256	C₂×C₁₃	1	2	yes	complemented
459	#3247	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3240	C₂×C₁₃	1	2	yes	complemented
461	#3228	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3114	C₂×C₁₃	1	2	yes	complemented
463	#3102	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3077	C₂×C₁₃	1	2	yes	complemented
465	#3076	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#2989	C₂×C₁₃	1	1	yes	characteristic, complemented
467	C₂³×C₁₃	—	2	1	no	—
468	C₂³×C₁₃	—	2	1	no	—
469	C₂³×C₁₃	—	2	2	no	—
470	C₂³×C₁₃	—	4	4	no	—
471	C₂³×C₁₃	—	4	4	no	—
472	C₂³×C₁₃	—	8	2	no	—
473	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
474	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
475	Q₈×C₁₃	—	2	2	no	—
476	Q₈×C₁₃	—	2	1	no	—
477	Q₈×C₁₃	—	2	1	no	—
478	Q₈×C₁₃	—	2	1	no	—
479	Q₈×C₁₃	—	2	1	no	—
480	Q₈×C₁₃	—	4	4	no	—
481	Q₈×C₁₃	—	4	2	no	—
482	Q₈×C₁₃	—	8	2	no	—
483	Q₈×C₁₃	—	8	1	no	—
484	Q₈×C₁₃	—	8	1	no	—
485	D₄×C₁₃	—	2	2	no	—
486	D₄×C₁₃	—	2	1	no	—
487	D₄×C₁₃	—	2	2	no	—
488	D₄×C₁₃	—	2	1	no	—
489	D₄×C₁₃	—	2	1	no	—
490	D₄×C₁₃	—	2	2	no	—
491	D₄×C₁₃	—	4	2	no	—
492	D₄×C₁₃	—	4	4	no	—
493	D₄×C₁₃	—	4	2	no	—
494	D₄×C₁₃	—	4	4	no	—
495	D₄×C₁₃	—	4	2	no	—
496	D₄×C₁₃	—	8	1	no	—
497	D₄×C₁₃	—	8	2	no	—
498	D₄×C₁₃	—	8	1	no	—
499	D₄×C₁₃	—	8	2	no	—
500	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
501	C₂×C₄×C₁₃	—	2	2	no	—
502	C₂×C₄×C₁₃	—	2	2	no	—
503	C₂×C₄×C₁₃	—	2	1	no	—
504	C₂×C₄×C₁₃	—	2	1	no	—
505	C₂×C₄×C₁₃	—	2	2	no	—
506	C₂×C₄×C₁₃	—	2	1	no	—
507	C₂×C₄×C₁₃	—	2	2	no	—
508	C₂×C₄×C₁₃	—	2	1	no	—
509	C₂×C₄×C₁₃	—	2	1	no	—
510	C₂×C₄×C₁₃	—	2	1	no	—
511	C₂×C₄×C₁₃	—	2	2	no	—
512	C₂×C₄×C₁₃	—	2	1	no	—
513	C₂×C₄×C₁₃	—	2	1	no	—
514	C₂×C₄×C₁₃	—	2	2	no	—
515	C₂×C₄×C₁₃	—	4	2	no	—
516	C₂×C₄×C₁₃	—	4	2	no	—
517	C₂×C₄×C₁₃	—	4	1	no	—
518	C₂×C₄×C₁₃	—	4	2	no	—
519	C₂×C₄×C₁₃	—	4	2	no	—
520	C₂×C₄×C₁₃	—	4	4	no	—
521	C₂×C₄×C₁₃	—	4	4	no	—
522	C₂×C₄×C₁₃	—	4	2	no	—
523	C₂×C₄×C₁₃	—	4	2	no	—
524	C₂×C₄×C₁₃	—	8	2	no	—
525	C₂×C₄×C₁₃	—	8	2	no	—
526	C₂×C₄×C₁₃	—	8	2	no	—
527	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
536	C₈×C₁₃	—	2	1	no	—
537	C₈×C₁₃	—	2	1	no	—
538	C₈×C₁₃	—	2	2	no	—
539	C₈×C₁₃	—	2	2	no	—
540	C₈×C₁₃	—	2	1	no	—
541	C₈×C₁₃	—	2	1	no	—
542	#559	C₂²×C₁₃	1	1	yes	characteristic
543	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
544	#556	—	2	1	no	—
545	#556	—	2	2	no	—
546	#556	C₂²×C₁₃	1	1	yes	characteristic
547	#556	C₂²×C₁₃	1	2	yes	complemented
548	#555	C₂²×C₁₃	1	1	yes	characteristic
549	#555	C₂²×C₁₃	1	2	yes	complemented
550	#554	C₂²×C₁₃	1	1	yes	characteristic
551	#554	C₂²×C₁₃	1	1	yes	characteristic
552	#553	—	2	1	no	—
553	#553	C₂²×C₁₃	1	2	yes	—
554	#551	—	2	2	no	—
555	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
556	#548	—	2	1	no	—
557	#546	—	2	1	no	—
558	#546	C₂²×C₁₃	1	2	yes	—
559	D₄²	C₂²×C₁₃	1	1	yes	characteristic
560	#542	—	2	1	no	—
561	#542	—	2	2	no	—
562	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
563	#533	C₂²×C₁₃	1	2	yes	complemented
564	#532	C₂²×C₁₃	1	1	yes	characteristic
565	#529	—	2	1	no	—
566	#529	C₂²×C₁₃	1	2	yes	—
567	#529	C₂²×C₁₃	1	1	yes	characteristic, complemented
568	#529	C₂²×C₁₃	1	2	yes	complemented
569	#525	—	2	2	no	—
570	#519	—	2	1	no	—
571	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
572	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
573	C₂×C₄×D₄	—	2	1	no	—
574	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
575	#501	C₂²×C₁₃	1	2	yes	complemented
576	#501	C₂²×C₁₃	1	2	yes	complemented
577	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
578	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
579	#489	C₂²×C₁₃	1	2	yes	complemented
580	#489	C₂²×C₁₃	1	2	yes	complemented
581	#486	C₂²×C₁₃	1	1	yes	characteristic
582	#486	C₂²×C₁₃	1	1	yes	characteristic
583	#485	C₂²×C₁₃	1	1	yes	characteristic, complemented
584	#485	C₂²×C₁₃	1	2	yes	complemented
585	#485	C₂²×C₁₃	1	2	yes	complemented
586	#483	C₂²×C₁₃	1	2	yes	complemented
587	#482	C₂²×C₁₃	1	2	yes	—
588	#482	C₂²×C₁₃	1	2	yes	—
589	#482	C₂²×C₁₃	1	1	yes	characteristic, complemented
590	#482	C₂²×C₁₃	1	2	yes	complemented
591	#482	C₂²×C₁₃	1	2	yes	complemented
592	#480	C₂²×C₁₃	1	2	yes	complemented
593	#479	C₂²×C₁₃	1	2	yes	complemented
594	#479	C₂²×C₁₃	1	2	yes	complemented
595	#479	C₂²×C₁₃	1	1	yes	characteristic, complemented
596	#478	C₂²×C₁₃	1	2	yes	—
597	#478	C₂²×C₁₃	1	1	yes	characteristic
598	#478	C₂²×C₁₃	1	2	yes	complemented
599	#478	C₂²×C₁₃	1	2	yes	complemented
600	#478	C₂²×C₁₃	1	2	yes	complemented
601	#478	C₂²×C₁₃	1	2	yes	complemented
602	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
603	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
604	#476	C₂²×C₁₃	1	1	yes	characteristic
605	#476	C₂²×C₁₃	1	2	yes	—
606	#476	C₂²×C₁₃	1	2	yes	complemented
607	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
608	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
609	#474	C₂²×C₁₃	1	1	yes	characteristic
610	#474	C₂²×C₁₃	1	2	yes	—
611	#474	C₂²×C₁₃	1	2	yes	complemented
612	#470	C₂²×C₁₃	1	2	yes	complemented
613	#469	C₂²×C₁₃	1	2	yes	—
614	#468	C₂²×C₁₃	1	2	yes	—
615	#468	C₂²×C₁₃	1	2	yes	complemented
616	#466	C₂²×C₁₃	1	2	yes	complemented
617	#465	C₂²×C₁₃	1	2	yes	complemented
618	#464	C₂²×C₁₃	1	1	yes	characteristic, complemented
619	#464	C₂²×C₁₃	1	2	yes	complemented
620	#463	C₂²×C₁₃	1	1	yes	characteristic
621	#463	C₂²×C₁₃	1	2	yes	complemented
622	#463	C₂²×C₁₃	1	2	yes	complemented
623	#460	C₂²×C₁₃	1	1	yes	characteristic
624	#459	C₂²×C₁₃	1	1	yes	characteristic
625	#452	C₂²×C₁₃	1	1	yes	characteristic
626	#450	C₂²×C₁₃	1	2	yes	—
627	#449	C₂²×C₁₃	1	1	yes	characteristic
628	#447	C₂²×C₁₃	1	2	yes	—
629	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
630	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
631	#442	C₂²×C₁₃	1	2	yes	—
632	#442	C₂²×C₁₃	1	2	yes	complemented
633	#440	C₂²×C₁₃	1	2	yes	—
634	#440	C₂²×C₁₃	1	2	yes	complemented
635	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
636	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
637	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
638	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
639	#436	C₂²×C₁₃	1	1	yes	characteristic
640	#436	C₂²×C₁₃	1	1	yes	characteristic
641	#435	C₂²×C₁₃	1	2	yes	complemented
642	#435	C₂²×C₁₃	1	2	yes	complemented
643	#432	C₂²×C₁₃	1	2	yes	complemented
644	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
645	#428	C₂²×C₁₃	1	2	yes	complemented
646	#428	C₂²×C₁₃	1	2	yes	complemented
647	#427	C₂²×C₁₃	1	2	yes	complemented
648	#423	C₂²×C₁₃	1	2	yes	complemented
649	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
650	#418	C₂²×C₁₃	1	2	yes	—
651	#418	C₂²×C₁₃	1	2	yes	—
652	#416	C₂²×C₁₃	1	2	yes	—
653	C₂²×C₁₃	—	2	2	no	—
654	C₂²×C₁₃	—	2	1	no	—
655	C₂²×C₁₃	—	2	1	no	—
656	C₂²×C₁₃	—	2	2	no	—
657	C₂²×C₁₃	—	2	2	no	—
658	C₂²×C₁₃	—	2	1	no	—
659	C₂²×C₁₃	—	2	2	no	—
660	C₂²×C₁₃	—	4	1	no	—
661	C₂²×C₁₃	—	4	1	no	—
662	C₂²×C₁₃	—	4	2	no	—
663	C₂²×C₁₃	—	4	1	no	—
664	C₂²×C₁₃	—	4	2	no	—
665	C₂²×C₁₃	—	4	1	no	—
666	C₂²×C₁₃	—	4	1	no	—
667	C₂²×C₁₃	—	4	2	no	—
668	C₂²×C₁₃	—	8	8	no	—
669	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
670	C₄×C₁₃	—	2	1	no	—
671	C₄×C₁₃	—	2	2	no	—
672	C₄×C₁₃	—	2	1	no	—
673	C₄×C₁₃	—	2	1	no	—
674	C₄×C₁₃	—	2	2	no	—
675	C₄×C₁₃	—	2	1	no	—
676	C₄×C₁₃	—	2	2	no	—
677	C₄×C₁₃	—	4	1	no	—
678	C₄×C₁₃	—	4	2	no	—
679	C₄×C₁₃	—	4	2	no	—
680	C₄×C₁₃	—	4	1	no	—
681	C₄×C₁₃	—	4	1	no	—
682	C₄×C₁₃	—	4	1	no	—
683	C₄×C₁₃	—	4	1	no	—
684	C₄×C₁₃	—	4	2	no	—
685	C₄×C₁₃	—	4	1	no	—
686	C₄×C₁₃	#575	1	2	yes	—
687	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
688	C₄×C₁₃	#585	1	1	yes	characteristic
689	C₂×#41	—	2	1	no	—
690	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
691	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
692	C₂²×Q₈	—	2	1	no	—
693	C₂²×D₄	—	2	1	no	—
694	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
695	C₂³×C₄	—	2	2	no	—
696	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
697	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
698	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
699	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
700	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
701	C₂×D₈	C₂³×C₁₃	1	2	yes	—
702	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
703	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
704	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
705	C₄⋊Q₈	—	2	1	no	—
706	C₄⋊Q₈	—	2	2	no	—
707	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
708	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
710	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
711	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
712	#127	C₂³×C₁₃	1	1	yes	characteristic
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	1	no	—
719	#126	—	2	2	no	—
720	#125	—	2	1	no	—
721	#125	C₂³×C₁₃	1	2	yes	—
722	#125	C₂³×C₁₃	1	1	yes	characteristic
723	#125	C₂³×C₁₃	1	2	yes	—
724	#124	—	2	1	no	—
725	#124	—	2	1	no	—
726	#124	—	2	2	no	—
727	#124	—	2	2	no	—
728	#124	—	2	2	no	—
729	#124	—	2	2	no	—
730	#124	—	2	1	no	—
731	#124	C₂³×C₁₃	1	2	yes	—
732	#124	C₂³×C₁₃	1	1	yes	characteristic
733	#123	—	2	2	no	—
734	#123	—	2	2	no	—
735	#123	—	2	1	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	C₂²⋊Q₈	—	2	1	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	1	no	—
742	C₂²⋊Q₈	—	2	1	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
749	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
750	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
751	#121	—	2	2	no	—
752	#121	—	2	1	no	—
753	#121	—	2	2	no	—
754	#121	—	2	1	no	—
755	#121	—	2	1	no	—
756	#121	—	2	2	no	—
757	#121	C₂³×C₁₃	1	2	yes	—
758	#121	C₂³×C₁₃	1	2	yes	—
759	#121	C₂³×C₁₃	1	1	yes	characteristic
760	#121	C₂³×C₁₃	1	2	yes	—
761	#120	—	2	2	no	—
762	#120	—	2	2	no	—
763	C₄×Q₈	—	2	1	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	2	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	2	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	2	no	—
770	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
771	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
772	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
774	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
775	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	1	no	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	—	2	2	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	2	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	2	no	—
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
788	C₄×D₄	D₄×C₁₃	1	2	yes	—
789	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
790	C₄×D₄	C₂³×C₁₃	1	2	yes	—
791	C₄×D₄	C₂³×C₁₃	1	2	yes	—
792	C₄×D₄	C₂³×C₁₃	1	2	yes	—
793	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
794	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
795	C₄×D₄	C₂³×C₁₃	1	2	yes	—
796	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₁₃	1	2	yes	—
798	#117	—	2	1	no	—
799	#117	—	2	2	no	—
800	#117	—	2	1	no	—
801	#117	—	2	1	no	—
802	#117	—	2	2	no	—
803	#117	—	2	2	no	—
804	#117	D₄×C₁₃	1	2	yes	—
805	#117	D₄×C₁₃	1	1	yes	characteristic
806	#117	C₂³×C₁₃	1	1	yes	characteristic
807	#117	C₂³×C₁₃	1	2	yes	—
808	#117	C₂³×C₁₃	1	2	yes	—
809	#117	C₂³×C₁₃	1	2	yes	—
810	C₂×C₄⋊C₄	—	2	1	no	—
811	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
812	C₂×C₂²⋊C₄	—	2	2	no	—
813	C₂×C₂²⋊C₄	—	2	2	no	—
814	C₂×C₄²	—	2	1	no	—
815	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
816	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
817	#107	C₂³×C₁₃	1	2	yes	—
818	#107	C₂³×C₁₃	1	2	yes	—
819	#107	C₂³×C₁₃	1	1	yes	characteristic
820	#107	C₂³×C₁₃	1	2	yes	—
821	#107	C₂³×C₁₃	1	2	yes	—
822	#107	C₂³×C₁₃	1	1	yes	characteristic
823	#107	C₂³×C₁₃	1	2	yes	—
824	#106	C₂³×C₁₃	1	2	yes	—
825	#106	C₂³×C₁₃	1	2	yes	—
826	#106	C₂³×C₁₃	1	1	yes	characteristic
827	#106	C₂³×C₁₃	1	2	yes	—
828	#106	C₂³×C₁₃	1	2	yes	—
829	#106	C₂³×C₁₃	1	1	yes	characteristic
830	#106	C₂³×C₁₃	1	2	yes	—
831	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
832	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
833	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
834	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
835	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
836	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
837	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
838	#103	C₂³×C₁₃	1	2	yes	—
839	#103	C₂³×C₁₃	1	2	yes	—
840	#103	C₂³×C₁₃	1	1	yes	characteristic
841	#103	C₂³×C₁₃	1	1	yes	characteristic
842	#103	C₂³×C₁₃	1	1	yes	characteristic
843	#103	C₂³×C₁₃	1	1	yes	characteristic
844	#103	C₂³×C₁₃	1	2	yes	—
845	#102	C₂³×C₁₃	1	2	yes	—
846	#102	C₂³×C₁₃	1	2	yes	—
847	#102	C₂³×C₁₃	1	1	yes	characteristic
848	#102	C₂³×C₁₃	1	1	yes	characteristic
849	#102	C₂³×C₁₃	1	2	yes	—
850	#102	C₂³×C₁₃	1	2	yes	—
851	#102	C₂³×C₁₃	1	2	yes	—
852	#102	C₂³×C₁₃	1	2	yes	—
853	#102	C₂³×C₁₃	1	1	yes	characteristic
854	#102	C₂³×C₁₃	1	1	yes	characteristic
855	#102	C₂³×C₁₃	1	2	yes	—
856	#102	C₂³×C₁₃	1	2	yes	—
857	#102	C₂³×C₁₃	1	2	yes	—
858	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
859	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
860	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
861	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
862	#97	C₂³×C₁₃	1	2	yes	—
863	#97	C₂³×C₁₃	1	2	yes	—
864	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
865	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
866	C₂×C₁₃	—	4	1	no	—
867	C₂×C₁₃	—	4	2	no	—
868	C₂×C₁₃	—	4	2	no	—
869	C₂×C₁₃	—	8	1	no	—
870	C₂×C₁₃	—	8	2	no	—
871	C₂×C₁₃	#3489	1	1	yes	characteristic
872	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
873	C₂×C₁₃	#3585	1	1	yes	characteristic
874	C₂⁴	—	2	2	no	—
875	#41	—	2	2	no	—
876	#41	—	4	2	no	—
877	#41	—	4	1	no	—
878	#41	—	8	2	no	—
879	C₂×Q₈	—	2	2	no	—
880	C₂×Q₈	—	2	1	no	—
881	C₂×Q₈	—	2	2	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	1	no	—
884	C₂×Q₈	—	4	4	no	—
885	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
886	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
887	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
888	C₂×D₄	—	2	4	no	—
889	C₂×D₄	—	2	1	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	4	2	no	—
898	C₂×D₄	—	4	4	no	—
899	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
900	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
901	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
902	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
903	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	8	4	no	—
914	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
915	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
916	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
917	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
919	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
920	Q₁₆	—	4	1	no	—
921	SD₁₆	—	2	2	no	—
922	SD₁₆	—	4	2	no	—
923	SD₁₆	—	4	1	no	—
924	D₈	—	2	2	no	—
925	D₈	—	4	2	no	—
926	M₁₆	—	4	2	no	—
927	M₁₆	—	4	2	no	—
928	C₂×C₈	—	4	2	no	—
929	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
930	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
934	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
955	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
956	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
957	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
958	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
959	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
960	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
961	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
962	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
963	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
964	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
988	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
989	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	2	no	—
994	C₄²	—	2	2	no	—
995	C₄²	—	2	2	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	1	no	—
998	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
999	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1000	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1001	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1002	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1003	C₄²	C₂⁴×C₁₃	1	2	yes	—
1004	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1005	C₁₃	#62122	1	1	yes	characteristic, direct product factor, Sylow
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	4	4	no	—
1010	C₂³	—	4	4	no	—
1011	C₂³	—	8	2	no	—
1012	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1013	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1014	Q₈	—	2	2	no	—
1015	Q₈	—	2	1	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	4	4	no	—
1020	Q₈	—	4	2	no	—
1021	Q₈	—	8	1	no	—
1022	Q₈	—	8	2	no	—
1023	Q₈	—	8	1	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	2	1	no	—
1026	D₄	—	2	2	no	—
1027	D₄	—	2	1	no	—
1028	D₄	—	2	1	no	—
1029	D₄	—	2	2	no	—
1030	D₄	—	4	2	no	—
1031	D₄	—	4	4	no	—
1032	D₄	—	4	2	no	—
1033	D₄	—	4	4	no	—
1034	D₄	—	4	2	no	—
1035	D₄	—	8	1	no	—
1036	D₄	—	8	2	no	—
1037	D₄	—	8	1	no	—
1038	D₄	—	8	2	no	—
1039	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	4	2	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	1	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	4	4	no	—
1060	C₂×C₄	—	4	4	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1068	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1069	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1070	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1072	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1073	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1074	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	2	no	—
1078	C₈	—	2	2	no	—
1079	C₈	—	2	1	no	—
1080	C₈	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	2	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	8	8	no	—
1097	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1098	C₄	—	2	1	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	1	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	1	no	—
1114	C₄	C₁₃×#575	1	2	yes	—
1115	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1116	C₄	C₁₃×#585	1	1	yes	characteristic
1117	C₂	—	4	2	no	—
1118	C₂	—	4	1	no	—
1119	C₂	—	4	2	no	—
1120	C₂	—	8	2	no	—
1121	C₂	—	8	1	no	—
1122	C₂	C₁₃×#3489	1	1	yes	characteristic
1123	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
1124	C₂	C₁₃×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3518	C₂	semidirect
2. C₁₃×#3481	C₂	semidirect
3. C₁₃×#3385	C₂	semidirect
4. C₁₃×#3384	C₂	semidirect
5. C₁₃×#3375	C₂	semidirect
6. C₁₃×#3373	C₂	semidirect
7. C₁₃×#3357	C₂	semidirect
8. C₁₃×#3356	C₂	semidirect
9. C₁₃×#3350	C₂	semidirect
10. C₁₃×#3347	C₂	semidirect
11. C₁₃×#3325	C₂	semidirect
12. C₁₃×#3324	C₂	semidirect
13. C₁₃×#3319	C₂	semidirect
14. C₁₃×#3311	C₂	semidirect
15. C₁₃×#3256	C₂	semidirect
16. C₁₃×#3247	C₂	semidirect
17. C₁₃×#3240	C₂	semidirect
18. C₁₃×#3228	C₂	semidirect
19. C₁₃×#3114	C₂	semidirect
20. C₁₃×#3102	C₂	semidirect
21. C₁₃×#3077	C₂	semidirect
22. C₁₃×#3076	C₂	semidirect
23. C₁₃×#2989	C₂	semidirect
25. Q₈²×C₁₃	C₂²	semidirect
29. C₁₃×#556	C₂²	semidirect
31. C₁₃×#555	C₂²	semidirect
37. D₄×Q₈×C₁₃	C₂²	semidirect
44. C₁₃×#533	C₂²	semidirect
45. C₁₃×#533	C₂²	semidirect
49. C₁₃×#529	C₂²	semidirect
50. C₁₃×#529	C₂²	semidirect
57. C₁₃×#501	C₂²	semidirect
58. C₁₃×#501	C₂²	semidirect
59. C₁₃×#500	C₂²	semidirect
60. C₁₃×#498	C₂²	semidirect
61. C₁₃×#489	C₂²	semidirect
62. C₁₃×#489	C₂²	semidirect
65. C₁₃×#485	C₂²	semidirect
66. C₁₃×#485	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
68. C₁₃×#483	C₂²	semidirect
71. C₁₃×#482	C₂²	semidirect
72. C₁₃×#482	C₂²	semidirect
73. C₁₃×#482	C₂²	semidirect
74. C₁₃×#480	C₂²	semidirect
75. C₁₃×#479	C₂²	semidirect
76. C₁₃×#479	C₂²	semidirect
77. C₁₃×#479	C₂²	semidirect
80. C₁₃×#478	C₂²	semidirect
81. C₁₃×#478	C₂²	semidirect
82. C₁₃×#478	C₂²	semidirect
83. C₁₃×#478	C₂²	semidirect
84. C₁₃×#477	C₂²	semidirect
85. C₁₃×#477	C₂²	semidirect
88. C₁₃×#476	C₂²	semidirect
89. C₁₃×#476	C₂²	semidirect
90. C₁₃×#475	C₂²	semidirect
93. C₁₃×#474	C₂²	semidirect
94. C₁₃×#470	C₂²	semidirect
97. C₁₃×#468	C₂²	semidirect
98. C₁₃×#466	C₂²	semidirect
99. C₁₃×#465	C₂²	semidirect
100. C₁₃×#464	C₂²	semidirect
101. C₁₃×#464	C₂²	semidirect
103. C₁₃×#463	C₂²	semidirect
104. C₁₃×#463	C₂²	semidirect
111. C₁₃×#446	C₂²	semidirect
112. C₁₃×#446	C₂²	semidirect
114. C₁₃×#442	C₂²	semidirect
116. C₁₃×#440	C₂²	semidirect
117. C₄×C₁₃×Q₁₆	C₂²	semidirect
119. C₄×C₁₃×SD₁₆	C₂²	semidirect
123. C₁₃×#435	C₂²	semidirect
124. C₁₃×#435	C₂²	semidirect
125. C₁₃×#432	C₂²	semidirect
126. C₁₃×#431	C₂²	semidirect
127. C₁₃×#428	C₂²	semidirect
128. C₁₃×#428	C₂²	semidirect
129. C₁₃×#427	C₂²	semidirect
130. C₁₃×#423	C₂²	semidirect
131. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
312. #62122	C₁₃	direct (N × H)
444. #3518	C₂×C₁₃	semidirect
445. #3481	C₂×C₁₃	semidirect
446. #3385	C₂×C₁₃	semidirect
447. #3384	C₂×C₁₃	semidirect
448. #3375	C₂×C₁₃	semidirect
449. #3373	C₂×C₁₃	semidirect
450. #3357	C₂×C₁₃	semidirect
451. #3356	C₂×C₁₃	semidirect
452. #3350	C₂×C₁₃	semidirect
453. #3347	C₂×C₁₃	semidirect
454. #3325	C₂×C₁₃	semidirect
455. #3324	C₂×C₁₃	semidirect
456. #3319	C₂×C₁₃	semidirect
457. #3311	C₂×C₁₃	semidirect
458. #3256	C₂×C₁₃	semidirect
459. #3247	C₂×C₁₃	semidirect
460. #3240	C₂×C₁₃	semidirect
461. #3228	C₂×C₁₃	semidirect
462. #3114	C₂×C₁₃	semidirect
463. #3102	C₂×C₁₃	semidirect
464. #3077	C₂×C₁₃	semidirect
465. #3076	C₂×C₁₃	semidirect
466. #2989	C₂×C₁₃	semidirect
543. Q₈²	C₂²×C₁₃	semidirect
547. #556	C₂²×C₁₃	semidirect
549. #555	C₂²×C₁₃	semidirect
555. D₄×Q₈	C₂²×C₁₃	semidirect
562. #533	C₂²×C₁₃	semidirect
563. #533	C₂²×C₁₃	semidirect
567. #529	C₂²×C₁₃	semidirect
568. #529	C₂²×C₁₃	semidirect
575. #501	C₂²×C₁₃	semidirect
576. #501	C₂²×C₁₃	semidirect
577. #500	C₂²×C₁₃	semidirect
578. #498	C₂²×C₁₃	semidirect
579. #489	C₂²×C₁₃	semidirect
580. #489	C₂²×C₁₃	semidirect
583. #485	C₂²×C₁₃	semidirect
584. #485	C₂²×C₁₃	semidirect
585. #485	C₂²×C₁₃	semidirect
586. #483	C₂²×C₁₃	semidirect
589. #482	C₂²×C₁₃	semidirect
590. #482	C₂²×C₁₃	semidirect
591. #482	C₂²×C₁₃	semidirect
592. #480	C₂²×C₁₃	semidirect
593. #479	C₂²×C₁₃	semidirect
594. #479	C₂²×C₁₃	semidirect
595. #479	C₂²×C₁₃	semidirect
598. #478	C₂²×C₁₃	semidirect
599. #478	C₂²×C₁₃	semidirect
600. #478	C₂²×C₁₃	semidirect
601. #478	C₂²×C₁₃	semidirect
602. #477	C₂²×C₁₃	semidirect
603. #477	C₂²×C₁₃	semidirect
606. #476	C₂²×C₁₃	semidirect
607. #476	C₂²×C₁₃	semidirect
608. #475	C₂²×C₁₃	semidirect
611. #474	C₂²×C₁₃	semidirect
612. #470	C₂²×C₁₃	semidirect
615. #468	C₂²×C₁₃	semidirect
616. #466	C₂²×C₁₃	semidirect
617. #465	C₂²×C₁₃	semidirect
618. #464	C₂²×C₁₃	semidirect
619. #464	C₂²×C₁₃	semidirect
621. #463	C₂²×C₁₃	semidirect
622. #463	C₂²×C₁₃	semidirect
629. #446	C₂²×C₁₃	semidirect
630. #446	C₂²×C₁₃	semidirect
632. #442	C₂²×C₁₃	semidirect
634. #440	C₂²×C₁₃	semidirect
635. C₄×Q₁₆	C₂²×C₁₃	semidirect
637. C₄×SD₁₆	C₂²×C₁₃	semidirect
641. #435	C₂²×C₁₃	semidirect
642. #435	C₂²×C₁₃	semidirect
643. #432	C₂²×C₁₃	semidirect
644. #431	C₂²×C₁₃	semidirect
645. #428	C₂²×C₁₃	semidirect
646. #428	C₂²×C₁₃	semidirect
647. #427	C₂²×C₁₃	semidirect
648. #423	C₂²×C₁₃	semidirect
649. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
1005. C₁₃	#62122	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×#3518	2
C₁₃×#3481	2
C₁₃×#3385	2
C₁₃×#3384	2
C₁₃×#3375	2
C₁₃×#3373	2
C₁₃×#3357	2
C₁₃×#3356	2
C₁₃×#3350	2
C₁₃×#3347	2
C₁₃×#3325	2
C₁₃×#3324	2
C₁₃×#3319	2
C₁₃×#3311	2
C₁₃×#3256	2
C₁₃×#3247	2
C₁₃×#3240	2
C₁₃×#3228	2
C₁₃×#3114	2
C₁₃×#3102	2
C₁₃×#3077	2
C₁₃×#3076	2
C₁₃×#2989	2
#62122	13

Subgroups — C13×#62122 #15748461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62122 #15748461