Subgroups — C₁₃×#61320 #15747659

Order 3328.

1804 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3480	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3377	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3374	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3371	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3368	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3365	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3364	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3142	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3080	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3037	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
15	Q₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₁₃×#137	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#137	C₂²	1	2	yes	—
20	C₁₃×#559	C₂²	1	1	yes	characteristic
21	C₁₃×#559	C₂²	1	2	yes	—
22	C₁₃×#557	—	2	1	no	—
23	C₁₃×#557	—	2	1	no	—
24	C₁₃×#557	—	2	2	no	—
25	C₁₃×#557	C₂²	1	1	yes	characteristic
26	C₁₃×#557	C₂²	1	2	yes	—
27	C₁₃×#557	C₂²	1	2	yes	—
28	C₁₃×#557	C₂²	1	4	yes	—
29	C₁₃×#556	C₂²	1	1	yes	characteristic
30	C₁₃×#556	C₂²	1	2	yes	—
31	C₁₃×#553	—	2	1	no	—
32	C₁₃×#553	—	2	2	no	—
33	C₁₃×#550	C₂²	1	1	yes	characteristic
34	C₁₃×#548	—	2	1	no	—
35	C₁₃×#532	C₂²	1	1	yes	characteristic
36	C₁₃×#532	C₂²	1	2	yes	—
37	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
38	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
39	C₁₃×#529	—	2	2	no	—
40	C₁₃×#529	—	2	1	no	—
41	C₂×C₁₃×#125	—	2	2	no	—
42	C₂×C₁₃×#125	C₂²	1	2	yes	—
43	C₄×C₁₃×#41	—	2	1	no	—
44	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
45	C₄×C₁₃×#41	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
47	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
48	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
50	C₁₃×#491	C₂²	1	4	yes	—
51	C₁₃×#490	C₂²	1	4	yes	—
52	C₁₃×#489	C₂²	1	4	yes	—
53	C₁₃×#488	C₂²	1	4	yes	—
54	C₁₃×#488	C₂²	1	4	yes	—
55	C₁₃×#487	C₂²	1	2	yes	—
56	C₁₃×#486	C₂²	1	2	yes	—
57	C₁₃×#479	C₂²	1	4	yes	—
58	C₁₃×#479	C₂²	1	4	yes	—
59	C₁₃×#478	C₂²	1	4	yes	—
60	C₁₃×#478	C₂²	1	4	yes	—
61	C₁₃×#477	C₂²	1	2	yes	—
62	C₁₃×#476	C₂²	1	2	yes	—
63	C₁₃×#475	C₂²	1	2	yes	—
64	C₁₃×#474	C₂²	1	2	yes	—
65	C₁₃×#464	C₂²	1	4	yes	—
66	C₁₃×#464	C₂²	1	4	yes	—
67	C₁₃×#464	C₂²	1	4	yes	—
68	C₁₃×#462	C₂²	1	2	yes	—
69	C₁₃×#462	C₂²	1	4	yes	—
70	C₁₃×#460	C₂²	1	2	yes	—
71	C₁₃×#460	C₂²	1	4	yes	—
72	C₁₃×#446	C₂²	1	2	yes	—
73	C₁₃×#446	C₂²	1	4	yes	—
74	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
75	C₁₃×#441	C₂²	1	4	yes	—
76	C₁₃×#441	C₂²	1	2	yes	—
77	C₁₃×#440	C₂²	1	4	yes	—
78	C₁₃×#440	C₂²	1	2	yes	—
79	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
80	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
81	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
82	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
83	C₁₃×#428	C₂²	1	2	yes	—
84	C₁₃×#428	C₂²	1	1	yes	characteristic
85	C₁₃×#423	C₂²	1	1	yes	characteristic
86	C₁₃×#423	C₂²	1	2	yes	—
87	C₁₃×#419	C₂²	1	1	yes	characteristic
88	C₁₃×#417	C₂²	1	2	yes	—
89	C₁₃×#417	C₂²	1	2	yes	—
90	C₁₃×#417	C₂²	1	2	yes	—
91	C₁₃×#417	C₂²	1	2	yes	—
92	C₁₃×#417	C₂²	1	1	yes	characteristic
93	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
94	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×#41	C₂³	1	2	yes	—
98	C₂²×Q₈×C₁₃	—	2	1	no	—
99	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
100	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×#137	—	2	4	no	—
102	C₁₃×#137	—	2	8	no	—
103	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
105	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
106	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
107	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
110	C₁₃×C₄⋊Q₈	—	2	2	no	—
111	C₁₃×C₄⋊Q₈	—	2	2	no	—
112	C₁₃×C₄⋊Q₈	—	2	4	no	—
113	C₁₃×C₄⋊Q₈	—	2	1	no	—
114	C₁₃×C₄⋊Q₈	—	2	1	no	—
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₁₃×#127	C₂³	1	1	yes	characteristic
120	C₁₃×#127	C₂³	1	2	yes	—
121	C₁₃×#126	—	2	2	no	—
122	C₁₃×#126	—	2	2	no	—
123	C₁₃×#126	—	2	2	no	—
124	C₁₃×#125	—	2	4	no	—
125	C₁₃×#125	—	2	4	no	—
126	C₁₃×#125	—	2	4	no	—
127	C₁₃×#125	—	2	4	no	—
128	C₁₃×#125	—	2	1	no	—
129	C₁₃×#125	—	2	2	no	—
130	C₁₃×#125	—	2	2	no	—
131	C₁₃×#125	—	2	2	no	—
132	C₁₃×#125	C₂³	1	4	yes	—
133	C₁₃×#125	C₂³	1	4	yes	—
134	C₁₃×#124	—	2	1	no	—
135	C₁₃×#124	—	2	2	no	—
136	C₁₃×#124	C₂³	1	2	yes	—
137	C₁₃×#124	C₂³	1	2	yes	—
138	C₁₃×#124	C₂³	1	2	yes	—
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×#123	—	2	2	no	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×C₂²⋊Q₈	—	2	1	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×#121	—	2	1	no	—
145	C₁₃×#121	—	2	2	no	—
146	C₁₃×#121	—	2	2	no	—
147	C₁₃×#121	—	2	1	no	—
148	C₁₃×#121	—	2	1	no	—
149	C₁₃×#121	—	2	2	no	—
150	C₄×Q₈×C₁₃	—	2	1	no	—
151	C₄×Q₈×C₁₃	—	2	2	no	—
152	C₄×Q₈×C₁₃	—	2	2	no	—
153	C₄×Q₈×C₁₃	—	2	4	no	—
154	C₄×Q₈×C₁₃	—	2	2	no	—
155	C₄×Q₈×C₁₃	—	2	2	no	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	—	2	1	no	—
158	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
159	C₄×Q₈×C₁₃	D₄	1	2	yes	—
160	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
162	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
163	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
165	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
166	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
167	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
172	C₄×D₄×C₁₃	—	2	1	no	—
173	C₄×D₄×C₁₃	—	2	2	no	—
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	2	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	—	2	1	no	—
180	C₄×D₄×C₁₃	—	2	2	no	—
181	C₄×D₄×C₁₃	—	2	1	no	—
182	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₁₃	C₂³	1	2	yes	—
184	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₁₃	C₂³	1	2	yes	—
186	C₁₃×#117	—	2	1	no	—
187	C₁₃×#117	—	2	2	no	—
188	C₁₃×#117	—	2	2	no	—
189	C₁₃×#117	—	2	1	no	—
190	C₁₃×#117	C₂³	1	1	yes	characteristic
191	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
194	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
197	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
198	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₄²×C₁₃	—	2	2	no	—
201	C₂×C₄²×C₁₃	—	2	1	no	—
202	C₂×C₄²×C₁₃	—	2	2	no	—
203	C₂×C₄²×C₁₃	—	2	1	no	—
204	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
205	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
206	C₁₃×#107	C₂³	1	4	yes	—
207	C₁₃×#107	C₂³	1	2	yes	—
208	C₁₃×#106	C₂³	1	4	yes	—
209	C₁₃×#106	C₂³	1	2	yes	—
210	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₁₃×#103	C₂³	1	4	yes	—
215	C₁₃×#103	C₂³	1	2	yes	—
216	C₁₃×#103	C₂³	1	4	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#103	C₂³	1	2	yes	—
220	C₁₃×#103	C₂³	1	2	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	2	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	4	yes	—
225	C₁₃×#102	C₂³	1	4	yes	—
226	C₁₃×#97	C₂³	1	2	yes	—
227	C₁₃×#97	C₂³	1	4	yes	—
228	C₄×C₈×C₁₃	C₂³	1	2	yes	—
229	C₄×C₈×C₁₃	C₂³	1	4	yes	—
230	#61320	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₁₃×#41	—	2	2	no	—
232	C₁₃×#41	—	2	4	no	—
233	C₁₃×#41	—	2	2	no	—
234	C₁₃×#41	—	2	4	no	—
235	C₁₃×#41	—	4	4	no	—
236	C₂×Q₈×C₁₃	—	2	1	no	—
237	C₂×Q₈×C₁₃	—	2	2	no	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	4	2	no	—
241	C₂×Q₈×C₁₃	—	4	4	no	—
242	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
245	C₂×Q₈×C₁₃	#41	1	4	yes	complemented
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×D₄×C₁₃	—	2	1	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	1	no	—
253	C₂×D₄×C₁₃	—	2	2	no	—
254	C₂×D₄×C₁₃	—	2	1	no	—
255	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	—	2	1	no	—
258	C₂²×C₄×C₁₃	—	2	1	no	—
259	C₂²×C₄×C₁₃	—	2	2	no	—
260	C₂²×C₄×C₁₃	—	2	2	no	—
261	C₂²×C₄×C₁₃	—	2	1	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	2	no	—
265	C₂²×C₄×C₁₃	—	2	1	no	—
266	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₁₃×Q₁₆	—	2	8	no	—
272	C₁₃×Q₁₆	—	2	4	no	—
273	C₁₃×SD₁₆	—	2	4	no	—
274	C₁₃×SD₁₆	—	2	8	no	—
275	C₁₃×M₁₆	—	2	2	no	—
276	C₁₃×M₁₆	—	2	4	no	—
277	C₁₃×M₁₆	—	2	2	no	—
278	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
279	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
280	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
281	C₁₃×C₄⋊C₄	—	2	4	no	—
282	C₁₃×C₄⋊C₄	—	2	4	no	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	2	no	—
285	C₁₃×C₄⋊C₄	—	2	4	no	—
286	C₁₃×C₄⋊C₄	—	2	4	no	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	4	no	—
290	C₁₃×C₄⋊C₄	—	2	4	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	1	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	—	2	2	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	C₂×D₄	1	1	yes	characteristic
302	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
303	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
304	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
305	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
306	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
307	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
311	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
312	C₁₃×C₂²⋊C₄	—	2	1	no	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	2	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	1	no	—
318	C₁₃×C₂²⋊C₄	—	2	1	no	—
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	C₄²×C₁₃	—	2	1	no	—
324	C₄²×C₁₃	—	2	2	no	—
325	C₄²×C₁₃	—	2	1	no	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	—	2	1	no	—
328	C₄²×C₁₃	—	2	4	no	—
329	C₄²×C₁₃	—	2	4	no	—
330	C₄²×C₁₃	—	2	2	no	—
331	C₄²×C₁₃	—	2	2	no	—
332	C₄²×C₁₃	C₂×D₄	1	2	yes	—
333	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₁₃	C₂×D₄	1	2	yes	—
335	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₁₃	C₂⁴	1	2	yes	—
337	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
338	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
339	C₄²×C₁₃	C₂⁴	1	2	yes	—
340	#3480	C₂×C₁₃	1	1	yes	characteristic
341	C₂×#557	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#3377	C₂×C₁₃	1	4	yes	complemented
343	#3374	C₂×C₁₃	1	2	yes	complemented
344	#3371	C₂×C₁₃	1	4	yes	complemented
345	#3368	C₂×C₁₃	1	2	yes	complemented
346	#3365	C₂×C₁₃	1	2	yes	complemented
347	#3364	C₂×C₁₃	1	2	yes	complemented
348	#3142	C₂×C₁₃	1	2	yes	complemented
349	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#3080	C₂×C₁₃	1	2	yes	complemented
351	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#3037	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3037	C₂×C₁₃	1	2	yes	complemented
354	Q₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
355	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
356	C₄×#137	C₂×C₁₃	1	2	yes	complemented
357	C₂³×C₁₃	—	2	2	no	—
358	C₂³×C₁₃	—	2	1	no	—
359	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
360	Q₈×C₁₃	—	2	4	no	—
361	Q₈×C₁₃	—	2	2	no	—
362	Q₈×C₁₃	—	2	2	no	—
363	Q₈×C₁₃	—	2	2	no	—
364	Q₈×C₁₃	—	2	2	no	—
365	Q₈×C₁₃	—	2	1	no	—
366	Q₈×C₁₃	—	2	2	no	—
367	Q₈×C₁₃	—	2	1	no	—
368	Q₈×C₁₃	—	4	2	no	—
369	Q₈×C₁₃	—	4	4	no	—
370	Q₈×C₁₃	—	4	4	no	—
371	Q₈×C₁₃	C₂×#41	1	4	yes	—
372	D₄×C₁₃	—	2	2	no	—
373	D₄×C₁₃	—	2	1	no	—
374	D₄×C₁₃	—	2	2	no	—
375	D₄×C₁₃	—	2	1	no	—
376	D₄×C₁₃	—	4	4	no	—
377	D₄×C₁₃	—	4	2	no	—
378	D₄×C₁₃	—	4	4	no	—
379	D₄×C₁₃	—	4	2	no	—
380	D₄×C₁₃	—	8	2	no	—
381	D₄×C₁₃	—	8	1	no	—
382	C₂×C₄×C₁₃	—	2	4	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	1	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	4	no	—
391	C₂×C₄×C₁₃	—	4	2	no	—
392	C₂×C₄×C₁₃	—	4	1	no	—
393	C₂×C₄×C₁₃	—	4	2	no	—
394	C₂×C₄×C₁₃	—	4	4	no	—
395	C₂×C₄×C₁₃	—	4	2	no	—
396	C₂×C₄×C₁₃	—	4	4	no	—
397	C₂×C₄×C₁₃	—	4	4	no	—
398	C₂×C₄×C₁₃	—	4	2	no	—
399	C₂×C₄×C₁₃	—	4	2	no	—
400	C₂×C₄×C₁₃	—	8	2	no	—
401	C₂×C₄×C₁₃	—	8	1	no	—
402	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
407	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
408	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
412	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
413	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
414	C₈×C₁₃	—	2	2	no	—
415	C₈×C₁₃	—	2	4	no	—
416	C₈×C₁₃	—	2	2	no	—
417	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×#137	C₂²×C₁₃	1	2	yes	—
419	#559	C₂²×C₁₃	1	1	yes	characteristic
420	#559	C₂²×C₁₃	1	2	yes	—
421	#557	—	2	1	no	—
422	#557	—	2	1	no	—
423	#557	—	2	2	no	—
424	#557	C₂²×C₁₃	1	1	yes	characteristic
425	#557	C₂²×C₁₃	1	2	yes	—
426	#557	C₂²×C₁₃	1	2	yes	—
427	#557	C₂²×C₁₃	1	4	yes	—
428	#556	C₂²×C₁₃	1	1	yes	characteristic
429	#556	C₂²×C₁₃	1	2	yes	—
430	#553	—	2	1	no	—
431	#553	—	2	2	no	—
432	#550	C₂²×C₁₃	1	1	yes	characteristic
433	#548	—	2	1	no	—
434	#532	C₂²×C₁₃	1	1	yes	characteristic
435	#532	C₂²×C₁₃	1	2	yes	—
436	C₂×C₄⋊Q₈	—	2	1	no	—
437	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
438	#529	—	2	2	no	—
439	#529	—	2	1	no	—
440	C₂×#125	—	2	2	no	—
441	C₂×#125	C₂²×C₁₃	1	2	yes	—
442	C₄×#41	—	2	1	no	—
443	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
444	C₄×#41	C₂²×C₁₃	1	2	yes	—
445	C₂×C₄×Q₈	—	2	1	no	—
446	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
447	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
448	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
449	#491	C₂²×C₁₃	1	4	yes	—
450	#490	C₂²×C₁₃	1	4	yes	—
451	#489	C₂²×C₁₃	1	4	yes	—
452	#488	C₂²×C₁₃	1	4	yes	—
453	#488	C₂²×C₁₃	1	4	yes	—
454	#487	C₂²×C₁₃	1	2	yes	—
455	#486	C₂²×C₁₃	1	2	yes	—
456	#479	C₂²×C₁₃	1	4	yes	—
457	#479	C₂²×C₁₃	1	4	yes	—
458	#478	C₂²×C₁₃	1	4	yes	—
459	#478	C₂²×C₁₃	1	4	yes	—
460	#477	C₂²×C₁₃	1	2	yes	—
461	#476	C₂²×C₁₃	1	2	yes	—
462	#475	C₂²×C₁₃	1	2	yes	—
463	#474	C₂²×C₁₃	1	2	yes	—
464	#464	C₂²×C₁₃	1	4	yes	—
465	#464	C₂²×C₁₃	1	4	yes	—
466	#464	C₂²×C₁₃	1	4	yes	—
467	#462	C₂²×C₁₃	1	2	yes	—
468	#462	C₂²×C₁₃	1	4	yes	—
469	#460	C₂²×C₁₃	1	2	yes	—
470	#460	C₂²×C₁₃	1	4	yes	—
471	#446	C₂²×C₁₃	1	2	yes	—
472	#446	C₂²×C₁₃	1	4	yes	—
473	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
474	#441	C₂²×C₁₃	1	4	yes	—
475	#441	C₂²×C₁₃	1	2	yes	—
476	#440	C₂²×C₁₃	1	4	yes	—
477	#440	C₂²×C₁₃	1	2	yes	—
478	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
479	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
480	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
481	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
482	#428	C₂²×C₁₃	1	2	yes	—
483	#428	C₂²×C₁₃	1	1	yes	characteristic
484	#423	C₂²×C₁₃	1	1	yes	characteristic
485	#423	C₂²×C₁₃	1	2	yes	—
486	#419	C₂²×C₁₃	1	1	yes	characteristic
487	#417	C₂²×C₁₃	1	2	yes	—
488	#417	C₂²×C₁₃	1	2	yes	—
489	#417	C₂²×C₁₃	1	2	yes	—
490	#417	C₂²×C₁₃	1	2	yes	—
491	#417	C₂²×C₁₃	1	1	yes	characteristic
492	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
493	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
494	C₂²×C₁₃	—	2	1	no	—
495	C₂²×C₁₃	—	2	1	no	—
496	C₂²×C₁₃	—	4	2	no	—
497	C₂²×C₁₃	—	4	1	no	—
498	C₂²×C₁₃	—	4	2	no	—
499	C₂²×C₁₃	—	4	1	no	—
500	C₂²×C₁₃	—	4	2	no	—
501	C₂²×C₁₃	—	4	1	no	—
502	C₂²×C₁₃	#548	1	2	yes	—
503	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
504	C₄×C₁₃	—	2	2	no	—
505	C₄×C₁₃	—	2	1	no	—
506	C₄×C₁₃	—	2	2	no	—
507	C₄×C₁₃	—	2	1	no	—
508	C₄×C₁₃	—	2	4	no	—
509	C₄×C₁₃	—	2	1	no	—
510	C₄×C₁₃	—	2	2	no	—
511	C₄×C₁₃	—	2	2	no	—
512	C₄×C₁₃	—	4	2	no	—
513	C₄×C₁₃	—	4	1	no	—
514	C₄×C₁₃	—	4	2	no	—
515	C₄×C₁₃	—	4	1	no	—
516	C₄×C₁₃	—	4	1	no	—
517	C₄×C₁₃	—	4	4	no	—
518	C₄×C₁₃	#548	1	2	yes	—
519	C₄×C₁₃	#575	1	2	yes	—
520	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
521	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
522	C₂×#41	—	2	1	no	—
523	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
524	C₂×#41	C₂³×C₁₃	1	2	yes	—
525	C₂²×Q₈	—	2	1	no	—
526	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
527	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
528	#137	—	2	4	no	—
529	#137	—	2	8	no	—
530	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
531	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
532	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
533	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
534	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
535	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
536	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
537	C₄⋊Q₈	—	2	2	no	—
538	C₄⋊Q₈	—	2	2	no	—
539	C₄⋊Q₈	—	2	4	no	—
540	C₄⋊Q₈	—	2	1	no	—
541	C₄⋊Q₈	—	2	1	no	—
542	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
543	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
544	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
545	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
546	#127	C₂³×C₁₃	1	1	yes	characteristic
547	#127	C₂³×C₁₃	1	2	yes	—
548	#126	—	2	2	no	—
549	#126	—	2	2	no	—
550	#126	—	2	2	no	—
551	#125	—	2	4	no	—
552	#125	—	2	4	no	—
553	#125	—	2	4	no	—
554	#125	—	2	4	no	—
555	#125	—	2	1	no	—
556	#125	—	2	2	no	—
557	#125	—	2	2	no	—
558	#125	—	2	2	no	—
559	#125	C₂³×C₁₃	1	4	yes	—
560	#125	C₂³×C₁₃	1	4	yes	—
561	#124	—	2	1	no	—
562	#124	—	2	2	no	—
563	#124	C₂³×C₁₃	1	2	yes	—
564	#124	C₂³×C₁₃	1	2	yes	—
565	#124	C₂³×C₁₃	1	2	yes	—
566	#123	—	2	2	no	—
567	#123	—	2	2	no	—
568	#123	—	2	2	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	#121	—	2	1	no	—
572	#121	—	2	2	no	—
573	#121	—	2	2	no	—
574	#121	—	2	1	no	—
575	#121	—	2	1	no	—
576	#121	—	2	2	no	—
577	C₄×Q₈	—	2	1	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	2	no	—
580	C₄×Q₈	—	2	4	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	—	2	2	no	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	—	2	1	no	—
585	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
586	C₄×Q₈	D₄×C₁₃	1	2	yes	—
587	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
588	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
589	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
590	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
591	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
592	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
593	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
594	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
595	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
596	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
597	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
598	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
599	C₄×D₄	—	2	1	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
610	C₄×D₄	C₂³×C₁₃	1	2	yes	—
611	C₄×D₄	C₂³×C₁₃	1	2	yes	—
612	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
613	#117	—	2	1	no	—
614	#117	—	2	2	no	—
615	#117	—	2	2	no	—
616	#117	—	2	1	no	—
617	#117	C₂³×C₁₃	1	1	yes	characteristic
618	C₂×C₄⋊C₄	—	2	2	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	2	no	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	—	2	2	no	—
623	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
624	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
627	C₂×C₄²	—	2	2	no	—
628	C₂×C₄²	—	2	1	no	—
629	C₂×C₄²	—	2	2	no	—
630	C₂×C₄²	—	2	1	no	—
631	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
632	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
633	#107	C₂³×C₁₃	1	4	yes	—
634	#107	C₂³×C₁₃	1	2	yes	—
635	#106	C₂³×C₁₃	1	4	yes	—
636	#106	C₂³×C₁₃	1	2	yes	—
637	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
638	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
639	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
640	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
641	#103	C₂³×C₁₃	1	4	yes	—
642	#103	C₂³×C₁₃	1	2	yes	—
643	#103	C₂³×C₁₃	1	4	yes	—
644	#103	C₂³×C₁₃	1	4	yes	—
645	#103	C₂³×C₁₃	1	4	yes	—
646	#103	C₂³×C₁₃	1	2	yes	—
647	#103	C₂³×C₁₃	1	2	yes	—
648	#102	C₂³×C₁₃	1	4	yes	—
649	#102	C₂³×C₁₃	1	2	yes	—
650	#102	C₂³×C₁₃	1	4	yes	—
651	#102	C₂³×C₁₃	1	4	yes	—
652	#102	C₂³×C₁₃	1	4	yes	—
653	#97	C₂³×C₁₃	1	2	yes	—
654	#97	C₂³×C₁₃	1	4	yes	—
655	C₄×C₈	C₂³×C₁₃	1	2	yes	—
656	C₄×C₈	C₂³×C₁₃	1	4	yes	—
657	C₂×C₁₃	—	2	2	no	—
658	C₂×C₁₃	—	8	2	no	—
659	C₂×C₁₃	—	8	1	no	—
660	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
661	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
662	C₂×C₁₃	#3586	1	1	yes	characteristic
663	#41	—	2	2	no	—
664	#41	—	2	4	no	—
665	#41	—	2	2	no	—
666	#41	—	2	4	no	—
667	#41	—	4	4	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	4	2	no	—
673	C₂×Q₈	—	4	4	no	—
674	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
675	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
676	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
677	C₂×Q₈	C₁₃×#41	1	4	yes	complemented
678	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
679	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
680	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
688	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
699	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
700	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
701	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
703	Q₁₆	—	2	8	no	—
704	Q₁₆	—	2	4	no	—
705	SD₁₆	—	2	4	no	—
706	SD₁₆	—	2	8	no	—
707	M₁₆	—	2	2	no	—
708	M₁₆	—	2	4	no	—
709	M₁₆	—	2	2	no	—
710	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
711	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
712	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
734	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
735	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
736	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
737	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
738	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
739	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
740	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
742	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
743	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₄²	—	2	1	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	1	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	4	no	—
761	C₄²	—	2	4	no	—
762	C₄²	—	2	2	no	—
763	C₄²	—	2	2	no	—
764	C₄²	C₂×D₄×C₁₃	1	2	yes	—
765	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
766	C₄²	C₂×D₄×C₁₃	1	2	yes	—
767	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
768	C₄²	C₂⁴×C₁₃	1	2	yes	—
769	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
770	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
771	C₄²	C₂⁴×C₁₃	1	2	yes	—
772	C₁₃	#61320	1	1	yes	characteristic, direct product factor, Sylow
773	C₂³	—	2	2	no	—
774	C₂³	—	2	1	no	—
775	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
776	Q₈	—	2	4	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	2	2	no	—
779	Q₈	—	2	2	no	—
780	Q₈	—	2	2	no	—
781	Q₈	—	2	1	no	—
782	Q₈	—	2	2	no	—
783	Q₈	—	2	1	no	—
784	Q₈	—	4	2	no	—
785	Q₈	—	4	4	no	—
786	Q₈	—	4	4	no	—
787	Q₈	C₂×C₁₃×#41	1	4	yes	—
788	D₄	—	2	2	no	—
789	D₄	—	2	1	no	—
790	D₄	—	2	2	no	—
791	D₄	—	2	1	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	2	no	—
794	D₄	—	4	4	no	—
795	D₄	—	4	2	no	—
796	D₄	—	8	2	no	—
797	D₄	—	8	1	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	4	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	4	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	8	2	no	—
817	C₂×C₄	—	8	1	no	—
818	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
819	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
820	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
821	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
822	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
823	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
827	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
828	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
829	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
830	C₈	—	2	2	no	—
831	C₈	—	2	4	no	—
832	C₈	—	2	2	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	1	no	—
841	C₂²	C₁₃×#548	1	2	yes	—
842	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
843	C₄	—	2	1	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	2	no	—
847	C₄	—	2	1	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	1	no	—
850	C₄	—	2	4	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	4	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	1	no	—
857	C₄	C₁₃×#548	1	2	yes	—
858	C₄	C₁₃×#575	1	2	yes	—
859	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
860	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
861	C₂	—	2	2	no	—
862	C₂	—	8	2	no	—
863	C₂	—	8	1	no	—
864	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
865	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
866	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3480	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#557	C₂	semidirect
3. C₁₃×#3377	C₂	semidirect
4. C₁₃×#3374	C₂	semidirect
5. C₁₃×#3371	C₂	semidirect
6. C₁₃×#3368	C₂	semidirect
7. C₁₃×#3365	C₂	semidirect
8. C₁₃×#3364	C₂	semidirect
9. C₁₃×#3142	C₂	semidirect
10. C₁₃×#3141	C₂	semidirect
11. C₁₃×#3080	C₂	semidirect
12. C₁₃×#3079	C₂	semidirect
13. C₁₃×#3037	C₂	semidirect
14. C₁₃×#3037	C₂	semidirect
15. Q₈×C₁₃×M₁₆	C₂	semidirect
16. C₄×C₁₃×#137	C₂	semidirect
17. C₄×C₁₃×#137	C₂	semidirect
230. #61320	C₁₃	direct (N × H)
245. C₂×Q₈×C₁₃	#41	semidirect
341. C₂×#557	C₂×C₁₃	semidirect
342. #3377	C₂×C₁₃	semidirect
343. #3374	C₂×C₁₃	semidirect
344. #3371	C₂×C₁₃	semidirect
345. #3368	C₂×C₁₃	semidirect
346. #3365	C₂×C₁₃	semidirect
347. #3364	C₂×C₁₃	semidirect
348. #3142	C₂×C₁₃	semidirect
349. #3141	C₂×C₁₃	semidirect
350. #3080	C₂×C₁₃	semidirect
351. #3079	C₂×C₁₃	semidirect
352. #3037	C₂×C₁₃	semidirect
353. #3037	C₂×C₁₃	semidirect
354. Q₈×M₁₆	C₂×C₁₃	semidirect
355. C₄×#137	C₂×C₁₃	semidirect
356. C₄×#137	C₂×C₁₃	semidirect
677. C₂×Q₈	C₁₃×#41	semidirect
772. C₁₃	#61320	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×#3480	2
C₂×C₁₃×#557	2
C₁₃×#3377	2
C₁₃×#3374	2
C₁₃×#3371	2
C₁₃×#3368	2
C₁₃×#3365	2
C₁₃×#3364	2
C₁₃×#3142	2
C₁₃×#3141	2
C₁₃×#3080	2
C₁₃×#3079	2
C₁₃×#3037	2
Q₈×C₁₃×M₁₆	2
C₄×C₁₃×#137	2
#61320	13

Subgroups — C13×#61320 #15747659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61320 #15747659