Subgroups — C₁₃×#62144 #15748483

Order 3328.

1774 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3481	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3381	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3365	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3356	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3351	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3324	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3323	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3252	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3233	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3101	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3077	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2991	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#559	C₂²	1	1	yes	characteristic
19	C₁₃×#557	—	2	1	no	—
20	C₁₃×#557	C₂²	1	2	yes	complemented
21	C₁₃×#556	—	2	1	no	—
22	C₁₃×#556	C₂²	1	2	yes	—
23	C₁₃×#554	C₂²	1	1	yes	characteristic
24	C₁₃×#554	C₂²	1	1	yes	characteristic
25	C₁₃×#553	—	2	1	no	—
26	C₁₃×#553	C₂²	1	2	yes	—
27	C₁₃×#552	—	2	2	no	—
28	C₁₃×#552	C₂²	1	4	yes	complemented
29	C₁₃×#551	—	2	2	no	—
30	C₁₃×#546	—	2	1	no	—
31	C₁₃×#546	C₂²	1	2	yes	—
32	D₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#541	—	2	2	no	—
34	C₁₃×#536	—	2	1	no	—
35	C₁₃×#533	C₂²	1	2	yes	complemented
36	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#533	C₂²	1	2	yes	complemented
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#529	—	2	1	no	—
41	C₁₃×#529	C₂²	1	2	yes	—
42	C₁₃×#525	—	2	2	no	—
43	C₁₃×#519	—	2	1	no	—
44	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
45	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	—	2	1	no	—
47	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
48	C₁₃×#499	C₂²	1	4	yes	complemented
49	C₁₃×#498	C₂²	1	2	yes	complemented
50	C₁₃×#488	C₂²	1	4	yes	complemented
51	C₁₃×#486	C₂²	1	2	yes	—
52	C₁₃×#485	C₂²	1	4	yes	complemented
53	C₁₃×#485	C₂²	1	2	yes	complemented
54	C₁₃×#483	C₂²	1	4	yes	complemented
55	C₁₃×#482	C₂²	1	4	yes	—
56	C₁₃×#481	C₂²	1	4	yes	complemented
57	C₁₃×#479	C₂²	1	4	yes	complemented
58	C₁₃×#478	C₂²	1	4	yes	—
59	C₁₃×#478	C₂²	1	4	yes	complemented
60	C₁₃×#477	C₂²	1	2	yes	complemented
61	C₁₃×#477	C₂²	1	2	yes	complemented
62	C₁₃×#476	C₂²	1	2	yes	—
63	C₁₃×#476	C₂²	1	2	yes	complemented
64	C₁₃×#476	C₂²	1	2	yes	complemented
65	C₁₃×#475	C₂²	1	2	yes	complemented
66	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#474	C₂²	1	2	yes	—
68	C₁₃×#474	C₂²	1	1	yes	characteristic
69	C₁₃×#474	C₂²	1	2	yes	complemented
70	C₁₃×#470	C₂²	1	4	yes	complemented
71	C₁₃×#468	C₂²	1	4	yes	—
72	C₁₃×#468	C₂²	1	4	yes	complemented
73	C₁₃×#464	C₂²	1	4	yes	complemented
74	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#461	C₂²	1	1	yes	characteristic
76	C₁₃×#461	C₂²	1	2	yes	complemented
77	C₁₃×#460	C₂²	1	2	yes	—
78	C₁₃×#452	C₂²	1	2	yes	—
79	C₁₃×#450	C₂²	1	4	yes	—
80	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
81	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
82	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
83	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
84	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
85	C₁₃×#436	C₂²	1	2	yes	—
86	C₁₃×#436	C₂²	1	4	yes	complemented
87	C₁₃×#431	C₂²	1	2	yes	complemented
88	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#428	C₂²	1	4	yes	complemented
90	C₁₃×#428	C₂²	1	2	yes	complemented
91	C₁₃×#423	C₂²	1	2	yes	complemented
92	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#418	C₂²	1	4	yes	—
94	C₁₃×#417	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
97	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₁₃	—	2	1	no	—
99	C₂²×D₄×C₁₃	—	2	1	no	—
100	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃	—	2	2	no	—
102	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
103	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
106	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
107	C₁₃×C₄⋊Q₈	—	2	2	no	—
108	C₁₃×C₄⋊Q₈	—	2	1	no	—
109	C₁₃×C₄⋊Q₈	—	2	1	no	—
110	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₃×#127	C₂³	1	1	yes	characteristic
116	C₁₃×#126	—	2	2	no	—
117	C₁₃×#126	—	2	4	no	—
118	C₁₃×#126	—	2	4	no	—
119	C₁₃×#126	—	2	2	no	—
120	C₁₃×#125	—	2	1	no	—
121	C₁₃×#125	—	2	4	no	—
122	C₁₃×#125	—	2	4	no	—
123	C₁₃×#125	—	2	1	no	—
124	C₁₃×#125	—	2	2	no	—
125	C₁₃×#125	C₂³	1	4	yes	—
126	C₁₃×#125	C₂³	1	2	yes	—
127	C₁₃×#124	—	2	1	no	—
128	C₁₃×#124	—	2	2	no	—
129	C₁₃×#124	—	2	1	no	—
130	C₁₃×#124	C₂³	1	2	yes	—
131	C₁₃×#123	—	2	4	no	—
132	C₁₃×#123	—	2	2	no	—
133	C₁₃×#123	—	2	2	no	—
134	C₁₃×#123	—	2	2	no	—
135	C₁₃×#123	—	2	2	no	—
136	C₁₃×C₂²⋊Q₈	—	2	1	no	—
137	C₁₃×C₂²⋊Q₈	—	2	2	no	—
138	C₁₃×C₂²⋊Q₈	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	1	no	—
140	C₁₃×C₂²⋊Q₈	—	2	2	no	—
141	C₁₃×C₂²⋊Q₈	—	2	2	no	—
142	C₁₃×C₂²⋊Q₈	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
144	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
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	C₁₃×#121	C₂³	1	2	yes	—
151	C₁₃×#121	C₂³	1	2	yes	—
152	C₁₃×#120	—	2	2	no	—
153	C₁₃×#120	—	2	2	no	—
154	C₄×Q₈×C₁₃	—	2	2	no	—
155	C₄×Q₈×C₁₃	—	2	2	no	—
156	C₄×Q₈×C₁₃	—	2	2	no	—
157	C₄×Q₈×C₁₃	—	2	2	no	—
158	C₄×Q₈×C₁₃	—	2	2	no	—
159	C₄×Q₈×C₁₃	—	2	1	no	—
160	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
162	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
163	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
166	C₄×D₄×C₁₃	—	2	1	no	—
167	C₄×D₄×C₁₃	—	2	2	no	—
168	C₄×D₄×C₁₃	—	2	1	no	—
169	C₄×D₄×C₁₃	—	2	1	no	—
170	C₄×D₄×C₁₃	—	2	1	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
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	D₄	1	1	yes	characteristic
176	C₄×D₄×C₁₃	D₄	1	2	yes	—
177	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₁₃	C₂³	1	2	yes	—
179	C₄×D₄×C₁₃	C₂³	1	2	yes	—
180	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₁₃	C₂³	1	2	yes	—
182	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₁₃	C₂³	1	2	yes	—
184	C₁₃×#117	—	2	1	no	—
185	C₁₃×#117	—	2	2	no	—
186	C₁₃×#117	—	2	4	no	—
187	C₁₃×#117	—	2	1	no	—
188	C₁₃×#117	—	2	2	no	—
189	C₁₃×#117	D₄	1	1	yes	characteristic
190	C₁₃×#117	D₄	1	2	yes	—
191	C₁₃×#117	C₂³	1	4	yes	—
192	C₁₃×#117	C₂³	1	1	yes	characteristic
193	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
198	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₄²×C₁₃	—	2	1	no	—
200	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₁₃×#107	C₂³	1	2	yes	—
203	C₁₃×#107	C₂³	1	4	yes	—
204	C₁₃×#107	C₂³	1	4	yes	—
205	C₁₃×#106	C₂³	1	4	yes	—
206	C₁₃×#106	C₂³	1	4	yes	—
207	C₁₃×#106	C₂³	1	2	yes	—
208	C₁₃×#106	C₂³	1	4	yes	—
209	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
210	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
211	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₁₃×#103	C₂³	1	4	yes	—
215	C₁₃×#103	C₂³	1	4	yes	—
216	C₁₃×#103	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	2	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	2	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
225	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₄×C₈×C₁₃	C₂³	1	2	yes	—
227	C₄×C₈×C₁₃	C₂³	1	4	yes	—
228	#62144	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂⁴×C₁₃	—	2	2	no	—
230	C₁₃×#41	—	2	2	no	—
231	C₁₃×#41	—	4	2	no	—
232	C₁₃×#41	—	4	1	no	—
233	C₁₃×#41	—	8	2	no	—
234	C₂×Q₈×C₁₃	—	2	1	no	—
235	C₂×Q₈×C₁₃	—	2	2	no	—
236	C₂×Q₈×C₁₃	—	2	2	no	—
237	C₂×Q₈×C₁₃	—	2	1	no	—
238	C₂×Q₈×C₁₃	—	4	4	no	—
239	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
242	C₂×D₄×C₁₃	—	2	4	no	—
243	C₂×D₄×C₁₃	—	2	1	no	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	2	1	no	—
248	C₂×D₄×C₁₃	—	2	1	no	—
249	C₂×D₄×C₁₃	—	4	2	no	—
250	C₂×D₄×C₁₃	—	4	4	no	—
251	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
252	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
253	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	2	no	—
257	C₂²×C₄×C₁₃	—	2	1	no	—
258	C₂²×C₄×C₁₃	—	2	1	no	—
259	C₂²×C₄×C₁₃	—	2	1	no	—
260	C₂²×C₄×C₁₃	—	2	2	no	—
261	C₂²×C₄×C₁₃	—	2	2	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	—	8	4	no	—
264	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
270	C₁₃×Q₁₆	—	4	2	no	—
271	C₁₃×SD₁₆	—	2	4	no	—
272	C₁₃×SD₁₆	—	4	4	no	—
273	C₁₃×M₁₆	—	4	2	no	—
274	C₁₃×M₁₆	—	4	4	no	—
275	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
276	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
277	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
278	C₁₃×C₄⋊C₄	—	2	2	no	—
279	C₁₃×C₄⋊C₄	—	2	1	no	—
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	—	2	1	no	—
286	C₁₃×C₄⋊C₄	—	2	1	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	—	2	1	no	—
289	C₁₃×C₄⋊C₄	—	2	4	no	—
290	C₁₃×C₄⋊C₄	—	2	4	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	4	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	4	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
298	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
299	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
300	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
301	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
304	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
306	C₁₃×C₂²⋊C₄	—	2	2	no	—
307	C₁₃×C₂²⋊C₄	—	2	2	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	2	1	no	—
310	C₁₃×C₂²⋊C₄	—	2	4	no	—
311	C₁₃×C₂²⋊C₄	—	2	1	no	—
312	C₁₃×C₂²⋊C₄	—	2	2	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	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
321	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
322	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
323	C₄²×C₁₃	—	2	1	no	—
324	C₄²×C₁₃	—	2	1	no	—
325	C₄²×C₁₃	—	2	1	no	—
326	C₄²×C₁₃	—	2	4	no	—
327	C₄²×C₁₃	—	2	4	no	—
328	C₄²×C₁₃	—	2	2	no	—
329	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₁₃	C₂×D₄	1	2	yes	—
332	C₄²×C₁₃	C₂×D₄	1	2	yes	—
333	C₄²×C₁₃	C₂⁴	1	2	yes	—
334	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
335	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
336	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#3481	C₂×C₁₃	1	1	yes	characteristic
338	#3381	C₂×C₁₃	1	2	yes	complemented
339	#3365	C₂×C₁₃	1	2	yes	complemented
340	#3356	C₂×C₁₃	1	2	yes	complemented
341	#3351	C₂×C₁₃	1	4	yes	complemented
342	#3324	C₂×C₁₃	1	2	yes	complemented
343	#3323	C₂×C₁₃	1	4	yes	complemented
344	#3254	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3252	C₂×C₁₃	1	2	yes	complemented
346	#3233	C₂×C₁₃	1	2	yes	complemented
347	#3227	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3107	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3101	C₂×C₁₃	1	2	yes	complemented
350	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#3077	C₂×C₁₃	1	2	yes	complemented
352	#2991	C₂×C₁₃	1	1	yes	characteristic, complemented
353	C₂³×C₁₃	—	2	1	no	—
354	C₂³×C₁₃	—	2	2	no	—
355	C₂³×C₁₃	—	4	4	no	—
356	C₂³×C₁₃	—	4	4	no	—
357	C₂³×C₁₃	—	8	2	no	—
358	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
359	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
360	Q₈×C₁₃	—	2	2	no	—
361	Q₈×C₁₃	—	2	2	no	—
362	Q₈×C₁₃	—	2	1	no	—
363	Q₈×C₁₃	—	2	2	no	—
364	Q₈×C₁₃	—	2	1	no	—
365	Q₈×C₁₃	—	4	4	no	—
366	Q₈×C₁₃	—	4	4	no	—
367	Q₈×C₁₃	—	4	2	no	—
368	Q₈×C₁₃	—	8	1	no	—
369	D₄×C₁₃	—	2	2	no	—
370	D₄×C₁₃	—	2	2	no	—
371	D₄×C₁₃	—	2	1	no	—
372	D₄×C₁₃	—	2	2	no	—
373	D₄×C₁₃	—	4	2	no	—
374	D₄×C₁₃	—	4	4	no	—
375	D₄×C₁₃	—	4	2	no	—
376	D₄×C₁₃	—	4	4	no	—
377	D₄×C₁₃	—	4	2	no	—
378	D₄×C₁₃	—	8	1	no	—
379	D₄×C₁₃	—	8	2	no	—
380	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
381	C₂×C₄×C₁₃	—	2	2	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	2	no	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	1	no	—
392	C₂×C₄×C₁₃	—	2	1	no	—
393	C₂×C₄×C₁₃	—	2	4	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	4	2	no	—
396	C₂×C₄×C₁₃	—	4	2	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	—	4	4	no	—
401	C₂×C₄×C₁₃	—	8	2	no	—
402	C₂×C₄×C₁₃	—	8	2	no	—
403	C₂×C₄×C₁₃	—	8	2	no	—
404	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
413	C₈×C₁₃	—	2	2	no	—
414	C₈×C₁₃	—	2	4	no	—
415	C₈×C₁₃	—	2	2	no	—
416	#559	C₂²×C₁₃	1	1	yes	characteristic
417	#557	—	2	1	no	—
418	#557	C₂²×C₁₃	1	2	yes	complemented
419	#556	—	2	1	no	—
420	#556	C₂²×C₁₃	1	2	yes	—
421	#554	C₂²×C₁₃	1	1	yes	characteristic
422	#554	C₂²×C₁₃	1	1	yes	characteristic
423	#553	—	2	1	no	—
424	#553	C₂²×C₁₃	1	2	yes	—
425	#552	—	2	2	no	—
426	#552	C₂²×C₁₃	1	4	yes	complemented
427	#551	—	2	2	no	—
428	#546	—	2	1	no	—
429	#546	C₂²×C₁₃	1	2	yes	—
430	D₄²	C₂²×C₁₃	1	1	yes	characteristic
431	#541	—	2	2	no	—
432	#536	—	2	1	no	—
433	#533	C₂²×C₁₃	1	2	yes	complemented
434	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
435	#533	C₂²×C₁₃	1	2	yes	complemented
436	#532	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
438	#529	—	2	1	no	—
439	#529	C₂²×C₁₃	1	2	yes	—
440	#525	—	2	2	no	—
441	#519	—	2	1	no	—
442	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
443	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
444	C₂×C₄×D₄	—	2	1	no	—
445	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
446	#499	C₂²×C₁₃	1	4	yes	complemented
447	#498	C₂²×C₁₃	1	2	yes	complemented
448	#488	C₂²×C₁₃	1	4	yes	complemented
449	#486	C₂²×C₁₃	1	2	yes	—
450	#485	C₂²×C₁₃	1	2	yes	complemented
451	#485	C₂²×C₁₃	1	4	yes	complemented
452	#483	C₂²×C₁₃	1	4	yes	complemented
453	#482	C₂²×C₁₃	1	4	yes	—
454	#481	C₂²×C₁₃	1	4	yes	complemented
455	#479	C₂²×C₁₃	1	4	yes	complemented
456	#478	C₂²×C₁₃	1	4	yes	—
457	#478	C₂²×C₁₃	1	4	yes	complemented
458	#477	C₂²×C₁₃	1	2	yes	complemented
459	#477	C₂²×C₁₃	1	2	yes	complemented
460	#476	C₂²×C₁₃	1	2	yes	—
461	#476	C₂²×C₁₃	1	2	yes	complemented
462	#476	C₂²×C₁₃	1	2	yes	complemented
463	#475	C₂²×C₁₃	1	2	yes	complemented
464	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
465	#474	C₂²×C₁₃	1	1	yes	characteristic
466	#474	C₂²×C₁₃	1	2	yes	—
467	#474	C₂²×C₁₃	1	2	yes	complemented
468	#470	C₂²×C₁₃	1	4	yes	complemented
469	#468	C₂²×C₁₃	1	4	yes	—
470	#468	C₂²×C₁₃	1	4	yes	complemented
471	#464	C₂²×C₁₃	1	4	yes	complemented
472	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
473	#461	C₂²×C₁₃	1	1	yes	characteristic
474	#461	C₂²×C₁₃	1	2	yes	complemented
475	#460	C₂²×C₁₃	1	2	yes	—
476	#452	C₂²×C₁₃	1	2	yes	—
477	#450	C₂²×C₁₃	1	4	yes	—
478	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
479	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
480	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
481	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
482	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
483	#436	C₂²×C₁₃	1	2	yes	—
484	#436	C₂²×C₁₃	1	4	yes	complemented
485	#431	C₂²×C₁₃	1	2	yes	complemented
486	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
487	#428	C₂²×C₁₃	1	4	yes	complemented
488	#428	C₂²×C₁₃	1	2	yes	complemented
489	#423	C₂²×C₁₃	1	2	yes	complemented
490	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
491	#418	C₂²×C₁₃	1	4	yes	—
492	#417	C₂²×C₁₃	1	2	yes	—
493	C₂²×C₁₃	—	2	1	no	—
494	C₂²×C₁₃	—	2	2	no	—
495	C₂²×C₁₃	—	2	2	no	—
496	C₂²×C₁₃	—	2	1	no	—
497	C₂²×C₁₃	—	2	2	no	—
498	C₂²×C₁₃	—	2	2	no	—
499	C₂²×C₁₃	—	2	1	no	—
500	C₂²×C₁₃	—	4	1	no	—
501	C₂²×C₁₃	—	4	1	no	—
502	C₂²×C₁₃	—	4	2	no	—
503	C₂²×C₁₃	—	4	2	no	—
504	C₂²×C₁₃	—	4	2	no	—
505	C₂²×C₁₃	—	8	8	no	—
506	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
507	C₄×C₁₃	—	2	1	no	—
508	C₄×C₁₃	—	2	2	no	—
509	C₄×C₁₃	—	2	1	no	—
510	C₄×C₁₃	—	2	2	no	—
511	C₄×C₁₃	—	2	2	no	—
512	C₄×C₁₃	—	2	1	no	—
513	C₄×C₁₃	—	4	1	no	—
514	C₄×C₁₃	—	4	2	no	—
515	C₄×C₁₃	—	4	1	no	—
516	C₄×C₁₃	—	4	4	no	—
517	C₄×C₁₃	—	4	1	no	—
518	C₄×C₁₃	—	4	2	no	—
519	C₄×C₁₃	—	4	2	no	—
520	C₄×C₁₃	#575	1	2	yes	—
521	C₄×C₁₃	#577	1	2	yes	—
522	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
523	C₄×C₁₃	#585	1	1	yes	characteristic
524	C₂×#41	—	2	1	no	—
525	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
526	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
527	C₂²×Q₈	—	2	1	no	—
528	C₂²×D₄	—	2	1	no	—
529	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
530	C₂³×C₄	—	2	2	no	—
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	2	yes	—
535	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
536	C₄⋊Q₈	—	2	2	no	—
537	C₄⋊Q₈	—	2	1	no	—
538	C₄⋊Q₈	—	2	1	no	—
539	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
540	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
541	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
542	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
543	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
544	#127	C₂³×C₁₃	1	1	yes	characteristic
545	#126	—	2	2	no	—
546	#126	—	2	4	no	—
547	#126	—	2	4	no	—
548	#126	—	2	2	no	—
549	#125	—	2	1	no	—
550	#125	—	2	4	no	—
551	#125	—	2	4	no	—
552	#125	—	2	1	no	—
553	#125	—	2	2	no	—
554	#125	C₂³×C₁₃	1	2	yes	—
555	#125	C₂³×C₁₃	1	4	yes	—
556	#124	—	2	1	no	—
557	#124	—	2	2	no	—
558	#124	—	2	1	no	—
559	#124	C₂³×C₁₃	1	2	yes	—
560	#123	—	2	4	no	—
561	#123	—	2	2	no	—
562	#123	—	2	2	no	—
563	#123	—	2	2	no	—
564	#123	—	2	2	no	—
565	C₂²⋊Q₈	—	2	1	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
573	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
574	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
575	#121	—	2	2	no	—
576	#121	—	2	1	no	—
577	#121	—	2	1	no	—
578	#121	—	2	2	no	—
579	#121	C₂³×C₁₃	1	2	yes	—
580	#121	C₂³×C₁₃	1	2	yes	—
581	#120	—	2	2	no	—
582	#120	—	2	2	no	—
583	C₄×Q₈	—	2	2	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	2	no	—
587	C₄×Q₈	—	2	2	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
590	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
591	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
593	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
594	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	1	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
605	C₄×D₄	D₄×C₁₃	1	2	yes	—
606	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
607	C₄×D₄	C₂³×C₁₃	1	2	yes	—
608	C₄×D₄	C₂³×C₁₃	1	2	yes	—
609	C₄×D₄	C₂³×C₁₃	1	2	yes	—
610	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
611	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
612	C₄×D₄	C₂³×C₁₃	1	2	yes	—
613	#117	—	2	1	no	—
614	#117	—	2	2	no	—
615	#117	—	2	4	no	—
616	#117	—	2	1	no	—
617	#117	—	2	2	no	—
618	#117	D₄×C₁₃	1	1	yes	characteristic
619	#117	D₄×C₁₃	1	2	yes	—
620	#117	C₂³×C₁₃	1	1	yes	characteristic
621	#117	C₂³×C₁₃	1	4	yes	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
626	C₂×C₂²⋊C₄	—	2	2	no	—
627	C₂×C₂²⋊C₄	—	2	2	no	—
628	C₂×C₄²	—	2	1	no	—
629	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
630	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
631	#107	C₂³×C₁₃	1	2	yes	—
632	#107	C₂³×C₁₃	1	4	yes	—
633	#107	C₂³×C₁₃	1	4	yes	—
634	#106	C₂³×C₁₃	1	4	yes	—
635	#106	C₂³×C₁₃	1	4	yes	—
636	#106	C₂³×C₁₃	1	2	yes	—
637	#106	C₂³×C₁₃	1	4	yes	—
638	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
639	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
640	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
641	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
642	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
643	#103	C₂³×C₁₃	1	4	yes	—
644	#103	C₂³×C₁₃	1	4	yes	—
645	#103	C₂³×C₁₃	1	2	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	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
654	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
655	C₄×C₈	C₂³×C₁₃	1	2	yes	—
656	C₄×C₈	C₂³×C₁₃	1	4	yes	—
657	C₂×C₁₃	—	4	1	no	—
658	C₂×C₁₃	—	4	2	no	—
659	C₂×C₁₃	—	4	2	no	—
660	C₂×C₁₃	—	8	2	no	—
661	C₂×C₁₃	#3489	1	1	yes	characteristic
662	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
663	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
664	C₂⁴	—	2	2	no	—
665	#41	—	2	2	no	—
666	#41	—	4	2	no	—
667	#41	—	4	1	no	—
668	#41	—	8	2	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	4	4	no	—
674	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
675	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
676	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	4	2	no	—
685	C₂×D₄	—	4	4	no	—
686	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
687	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
688	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
689	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	8	4	no	—
699	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
700	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
701	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
702	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
705	Q₁₆	—	4	2	no	—
706	SD₁₆	—	2	4	no	—
707	SD₁₆	—	4	4	no	—
708	M₁₆	—	4	2	no	—
709	M₁₆	—	4	4	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	2	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
733	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
734	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
735	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
736	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
737	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
739	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
740	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
756	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
757	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
758	C₄²	—	2	1	no	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	1	no	—
761	C₄²	—	2	4	no	—
762	C₄²	—	2	4	no	—
763	C₄²	—	2	2	no	—
764	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
765	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
766	C₄²	C₂×D₄×C₁₃	1	2	yes	—
767	C₄²	C₂×D₄×C₁₃	1	2	yes	—
768	C₄²	C₂⁴×C₁₃	1	2	yes	—
769	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
770	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
771	C₁₃	#62144	1	1	yes	characteristic, direct product factor, Sylow
772	C₂³	—	2	1	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	4	4	no	—
775	C₂³	—	4	4	no	—
776	C₂³	—	8	2	no	—
777	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
778	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
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	4	no	—
785	Q₈	—	4	4	no	—
786	Q₈	—	4	2	no	—
787	Q₈	—	8	1	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	2	no	—
790	D₄	—	2	1	no	—
791	D₄	—	2	2	no	—
792	D₄	—	4	2	no	—
793	D₄	—	4	4	no	—
794	D₄	—	4	2	no	—
795	D₄	—	4	4	no	—
796	D₄	—	4	2	no	—
797	D₄	—	8	1	no	—
798	D₄	—	8	2	no	—
799	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	—	8	2	no	—
821	C₂×C₄	—	8	2	no	—
822	C₂×C₄	—	8	2	no	—
823	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
825	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
828	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
829	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
831	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
832	C₈	—	2	2	no	—
833	C₈	—	2	4	no	—
834	C₈	—	2	2	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	2	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	8	8	no	—
848	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
849	C₄	—	2	1	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	1	no	—
854	C₄	—	2	2	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	4	no	—
857	C₄	—	4	1	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	2	no	—
862	C₄	C₁₃×#575	1	2	yes	—
863	C₄	C₁₃×#577	1	2	yes	—
864	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
865	C₄	C₁₃×#585	1	1	yes	characteristic
866	C₂	—	4	2	no	—
867	C₂	—	4	1	no	—
868	C₂	—	4	2	no	—
869	C₂	—	8	2	no	—
870	C₂	C₁₃×#3489	1	1	yes	characteristic
871	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
872	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3481	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
1. C₁₃×#3509	C₂	semidirect
3. C₁₃×#3381	C₂	semidirect
4. C₁₃×#3365	C₂	semidirect
5. C₁₃×#3356	C₂	semidirect
6. C₁₃×#3351	C₂	semidirect
7. C₁₃×#3324	C₂	semidirect
8. C₁₃×#3323	C₂	semidirect
9. C₁₃×#3254	C₂	semidirect
10. C₁₃×#3252	C₂	semidirect
11. C₁₃×#3233	C₂	semidirect
12. C₁₃×#3227	C₂	semidirect
13. C₁₃×#3107	C₂	semidirect
14. C₁₃×#3101	C₂	semidirect
15. C₁₃×#3079	C₂	semidirect
16. C₁₃×#3077	C₂	semidirect
17. C₁₃×#2991	C₂	semidirect
20. C₁₃×#557	C₂²	semidirect
28. C₁₃×#552	C₂²	semidirect
35. C₁₃×#533	C₂²	semidirect
36. C₁₃×#533	C₂²	semidirect
37. C₁₃×#533	C₂²	semidirect
39. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
48. C₁₃×#499	C₂²	semidirect
49. C₁₃×#498	C₂²	semidirect
50. C₁₃×#488	C₂²	semidirect
52. C₁₃×#485	C₂²	semidirect
53. C₁₃×#485	C₂²	semidirect
54. C₁₃×#483	C₂²	semidirect
56. C₁₃×#481	C₂²	semidirect
57. C₁₃×#479	C₂²	semidirect
59. C₁₃×#478	C₂²	semidirect
60. C₁₃×#477	C₂²	semidirect
61. C₁₃×#477	C₂²	semidirect
63. C₁₃×#476	C₂²	semidirect
64. C₁₃×#476	C₂²	semidirect
65. C₁₃×#475	C₂²	semidirect
66. C₁₃×#475	C₂²	semidirect
69. C₁₃×#474	C₂²	semidirect
70. C₁₃×#470	C₂²	semidirect
72. C₁₃×#468	C₂²	semidirect
73. C₁₃×#464	C₂²	semidirect
74. C₁₃×#462	C₂²	semidirect
76. C₁₃×#461	C₂²	semidirect
80. C₈×Q₈×C₁₃	C₂²	semidirect
81. C₄×C₁₃×Q₁₆	C₂²	semidirect
84. C₄×C₁₃×SD₁₆	C₂²	semidirect
86. C₁₃×#436	C₂²	semidirect
87. C₁₃×#431	C₂²	semidirect
88. C₁₃×#431	C₂²	semidirect
89. C₁₃×#428	C₂²	semidirect
90. C₁₃×#428	C₂²	semidirect
91. C₁₃×#423	C₂²	semidirect
92. C₁₃×#423	C₂²	semidirect
228. #62144	C₁₃	direct (N × H)
336. #3509	C₂×C₁₃	semidirect
338. #3381	C₂×C₁₃	semidirect
339. #3365	C₂×C₁₃	semidirect
340. #3356	C₂×C₁₃	semidirect
341. #3351	C₂×C₁₃	semidirect
342. #3324	C₂×C₁₃	semidirect
343. #3323	C₂×C₁₃	semidirect
344. #3254	C₂×C₁₃	semidirect
345. #3252	C₂×C₁₃	semidirect
346. #3233	C₂×C₁₃	semidirect
347. #3227	C₂×C₁₃	semidirect
348. #3107	C₂×C₁₃	semidirect
349. #3101	C₂×C₁₃	semidirect
350. #3079	C₂×C₁₃	semidirect
351. #3077	C₂×C₁₃	semidirect
352. #2991	C₂×C₁₃	semidirect
418. #557	C₂²×C₁₃	semidirect
426. #552	C₂²×C₁₃	semidirect
433. #533	C₂²×C₁₃	semidirect
434. #533	C₂²×C₁₃	semidirect
435. #533	C₂²×C₁₃	semidirect
437. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
446. #499	C₂²×C₁₃	semidirect
447. #498	C₂²×C₁₃	semidirect
448. #488	C₂²×C₁₃	semidirect
450. #485	C₂²×C₁₃	semidirect
451. #485	C₂²×C₁₃	semidirect
452. #483	C₂²×C₁₃	semidirect
454. #481	C₂²×C₁₃	semidirect
455. #479	C₂²×C₁₃	semidirect
457. #478	C₂²×C₁₃	semidirect
458. #477	C₂²×C₁₃	semidirect
459. #477	C₂²×C₁₃	semidirect
461. #476	C₂²×C₁₃	semidirect
462. #476	C₂²×C₁₃	semidirect
463. #475	C₂²×C₁₃	semidirect
464. #475	C₂²×C₁₃	semidirect
467. #474	C₂²×C₁₃	semidirect
468. #470	C₂²×C₁₃	semidirect
470. #468	C₂²×C₁₃	semidirect
471. #464	C₂²×C₁₃	semidirect
472. #462	C₂²×C₁₃	semidirect
474. #461	C₂²×C₁₃	semidirect
478. C₈×Q₈	C₂²×C₁₃	semidirect
479. C₄×Q₁₆	C₂²×C₁₃	semidirect
482. C₄×SD₁₆	C₂²×C₁₃	semidirect
484. #436	C₂²×C₁₃	semidirect
485. #431	C₂²×C₁₃	semidirect
486. #431	C₂²×C₁₃	semidirect
487. #428	C₂²×C₁₃	semidirect
488. #428	C₂²×C₁₃	semidirect
489. #423	C₂²×C₁₃	semidirect
490. #423	C₂²×C₁₃	semidirect
771. C₁₃	#62144	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×#3509	2
C₁₃×#3481	2
C₁₃×#3381	2
C₁₃×#3365	2
C₁₃×#3356	2
C₁₃×#3351	2
C₁₃×#3324	2
C₁₃×#3323	2
C₁₃×#3254	2
C₁₃×#3252	2
C₁₃×#3233	2
C₁₃×#3227	2
C₁₃×#3107	2
C₁₃×#3101	2
C₁₃×#3079	2
C₁₃×#3077	2
C₁₃×#2991	2
#62144	13

Subgroups — C13×#62144 #15748483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62144 #15748483