Subgroups — C₁₃×#61965 #15748304

Order 3328.

1888 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3400	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3375	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3333	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3314	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3278	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3266	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3254	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3249	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3216	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3112	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3037	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
19	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
20	C₁₃×#559	—	2	1	no	—
21	C₁₃×#559	C₂²	1	2	yes	—
22	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#557	—	2	1	no	—
24	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#554	—	2	2	no	—
26	C₁₃×#554	—	2	1	no	—
27	C₁₃×#554	C₂²	1	2	yes	—
28	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#550	—	2	1	no	—
30	C₁₃×#550	C₂²	1	2	yes	—
31	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
32	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#546	—	2	2	no	—
34	C₁₃×#546	C₂²	1	4	yes	—
35	C₁₃×#540	—	2	2	no	—
36	C₁₃×#535	—	2	1	no	—
37	C₁₃×#533	—	2	1	no	—
38	C₁₃×#533	—	2	2	no	—
39	C₁₃×#533	C₂²	1	1	yes	characteristic
40	C₁₃×#533	C₂²	1	1	yes	characteristic
41	C₁₃×#533	C₂²	1	2	yes	complemented
42	C₁₃×#532	C₂²	1	2	yes	—
43	C₁₃×#532	C₂²	1	2	yes	—
44	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
45	C₁₃×#518	—	2	1	no	—
46	C₄×C₁₃×#41	—	2	1	no	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
50	C₁₃×#497	C₂²	1	4	yes	complemented
51	C₁₃×#492	C₂²	1	2	yes	—
52	C₁₃×#489	C₂²	1	4	yes	complemented
53	C₁₃×#486	C₂²	1	2	yes	—
54	C₁₃×#484	C₂²	1	2	yes	—
55	C₁₃×#480	C₂²	1	4	yes	complemented
56	C₁₃×#477	C₂²	1	2	yes	complemented
57	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#477	C₂²	1	2	yes	complemented
60	C₁₃×#474	C₂²	1	4	yes	complemented
61	C₁₃×#468	C₂²	1	4	yes	complemented
62	C₁₃×#468	C₂²	1	4	yes	complemented
63	C₁₃×#467	C₂²	1	4	yes	—
64	C₁₃×#464	C₂²	1	4	yes	complemented
65	C₁₃×#464	C₂²	1	4	yes	complemented
66	C₁₃×#462	C₂²	1	2	yes	complemented
67	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#462	C₂²	1	2	yes	complemented
69	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#461	C₂²	1	4	yes	complemented
71	C₁₃×#460	C₂²	1	2	yes	—
72	C₁₃×#460	C₂²	1	2	yes	—
73	C₁₃×#460	C₂²	1	2	yes	—
74	C₁₃×#460	C₂²	1	2	yes	—
75	C₁₃×#460	C₂²	1	2	yes	—
76	C₁₃×#460	C₂²	1	2	yes	—
77	C₁₃×#452	C₂²	1	4	yes	complemented
78	C₁₃×#452	C₂²	1	4	yes	complemented
79	C₁₃×#451	C₂²	1	2	yes	—
80	C₁₃×#450	C₂²	1	4	yes	—
81	C₁₃×#448	C₂²	1	4	yes	complemented
82	C₁₃×#446	C₂²	1	2	yes	complemented
83	C₁₃×#440	C₂²	1	4	yes	complemented
84	C₁₃×#440	C₂²	1	4	yes	complemented
85	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
86	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
87	C₁₃×#436	C₂²	1	2	yes	complemented
88	C₁₃×#435	C₂²	1	4	yes	—
89	C₁₃×#432	C₂²	1	2	yes	complemented
90	C₁₃×#431	C₂²	1	1	yes	characteristic
91	C₁₃×#423	C₂²	1	2	yes	complemented
92	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
93	C₁₃×#417	C₂²	1	4	yes	complemented
94	C₂×C₁₃×#102	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	2	no	—
96	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
97	C₂×C₁₃×#41	C₂³	1	4	yes	—
98	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
99	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	—	2	1	no	—
102	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
103	C₁₃×#137	—	4	8	no	—
104	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
105	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
106	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
107	C₂×C₁₃×SD₁₆	—	4	4	no	—
108	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
109	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
111	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
112	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
113	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
114	C₁₃×C₄⋊Q₈	—	2	2	no	—
115	C₁₃×C₄⋊Q₈	—	2	1	no	—
116	C₁₃×C₄⋊Q₈	—	2	1	no	—
117	C₁₃×C₄⋊Q₈	—	2	2	no	—
118	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
124	C₁₃×#127	—	2	2	no	—
125	C₁₃×#127	—	2	1	no	—
126	C₁₃×#127	—	2	1	no	—
127	C₁₃×#127	C₂³	1	2	yes	—
128	C₁₃×#127	C₂³	1	2	yes	—
129	C₁₃×#125	—	2	1	no	—
130	C₁₃×#125	—	2	2	no	—
131	C₁₃×#125	—	2	2	no	—
132	C₁₃×#125	—	2	1	no	—
133	C₁₃×#125	—	2	1	no	—
134	C₁₃×#125	—	2	1	no	—
135	C₁₃×#125	—	2	2	no	—
136	C₁₃×#124	—	2	2	no	—
137	C₁₃×#124	—	2	2	no	—
138	C₁₃×#124	C₂³	1	4	yes	—
139	C₁₃×#123	—	2	4	no	—
140	C₁₃×#123	—	2	4	no	—
141	C₁₃×C₂²⋊Q₈	—	2	1	no	—
142	C₁₃×C₂²⋊Q₈	—	2	1	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	—	2	2	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	4	no	—
158	C₁₃×#121	—	2	4	no	—
159	C₁₃×#121	C₂³	1	4	yes	—
160	C₁₃×#120	—	2	4	no	—
161	C₄×Q₈×C₁₃	—	2	1	no	—
162	C₄×Q₈×C₁₃	—	2	1	no	—
163	C₄×Q₈×C₁₃	—	2	1	no	—
164	C₄×Q₈×C₁₃	—	2	1	no	—
165	C₄×Q₈×C₁₃	—	2	2	no	—
166	C₄×Q₈×C₁₃	—	2	2	no	—
167	C₄×Q₈×C₁₃	—	2	1	no	—
168	C₄×Q₈×C₁₃	—	2	2	no	—
169	C₄×Q₈×C₁₃	—	2	1	no	—
170	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
171	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
173	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
174	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
175	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
176	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
177	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
178	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
179	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₁₃	—	2	2	no	—
181	C₄×D₄×C₁₃	—	2	1	no	—
182	C₄×D₄×C₁₃	—	2	2	no	—
183	C₄×D₄×C₁₃	—	2	1	no	—
184	C₄×D₄×C₁₃	—	2	2	no	—
185	C₄×D₄×C₁₃	—	2	2	no	—
186	C₄×D₄×C₁₃	—	2	2	no	—
187	C₄×D₄×C₁₃	—	2	2	no	—
188	C₄×D₄×C₁₃	—	2	2	no	—
189	C₄×D₄×C₁₃	D₄	1	2	yes	—
190	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
191	C₄×D₄×C₁₃	C₂³	1	4	yes	—
192	C₄×D₄×C₁₃	C₂³	1	2	yes	—
193	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
194	C₁₃×#117	—	2	1	no	—
195	C₁₃×#117	—	2	2	no	—
196	C₁₃×#117	—	2	1	no	—
197	C₁₃×#117	D₄	1	1	yes	characteristic
198	C₁₃×#117	D₄	1	2	yes	—
199	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₂×C₄²×C₁₃	—	2	1	no	—
205	C₂×C₄²×C₁₃	—	2	2	no	—
206	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
208	C₁₃×#107	C₂³	1	2	yes	—
209	C₁₃×#107	C₂³	1	2	yes	—
210	C₁₃×#107	C₂³	1	4	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₁₃×#103	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	2	yes	—
219	C₁₃×#103	C₂³	1	2	yes	—
220	C₁₃×#103	C₂³	1	2	yes	—
221	C₁₃×#103	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	4	yes	—
225	C₁₃×#102	C₂³	1	4	yes	—
226	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₁₃×#97	C₂³	1	4	yes	—
229	C₄×C₈×C₁₃	C₂³	1	2	yes	—
230	#61965	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂⁴×C₁₃	—	2	2	no	—
232	C₁₃×#41	—	2	4	no	—
233	C₁₃×#41	—	4	4	no	—
234	C₁₃×#41	—	4	4	no	—
235	C₁₃×#41	—	8	4	no	—
236	C₂×Q₈×C₁₃	—	2	2	no	—
237	C₂×Q₈×C₁₃	—	2	1	no	—
238	C₂×Q₈×C₁₃	—	2	1	no	—
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	2	1	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	2	4	no	—
243	C₂×Q₈×C₁₃	—	4	1	no	—
244	C₂×Q₈×C₁₃	—	4	2	no	—
245	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
247	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
249	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂×D₄×C₁₃	—	2	4	no	—
251	C₂×D₄×C₁₃	—	2	4	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	2	no	—
254	C₂×D₄×C₁₃	—	2	2	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	2	2	no	—
257	C₂×D₄×C₁₃	—	4	2	no	—
258	C₂×D₄×C₁₃	—	4	2	no	—
259	C₂×D₄×C₁₃	—	4	4	no	—
260	C₂×D₄×C₁₃	—	8	2	no	—
261	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
262	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
264	C₂²×C₄×C₁₃	—	2	2	no	—
265	C₂²×C₄×C₁₃	—	2	1	no	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	1	no	—
268	C₂²×C₄×C₁₃	—	2	4	no	—
269	C₂²×C₄×C₁₃	—	2	4	no	—
270	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
272	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₁₃×Q₁₆	—	2	4	no	—
277	C₁₃×Q₁₆	—	4	2	no	—
278	C₁₃×Q₁₆	—	4	4	no	—
279	C₁₃×SD₁₆	—	2	8	no	—
280	C₁₃×SD₁₆	—	4	4	no	—
281	C₁₃×SD₁₆	—	4	4	no	—
282	C₁₃×SD₁₆	—	4	4	no	—
283	C₁₃×M₁₆	—	4	4	no	—
284	C₂×C₈×C₁₃	—	4	2	no	—
285	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
286	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
287	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
288	C₁₃×C₄⋊C₄	—	2	1	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	1	no	—
291	C₁₃×C₄⋊C₄	—	2	1	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	1	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	1	no	—
297	C₁₃×C₄⋊C₄	—	2	1	no	—
298	C₁₃×C₄⋊C₄	—	2	1	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	2	1	no	—
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	—	2	1	no	—
303	C₁₃×C₄⋊C₄	—	2	1	no	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	2	no	—
306	C₁₃×C₄⋊C₄	—	2	1	no	—
307	C₁₃×C₄⋊C₄	—	2	2	no	—
308	C₁₃×C₄⋊C₄	—	2	2	no	—
309	C₁₃×C₄⋊C₄	—	2	2	no	—
310	C₁₃×C₄⋊C₄	—	2	2	no	—
311	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
312	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
313	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
314	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
316	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
317	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
318	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	2	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	—	2	4	no	—
324	C₁₃×C₂²⋊C₄	—	2	4	no	—
325	C₁₃×C₂²⋊C₄	—	2	4	no	—
326	C₁₃×C₂²⋊C₄	—	2	4	no	—
327	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
328	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
329	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
330	C₄²×C₁₃	—	2	1	no	—
331	C₄²×C₁₃	—	2	1	no	—
332	C₄²×C₁₃	—	2	2	no	—
333	C₄²×C₁₃	—	2	2	no	—
334	C₄²×C₁₃	—	2	1	no	—
335	C₄²×C₁₃	—	2	2	no	—
336	C₄²×C₁₃	—	2	1	no	—
337	C₄²×C₁₃	—	2	2	no	—
338	C₄²×C₁₃	C₂×D₄	1	2	yes	—
339	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₁₃	C₂×D₄	1	2	yes	—
341	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
343	C₄²×C₁₃	C₂⁴	1	2	yes	—
344	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
345	#3508	C₂×C₁₃	1	1	yes	characteristic
346	Q₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#3400	C₂×C₁₃	1	2	yes	complemented
348	#3375	C₂×C₁₃	1	2	yes	complemented
349	#3333	C₂×C₁₃	1	2	yes	complemented
350	#3314	C₂×C₁₃	1	4	yes	complemented
351	#3278	C₂×C₁₃	1	2	yes	complemented
352	#3266	C₂×C₁₃	1	4	yes	complemented
353	#3254	C₂×C₁₃	1	2	yes	complemented
354	#3249	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#3216	C₂×C₁₃	1	2	yes	complemented
356	#3208	C₂×C₁₃	1	1	yes	characteristic, complemented
357	#3112	C₂×C₁₃	1	2	yes	complemented
358	#3104	C₂×C₁₃	1	1	yes	characteristic, complemented
359	#3037	C₂×C₁₃	1	2	yes	complemented
360	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
361	#2989	C₂×C₁₃	1	1	yes	characteristic, complemented
362	C₂³×C₁₃	—	2	4	no	—
363	C₂³×C₁₃	—	4	4	no	—
364	C₂³×C₁₃	—	8	2	no	—
365	C₂³×C₁₃	—	8	2	no	—
366	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
367	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
368	Q₈×C₁₃	—	2	2	no	—
369	Q₈×C₁₃	—	2	1	no	—
370	Q₈×C₁₃	—	2	1	no	—
371	Q₈×C₁₃	—	2	2	no	—
372	Q₈×C₁₃	—	2	2	no	—
373	Q₈×C₁₃	—	2	2	no	—
374	Q₈×C₁₃	—	2	1	no	—
375	Q₈×C₁₃	—	2	2	no	—
376	Q₈×C₁₃	—	4	4	no	—
377	Q₈×C₁₃	—	4	2	no	—
378	Q₈×C₁₃	—	4	2	no	—
379	Q₈×C₁₃	—	8	2	no	—
380	Q₈×C₁₃	—	8	1	no	—
381	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
382	D₄×C₁₃	—	2	4	no	—
383	D₄×C₁₃	—	2	2	no	—
384	D₄×C₁₃	—	2	4	no	—
385	D₄×C₁₃	—	2	4	no	—
386	D₄×C₁₃	—	4	4	no	—
387	D₄×C₁₃	—	4	4	no	—
388	D₄×C₁₃	—	4	4	no	—
389	D₄×C₁₃	—	8	2	no	—
390	D₄×C₁₃	—	8	2	no	—
391	D₄×C₁₃	—	8	4	no	—
392	D₄×C₁₃	—	8	4	no	—
393	C₂×C₄×C₁₃	—	2	1	no	—
394	C₂×C₄×C₁₃	—	2	4	no	—
395	C₂×C₄×C₁₃	—	2	1	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	1	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	4	1	no	—
407	C₂×C₄×C₁₃	—	4	2	no	—
408	C₂×C₄×C₁₃	—	4	2	no	—
409	C₂×C₄×C₁₃	—	4	4	no	—
410	C₂×C₄×C₁₃	—	8	4	no	—
411	C₂×C₄×C₁₃	—	8	4	no	—
412	C₂×C₄×C₁₃	—	8	1	no	—
413	C₂×C₄×C₁₃	—	8	2	no	—
414	C₂×C₄×C₁₃	#137	1	4	yes	complemented
415	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
424	C₈×C₁₃	—	2	4	no	—
425	C₈×C₁₃	—	2	2	no	—
426	C₈×C₁₃	—	2	2	no	—
427	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
428	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
429	#559	—	2	1	no	—
430	#559	C₂²×C₁₃	1	2	yes	—
431	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
432	#557	—	2	1	no	—
433	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
434	#554	—	2	2	no	—
435	#554	—	2	1	no	—
436	#554	C₂²×C₁₃	1	2	yes	—
437	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
438	#550	—	2	1	no	—
439	#550	C₂²×C₁₃	1	2	yes	—
440	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
441	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
442	#546	—	2	2	no	—
443	#546	C₂²×C₁₃	1	4	yes	—
444	#540	—	2	2	no	—
445	#535	—	2	1	no	—
446	#533	—	2	1	no	—
447	#533	—	2	2	no	—
448	#533	C₂²×C₁₃	1	1	yes	characteristic
449	#533	C₂²×C₁₃	1	1	yes	characteristic
450	#533	C₂²×C₁₃	1	2	yes	complemented
451	#532	C₂²×C₁₃	1	2	yes	—
452	#532	C₂²×C₁₃	1	2	yes	—
453	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
454	#518	—	2	1	no	—
455	C₄×#41	—	2	1	no	—
456	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
457	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
458	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
459	#497	C₂²×C₁₃	1	4	yes	complemented
460	#492	C₂²×C₁₃	1	2	yes	—
461	#489	C₂²×C₁₃	1	4	yes	complemented
462	#486	C₂²×C₁₃	1	2	yes	—
463	#484	C₂²×C₁₃	1	2	yes	—
464	#480	C₂²×C₁₃	1	4	yes	complemented
465	#477	C₂²×C₁₃	1	2	yes	complemented
466	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
467	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
468	#477	C₂²×C₁₃	1	2	yes	complemented
469	#474	C₂²×C₁₃	1	4	yes	complemented
470	#468	C₂²×C₁₃	1	4	yes	complemented
471	#468	C₂²×C₁₃	1	4	yes	complemented
472	#467	C₂²×C₁₃	1	4	yes	—
473	#464	C₂²×C₁₃	1	4	yes	complemented
474	#464	C₂²×C₁₃	1	4	yes	complemented
475	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
476	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
477	#462	C₂²×C₁₃	1	2	yes	complemented
478	#462	C₂²×C₁₃	1	2	yes	complemented
479	#461	C₂²×C₁₃	1	4	yes	complemented
480	#460	C₂²×C₁₃	1	2	yes	—
481	#460	C₂²×C₁₃	1	2	yes	—
482	#460	C₂²×C₁₃	1	2	yes	—
483	#460	C₂²×C₁₃	1	2	yes	—
484	#460	C₂²×C₁₃	1	2	yes	—
485	#460	C₂²×C₁₃	1	2	yes	—
486	#452	C₂²×C₁₃	1	4	yes	complemented
487	#452	C₂²×C₁₃	1	4	yes	complemented
488	#451	C₂²×C₁₃	1	2	yes	—
489	#450	C₂²×C₁₃	1	4	yes	—
490	#448	C₂²×C₁₃	1	4	yes	complemented
491	#446	C₂²×C₁₃	1	2	yes	complemented
492	#440	C₂²×C₁₃	1	4	yes	complemented
493	#440	C₂²×C₁₃	1	4	yes	complemented
494	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
495	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
496	#436	C₂²×C₁₃	1	2	yes	complemented
497	#435	C₂²×C₁₃	1	4	yes	—
498	#432	C₂²×C₁₃	1	2	yes	complemented
499	#431	C₂²×C₁₃	1	1	yes	characteristic
500	#423	C₂²×C₁₃	1	2	yes	complemented
501	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
502	#417	C₂²×C₁₃	1	4	yes	complemented
503	C₂×#102	C₂²×C₁₃	1	2	yes	—
504	C₂²×C₁₃	—	2	1	no	—
505	C₂²×C₁₃	—	2	1	no	—
506	C₂²×C₁₃	—	2	2	no	—
507	C₂²×C₁₃	—	2	2	no	—
508	C₂²×C₁₃	—	2	2	no	—
509	C₂²×C₁₃	—	4	4	no	—
510	C₂²×C₁₃	—	4	4	no	—
511	C₂²×C₁₃	—	4	4	no	—
512	C₂²×C₁₃	—	16	4	no	—
513	C₂²×C₁₃	C₂×#137	1	2	yes	—
514	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
515	C₄×C₁₃	—	2	1	no	—
516	C₄×C₁₃	—	2	2	no	—
517	C₄×C₁₃	—	2	1	no	—
518	C₄×C₁₃	—	2	2	no	—
519	C₄×C₁₃	—	2	1	no	—
520	C₄×C₁₃	—	2	2	no	—
521	C₄×C₁₃	—	2	2	no	—
522	C₄×C₁₃	—	4	1	no	—
523	C₄×C₁₃	—	4	2	no	—
524	C₄×C₁₃	—	4	1	no	—
525	C₄×C₁₃	—	4	2	no	—
526	C₄×C₁₃	—	4	1	no	—
527	C₄×C₁₃	—	4	2	no	—
528	C₄×C₁₃	—	4	2	no	—
529	C₄×C₁₃	C₂×#137	1	2	yes	—
530	C₄×C₁₃	C₂×#137	1	2	yes	—
531	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
532	C₄×C₁₃	#585	1	1	yes	characteristic
533	C₂×#41	—	2	2	no	—
534	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
535	C₂×#41	C₂³×C₁₃	1	4	yes	—
536	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
537	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
538	C₂²×D₄	—	2	1	no	—
539	C₂²×D₄	—	2	1	no	—
540	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
541	#137	—	4	8	no	—
542	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
543	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
544	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
545	C₂×SD₁₆	—	4	4	no	—
546	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
547	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
548	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
549	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
550	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
551	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
552	C₄⋊Q₈	—	2	2	no	—
553	C₄⋊Q₈	—	2	1	no	—
554	C₄⋊Q₈	—	2	1	no	—
555	C₄⋊Q₈	—	2	2	no	—
556	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
557	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
558	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
559	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
560	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
561	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
562	#127	—	2	2	no	—
563	#127	—	2	1	no	—
564	#127	—	2	1	no	—
565	#127	C₂³×C₁₃	1	2	yes	—
566	#127	C₂³×C₁₃	1	2	yes	—
567	#125	—	2	1	no	—
568	#125	—	2	2	no	—
569	#125	—	2	2	no	—
570	#125	—	2	1	no	—
571	#125	—	2	1	no	—
572	#125	—	2	1	no	—
573	#125	—	2	2	no	—
574	#124	—	2	2	no	—
575	#124	—	2	2	no	—
576	#124	C₂³×C₁₃	1	4	yes	—
577	#123	—	2	4	no	—
578	#123	—	2	4	no	—
579	C₂²⋊Q₈	—	2	1	no	—
580	C₂²⋊Q₈	—	2	1	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
589	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
590	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
591	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
592	#121	—	2	2	no	—
593	#121	—	2	2	no	—
594	#121	—	2	2	no	—
595	#121	—	2	4	no	—
596	#121	—	2	4	no	—
597	#121	C₂³×C₁₃	1	4	yes	—
598	#120	—	2	4	no	—
599	C₄×Q₈	—	2	1	no	—
600	C₄×Q₈	—	2	1	no	—
601	C₄×Q₈	—	2	1	no	—
602	C₄×Q₈	—	2	1	no	—
603	C₄×Q₈	—	2	2	no	—
604	C₄×Q₈	—	2	2	no	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	—	2	2	no	—
607	C₄×Q₈	—	2	1	no	—
608	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
609	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
610	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
611	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
612	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
613	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
614	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
615	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
616	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
617	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	D₄×C₁₃	1	2	yes	—
628	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
629	C₄×D₄	C₂³×C₁₃	1	4	yes	—
630	C₄×D₄	C₂³×C₁₃	1	2	yes	—
631	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
632	#117	—	2	1	no	—
633	#117	—	2	2	no	—
634	#117	—	2	1	no	—
635	#117	D₄×C₁₃	1	1	yes	characteristic
636	#117	D₄×C₁₃	1	2	yes	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	—	2	2	no	—
639	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
641	C₂×C₂²⋊C₄	—	2	4	no	—
642	C₂×C₄²	—	2	1	no	—
643	C₂×C₄²	—	2	2	no	—
644	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
646	#107	C₂³×C₁₃	1	2	yes	—
647	#107	C₂³×C₁₃	1	2	yes	—
648	#107	C₂³×C₁₃	1	4	yes	—
649	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
650	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
651	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
652	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
653	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
654	#103	C₂³×C₁₃	1	2	yes	—
655	#103	C₂³×C₁₃	1	4	yes	—
656	#103	C₂³×C₁₃	1	2	yes	—
657	#103	C₂³×C₁₃	1	2	yes	—
658	#103	C₂³×C₁₃	1	2	yes	—
659	#103	C₂³×C₁₃	1	4	yes	—
660	#102	C₂³×C₁₃	1	4	yes	—
661	#102	C₂³×C₁₃	1	4	yes	—
662	#102	C₂³×C₁₃	1	4	yes	—
663	#102	C₂³×C₁₃	1	4	yes	—
664	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
665	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
666	#97	C₂³×C₁₃	1	4	yes	—
667	C₄×C₈	C₂³×C₁₃	1	2	yes	—
668	C₂×C₁₃	—	2	2	no	—
669	C₂×C₁₃	—	4	2	no	—
670	C₂×C₁₃	—	8	4	no	—
671	C₂×C₁₃	#3488	1	1	yes	characteristic
672	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
673	C₂×C₁₃	#3585	1	1	yes	characteristic
674	C₂⁴	—	2	2	no	—
675	#41	—	2	4	no	—
676	#41	—	4	4	no	—
677	#41	—	4	4	no	—
678	#41	—	8	4	no	—
679	C₂×Q₈	—	2	2	no	—
680	C₂×Q₈	—	2	1	no	—
681	C₂×Q₈	—	2	1	no	—
682	C₂×Q₈	—	2	2	no	—
683	C₂×Q₈	—	2	1	no	—
684	C₂×Q₈	—	2	2	no	—
685	C₂×Q₈	—	2	4	no	—
686	C₂×Q₈	—	4	1	no	—
687	C₂×Q₈	—	4	2	no	—
688	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
689	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
690	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
691	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
692	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
693	C₂×D₄	—	2	4	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	4	2	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	4	4	no	—
703	C₂×D₄	—	8	2	no	—
704	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
705	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
706	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	2	4	no	—
713	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
714	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
715	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
716	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
719	Q₁₆	—	2	4	no	—
720	Q₁₆	—	4	4	no	—
721	Q₁₆	—	4	2	no	—
722	SD₁₆	—	2	8	no	—
723	SD₁₆	—	4	4	no	—
724	SD₁₆	—	4	4	no	—
725	SD₁₆	—	4	4	no	—
726	M₁₆	—	4	4	no	—
727	C₂×C₈	—	4	2	no	—
728	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
729	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
730	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
755	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
756	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
757	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
758	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
759	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
760	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
761	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
771	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
772	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
773	C₄²	—	2	1	no	—
774	C₄²	—	2	1	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	1	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	1	no	—
780	C₄²	—	2	2	no	—
781	C₄²	C₂×D₄×C₁₃	1	2	yes	—
782	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
783	C₄²	C₂×D₄×C₁₃	1	2	yes	—
784	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
785	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
786	C₄²	C₂⁴×C₁₃	1	2	yes	—
787	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
788	C₁₃	#61965	1	1	yes	characteristic, direct product factor, Sylow
789	C₂³	—	2	4	no	—
790	C₂³	—	4	4	no	—
791	C₂³	—	8	2	no	—
792	C₂³	—	8	2	no	—
793	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
794	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
795	Q₈	—	2	2	no	—
796	Q₈	—	2	1	no	—
797	Q₈	—	2	1	no	—
798	Q₈	—	2	2	no	—
799	Q₈	—	2	2	no	—
800	Q₈	—	2	2	no	—
801	Q₈	—	2	1	no	—
802	Q₈	—	2	2	no	—
803	Q₈	—	4	4	no	—
804	Q₈	—	4	2	no	—
805	Q₈	—	4	2	no	—
806	Q₈	—	8	2	no	—
807	Q₈	—	8	1	no	—
808	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
809	D₄	—	2	4	no	—
810	D₄	—	2	2	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	4	no	—
813	D₄	—	4	4	no	—
814	D₄	—	4	4	no	—
815	D₄	—	4	4	no	—
816	D₄	—	8	2	no	—
817	D₄	—	8	2	no	—
818	D₄	—	8	4	no	—
819	D₄	—	8	4	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	2	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	8	4	no	—
838	C₂×C₄	—	8	4	no	—
839	C₂×C₄	—	8	1	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	C₁₃×#137	1	4	yes	complemented
842	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
843	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
845	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
850	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
851	C₈	—	2	4	no	—
852	C₈	—	2	2	no	—
853	C₈	—	2	2	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	4	4	no	—
860	C₂²	—	4	4	no	—
861	C₂²	—	4	4	no	—
862	C₂²	—	16	4	no	—
863	C₂²	C₂×C₁₃×#137	1	2	yes	—
864	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
865	C₄	—	2	2	no	—
866	C₄	—	2	1	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	1	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	2	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₄	C₂×C₁₃×#137	1	2	yes	—
880	C₄	C₂×C₁₃×#137	1	2	yes	—
881	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
882	C₄	C₁₃×#585	1	1	yes	characteristic
883	C₂	—	2	2	no	—
884	C₂	—	4	2	no	—
885	C₂	—	8	4	no	—
886	C₂	C₁₃×#3488	1	1	yes	characteristic
887	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
888	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3508	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×C₁₃×#41	C₂	semidirect
3. C₁₃×#3400	C₂	semidirect
4. C₁₃×#3375	C₂	semidirect
5. C₁₃×#3333	C₂	semidirect
6. C₁₃×#3314	C₂	semidirect
7. C₁₃×#3278	C₂	semidirect
8. C₁₃×#3266	C₂	semidirect
9. C₁₃×#3254	C₂	semidirect
10. C₁₃×#3249	C₂	semidirect
11. C₁₃×#3216	C₂	semidirect
12. C₁₃×#3208	C₂	semidirect
13. C₁₃×#3112	C₂	semidirect
14. C₁₃×#3104	C₂	semidirect
15. C₁₃×#3037	C₂	semidirect
16. C₂×C₁₃×#460	C₂	semidirect
17. C₁₃×#2989	C₂	semidirect
18. C₂×C₁₃×#137	C₂²	semidirect
22. Q₈²×C₁₃	C₂²	semidirect
24. C₁₃×#557	C₂²	semidirect
28. C₁₃×#554	C₂²	semidirect
32. D₄×Q₈×C₁₃	C₂²	semidirect
41. C₁₃×#533	C₂²	semidirect
49. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
50. C₁₃×#497	C₂²	semidirect
52. C₁₃×#489	C₂²	semidirect
55. C₁₃×#480	C₂²	semidirect
56. C₁₃×#477	C₂²	semidirect
57. C₁₃×#477	C₂²	semidirect
58. C₁₃×#477	C₂²	semidirect
59. C₁₃×#477	C₂²	semidirect
60. C₁₃×#474	C₂²	semidirect
61. C₁₃×#468	C₂²	semidirect
62. C₁₃×#468	C₂²	semidirect
64. C₁₃×#464	C₂²	semidirect
65. C₁₃×#464	C₂²	semidirect
66. C₁₃×#462	C₂²	semidirect
67. C₁₃×#462	C₂²	semidirect
68. C₁₃×#462	C₂²	semidirect
69. C₁₃×#462	C₂²	semidirect
70. C₁₃×#461	C₂²	semidirect
77. C₁₃×#452	C₂²	semidirect
78. C₁₃×#452	C₂²	semidirect
81. C₁₃×#448	C₂²	semidirect
82. C₁₃×#446	C₂²	semidirect
83. C₁₃×#440	C₂²	semidirect
84. C₁₃×#440	C₂²	semidirect
85. C₄×C₁₃×Q₁₆	C₂²	semidirect
86. C₄×C₁₃×Q₁₆	C₂²	semidirect
87. C₁₃×#436	C₂²	semidirect
89. C₁₃×#432	C₂²	semidirect
91. C₁₃×#423	C₂²	semidirect
93. C₁₃×#417	C₂²	semidirect
230. #61965	C₁₃	direct (N × H)
346. Q₈×#41	C₂×C₁₃	semidirect
347. #3400	C₂×C₁₃	semidirect
348. #3375	C₂×C₁₃	semidirect
349. #3333	C₂×C₁₃	semidirect
350. #3314	C₂×C₁₃	semidirect
351. #3278	C₂×C₁₃	semidirect
352. #3266	C₂×C₁₃	semidirect
353. #3254	C₂×C₁₃	semidirect
354. #3249	C₂×C₁₃	semidirect
355. #3216	C₂×C₁₃	semidirect
356. #3208	C₂×C₁₃	semidirect
357. #3112	C₂×C₁₃	semidirect
358. #3104	C₂×C₁₃	semidirect
359. #3037	C₂×C₁₃	semidirect
360. C₂×#460	C₂×C₁₃	semidirect
361. #2989	C₂×C₁₃	semidirect
414. C₂×C₄×C₁₃	#137	semidirect
427. C₂×#137	C₂²×C₁₃	semidirect
431. Q₈²	C₂²×C₁₃	semidirect
433. #557	C₂²×C₁₃	semidirect
437. #554	C₂²×C₁₃	semidirect
441. D₄×Q₈	C₂²×C₁₃	semidirect
450. #533	C₂²×C₁₃	semidirect
458. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
459. #497	C₂²×C₁₃	semidirect
461. #489	C₂²×C₁₃	semidirect
464. #480	C₂²×C₁₃	semidirect
465. #477	C₂²×C₁₃	semidirect
466. #477	C₂²×C₁₃	semidirect
467. #477	C₂²×C₁₃	semidirect
468. #477	C₂²×C₁₃	semidirect
469. #474	C₂²×C₁₃	semidirect
470. #468	C₂²×C₁₃	semidirect
471. #468	C₂²×C₁₃	semidirect
473. #464	C₂²×C₁₃	semidirect
474. #464	C₂²×C₁₃	semidirect
475. #462	C₂²×C₁₃	semidirect
476. #462	C₂²×C₁₃	semidirect
477. #462	C₂²×C₁₃	semidirect
478. #462	C₂²×C₁₃	semidirect
479. #461	C₂²×C₁₃	semidirect
486. #452	C₂²×C₁₃	semidirect
487. #452	C₂²×C₁₃	semidirect
490. #448	C₂²×C₁₃	semidirect
491. #446	C₂²×C₁₃	semidirect
492. #440	C₂²×C₁₃	semidirect
493. #440	C₂²×C₁₃	semidirect
494. C₄×Q₁₆	C₂²×C₁₃	semidirect
495. C₄×Q₁₆	C₂²×C₁₃	semidirect
496. #436	C₂²×C₁₃	semidirect
498. #432	C₂²×C₁₃	semidirect
500. #423	C₂²×C₁₃	semidirect
502. #417	C₂²×C₁₃	semidirect
788. C₁₃	#61965	direct (N × H)
841. 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
C₁₃×#3508	2
Q₈×C₁₃×#41	2
C₁₃×#3400	2
C₁₃×#3375	2
C₁₃×#3333	2
C₁₃×#3314	2
C₁₃×#3278	2
C₁₃×#3266	2
C₁₃×#3254	2
C₁₃×#3249	2
C₁₃×#3216	2
C₁₃×#3208	2
C₁₃×#3112	2
C₁₃×#3104	2
C₁₃×#3037	2
C₂×C₁₃×#460	2
C₁₃×#2989	2
#61965	13

Subgroups — C13×#61965 #15748304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61965 #15748304