Subgroups — C₁₃×#62094 #15748433

Order 3328.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3517	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3397	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3377	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3322	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3320	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3308	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3278	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3271	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3268	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3257	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3254	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3221	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3124	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3046	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2995	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
22	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#135	C₂²	1	2	yes	—
24	C₁₃×#563	—	2	1	no	—
25	C₁₃×#562	—	2	1	no	—
26	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#556	C₂²	1	2	yes	—
28	C₁₃×#553	—	2	2	no	—
29	C₁₃×#553	C₂²	1	2	yes	—
30	C₁₃×#551	—	2	2	no	—
31	C₁₃×#550	—	2	1	no	—
32	C₁₃×#550	C₂²	1	2	yes	—
33	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
36	C₁₃×#548	C₂²	1	2	yes	—
37	C₁₃×#547	—	2	1	no	—
38	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#546	C₂²	1	2	yes	—
40	C₁₃×#543	—	2	1	no	—
41	C₁₃×#542	—	2	2	no	—
42	C₁₃×#542	C₂²	1	2	yes	—
43	C₁₃×#540	—	2	2	no	—
44	C₁₃×#540	C₂²	1	2	yes	complemented
45	C₁₃×#538	—	2	1	no	—
46	C₁₃×#536	C₂²	1	2	yes	—
47	C₁₃×#533	C₂²	1	1	yes	characteristic
48	C₁₃×#532	—	2	1	no	—
49	C₁₃×#532	C₂²	1	1	yes	characteristic
50	C₁₃×#529	—	2	1	no	—
51	C₁₃×#529	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
53	C₁₃×#520	C₂²	1	2	yes	complemented
54	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
55	C₁₃×#496	C₂²	1	2	yes	—
56	C₁₃×#496	C₂²	1	2	yes	—
57	C₁₃×#492	C₂²	1	2	yes	complemented
58	C₁₃×#491	C₂²	1	2	yes	complemented
59	C₁₃×#489	C₂²	1	2	yes	—
60	C₁₃×#488	C₂²	1	2	yes	—
61	C₁₃×#485	C₂²	1	2	yes	—
62	C₁₃×#484	C₂²	1	2	yes	complemented
63	C₁₃×#480	C₂²	1	2	yes	—
64	C₁₃×#479	C₂²	1	2	yes	complemented
65	C₁₃×#478	C₂²	1	2	yes	—
66	C₁₃×#477	C₂²	1	2	yes	complemented
67	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#474	C₂²	1	2	yes	complemented
70	C₁₃×#469	C₂²	1	2	yes	—
71	C₁₃×#468	C₂²	1	2	yes	—
72	C₁₃×#468	C₂²	1	2	yes	—
73	C₁₃×#468	C₂²	1	2	yes	complemented
74	C₁₃×#466	C₂²	1	2	yes	—
75	C₁₃×#465	C₂²	1	2	yes	complemented
76	C₁₃×#464	C₂²	1	2	yes	—
77	C₁₃×#464	C₂²	1	2	yes	—
78	C₁₃×#464	C₂²	1	2	yes	—
79	C₁₃×#463	C₂²	1	2	yes	—
80	C₁₃×#463	C₂²	1	2	yes	—
81	C₁₃×#463	C₂²	1	2	yes	—
82	C₁₃×#463	C₂²	1	2	yes	—
83	C₁₃×#463	C₂²	1	2	yes	—
84	C₁₃×#462	C₂²	1	2	yes	complemented
85	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
86	C₁₃×#461	C₂²	1	2	yes	complemented
87	C₁₃×#461	C₂²	1	2	yes	complemented
88	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#460	C₂²	1	2	yes	complemented
90	C₁₃×#460	C₂²	1	2	yes	complemented
91	C₁₃×#459	C₂²	1	2	yes	—
92	C₁₃×#452	C₂²	1	2	yes	—
93	C₁₃×#452	C₂²	1	2	yes	complemented
94	C₁₃×#449	C₂²	1	2	yes	—
95	C₁₃×#449	C₂²	1	2	yes	—
96	C₁₃×#449	C₂²	1	2	yes	—
97	C₁₃×#448	C₂²	1	2	yes	—
98	C₁₃×#448	C₂²	1	2	yes	complemented
99	C₁₃×#448	C₂²	1	2	yes	complemented
100	C₁₃×#447	C₂²	1	2	yes	—
101	C₁₃×#446	C₂²	1	2	yes	complemented
102	C₁₃×#441	C₂²	1	2	yes	complemented
103	C₁₃×#440	C₂²	1	2	yes	—
104	C₁₃×#440	C₂²	1	2	yes	complemented
105	C₁₃×#440	C₂²	1	2	yes	complemented
106	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
107	C₄×C₁₃×D₈	C₂²	1	2	yes	—
108	C₁₃×#436	C₂²	1	2	yes	—
109	C₁₃×#435	C₂²	1	2	yes	—
110	C₁₃×#435	C₂²	1	2	yes	complemented
111	C₁₃×#433	C₂²	1	2	yes	complemented
112	C₁₃×#432	C₂²	1	1	yes	characteristic
113	C₁₃×#424	C₂²	1	2	yes	complemented
114	C₁₃×#423	C₂²	1	1	yes	characteristic
115	C₁₃×#419	C₂²	1	1	yes	characteristic
116	C₁₃×#418	C₂²	1	1	yes	characteristic
117	C₁₃×#417	C₂²	1	2	yes	—
118	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
119	C₂×C₁₃×#41	—	2	1	no	—
120	C₂×C₁₃×#41	—	2	1	no	—
121	C₂×C₁₃×#41	—	2	1	no	—
122	C₂×C₁₃×#41	C₂³	1	2	yes	—
123	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
124	C₂×C₁₃×#41	C₂³	1	2	yes	—
125	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
126	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₁₃×#137	—	4	2	no	—
129	C₁₃×#137	—	4	4	no	—
130	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
131	C₁₃×#135	—	4	4	no	—
132	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
133	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
134	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
135	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
136	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
137	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
138	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
139	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
140	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
141	C₂×C₁₃×D₈	C₂³	1	2	yes	—
142	C₂×C₁₃×D₈	C₂³	1	2	yes	—
143	C₂×C₁₃×D₈	C₂³	1	2	yes	—
144	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
145	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
147	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
148	C₁₃×C₄⋊Q₈	—	2	1	no	—
149	C₁₃×C₄⋊Q₈	—	2	2	no	—
150	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
151	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
152	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₁₃×#127	—	2	1	no	—
155	C₁₃×#127	—	2	2	no	—
156	C₁₃×#127	C₂³	1	2	yes	—
157	C₁₃×#127	C₂³	1	1	yes	characteristic
158	C₁₃×#126	—	2	2	no	—
159	C₁₃×#126	—	2	2	no	—
160	C₁₃×#126	—	2	2	no	—
161	C₁₃×#126	—	2	2	no	—
162	C₁₃×#126	D₄	1	2	yes	—
163	C₁₃×#125	—	2	2	no	—
164	C₁₃×#125	—	2	1	no	—
165	C₁₃×#125	D₄	1	1	yes	characteristic
166	C₁₃×#125	C₂³	1	2	yes	—
167	C₁₃×#124	—	2	2	no	—
168	C₁₃×#124	—	2	2	no	—
169	C₁₃×#124	—	2	1	no	—
170	C₁₃×#124	—	2	1	no	—
171	C₁₃×#124	—	2	1	no	—
172	C₁₃×#124	D₄	1	1	yes	characteristic
173	C₁₃×#124	C₂³	1	2	yes	—
174	C₁₃×#124	C₂³	1	2	yes	—
175	C₁₃×#124	C₂³	1	2	yes	—
176	C₁₃×#123	—	2	2	no	—
177	C₁₃×#123	—	2	2	no	—
178	C₁₃×#123	—	2	2	no	—
179	C₁₃×#123	—	2	2	no	—
180	C₁₃×#123	—	2	2	no	—
181	C₁₃×#123	—	2	2	no	—
182	C₁₃×#123	—	2	2	no	—
183	C₁₃×#123	—	2	2	no	—
184	C₁₃×#123	D₄	1	2	yes	—
185	C₁₃×C₂²⋊Q₈	—	2	2	no	—
186	C₁₃×C₂²⋊Q₈	—	2	1	no	—
187	C₁₃×C₂²⋊Q₈	—	2	1	no	—
188	C₁₃×C₂²⋊Q₈	—	2	2	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	D₄	1	1	yes	characteristic
195	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₁₃×#121	—	2	2	no	—
198	C₁₃×#121	—	2	2	no	—
199	C₁₃×#121	—	2	1	no	—
200	C₁₃×#121	—	2	1	no	—
201	C₁₃×#121	—	2	2	no	—
202	C₁₃×#121	—	2	2	no	—
203	C₁₃×#121	—	2	2	no	—
204	C₁₃×#121	—	2	2	no	—
205	C₁₃×#121	—	2	2	no	—
206	C₁₃×#121	—	2	2	no	—
207	C₁₃×#121	—	2	2	no	—
208	C₁₃×#121	D₄	1	1	yes	characteristic
209	C₁₃×#121	C₂³	1	2	yes	—
210	C₁₃×#121	C₂³	1	2	yes	—
211	C₁₃×#121	C₂³	1	2	yes	—
212	C₁₃×#121	C₂³	1	2	yes	—
213	C₁₃×#120	—	2	2	no	—
214	C₄×Q₈×C₁₃	—	2	1	no	—
215	C₄×Q₈×C₁₃	—	2	1	no	—
216	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
217	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
218	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
219	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
222	C₄×D₄×C₁₃	—	2	2	no	—
223	C₄×D₄×C₁₃	—	2	1	no	—
224	C₄×D₄×C₁₃	—	2	1	no	—
225	C₄×D₄×C₁₃	—	2	1	no	—
226	C₄×D₄×C₁₃	—	2	2	no	—
227	C₄×D₄×C₁₃	—	2	2	no	—
228	C₄×D₄×C₁₃	—	2	2	no	—
229	C₄×D₄×C₁₃	—	2	2	no	—
230	C₄×D₄×C₁₃	—	2	2	no	—
231	C₄×D₄×C₁₃	—	2	1	no	—
232	C₄×D₄×C₁₃	C₂³	1	2	yes	—
233	C₄×D₄×C₁₃	C₂³	1	2	yes	—
234	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₁₃	C₂³	1	2	yes	—
236	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₁₃	C₂³	1	2	yes	—
238	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
239	C₁₃×#117	—	2	1	no	—
240	C₁₃×#117	—	2	2	no	—
241	C₁₃×#117	—	2	2	no	—
242	C₁₃×#117	—	2	1	no	—
243	C₁₃×#117	C₂³	1	1	yes	characteristic
244	C₁₃×#117	C₂³	1	2	yes	—
245	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
246	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
247	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
248	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₄²×C₁₃	—	2	1	no	—
251	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
252	C₁₃×#107	C₂³	1	2	yes	—
253	C₁₃×#107	C₂³	1	2	yes	—
254	C₁₃×#107	C₂³	1	2	yes	—
255	C₁₃×#106	C₂³	1	2	yes	—
256	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
257	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
258	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
260	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
261	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₁₃×#103	C₂³	1	2	yes	—
263	C₁₃×#103	C₂³	1	2	yes	—
264	C₁₃×#103	C₂³	1	2	yes	—
265	C₁₃×#103	C₂³	1	2	yes	—
266	C₁₃×#103	C₂³	1	2	yes	—
267	C₁₃×#103	C₂³	1	2	yes	—
268	C₁₃×#103	C₂³	1	2	yes	—
269	C₁₃×#103	C₂³	1	2	yes	—
270	C₁₃×#103	C₂³	1	2	yes	—
271	C₁₃×#102	C₂³	1	2	yes	—
272	C₁₃×#102	C₂³	1	2	yes	—
273	C₁₃×#102	C₂³	1	2	yes	—
274	C₁₃×#102	C₂³	1	2	yes	—
275	C₁₃×#102	C₂³	1	2	yes	—
276	C₁₃×#102	C₂³	1	2	yes	—
277	C₁₃×#102	C₂³	1	2	yes	—
278	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
279	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₁₃×#97	C₂³	1	2	yes	—
282	C₁₃×#97	C₂³	1	2	yes	—
283	C₄×C₈×C₁₃	C₂³	1	2	yes	—
284	#62094	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
285	C₂⁴×C₁₃	—	2	1	no	—
286	C₁₃×#41	—	2	4	no	—
287	C₁₃×#41	—	2	2	no	—
288	C₁₃×#41	—	4	1	no	—
289	C₁₃×#41	—	4	2	no	—
290	C₁₃×#41	—	4	2	no	—
291	C₁₃×#41	—	4	2	no	—
292	C₁₃×#41	—	8	2	no	—
293	C₁₃×#41	—	8	2	no	—
294	C₁₃×#41	—	8	2	no	—
295	C₂×Q₈×C₁₃	—	2	1	no	—
296	C₂×Q₈×C₁₃	—	2	1	no	—
297	C₂×Q₈×C₁₃	—	2	2	no	—
298	C₂×Q₈×C₁₃	—	2	1	no	—
299	C₂×Q₈×C₁₃	—	4	2	no	—
300	C₂×Q₈×C₁₃	—	4	1	no	—
301	C₂×Q₈×C₁₃	—	4	1	no	—
302	C₂×Q₈×C₁₃	—	4	2	no	—
303	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
305	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
306	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
307	C₂×D₄×C₁₃	—	2	1	no	—
308	C₂×D₄×C₁₃	—	2	2	no	—
309	C₂×D₄×C₁₃	—	2	2	no	—
310	C₂×D₄×C₁₃	—	2	2	no	—
311	C₂×D₄×C₁₃	—	2	2	no	—
312	C₂×D₄×C₁₃	—	2	2	no	—
313	C₂×D₄×C₁₃	—	2	2	no	—
314	C₂×D₄×C₁₃	—	2	1	no	—
315	C₂×D₄×C₁₃	—	2	1	no	—
316	C₂×D₄×C₁₃	—	2	2	no	—
317	C₂×D₄×C₁₃	—	2	2	no	—
318	C₂×D₄×C₁₃	—	2	1	no	—
319	C₂×D₄×C₁₃	—	4	1	no	—
320	C₂×D₄×C₁₃	—	4	1	no	—
321	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
322	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
323	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
324	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₁₃	—	2	1	no	—
327	C₂²×C₄×C₁₃	—	2	2	no	—
328	C₂²×C₄×C₁₃	—	2	2	no	—
329	C₂²×C₄×C₁₃	—	2	1	no	—
330	C₂²×C₄×C₁₃	—	2	1	no	—
331	C₂²×C₄×C₁₃	—	2	2	no	—
332	C₂²×C₄×C₁₃	—	2	1	no	—
333	C₂²×C₄×C₁₃	—	2	2	no	—
334	C₂²×C₄×C₁₃	—	2	2	no	—
335	C₂²×C₄×C₁₃	—	2	2	no	—
336	C₂²×C₄×C₁₃	—	2	2	no	—
337	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
338	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
339	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
341	C₁₃×Q₁₆	—	2	4	no	—
342	C₁₃×Q₁₆	—	2	4	no	—
343	C₁₃×SD₁₆	—	2	4	no	—
344	C₁₃×SD₁₆	—	4	2	no	—
345	C₁₃×SD₁₆	—	4	2	no	—
346	C₁₃×SD₁₆	—	4	2	no	—
347	C₁₃×SD₁₆	—	4	2	no	—
348	C₁₃×SD₁₆	—	4	2	no	—
349	C₁₃×SD₁₆	—	4	2	no	—
350	C₁₃×D₈	—	4	2	no	—
351	C₁₃×D₈	—	4	2	no	—
352	C₁₃×D₈	—	4	2	no	—
353	C₁₃×M₁₆	—	4	1	no	—
354	C₁₃×M₁₆	—	4	2	no	—
355	C₁₃×M₁₆	—	4	1	no	—
356	C₂×C₈×C₁₃	—	4	2	no	—
357	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
358	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
359	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
360	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
361	C₁₃×C₄⋊C₄	—	2	1	no	—
362	C₁₃×C₄⋊C₄	—	2	2	no	—
363	C₁₃×C₄⋊C₄	—	2	2	no	—
364	C₁₃×C₄⋊C₄	—	2	1	no	—
365	C₁₃×C₄⋊C₄	—	2	2	no	—
366	C₁₃×C₄⋊C₄	—	2	1	no	—
367	C₁₃×C₄⋊C₄	—	2	1	no	—
368	C₁₃×C₄⋊C₄	—	2	1	no	—
369	C₁₃×C₄⋊C₄	—	2	2	no	—
370	C₁₃×C₄⋊C₄	—	2	2	no	—
371	C₁₃×C₄⋊C₄	—	2	2	no	—
372	C₁₃×C₄⋊C₄	—	2	2	no	—
373	C₁₃×C₄⋊C₄	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
378	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
379	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
380	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
381	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
382	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
383	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
384	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
385	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
386	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
387	C₁₃×C₂²⋊C₄	—	2	2	no	—
388	C₁₃×C₂²⋊C₄	—	2	1	no	—
389	C₁₃×C₂²⋊C₄	—	2	2	no	—
390	C₁₃×C₂²⋊C₄	—	2	2	no	—
391	C₁₃×C₂²⋊C₄	—	2	2	no	—
392	C₁₃×C₂²⋊C₄	—	2	2	no	—
393	C₁₃×C₂²⋊C₄	—	2	2	no	—
394	C₁₃×C₂²⋊C₄	—	2	2	no	—
395	C₁₃×C₂²⋊C₄	—	2	2	no	—
396	C₁₃×C₂²⋊C₄	—	2	2	no	—
397	C₁₃×C₂²⋊C₄	—	2	1	no	—
398	C₁₃×C₂²⋊C₄	—	2	1	no	—
399	C₁₃×C₂²⋊C₄	—	2	2	no	—
400	C₁₃×C₂²⋊C₄	—	2	2	no	—
401	C₁₃×C₂²⋊C₄	—	2	2	no	—
402	C₁₃×C₂²⋊C₄	—	2	2	no	—
403	C₁₃×C₂²⋊C₄	—	2	2	no	—
404	C₁₃×C₂²⋊C₄	—	2	2	no	—
405	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
406	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
407	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
408	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
409	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
410	C₄²×C₁₃	—	2	1	no	—
411	C₄²×C₁₃	—	2	1	no	—
412	C₄²×C₁₃	—	2	1	no	—
413	C₄²×C₁₃	—	2	2	no	—
414	C₄²×C₁₃	—	2	2	no	—
415	C₄²×C₁₃	—	2	2	no	—
416	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
417	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
418	C₄²×C₁₃	C₂⁴	1	2	yes	—
419	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
420	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
421	#3561	C₂×C₁₃	1	1	yes	characteristic, complemented
422	#3517	C₂×C₁₃	1	1	yes	characteristic, complemented
423	#3397	C₂×C₁₃	1	2	yes	complemented
424	#3377	C₂×C₁₃	1	2	yes	complemented
425	#3322	C₂×C₁₃	1	2	yes	complemented
426	#3320	C₂×C₁₃	1	2	yes	complemented
427	#3308	C₂×C₁₃	1	2	yes	complemented
428	#3278	C₂×C₁₃	1	2	yes	complemented
429	#3271	C₂×C₁₃	1	2	yes	complemented
430	#3268	C₂×C₁₃	1	2	yes	complemented
431	#3257	C₂×C₁₃	1	2	yes	complemented
432	#3254	C₂×C₁₃	1	1	yes	characteristic, complemented
433	#3221	C₂×C₁₃	1	2	yes	complemented
434	#3213	C₂×C₁₃	1	1	yes	characteristic, complemented
435	#3124	C₂×C₁₃	1	2	yes	complemented
436	#3116	C₂×C₁₃	1	1	yes	characteristic, complemented
437	#3046	C₂×C₁₃	1	2	yes	complemented
438	#3040	C₂×C₁₃	1	1	yes	characteristic, complemented
439	#2995	C₂×C₁₃	1	1	yes	characteristic, complemented
440	C₂³×C₁₃	—	2	2	no	—
441	C₂³×C₁₃	—	2	1	no	—
442	C₂³×C₁₃	—	2	2	no	—
443	C₂³×C₁₃	—	4	2	no	—
444	C₂³×C₁₃	—	8	1	no	—
445	C₂³×C₁₃	—	8	1	no	—
446	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
447	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
448	Q₈×C₁₃	—	2	1	no	—
449	Q₈×C₁₃	—	2	2	no	—
450	Q₈×C₁₃	—	2	2	no	—
451	Q₈×C₁₃	—	2	2	no	—
452	Q₈×C₁₃	—	2	2	no	—
453	Q₈×C₁₃	—	4	1	no	—
454	Q₈×C₁₃	—	4	2	no	—
455	Q₈×C₁₃	—	8	1	no	—
456	Q₈×C₁₃	—	8	2	no	—
457	Q₈×C₁₃	—	8	1	no	—
458	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
459	D₄×C₁₃	—	2	2	no	—
460	D₄×C₁₃	—	2	1	no	—
461	D₄×C₁₃	—	2	2	no	—
462	D₄×C₁₃	—	2	2	no	—
463	D₄×C₁₃	—	2	2	no	—
464	D₄×C₁₃	—	2	1	no	—
465	D₄×C₁₃	—	4	2	no	—
466	D₄×C₁₃	—	4	1	no	—
467	D₄×C₁₃	—	4	4	no	—
468	D₄×C₁₃	—	4	2	no	—
469	D₄×C₁₃	—	4	2	no	—
470	D₄×C₁₃	—	8	1	no	—
471	D₄×C₁₃	—	8	2	no	—
472	D₄×C₁₃	—	8	1	no	—
473	D₄×C₁₃	—	8	2	no	—
474	D₄×C₁₃	—	8	2	no	—
475	D₄×C₁₃	—	8	2	no	—
476	D₄×C₁₃	—	8	2	no	—
477	D₄×C₁₃	—	8	2	no	—
478	D₄×C₁₃	—	8	2	no	—
479	C₂×C₄×C₁₃	—	2	1	no	—
480	C₂×C₄×C₁₃	—	2	2	no	—
481	C₂×C₄×C₁₃	—	2	1	no	—
482	C₂×C₄×C₁₃	—	2	1	no	—
483	C₂×C₄×C₁₃	—	2	2	no	—
484	C₂×C₄×C₁₃	—	2	1	no	—
485	C₂×C₄×C₁₃	—	2	2	no	—
486	C₂×C₄×C₁₃	—	2	1	no	—
487	C₂×C₄×C₁₃	—	2	2	no	—
488	C₂×C₄×C₁₃	—	2	2	no	—
489	C₂×C₄×C₁₃	—	2	2	no	—
490	C₂×C₄×C₁₃	—	4	1	no	—
491	C₂×C₄×C₁₃	—	4	1	no	—
492	C₂×C₄×C₁₃	—	4	4	no	—
493	C₂×C₄×C₁₃	—	4	2	no	—
494	C₂×C₄×C₁₃	—	4	2	no	—
495	C₂×C₄×C₁₃	—	8	2	no	—
496	C₂×C₄×C₁₃	—	8	1	no	—
497	C₂×C₄×C₁₃	—	8	2	no	—
498	C₂×C₄×C₁₃	—	8	2	no	—
499	C₂×C₄×C₁₃	—	8	2	no	—
500	C₂×C₄×C₁₃	—	8	2	no	—
501	C₂×C₄×C₁₃	—	8	1	no	—
502	C₂×C₄×C₁₃	—	8	2	no	—
503	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
512	C₈×C₁₃	—	2	2	no	—
513	C₈×C₁₃	—	2	2	no	—
514	C₈×C₁₃	—	2	2	no	—
515	C₈×C₁₃	—	2	2	no	—
516	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
517	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
518	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
519	C₂×#135	C₂²×C₁₃	1	2	yes	—
520	#563	—	2	1	no	—
521	#562	—	2	1	no	—
522	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
523	#556	C₂²×C₁₃	1	2	yes	—
524	#553	—	2	2	no	—
525	#553	C₂²×C₁₃	1	2	yes	—
526	#551	—	2	2	no	—
527	#550	—	2	1	no	—
528	#550	C₂²×C₁₃	1	2	yes	—
529	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
530	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
531	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
532	#548	C₂²×C₁₃	1	2	yes	—
533	#547	—	2	1	no	—
534	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
535	#546	C₂²×C₁₃	1	2	yes	—
536	#543	—	2	1	no	—
537	#542	—	2	2	no	—
538	#542	C₂²×C₁₃	1	2	yes	—
539	#540	—	2	2	no	—
540	#540	C₂²×C₁₃	1	2	yes	complemented
541	#538	—	2	1	no	—
542	#536	C₂²×C₁₃	1	2	yes	—
543	#533	C₂²×C₁₃	1	1	yes	characteristic
544	#532	—	2	1	no	—
545	#532	C₂²×C₁₃	1	1	yes	characteristic
546	#529	—	2	1	no	—
547	#529	C₂²×C₁₃	1	1	yes	characteristic
548	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
549	#520	C₂²×C₁₃	1	2	yes	complemented
550	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
551	#496	C₂²×C₁₃	1	2	yes	—
552	#496	C₂²×C₁₃	1	2	yes	—
553	#492	C₂²×C₁₃	1	2	yes	complemented
554	#491	C₂²×C₁₃	1	2	yes	complemented
555	#489	C₂²×C₁₃	1	2	yes	—
556	#488	C₂²×C₁₃	1	2	yes	—
557	#485	C₂²×C₁₃	1	2	yes	—
558	#484	C₂²×C₁₃	1	2	yes	complemented
559	#480	C₂²×C₁₃	1	2	yes	—
560	#479	C₂²×C₁₃	1	2	yes	complemented
561	#478	C₂²×C₁₃	1	2	yes	—
562	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
563	#477	C₂²×C₁₃	1	2	yes	complemented
564	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
565	#474	C₂²×C₁₃	1	2	yes	complemented
566	#469	C₂²×C₁₃	1	2	yes	—
567	#468	C₂²×C₁₃	1	2	yes	—
568	#468	C₂²×C₁₃	1	2	yes	—
569	#468	C₂²×C₁₃	1	2	yes	complemented
570	#466	C₂²×C₁₃	1	2	yes	—
571	#465	C₂²×C₁₃	1	2	yes	complemented
572	#464	C₂²×C₁₃	1	2	yes	—
573	#464	C₂²×C₁₃	1	2	yes	—
574	#464	C₂²×C₁₃	1	2	yes	—
575	#463	C₂²×C₁₃	1	2	yes	—
576	#463	C₂²×C₁₃	1	2	yes	—
577	#463	C₂²×C₁₃	1	2	yes	—
578	#463	C₂²×C₁₃	1	2	yes	—
579	#463	C₂²×C₁₃	1	2	yes	—
580	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
581	#462	C₂²×C₁₃	1	2	yes	complemented
582	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
583	#461	C₂²×C₁₃	1	2	yes	complemented
584	#461	C₂²×C₁₃	1	2	yes	complemented
585	#460	C₂²×C₁₃	1	2	yes	complemented
586	#460	C₂²×C₁₃	1	2	yes	complemented
587	#459	C₂²×C₁₃	1	2	yes	—
588	#452	C₂²×C₁₃	1	2	yes	—
589	#452	C₂²×C₁₃	1	2	yes	complemented
590	#449	C₂²×C₁₃	1	2	yes	—
591	#449	C₂²×C₁₃	1	2	yes	—
592	#449	C₂²×C₁₃	1	2	yes	—
593	#448	C₂²×C₁₃	1	2	yes	—
594	#448	C₂²×C₁₃	1	2	yes	complemented
595	#448	C₂²×C₁₃	1	2	yes	complemented
596	#447	C₂²×C₁₃	1	2	yes	—
597	#446	C₂²×C₁₃	1	2	yes	complemented
598	#441	C₂²×C₁₃	1	2	yes	complemented
599	#440	C₂²×C₁₃	1	2	yes	—
600	#440	C₂²×C₁₃	1	2	yes	complemented
601	#440	C₂²×C₁₃	1	2	yes	complemented
602	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
603	C₄×D₈	C₂²×C₁₃	1	2	yes	—
604	#436	C₂²×C₁₃	1	2	yes	—
605	#435	C₂²×C₁₃	1	2	yes	—
606	#435	C₂²×C₁₃	1	2	yes	complemented
607	#433	C₂²×C₁₃	1	2	yes	complemented
608	#432	C₂²×C₁₃	1	1	yes	characteristic
609	#424	C₂²×C₁₃	1	2	yes	complemented
610	#423	C₂²×C₁₃	1	1	yes	characteristic
611	#419	C₂²×C₁₃	1	1	yes	characteristic
612	#418	C₂²×C₁₃	1	1	yes	characteristic
613	#417	C₂²×C₁₃	1	2	yes	—
614	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
615	C₂²×C₁₃	—	2	1	no	—
616	C₂²×C₁₃	—	2	2	no	—
617	C₂²×C₁₃	—	2	1	no	—
618	C₂²×C₁₃	—	2	2	no	—
619	C₂²×C₁₃	—	2	2	no	—
620	C₂²×C₁₃	—	2	1	no	—
621	C₂²×C₁₃	—	4	1	no	—
622	C₂²×C₁₃	—	4	2	no	—
623	C₂²×C₁₃	—	4	2	no	—
624	C₂²×C₁₃	—	4	1	no	—
625	C₂²×C₁₃	—	4	2	no	—
626	C₂²×C₁₃	—	4	2	no	—
627	C₂²×C₁₃	—	4	1	no	—
628	C₂²×C₁₃	—	4	2	no	—
629	C₂²×C₁₃	—	4	2	no	—
630	C₂²×C₁₃	—	16	2	no	—
631	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
632	C₄×C₁₃	—	2	1	no	—
633	C₄×C₁₃	—	2	1	no	—
634	C₄×C₁₃	—	2	2	no	—
635	C₄×C₁₃	—	2	1	no	—
636	C₄×C₁₃	—	2	1	no	—
637	C₄×C₁₃	—	2	2	no	—
638	C₄×C₁₃	—	2	2	no	—
639	C₄×C₁₃	—	2	1	no	—
640	C₄×C₁₃	—	2	2	no	—
641	C₄×C₁₃	—	4	1	no	—
642	C₄×C₁₃	—	4	2	no	—
643	C₄×C₁₃	—	4	2	no	—
644	C₄×C₁₃	—	4	1	no	—
645	C₄×C₁₃	—	4	2	no	—
646	C₄×C₁₃	—	4	2	no	—
647	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
648	C₄×C₁₃	#585	1	1	yes	characteristic
649	C₂×#41	—	2	1	no	—
650	C₂×#41	—	2	1	no	—
651	C₂×#41	—	2	1	no	—
652	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
653	C₂×#41	C₂³×C₁₃	1	2	yes	—
654	C₂×#41	C₂³×C₁₃	1	2	yes	—
655	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
656	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
657	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
658	#137	—	4	2	no	—
659	#137	—	4	4	no	—
660	AGL(1,ℤ/8)	—	4	2	no	—
661	#135	—	4	4	no	—
662	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
663	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
664	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
665	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
666	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
667	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
668	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
669	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
670	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
671	C₂×D₈	C₂³×C₁₃	1	2	yes	—
672	C₂×D₈	C₂³×C₁₃	1	2	yes	—
673	C₂×D₈	C₂³×C₁₃	1	2	yes	—
674	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
675	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
676	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
677	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
678	C₄⋊Q₈	—	2	1	no	—
679	C₄⋊Q₈	—	2	2	no	—
680	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
681	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
682	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
683	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
684	#127	—	2	1	no	—
685	#127	—	2	2	no	—
686	#127	C₂³×C₁₃	1	1	yes	characteristic
687	#127	C₂³×C₁₃	1	2	yes	—
688	#126	—	2	2	no	—
689	#126	—	2	2	no	—
690	#126	—	2	2	no	—
691	#126	—	2	2	no	—
692	#126	D₄×C₁₃	1	2	yes	—
693	#125	—	2	2	no	—
694	#125	—	2	1	no	—
695	#125	D₄×C₁₃	1	1	yes	characteristic
696	#125	C₂³×C₁₃	1	2	yes	—
697	#124	—	2	2	no	—
698	#124	—	2	2	no	—
699	#124	—	2	1	no	—
700	#124	—	2	1	no	—
701	#124	—	2	1	no	—
702	#124	D₄×C₁₃	1	1	yes	characteristic
703	#124	C₂³×C₁₃	1	2	yes	—
704	#124	C₂³×C₁₃	1	2	yes	—
705	#124	C₂³×C₁₃	1	2	yes	—
706	#123	—	2	2	no	—
707	#123	—	2	2	no	—
708	#123	—	2	2	no	—
709	#123	—	2	2	no	—
710	#123	—	2	2	no	—
711	#123	—	2	2	no	—
712	#123	—	2	2	no	—
713	#123	—	2	2	no	—
714	#123	D₄×C₁₃	1	2	yes	—
715	C₂²⋊Q₈	—	2	2	no	—
716	C₂²⋊Q₈	—	2	1	no	—
717	C₂²⋊Q₈	—	2	1	no	—
718	C₂²⋊Q₈	—	2	2	no	—
719	C₂²⋊Q₈	—	2	2	no	—
720	C₂²⋊Q₈	—	2	2	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
725	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
726	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
727	#121	—	2	2	no	—
728	#121	—	2	2	no	—
729	#121	—	2	1	no	—
730	#121	—	2	1	no	—
731	#121	—	2	2	no	—
732	#121	—	2	2	no	—
733	#121	—	2	2	no	—
734	#121	—	2	2	no	—
735	#121	—	2	2	no	—
736	#121	—	2	2	no	—
737	#121	—	2	2	no	—
738	#121	D₄×C₁₃	1	1	yes	characteristic
739	#121	C₂³×C₁₃	1	2	yes	—
740	#121	C₂³×C₁₃	1	2	yes	—
741	#121	C₂³×C₁₃	1	2	yes	—
742	#121	C₂³×C₁₃	1	2	yes	—
743	#120	—	2	2	no	—
744	C₄×Q₈	—	2	1	no	—
745	C₄×Q₈	—	2	1	no	—
746	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
747	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
748	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
749	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
750	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
751	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
752	C₄×D₄	—	2	2	no	—
753	C₄×D₄	—	2	1	no	—
754	C₄×D₄	—	2	1	no	—
755	C₄×D₄	—	2	1	no	—
756	C₄×D₄	—	2	2	no	—
757	C₄×D₄	—	2	2	no	—
758	C₄×D₄	—	2	2	no	—
759	C₄×D₄	—	2	2	no	—
760	C₄×D₄	—	2	2	no	—
761	C₄×D₄	—	2	1	no	—
762	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
763	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
764	C₄×D₄	C₂³×C₁₃	1	2	yes	—
765	C₄×D₄	C₂³×C₁₃	1	2	yes	—
766	C₄×D₄	C₂³×C₁₃	1	2	yes	—
767	C₄×D₄	C₂³×C₁₃	1	2	yes	—
768	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
769	#117	—	2	1	no	—
770	#117	—	2	2	no	—
771	#117	—	2	2	no	—
772	#117	—	2	1	no	—
773	#117	C₂³×C₁₃	1	1	yes	characteristic
774	#117	C₂³×C₁₃	1	2	yes	—
775	C₂×C₄⋊C₄	—	2	2	no	—
776	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
777	C₂×C₂²⋊C₄	—	2	1	no	—
778	C₂×C₂²⋊C₄	—	2	1	no	—
779	C₂×C₂²⋊C₄	—	2	2	no	—
780	C₂×C₄²	—	2	1	no	—
781	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
782	#107	C₂³×C₁₃	1	2	yes	—
783	#107	C₂³×C₁₃	1	2	yes	—
784	#107	C₂³×C₁₃	1	2	yes	—
785	#106	C₂³×C₁₃	1	2	yes	—
786	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
787	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
788	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
789	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
790	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
791	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
792	#103	C₂³×C₁₃	1	2	yes	—
793	#103	C₂³×C₁₃	1	2	yes	—
794	#103	C₂³×C₁₃	1	2	yes	—
795	#103	C₂³×C₁₃	1	2	yes	—
796	#103	C₂³×C₁₃	1	2	yes	—
797	#103	C₂³×C₁₃	1	2	yes	—
798	#103	C₂³×C₁₃	1	2	yes	—
799	#103	C₂³×C₁₃	1	2	yes	—
800	#103	C₂³×C₁₃	1	2	yes	—
801	#102	C₂³×C₁₃	1	2	yes	—
802	#102	C₂³×C₁₃	1	2	yes	—
803	#102	C₂³×C₁₃	1	2	yes	—
804	#102	C₂³×C₁₃	1	2	yes	—
805	#102	C₂³×C₁₃	1	2	yes	—
806	#102	C₂³×C₁₃	1	2	yes	—
807	#102	C₂³×C₁₃	1	2	yes	—
808	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
809	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
810	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
811	#97	C₂³×C₁₃	1	2	yes	—
812	#97	C₂³×C₁₃	1	2	yes	—
813	C₄×C₈	C₂³×C₁₃	1	2	yes	—
814	C₂×C₁₃	—	4	2	no	—
815	C₂×C₁₃	—	4	1	no	—
816	C₂×C₁₃	—	8	1	no	—
817	C₂×C₁₃	—	8	2	no	—
818	C₂×C₁₃	—	8	2	no	—
819	C₂×C₁₃	#3488	1	1	yes	characteristic
820	C₂×C₁₃	#3585	1	1	yes	characteristic
821	C₂×C₁₃	#3586	1	1	yes	characteristic
822	C₂⁴	—	2	1	no	—
823	#41	—	2	4	no	—
824	#41	—	2	2	no	—
825	#41	—	4	1	no	—
826	#41	—	4	2	no	—
827	#41	—	4	2	no	—
828	#41	—	4	2	no	—
829	#41	—	8	2	no	—
830	#41	—	8	2	no	—
831	#41	—	8	2	no	—
832	C₂×Q₈	—	2	1	no	—
833	C₂×Q₈	—	2	1	no	—
834	C₂×Q₈	—	2	2	no	—
835	C₂×Q₈	—	2	1	no	—
836	C₂×Q₈	—	4	2	no	—
837	C₂×Q₈	—	4	1	no	—
838	C₂×Q₈	—	4	1	no	—
839	C₂×Q₈	—	4	2	no	—
840	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
841	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
842	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
843	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
844	C₂×D₄	—	2	1	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	2	2	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	2	1	no	—
852	C₂×D₄	—	2	1	no	—
853	C₂×D₄	—	2	2	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	—	2	1	no	—
856	C₂×D₄	—	4	1	no	—
857	C₂×D₄	—	4	1	no	—
858	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
859	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
860	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
861	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
862	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	2	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	2	no	—
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
875	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
878	Q₁₆	—	2	4	no	—
879	Q₁₆	—	2	4	no	—
880	SD₁₆	—	2	4	no	—
881	SD₁₆	—	4	2	no	—
882	SD₁₆	—	4	2	no	—
883	SD₁₆	—	4	2	no	—
884	SD₁₆	—	4	2	no	—
885	SD₁₆	—	4	2	no	—
886	SD₁₆	—	4	2	no	—
887	D₈	—	4	2	no	—
888	D₈	—	4	2	no	—
889	D₈	—	4	2	no	—
890	M₁₆	—	4	1	no	—
891	M₁₆	—	4	2	no	—
892	M₁₆	—	4	1	no	—
893	C₂×C₈	—	4	2	no	—
894	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
895	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
896	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
897	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
915	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
916	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
917	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
918	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
919	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
920	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
921	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
922	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
923	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	1	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	—	2	1	no	—
935	C₂²⋊C₄	—	2	1	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
943	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
944	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
945	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
946	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
947	C₄²	—	2	1	no	—
948	C₄²	—	2	1	no	—
949	C₄²	—	2	1	no	—
950	C₄²	—	2	2	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	2	2	no	—
953	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
954	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
955	C₄²	C₂⁴×C₁₃	1	2	yes	—
956	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
957	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
958	C₁₃	#62094	1	1	yes	characteristic, direct product factor, Sylow
959	C₂³	—	2	2	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	4	2	no	—
963	C₂³	—	8	1	no	—
964	C₂³	—	8	1	no	—
965	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
966	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
967	Q₈	—	2	1	no	—
968	Q₈	—	2	2	no	—
969	Q₈	—	2	2	no	—
970	Q₈	—	2	2	no	—
971	Q₈	—	2	2	no	—
972	Q₈	—	4	1	no	—
973	Q₈	—	4	2	no	—
974	Q₈	—	8	2	no	—
975	Q₈	—	8	1	no	—
976	Q₈	—	8	1	no	—
977	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
978	D₄	—	2	2	no	—
979	D₄	—	2	1	no	—
980	D₄	—	2	2	no	—
981	D₄	—	2	2	no	—
982	D₄	—	2	2	no	—
983	D₄	—	2	1	no	—
984	D₄	—	4	2	no	—
985	D₄	—	4	1	no	—
986	D₄	—	4	4	no	—
987	D₄	—	4	2	no	—
988	D₄	—	4	2	no	—
989	D₄	—	8	1	no	—
990	D₄	—	8	1	no	—
991	D₄	—	8	2	no	—
992	D₄	—	8	2	no	—
993	D₄	—	8	2	no	—
994	D₄	—	8	2	no	—
995	D₄	—	8	2	no	—
996	D₄	—	8	2	no	—
997	D₄	—	8	2	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	4	1	no	—
1010	C₂×C₄	—	4	1	no	—
1011	C₂×C₄	—	4	4	no	—
1012	C₂×C₄	—	4	2	no	—
1013	C₂×C₄	—	4	2	no	—
1014	C₂×C₄	—	8	2	no	—
1015	C₂×C₄	—	8	1	no	—
1016	C₂×C₄	—	8	2	no	—
1017	C₂×C₄	—	8	2	no	—
1018	C₂×C₄	—	8	2	no	—
1019	C₂×C₄	—	8	2	no	—
1020	C₂×C₄	—	8	1	no	—
1021	C₂×C₄	—	8	2	no	—
1022	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1024	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1025	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1026	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1027	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1028	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1029	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1030	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1031	C₈	—	2	2	no	—
1032	C₈	—	2	2	no	—
1033	C₈	—	2	2	no	—
1034	C₈	—	2	2	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	2	1	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	2	no	—
1043	C₂²	—	4	2	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	16	2	no	—
1051	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	2	2	no	—
1058	C₄	—	2	2	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	2	no	—
1067	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1068	C₄	C₁₃×#585	1	1	yes	characteristic
1069	C₂	—	4	1	no	—
1070	C₂	—	4	2	no	—
1071	C₂	—	8	2	no	—
1072	C₂	—	8	1	no	—
1073	C₂	—	8	2	no	—
1074	C₂	C₁₃×#3488	1	1	yes	characteristic
1075	C₂	C₁₃×#3585	1	1	yes	characteristic
1076	C₂	C₁₃×#3586	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 ◁ C₁₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3561	C₂	semidirect
2. C₁₃×#3517	C₂	semidirect
3. C₁₃×#3397	C₂	semidirect
4. C₁₃×#3377	C₂	semidirect
5. C₁₃×#3322	C₂	semidirect
6. C₁₃×#3320	C₂	semidirect
7. C₁₃×#3308	C₂	semidirect
8. C₁₃×#3278	C₂	semidirect
9. C₁₃×#3271	C₂	semidirect
10. C₁₃×#3268	C₂	semidirect
11. C₁₃×#3257	C₂	semidirect
12. C₁₃×#3254	C₂	semidirect
13. C₁₃×#3221	C₂	semidirect
14. C₁₃×#3213	C₂	semidirect
15. C₁₃×#3124	C₂	semidirect
16. C₁₃×#3116	C₂	semidirect
17. C₁₃×#3046	C₂	semidirect
18. C₁₃×#3040	C₂	semidirect
19. C₁₃×#2995	C₂	semidirect
21. C₂×C₁₃×#137	C₂²	semidirect
26. C₁₃×#557	C₂²	semidirect
33. C₁₃×#550	C₂²	semidirect
34. C₁₃×#550	C₂²	semidirect
38. C₁₃×#547	C₂²	semidirect
44. C₁₃×#540	C₂²	semidirect
53. C₁₃×#520	C₂²	semidirect
57. C₁₃×#492	C₂²	semidirect
58. C₁₃×#491	C₂²	semidirect
62. C₁₃×#484	C₂²	semidirect
64. C₁₃×#479	C₂²	semidirect
66. C₁₃×#477	C₂²	semidirect
67. C₁₃×#477	C₂²	semidirect
68. C₁₃×#476	C₂²	semidirect
69. C₁₃×#474	C₂²	semidirect
73. C₁₃×#468	C₂²	semidirect
75. C₁₃×#465	C₂²	semidirect
84. C₁₃×#462	C₂²	semidirect
85. C₁₃×#462	C₂²	semidirect
86. C₁₃×#461	C₂²	semidirect
87. C₁₃×#461	C₂²	semidirect
88. C₁₃×#461	C₂²	semidirect
89. C₁₃×#460	C₂²	semidirect
90. C₁₃×#460	C₂²	semidirect
93. C₁₃×#452	C₂²	semidirect
98. C₁₃×#448	C₂²	semidirect
99. C₁₃×#448	C₂²	semidirect
101. C₁₃×#446	C₂²	semidirect
102. C₁₃×#441	C₂²	semidirect
104. C₁₃×#440	C₂²	semidirect
105. C₁₃×#440	C₂²	semidirect
106. C₄×C₁₃×Q₁₆	C₂²	semidirect
110. C₁₃×#435	C₂²	semidirect
111. C₁₃×#433	C₂²	semidirect
113. C₁₃×#424	C₂²	semidirect
118. C₂×C₁₃×#103	C₂²	semidirect
284. #62094	C₁₃	direct (N × H)
421. #3561	C₂×C₁₃	semidirect
422. #3517	C₂×C₁₃	semidirect
423. #3397	C₂×C₁₃	semidirect
424. #3377	C₂×C₁₃	semidirect
425. #3322	C₂×C₁₃	semidirect
426. #3320	C₂×C₁₃	semidirect
427. #3308	C₂×C₁₃	semidirect
428. #3278	C₂×C₁₃	semidirect
429. #3271	C₂×C₁₃	semidirect
430. #3268	C₂×C₁₃	semidirect
431. #3257	C₂×C₁₃	semidirect
432. #3254	C₂×C₁₃	semidirect
433. #3221	C₂×C₁₃	semidirect
434. #3213	C₂×C₁₃	semidirect
435. #3124	C₂×C₁₃	semidirect
436. #3116	C₂×C₁₃	semidirect
437. #3046	C₂×C₁₃	semidirect
438. #3040	C₂×C₁₃	semidirect
439. #2995	C₂×C₁₃	semidirect
517. C₂×#137	C₂²×C₁₃	semidirect
522. #557	C₂²×C₁₃	semidirect
529. #550	C₂²×C₁₃	semidirect
530. #550	C₂²×C₁₃	semidirect
534. #547	C₂²×C₁₃	semidirect
540. #540	C₂²×C₁₃	semidirect
549. #520	C₂²×C₁₃	semidirect
553. #492	C₂²×C₁₃	semidirect
554. #491	C₂²×C₁₃	semidirect
558. #484	C₂²×C₁₃	semidirect
560. #479	C₂²×C₁₃	semidirect
562. #477	C₂²×C₁₃	semidirect
563. #477	C₂²×C₁₃	semidirect
564. #476	C₂²×C₁₃	semidirect
565. #474	C₂²×C₁₃	semidirect
569. #468	C₂²×C₁₃	semidirect
571. #465	C₂²×C₁₃	semidirect
580. #462	C₂²×C₁₃	semidirect
581. #462	C₂²×C₁₃	semidirect
582. #461	C₂²×C₁₃	semidirect
583. #461	C₂²×C₁₃	semidirect
584. #461	C₂²×C₁₃	semidirect
585. #460	C₂²×C₁₃	semidirect
586. #460	C₂²×C₁₃	semidirect
589. #452	C₂²×C₁₃	semidirect
594. #448	C₂²×C₁₃	semidirect
595. #448	C₂²×C₁₃	semidirect
597. #446	C₂²×C₁₃	semidirect
598. #441	C₂²×C₁₃	semidirect
600. #440	C₂²×C₁₃	semidirect
601. #440	C₂²×C₁₃	semidirect
602. C₄×Q₁₆	C₂²×C₁₃	semidirect
606. #435	C₂²×C₁₃	semidirect
607. #433	C₂²×C₁₃	semidirect
609. #424	C₂²×C₁₃	semidirect
614. C₂×#103	C₂²×C₁₃	semidirect
958. C₁₃	#62094	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×#3561	2
C₁₃×#3517	2
C₁₃×#3397	2
C₁₃×#3377	2
C₁₃×#3322	2
C₁₃×#3320	2
C₁₃×#3308	2
C₁₃×#3278	2
C₁₃×#3271	2
C₁₃×#3268	2
C₁₃×#3257	2
C₁₃×#3254	2
C₁₃×#3221	2
C₁₃×#3213	2
C₁₃×#3124	2
C₁₃×#3116	2
C₁₃×#3046	2
C₁₃×#3040	2
C₁₃×#2995	2
#62094	13

Subgroups — C13×#62094 #15748433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62094 #15748433