Subgroups — C₁₃×#62143 #15748482

Order 3328.

1830 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3380	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3361	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3357	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3355	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3325	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3322	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3253	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3251	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3233	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3100	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×#556	—	2	1	no	—
20	C₁₃×#555	C₂²	1	2	yes	—
21	C₁₃×#554	C₂²	1	1	yes	characteristic
22	C₁₃×#554	C₂²	1	1	yes	characteristic
23	C₁₃×#554	C₂²	1	2	yes	complemented
24	C₁₃×#553	—	2	1	no	—
25	C₁₃×#553	C₂²	1	2	yes	—
26	C₁₃×#553	C₂²	1	4	yes	complemented
27	C₁₃×#551	—	2	2	no	—
28	C₁₃×#548	—	2	2	no	—
29	C₁₃×#547	—	2	1	no	—
30	C₁₃×#546	—	2	1	no	—
31	C₁₃×#546	C₂²	1	2	yes	—
32	D₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#542	—	2	2	no	—
34	C₁₃×#537	—	2	1	no	—
35	C₁₃×#533	C₂²	1	2	yes	complemented
36	C₁₃×#532	C₂²	1	1	yes	characteristic
37	C₁₃×#532	C₂²	1	2	yes	complemented
38	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
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×#520	—	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×#500	C₂²	1	2	yes	complemented
49	C₁₃×#499	C₂²	1	4	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×#482	C₂²	1	4	yes	—
54	C₁₃×#482	C₂²	1	2	yes	complemented
55	C₁₃×#480	C₂²	1	4	yes	complemented
56	C₁₃×#480	C₂²	1	4	yes	complemented
57	C₁₃×#478	C₂²	1	4	yes	—
58	C₁₃×#478	C₂²	1	4	yes	complemented
59	C₁₃×#478	C₂²	1	4	yes	complemented
60	C₁₃×#477	C₂²	1	2	yes	complemented
61	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#476	C₂²	1	2	yes	—
63	C₁₃×#476	C₂²	1	1	yes	characteristic
64	C₁₃×#476	C₂²	1	2	yes	complemented
65	C₁₃×#476	C₂²	1	2	yes	complemented
66	C₁₃×#475	C₂²	1	2	yes	complemented
67	C₁₃×#474	C₂²	1	2	yes	—
68	C₁₃×#474	C₂²	1	2	yes	complemented
69	C₁₃×#474	C₂²	1	2	yes	complemented
70	C₁₃×#469	C₂²	1	4	yes	—
71	C₁₃×#469	C₂²	1	4	yes	complemented
72	C₁₃×#468	C₂²	1	4	yes	complemented
73	C₁₃×#463	C₂²	1	4	yes	complemented
74	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#459	C₂²	1	2	yes	—
76	C₁₃×#459	C₂²	1	1	yes	characteristic
77	C₁₃×#459	C₂²	1	2	yes	complemented
78	C₁₃×#449	C₂²	1	2	yes	—
79	C₁₃×#447	C₂²	1	4	yes	—
80	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
81	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
82	C₄×C₁₃×D₈	C₂²	1	4	yes	—
83	C₄×C₁₃×D₈	C₂²	1	2	yes	—
84	C₄×C₁₃×D₈	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	—	2	1	no	—
97	C₂×C₁₃×#41	—	2	2	no	—
98	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
99	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	—	2	1	no	—
102	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃	—	2	2	no	—
104	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
105	C₂×C₁₃×D₈	C₂³	1	2	yes	—
106	C₂×C₁₃×D₈	C₂³	1	4	yes	—
107	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
108	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
109	C₁₃×C₄⋊Q₈	—	2	1	no	—
110	C₁₃×C₄⋊Q₈	—	2	1	no	—
111	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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×#127	C₂³	1	1	yes	characteristic
117	C₁₃×#126	—	2	2	no	—
118	C₁₃×#126	—	2	4	no	—
119	C₁₃×#126	—	2	2	no	—
120	C₁₃×#125	—	2	1	no	—
121	C₁₃×#125	C₂³	1	4	yes	—
122	C₁₃×#125	C₂³	1	2	yes	—
123	C₁₃×#124	—	2	1	no	—
124	C₁₃×#124	—	2	4	no	—
125	C₁₃×#124	—	2	1	no	—
126	C₁₃×#124	—	2	1	no	—
127	C₁₃×#124	—	2	2	no	—
128	C₁₃×#124	C₂³	1	2	yes	—
129	C₁₃×#123	—	2	2	no	—
130	C₁₃×#123	—	2	2	no	—
131	C₁₃×#123	—	2	2	no	—
132	C₁₃×#123	—	2	2	no	—
133	C₁₃×#123	—	2	4	no	—
134	C₁₃×C₂²⋊Q₈	—	2	1	no	—
135	C₁₃×C₂²⋊Q₈	—	2	2	no	—
136	C₁₃×C₂²⋊Q₈	—	2	2	no	—
137	C₁₃×C₂²⋊Q₈	—	2	2	no	—
138	C₁₃×C₂²⋊Q₈	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	4	no	—
140	C₁₃×C₂²⋊Q₈	—	2	2	no	—
141	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₁₃×#121	—	2	2	no	—
143	C₁₃×#121	—	2	2	no	—
144	C₁₃×#121	—	2	4	no	—
145	C₁₃×#121	—	2	1	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	C₁₃×#121	C₂³	1	4	yes	—
151	C₁₃×#121	C₂³	1	2	yes	—
152	C₁₃×#121	C₂³	1	2	yes	—
153	C₁₃×#121	C₂³	1	2	yes	—
154	C₁₃×#120	—	2	2	no	—
155	C₁₃×#120	—	2	2	no	—
156	C₄×Q₈×C₁₃	—	2	2	no	—
157	C₄×Q₈×C₁₃	—	2	2	no	—
158	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
159	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
160	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
162	C₄×D₄×C₁₃	—	2	1	no	—
163	C₄×D₄×C₁₃	—	2	2	no	—
164	C₄×D₄×C₁₃	—	2	1	no	—
165	C₄×D₄×C₁₃	—	2	1	no	—
166	C₄×D₄×C₁₃	—	2	1	no	—
167	C₄×D₄×C₁₃	—	2	2	no	—
168	C₄×D₄×C₁₃	—	2	4	no	—
169	C₄×D₄×C₁₃	—	2	1	no	—
170	C₄×D₄×C₁₃	—	2	2	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	—	2	2	no	—
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
175	C₄×D₄×C₁₃	D₄	1	2	yes	—
176	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₁₃	C₂³	1	2	yes	—
178	C₄×D₄×C₁₃	C₂³	1	4	yes	—
179	C₄×D₄×C₁₃	C₂³	1	2	yes	—
180	C₄×D₄×C₁₃	C₂³	1	2	yes	—
181	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₁₃	C₂³	1	2	yes	—
183	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₁₃	C₂³	1	2	yes	—
185	C₁₃×#117	—	2	2	no	—
186	C₁₃×#117	—	2	1	no	—
187	C₁₃×#117	—	2	2	no	—
188	C₁₃×#117	D₄	1	1	yes	characteristic
189	C₁₃×#117	D₄	1	2	yes	—
190	C₁₃×#117	C₂³	1	4	yes	—
191	C₁₃×#117	C₂³	1	1	yes	characteristic
192	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₂×C₁₃×C₄⋊C₄	—	2	2	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	4	yes	—
203	C₁₃×#107	C₂³	1	4	yes	—
204	C₁₃×#107	C₂³	1	4	yes	—
205	C₁₃×#107	C₂³	1	2	yes	—
206	C₁₃×#106	C₂³	1	2	yes	—
207	C₁₃×#106	C₂³	1	4	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	2	yes	—
216	C₁₃×#102	C₂³	1	4	yes	—
217	C₁₃×#102	C₂³	1	2	yes	—
218	C₁₃×#102	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	2	yes	—
222	C₁₃×#102	C₂³	1	2	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	#62143	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	—	4	4	no	—
234	C₁₃×#41	—	8	2	no	—
235	C₁₃×#41	—	8	4	no	—
236	C₂×Q₈×C₁₃	—	2	1	no	—
237	C₂×Q₈×C₁₃	—	2	2	no	—
238	C₂×Q₈×C₁₃	—	2	1	no	—
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	8	2	no	—
241	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
242	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂×D₄×C₁₃	—	2	4	no	—
244	C₂×D₄×C₁₃	—	2	1	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	2	4	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	1	no	—
251	C₂×D₄×C₁₃	—	2	1	no	—
252	C₂×D₄×C₁₃	—	2	1	no	—
253	C₂×D₄×C₁₃	—	2	1	no	—
254	C₂×D₄×C₁₃	—	4	2	no	—
255	C₂×D₄×C₁₃	—	4	4	no	—
256	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
257	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
258	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	—	2	2	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	1	no	—
265	C₂²×C₄×C₁₃	—	2	1	no	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	2	no	—
268	C₂²×C₄×C₁₃	—	2	2	no	—
269	C₂²×C₄×C₁₃	—	2	4	no	—
270	C₂²×C₄×C₁₃	—	2	2	no	—
271	C₂²×C₄×C₁₃	—	8	4	no	—
272	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
278	C₁₃×SD₁₆	—	4	2	no	—
279	C₁₃×D₈	—	2	4	no	—
280	C₁₃×D₈	—	4	4	no	—
281	C₁₃×M₁₆	—	4	2	no	—
282	C₁₃×M₁₆	—	4	4	no	—
283	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
284	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
285	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	2	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	1	no	—
294	C₁₃×C₄⋊C₄	—	2	1	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	—	2	1	no	—
298	C₁₃×C₄⋊C₄	—	2	4	no	—
299	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
300	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
301	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
306	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
307	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
308	C₁₃×C₂²⋊C₄	—	2	2	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	4	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	4	no	—
323	C₁₃×C₂²⋊C₄	—	2	2	no	—
324	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
325	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
326	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
327	C₄²×C₁₃	—	2	1	no	—
328	C₄²×C₁₃	—	2	1	no	—
329	C₄²×C₁₃	—	2	1	no	—
330	C₄²×C₁₃	—	2	4	no	—
331	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₁₃	C₂×D₄	1	2	yes	—
334	C₄²×C₁₃	C₂×D₄	1	2	yes	—
335	C₄²×C₁₃	C₂⁴	1	2	yes	—
336	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
337	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
338	#3511	C₂×C₁₃	1	1	yes	characteristic, complemented
339	#3481	C₂×C₁₃	1	1	yes	characteristic, complemented
340	#3380	C₂×C₁₃	1	2	yes	complemented
341	#3361	C₂×C₁₃	1	2	yes	complemented
342	#3357	C₂×C₁₃	1	2	yes	complemented
343	#3355	C₂×C₁₃	1	4	yes	complemented
344	#3325	C₂×C₁₃	1	2	yes	complemented
345	#3322	C₂×C₁₃	1	4	yes	complemented
346	#3253	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#3251	C₂×C₁₃	1	2	yes	complemented
348	#3233	C₂×C₁₃	1	2	yes	complemented
349	#3226	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#3106	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#3100	C₂×C₁₃	1	2	yes	complemented
352	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3077	C₂×C₁₃	1	2	yes	complemented
354	#2991	C₂×C₁₃	1	1	yes	characteristic, complemented
355	C₂³×C₁₃	—	2	1	no	—
356	C₂³×C₁₃	—	2	2	no	—
357	C₂³×C₁₃	—	2	2	no	—
358	C₂³×C₁₃	—	4	4	no	—
359	C₂³×C₁₃	—	4	4	no	—
360	C₂³×C₁₃	—	8	2	no	—
361	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
362	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
363	Q₈×C₁₃	—	2	2	no	—
364	Q₈×C₁₃	—	2	1	no	—
365	Q₈×C₁₃	—	2	1	no	—
366	Q₈×C₁₃	—	4	2	no	—
367	Q₈×C₁₃	—	4	4	no	—
368	Q₈×C₁₃	—	8	2	no	—
369	Q₈×C₁₃	—	8	1	no	—
370	D₄×C₁₃	—	2	2	no	—
371	D₄×C₁₃	—	2	2	no	—
372	D₄×C₁₃	—	2	2	no	—
373	D₄×C₁₃	—	2	1	no	—
374	D₄×C₁₃	—	2	2	no	—
375	D₄×C₁₃	—	2	2	no	—
376	D₄×C₁₃	—	4	2	no	—
377	D₄×C₁₃	—	4	4	no	—
378	D₄×C₁₃	—	4	2	no	—
379	D₄×C₁₃	—	4	2	no	—
380	D₄×C₁₃	—	4	4	no	—
381	D₄×C₁₃	—	4	4	no	—
382	D₄×C₁₃	—	4	2	no	—
383	D₄×C₁₃	—	4	2	no	—
384	D₄×C₁₃	—	8	1	no	—
385	D₄×C₁₃	—	8	2	no	—
386	D₄×C₁₃	—	8	4	no	—
387	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	4	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	1	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	1	no	—
395	C₂×C₄×C₁₃	—	2	1	no	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	4	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	4	2	no	—
402	C₂×C₄×C₁₃	—	4	2	no	—
403	C₂×C₄×C₁₃	—	4	2	no	—
404	C₂×C₄×C₁₃	—	4	4	no	—
405	C₂×C₄×C₁₃	—	4	2	no	—
406	C₂×C₄×C₁₃	—	4	4	no	—
407	C₂×C₄×C₁₃	—	8	2	no	—
408	C₂×C₄×C₁₃	—	8	2	no	—
409	C₂×C₄×C₁₃	—	8	4	no	—
410	C₂×C₄×C₁₃	—	8	2	no	—
411	C₂×C₄×C₁₃	—	8	2	no	—
412	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
420	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
421	C₈×C₁₃	—	2	2	no	—
422	C₈×C₁₃	—	2	4	no	—
423	C₈×C₁₃	—	2	2	no	—
424	#559	C₂²×C₁₃	1	1	yes	characteristic
425	#556	—	2	1	no	—
426	#555	C₂²×C₁₃	1	2	yes	—
427	#554	C₂²×C₁₃	1	1	yes	characteristic
428	#554	C₂²×C₁₃	1	1	yes	characteristic
429	#554	C₂²×C₁₃	1	2	yes	complemented
430	#553	—	2	1	no	—
431	#553	C₂²×C₁₃	1	2	yes	—
432	#553	C₂²×C₁₃	1	4	yes	complemented
433	#551	—	2	2	no	—
434	#548	—	2	2	no	—
435	#547	—	2	1	no	—
436	#546	—	2	1	no	—
437	#546	C₂²×C₁₃	1	2	yes	—
438	D₄²	C₂²×C₁₃	1	1	yes	characteristic
439	#542	—	2	2	no	—
440	#537	—	2	1	no	—
441	#533	C₂²×C₁₃	1	2	yes	complemented
442	#532	C₂²×C₁₃	1	1	yes	characteristic
443	#532	C₂²×C₁₃	1	2	yes	complemented
444	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
445	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
446	#529	—	2	1	no	—
447	#529	C₂²×C₁₃	1	2	yes	—
448	#525	—	2	2	no	—
449	#520	—	2	1	no	—
450	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
451	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
452	C₂×C₄×D₄	—	2	1	no	—
453	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
454	#500	C₂²×C₁₃	1	2	yes	complemented
455	#499	C₂²×C₁₃	1	4	yes	complemented
456	#488	C₂²×C₁₃	1	4	yes	complemented
457	#486	C₂²×C₁₃	1	2	yes	—
458	#485	C₂²×C₁₃	1	4	yes	complemented
459	#482	C₂²×C₁₃	1	4	yes	—
460	#482	C₂²×C₁₃	1	2	yes	complemented
461	#480	C₂²×C₁₃	1	4	yes	complemented
462	#480	C₂²×C₁₃	1	4	yes	complemented
463	#478	C₂²×C₁₃	1	4	yes	—
464	#478	C₂²×C₁₃	1	4	yes	complemented
465	#478	C₂²×C₁₃	1	4	yes	complemented
466	#477	C₂²×C₁₃	1	2	yes	complemented
467	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
468	#476	C₂²×C₁₃	1	1	yes	characteristic
469	#476	C₂²×C₁₃	1	2	yes	—
470	#476	C₂²×C₁₃	1	2	yes	complemented
471	#476	C₂²×C₁₃	1	2	yes	complemented
472	#475	C₂²×C₁₃	1	2	yes	complemented
473	#474	C₂²×C₁₃	1	2	yes	—
474	#474	C₂²×C₁₃	1	2	yes	complemented
475	#474	C₂²×C₁₃	1	2	yes	complemented
476	#469	C₂²×C₁₃	1	4	yes	—
477	#469	C₂²×C₁₃	1	4	yes	complemented
478	#468	C₂²×C₁₃	1	4	yes	complemented
479	#463	C₂²×C₁₃	1	4	yes	complemented
480	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
481	#459	C₂²×C₁₃	1	1	yes	characteristic
482	#459	C₂²×C₁₃	1	2	yes	—
483	#459	C₂²×C₁₃	1	2	yes	complemented
484	#449	C₂²×C₁₃	1	2	yes	—
485	#447	C₂²×C₁₃	1	4	yes	—
486	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
487	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
488	C₄×D₈	C₂²×C₁₃	1	4	yes	—
489	C₄×D₈	C₂²×C₁₃	1	2	yes	—
490	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
491	#436	C₂²×C₁₃	1	2	yes	—
492	#436	C₂²×C₁₃	1	4	yes	complemented
493	#431	C₂²×C₁₃	1	2	yes	complemented
494	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
495	#428	C₂²×C₁₃	1	4	yes	complemented
496	#428	C₂²×C₁₃	1	2	yes	complemented
497	#423	C₂²×C₁₃	1	2	yes	complemented
498	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
499	#418	C₂²×C₁₃	1	4	yes	—
500	#417	C₂²×C₁₃	1	2	yes	—
501	C₂²×C₁₃	—	2	1	no	—
502	C₂²×C₁₃	—	2	2	no	—
503	C₂²×C₁₃	—	2	2	no	—
504	C₂²×C₁₃	—	2	1	no	—
505	C₂²×C₁₃	—	2	2	no	—
506	C₂²×C₁₃	—	2	1	no	—
507	C₂²×C₁₃	—	2	2	no	—
508	C₂²×C₁₃	—	4	1	no	—
509	C₂²×C₁₃	—	4	1	no	—
510	C₂²×C₁₃	—	4	2	no	—
511	C₂²×C₁₃	—	4	2	no	—
512	C₂²×C₁₃	—	4	2	no	—
513	C₂²×C₁₃	—	4	2	no	—
514	C₂²×C₁₃	—	4	2	no	—
515	C₂²×C₁₃	—	4	2	no	—
516	C₂²×C₁₃	—	8	8	no	—
517	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
518	C₄×C₁₃	—	2	1	no	—
519	C₄×C₁₃	—	2	2	no	—
520	C₄×C₁₃	—	2	1	no	—
521	C₄×C₁₃	—	2	2	no	—
522	C₄×C₁₃	—	2	2	no	—
523	C₄×C₁₃	—	2	1	no	—
524	C₄×C₁₃	—	4	1	no	—
525	C₄×C₁₃	—	4	1	no	—
526	C₄×C₁₃	—	4	2	no	—
527	C₄×C₁₃	—	4	1	no	—
528	C₄×C₁₃	—	4	2	no	—
529	C₄×C₁₃	—	4	4	no	—
530	C₄×C₁₃	#575	1	2	yes	—
531	C₄×C₁₃	#576	1	2	yes	—
532	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
533	C₄×C₁₃	#585	1	1	yes	characteristic
534	C₂×#41	—	2	1	no	—
535	C₂×#41	—	2	1	no	—
536	C₂×#41	—	2	2	no	—
537	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
538	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
539	C₂²×Q₈	—	2	1	no	—
540	C₂²×D₄	—	2	1	no	—
541	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
542	C₂³×C₄	—	2	2	no	—
543	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
544	C₂×D₈	C₂³×C₁₃	1	2	yes	—
545	C₂×D₈	C₂³×C₁₃	1	4	yes	—
546	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
547	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
548	C₄⋊Q₈	—	2	1	no	—
549	C₄⋊Q₈	—	2	1	no	—
550	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
551	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
552	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
553	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
554	#127	C₂³×C₁₃	1	1	yes	characteristic
555	#127	C₂³×C₁₃	1	1	yes	characteristic
556	#126	—	2	2	no	—
557	#126	—	2	4	no	—
558	#126	—	2	2	no	—
559	#125	—	2	1	no	—
560	#125	C₂³×C₁₃	1	2	yes	—
561	#125	C₂³×C₁₃	1	4	yes	—
562	#124	—	2	1	no	—
563	#124	—	2	4	no	—
564	#124	—	2	1	no	—
565	#124	—	2	1	no	—
566	#124	—	2	2	no	—
567	#124	C₂³×C₁₃	1	2	yes	—
568	#123	—	2	2	no	—
569	#123	—	2	2	no	—
570	#123	—	2	2	no	—
571	#123	—	2	2	no	—
572	#123	—	2	4	no	—
573	C₂²⋊Q₈	—	2	1	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	4	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
581	#121	—	2	2	no	—
582	#121	—	2	2	no	—
583	#121	—	2	4	no	—
584	#121	—	2	1	no	—
585	#121	—	2	2	no	—
586	#121	—	2	1	no	—
587	#121	—	2	1	no	—
588	#121	—	2	2	no	—
589	#121	C₂³×C₁₃	1	2	yes	—
590	#121	C₂³×C₁₃	1	2	yes	—
591	#121	C₂³×C₁₃	1	2	yes	—
592	#121	C₂³×C₁₃	1	4	yes	—
593	#120	—	2	2	no	—
594	#120	—	2	2	no	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	—	2	2	no	—
597	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
598	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	4	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
614	C₄×D₄	D₄×C₁₃	1	2	yes	—
615	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₁₃	1	2	yes	—
617	C₄×D₄	C₂³×C₁₃	1	2	yes	—
618	C₄×D₄	C₂³×C₁₃	1	2	yes	—
619	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
620	C₄×D₄	C₂³×C₁₃	1	4	yes	—
621	C₄×D₄	C₂³×C₁₃	1	2	yes	—
622	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
623	C₄×D₄	C₂³×C₁₃	1	2	yes	—
624	#117	—	2	2	no	—
625	#117	—	2	1	no	—
626	#117	—	2	2	no	—
627	#117	D₄×C₁₃	1	1	yes	characteristic
628	#117	D₄×C₁₃	1	2	yes	—
629	#117	C₂³×C₁₃	1	1	yes	characteristic
630	#117	C₂³×C₁₃	1	4	yes	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	2	no	—
634	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
636	C₂×C₂²⋊C₄	—	2	2	no	—
637	C₂×C₂²⋊C₄	—	2	2	no	—
638	C₂×C₄²	—	2	1	no	—
639	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
640	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
641	#107	C₂³×C₁₃	1	4	yes	—
642	#107	C₂³×C₁₃	1	4	yes	—
643	#107	C₂³×C₁₃	1	4	yes	—
644	#107	C₂³×C₁₃	1	2	yes	—
645	#106	C₂³×C₁₃	1	2	yes	—
646	#106	C₂³×C₁₃	1	4	yes	—
647	#106	C₂³×C₁₃	1	4	yes	—
648	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
649	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
650	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
651	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
652	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
653	#103	C₂³×C₁₃	1	4	yes	—
654	#103	C₂³×C₁₃	1	2	yes	—
655	#102	C₂³×C₁₃	1	4	yes	—
656	#102	C₂³×C₁₃	1	2	yes	—
657	#102	C₂³×C₁₃	1	4	yes	—
658	#102	C₂³×C₁₃	1	4	yes	—
659	#102	C₂³×C₁₃	1	4	yes	—
660	#102	C₂³×C₁₃	1	2	yes	—
661	#102	C₂³×C₁₃	1	2	yes	—
662	#102	C₂³×C₁₃	1	4	yes	—
663	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
664	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
665	C₄×C₈	C₂³×C₁₃	1	2	yes	—
666	C₄×C₈	C₂³×C₁₃	1	4	yes	—
667	C₂×C₁₃	—	4	1	no	—
668	C₂×C₁₃	—	4	2	no	—
669	C₂×C₁₃	—	4	2	no	—
670	C₂×C₁₃	—	8	2	no	—
671	C₂×C₁₃	—	8	2	no	—
672	C₂×C₁₃	#3489	1	1	yes	characteristic
673	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
674	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
675	C₂⁴	—	2	2	no	—
676	#41	—	2	2	no	—
677	#41	—	4	2	no	—
678	#41	—	4	1	no	—
679	#41	—	4	4	no	—
680	#41	—	8	2	no	—
681	#41	—	8	4	no	—
682	C₂×Q₈	—	2	1	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	1	no	—
685	C₂×Q₈	—	2	2	no	—
686	C₂×Q₈	—	8	2	no	—
687	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
688	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	4	2	no	—
701	C₂×D₄	—	4	4	no	—
702	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
703	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
704	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
705	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
706	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	8	4	no	—
718	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
719	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
721	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
724	SD₁₆	—	4	2	no	—
725	D₈	—	2	4	no	—
726	D₈	—	4	4	no	—
727	M₁₆	—	4	2	no	—
728	M₁₆	—	4	4	no	—
729	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
730	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
731	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
746	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
747	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
748	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
749	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
750	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
751	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
752	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
753	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	1	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	2	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	1	no	—
776	C₄²	—	2	4	no	—
777	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
778	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
779	C₄²	C₂×D₄×C₁₃	1	2	yes	—
780	C₄²	C₂×D₄×C₁₃	1	2	yes	—
781	C₄²	C₂⁴×C₁₃	1	2	yes	—
782	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
783	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
784	C₁₃	#62143	1	1	yes	characteristic, direct product factor, Sylow
785	C₂³	—	2	1	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	4	4	no	—
789	C₂³	—	4	4	no	—
790	C₂³	—	8	2	no	—
791	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
792	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
793	Q₈	—	2	2	no	—
794	Q₈	—	2	1	no	—
795	Q₈	—	2	1	no	—
796	Q₈	—	4	2	no	—
797	Q₈	—	4	4	no	—
798	Q₈	—	8	2	no	—
799	Q₈	—	8	1	no	—
800	D₄	—	2	2	no	—
801	D₄	—	2	2	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	1	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	2	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	4	no	—
808	D₄	—	4	2	no	—
809	D₄	—	4	2	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	4	no	—
812	D₄	—	4	2	no	—
813	D₄	—	4	2	no	—
814	D₄	—	8	1	no	—
815	D₄	—	8	2	no	—
816	D₄	—	8	4	no	—
817	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	4	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	8	2	no	—
838	C₂×C₄	—	8	2	no	—
839	C₂×C₄	—	8	4	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	—	8	2	no	—
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	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
846	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
847	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
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	2	no	—
852	C₈	—	2	4	no	—
853	C₈	—	2	2	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	2	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	8	8	no	—
870	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
871	C₄	—	2	1	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	2	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	4	no	—
882	C₄	—	4	1	no	—
883	C₄	C₁₃×#575	1	2	yes	—
884	C₄	C₁₃×#576	1	2	yes	—
885	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
886	C₄	C₁₃×#585	1	1	yes	characteristic
887	C₂	—	4	2	no	—
888	C₂	—	4	1	no	—
889	C₂	—	4	2	no	—
890	C₂	—	8	2	no	—
891	C₂	—	8	2	no	—
892	C₂	C₁₃×#3489	1	1	yes	characteristic
893	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
894	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3511	C₂	semidirect
2. C₁₃×#3481	C₂	semidirect
3. C₁₃×#3380	C₂	semidirect
4. C₁₃×#3361	C₂	semidirect
5. C₁₃×#3357	C₂	semidirect
6. C₁₃×#3355	C₂	semidirect
7. C₁₃×#3325	C₂	semidirect
8. C₁₃×#3322	C₂	semidirect
9. C₁₃×#3253	C₂	semidirect
10. C₁₃×#3251	C₂	semidirect
11. C₁₃×#3233	C₂	semidirect
12. C₁₃×#3226	C₂	semidirect
13. C₁₃×#3106	C₂	semidirect
14. C₁₃×#3100	C₂	semidirect
15. C₁₃×#3079	C₂	semidirect
16. C₁₃×#3077	C₂	semidirect
17. C₁₃×#2991	C₂	semidirect
23. C₁₃×#554	C₂²	semidirect
26. C₁₃×#553	C₂²	semidirect
35. C₁₃×#533	C₂²	semidirect
37. C₁₃×#532	C₂²	semidirect
38. C₁₃×#532	C₂²	semidirect
39. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
48. C₁₃×#500	C₂²	semidirect
49. C₁₃×#499	C₂²	semidirect
50. C₁₃×#488	C₂²	semidirect
52. C₁₃×#485	C₂²	semidirect
54. C₁₃×#482	C₂²	semidirect
55. C₁₃×#480	C₂²	semidirect
56. C₁₃×#480	C₂²	semidirect
58. C₁₃×#478	C₂²	semidirect
59. C₁₃×#478	C₂²	semidirect
60. C₁₃×#477	C₂²	semidirect
61. C₁₃×#477	C₂²	semidirect
64. C₁₃×#476	C₂²	semidirect
65. C₁₃×#476	C₂²	semidirect
66. C₁₃×#475	C₂²	semidirect
68. C₁₃×#474	C₂²	semidirect
69. C₁₃×#474	C₂²	semidirect
71. C₁₃×#469	C₂²	semidirect
72. C₁₃×#468	C₂²	semidirect
73. C₁₃×#463	C₂²	semidirect
74. C₁₃×#460	C₂²	semidirect
77. C₁₃×#459	C₂²	semidirect
80. C₈×Q₈×C₁₃	C₂²	semidirect
81. C₄×C₁₃×SD₁₆	C₂²	semidirect
84. C₄×C₁₃×D₈	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. #62143	C₁₃	direct (N × H)
338. #3511	C₂×C₁₃	semidirect
339. #3481	C₂×C₁₃	semidirect
340. #3380	C₂×C₁₃	semidirect
341. #3361	C₂×C₁₃	semidirect
342. #3357	C₂×C₁₃	semidirect
343. #3355	C₂×C₁₃	semidirect
344. #3325	C₂×C₁₃	semidirect
345. #3322	C₂×C₁₃	semidirect
346. #3253	C₂×C₁₃	semidirect
347. #3251	C₂×C₁₃	semidirect
348. #3233	C₂×C₁₃	semidirect
349. #3226	C₂×C₁₃	semidirect
350. #3106	C₂×C₁₃	semidirect
351. #3100	C₂×C₁₃	semidirect
352. #3079	C₂×C₁₃	semidirect
353. #3077	C₂×C₁₃	semidirect
354. #2991	C₂×C₁₃	semidirect
429. #554	C₂²×C₁₃	semidirect
432. #553	C₂²×C₁₃	semidirect
441. #533	C₂²×C₁₃	semidirect
443. #532	C₂²×C₁₃	semidirect
444. #532	C₂²×C₁₃	semidirect
445. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
454. #500	C₂²×C₁₃	semidirect
455. #499	C₂²×C₁₃	semidirect
456. #488	C₂²×C₁₃	semidirect
458. #485	C₂²×C₁₃	semidirect
460. #482	C₂²×C₁₃	semidirect
461. #480	C₂²×C₁₃	semidirect
462. #480	C₂²×C₁₃	semidirect
464. #478	C₂²×C₁₃	semidirect
465. #478	C₂²×C₁₃	semidirect
466. #477	C₂²×C₁₃	semidirect
467. #477	C₂²×C₁₃	semidirect
470. #476	C₂²×C₁₃	semidirect
471. #476	C₂²×C₁₃	semidirect
472. #475	C₂²×C₁₃	semidirect
474. #474	C₂²×C₁₃	semidirect
475. #474	C₂²×C₁₃	semidirect
477. #469	C₂²×C₁₃	semidirect
478. #468	C₂²×C₁₃	semidirect
479. #463	C₂²×C₁₃	semidirect
480. #460	C₂²×C₁₃	semidirect
483. #459	C₂²×C₁₃	semidirect
486. C₈×Q₈	C₂²×C₁₃	semidirect
487. C₄×SD₁₆	C₂²×C₁₃	semidirect
490. C₄×D₈	C₂²×C₁₃	semidirect
492. #436	C₂²×C₁₃	semidirect
493. #431	C₂²×C₁₃	semidirect
494. #431	C₂²×C₁₃	semidirect
495. #428	C₂²×C₁₃	semidirect
496. #428	C₂²×C₁₃	semidirect
497. #423	C₂²×C₁₃	semidirect
498. #423	C₂²×C₁₃	semidirect
784. C₁₃	#62143	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×#3511	2
C₁₃×#3481	2
C₁₃×#3380	2
C₁₃×#3361	2
C₁₃×#3357	2
C₁₃×#3355	2
C₁₃×#3325	2
C₁₃×#3322	2
C₁₃×#3253	2
C₁₃×#3251	2
C₁₃×#3233	2
C₁₃×#3226	2
C₁₃×#3106	2
C₁₃×#3100	2
C₁₃×#3079	2
C₁₃×#3077	2
C₁₃×#2991	2
#62143	13

Subgroups — C13×#62143 #15748482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62143 #15748482