Subgroups — C₁₃×#62583 #15748922

Order 3328.

1978 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×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3373	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3367	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3308	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3306	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3298	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3294	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3239	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3238	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3213	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3180	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3171	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#489	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×2₋¹⁺⁴	—	2	1	no	—
19	C₁₃×#559	C₂²	1	1	yes	characteristic
20	C₁₃×#556	C₂²	1	1	yes	characteristic
21	C₁₃×#555	—	2	1	no	—
22	C₁₃×#551	—	2	2	no	—
23	D₄×Q₈×C₁₃	—	2	1	no	—
24	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
26	C₁₃×#548	C₂²	1	2	yes	—
27	C₁₃×#547	—	2	1	no	—
28	C₁₃×#547	—	2	2	no	—
29	C₁₃×#547	C₂²	1	2	yes	—
30	C₁₃×#547	C₂²	1	4	yes	complemented
31	C₁₃×#546	—	2	1	no	—
32	C₁₃×#546	C₂²	1	2	yes	—
33	D₄²×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#542	—	2	1	no	—
35	C₁₃×#538	—	2	2	no	—
36	C₁₃×#536	—	2	2	no	—
37	C₁₃×#536	—	2	1	no	—
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#532	C₂²	1	2	yes	complemented
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
42	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#529	C₂²	1	1	yes	characteristic
44	C₁₃×#529	C₂²	1	2	yes	—
45	C₂×C₁₃×#124	C₂²	1	2	yes	—
46	C₁₃×#518	—	2	1	no	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₁₃×#501	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#501	C₂²	1	2	yes	complemented
50	C₁₃×#496	C₂²	1	1	yes	characteristic
51	C₁₃×#496	C₂²	1	2	yes	complemented
52	C₁₃×#490	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#489	C₂²	1	4	yes	—
54	C₁₃×#489	C₂²	1	1	yes	characteristic
55	C₁₃×#489	C₂²	1	2	yes	—
56	C₁₃×#489	C₂²	1	4	yes	complemented
57	C₁₃×#489	C₂²	1	2	yes	complemented
58	C₁₃×#489	C₂²	1	2	yes	complemented
59	C₁₃×#489	C₂²	1	2	yes	complemented
60	C₁₃×#487	C₂²	1	2	yes	complemented
61	C₁₃×#486	C₂²	1	2	yes	—
62	C₁₃×#484	C₂²	1	2	yes	complemented
63	C₁₃×#483	C₂²	1	4	yes	complemented
64	C₁₃×#481	C₂²	1	2	yes	—
65	C₁₃×#480	C₂²	1	4	yes	—
66	C₁₃×#477	C₂²	1	4	yes	complemented
67	C₁₃×#476	C₂²	1	4	yes	complemented
68	C₁₃×#475	C₂²	1	2	yes	complemented
69	C₁₃×#474	C₂²	1	2	yes	—
70	C₁₃×#469	C₂²	1	2	yes	—
71	C₁₃×#468	C₂²	1	2	yes	complemented
72	C₁₃×#466	C₂²	1	4	yes	—
73	C₁₃×#465	C₂²	1	4	yes	complemented
74	C₁₃×#463	C₂²	1	4	yes	—
75	C₁₃×#463	C₂²	1	4	yes	complemented
76	C₁₃×#461	C₂²	1	2	yes	complemented
77	C₁₃×#459	C₂²	1	2	yes	—
78	C₁₃×#449	C₂²	1	4	yes	complemented
79	C₁₃×#448	C₂²	1	4	yes	complemented
80	C₁₃×#447	C₂²	1	4	yes	—
81	C₁₃×#446	C₂²	1	2	yes	complemented
82	C₁₃×#442	C₂²	1	4	yes	complemented
83	C₁₃×#440	C₂²	1	4	yes	complemented
84	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
85	C₄×C₁₃×D₈	C₂²	1	2	yes	—
86	C₁₃×#435	C₂²	1	4	yes	complemented
87	C₈×D₄×C₁₃	C₂²	1	2	yes	—
88	C₁₃×#432	C₂²	1	2	yes	complemented
89	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#417	C₂²	1	4	yes	complemented
91	C₂×C₁₃×#103	C₂²	1	4	yes	complemented
92	C₂×C₁₃×#102	C₂²	1	4	yes	—
93	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
95	C₁₃×2₋¹⁺⁴	—	4	8	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	—	2	4	no	—
98	C₂×C₁₃×#41	—	2	2	no	—
99	C₂×C₁₃×#41	—	2	1	no	—
100	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
101	C₂×C₁₃×#41	C₂³	1	2	yes	—
102	C₂²×Q₈×C₁₃	—	2	2	no	—
103	C₂²×Q₈×C₁₃	—	2	2	no	—
104	C₂²×Q₈×C₁₃	—	2	1	no	—
105	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
106	C₂²×D₄×C₁₃	—	2	1	no	—
107	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
108	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
109	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×D₈	C₂³	1	2	yes	—
111	C₂×C₁₃×D₈	C₂³	1	4	yes	—
112	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
113	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
114	C₁₃×C₄⋊Q₈	—	2	1	no	—
115	C₁₃×C₄⋊Q₈	—	2	2	no	—
116	C₁₃×C₄⋊Q₈	—	2	1	no	—
117	C₁₃×C₄⋊Q₈	—	2	1	no	—
118	C₁₃×C₄⋊Q₈	—	2	2	no	—
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
122	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
124	C₁₃×#127	C₂³	1	1	yes	characteristic
125	C₁₃×#127	C₂³	1	1	yes	characteristic
126	C₁₃×#126	—	2	2	no	—
127	C₁₃×#126	—	2	2	no	—
128	C₁₃×#126	—	2	1	no	—
129	C₁₃×#125	C₂³	1	1	yes	characteristic
130	C₁₃×#124	—	2	1	no	—
131	C₁₃×#124	—	2	2	no	—
132	C₁₃×#124	—	2	2	no	—
133	C₁₃×#124	—	2	2	no	—
134	C₁₃×#124	—	2	2	no	—
135	C₁₃×#124	—	2	1	no	—
136	C₁₃×#124	C₂³	1	2	yes	—
137	C₁₃×#124	C₂³	1	2	yes	—
138	C₁₃×#124	C₂³	1	1	yes	characteristic
139	C₁₃×#124	C₂³	1	2	yes	—
140	C₁₃×#123	—	2	1	no	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×#123	—	2	2	no	—
143	C₁₃×#123	—	2	2	no	—
144	C₁₃×#123	—	2	4	no	—
145	C₁₃×#123	—	2	4	no	—
146	C₁₃×#123	—	2	4	no	—
147	C₁₃×C₂²⋊Q₈	—	2	1	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	—	2	4	no	—
150	C₁₃×C₂²⋊Q₈	—	2	2	no	—
151	C₁₃×C₂²⋊Q₈	—	2	4	no	—
152	C₁₃×C₂²⋊Q₈	—	2	2	no	—
153	C₁₃×C₂²⋊Q₈	—	2	2	no	—
154	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
155	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	1	no	—
158	C₁₃×#121	—	2	1	no	—
159	C₁₃×#121	—	2	2	no	—
160	C₁₃×#121	—	2	1	no	—
161	C₁₃×#121	—	2	1	no	—
162	C₁₃×#121	—	2	2	no	—
163	C₁₃×#121	C₂³	1	4	yes	—
164	C₁₃×#121	C₂³	1	2	yes	—
165	C₁₃×#121	C₂³	1	2	yes	—
166	C₁₃×#121	C₂³	1	1	yes	characteristic
167	C₁₃×#120	—	2	2	no	—
168	C₁₃×#120	—	2	2	no	—
169	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
170	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
172	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₁₃	—	2	1	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	1	no	—
179	C₄×D₄×C₁₃	—	2	1	no	—
180	C₄×D₄×C₁₃	—	2	1	no	—
181	C₄×D₄×C₁₃	—	2	2	no	—
182	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
183	C₄×D₄×C₁₃	D₄	1	2	yes	—
184	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₁₃	C₂³	1	2	yes	—
186	C₄×D₄×C₁₃	C₂³	1	4	yes	—
187	C₄×D₄×C₁₃	C₂³	1	2	yes	—
188	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₁₃	C₂³	1	2	yes	—
190	C₁₃×#117	—	2	1	no	—
191	C₁₃×#117	—	2	1	no	—
192	C₁₃×#117	—	2	2	no	—
193	C₁₃×#117	D₄	1	2	yes	—
194	C₁₃×#117	D₄	1	1	yes	characteristic
195	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
198	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
202	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
204	C₁₃×#107	C₂³	1	2	yes	—
205	C₁₃×#107	C₂³	1	4	yes	—
206	C₁₃×#106	C₂³	1	2	yes	—
207	C₁₃×#106	C₂³	1	4	yes	—
208	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
209	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
210	C₁₃×#103	C₂³	1	2	yes	—
211	C₁₃×#103	C₂³	1	4	yes	—
212	C₁₃×#103	C₂³	1	4	yes	—
213	C₁₃×#103	C₂³	1	4	yes	—
214	C₁₃×#103	C₂³	1	4	yes	—
215	C₁₃×#102	C₂³	1	2	yes	—
216	C₁₃×#102	C₂³	1	4	yes	—
217	C₁₃×#102	C₂³	1	4	yes	—
218	C₁₃×#102	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	2	yes	—
221	C₁₃×#102	C₂³	1	2	yes	—
222	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
223	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
224	C₁₃×#97	C₂³	1	1	yes	characteristic
225	C₁₃×#97	C₂³	1	2	yes	—
226	C₁₃×#97	C₂³	1	4	yes	—
227	C₁₃×#97	C₂³	1	1	yes	characteristic
228	C₄×C₈×C₁₃	C₂³	1	2	yes	—
229	#62583	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂⁴×C₁₃	—	2	2	no	—
231	C₁₃×#41	—	2	4	no	—
232	C₁₃×#41	—	4	8	no	—
233	C₁₃×#41	—	4	4	no	—
234	C₁₃×#41	—	4	4	no	—
235	C₁₃×#41	—	4	16	no	—
236	C₁₃×#41	—	4	8	no	—
237	C₂×Q₈×C₁₃	—	2	4	no	—
238	C₂×Q₈×C₁₃	—	2	2	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	—	4	8	no	—
243	C₂×Q₈×C₁₃	—	4	4	no	—
244	C₂×Q₈×C₁₃	—	4	4	no	—
245	C₂×Q₈×C₁₃	—	4	8	no	—
246	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	4	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	—	2	1	no	—
256	C₂×D₄×C₁₃	—	2	1	no	—
257	C₂×D₄×C₁₃	—	2	1	no	—
258	C₂×D₄×C₁₃	—	2	2	no	—
259	C₂×D₄×C₁₃	—	4	4	no	—
260	C₂×D₄×C₁₃	—	4	4	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	1	yes	characteristic
264	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	4	no	—
268	C₂²×C₄×C₁₃	—	2	2	no	—
269	C₂²×C₄×C₁₃	—	2	1	no	—
270	C₂²×C₄×C₁₃	—	2	4	no	—
271	C₂²×C₄×C₁₃	—	2	2	no	—
272	C₂²×C₄×C₁₃	—	2	2	no	—
273	C₂²×C₄×C₁₃	—	2	2	no	—
274	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
280	C₁₃×SD₁₆	—	4	4	no	—
281	C₁₃×SD₁₆	—	4	2	no	—
282	C₁₃×D₈	—	4	4	no	—
283	C₁₃×D₈	—	4	2	no	—
284	C₁₃×M₁₆	—	4	2	no	—
285	C₂×C₈×C₁₃	—	4	4	no	—
286	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
287	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
288	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
289	C₁₃×C₄⋊C₄	—	2	1	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	4	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	4	no	—
295	C₁₃×C₄⋊C₄	—	2	1	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	C₂×D₄	1	1	yes	characteristic
304	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
305	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
306	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
307	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
310	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
311	C₁₃×C₂²⋊C₄	—	2	2	no	—
312	C₁₃×C₂²⋊C₄	—	2	1	no	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	1	no	—
315	C₁₃×C₂²⋊C₄	—	2	1	no	—
316	C₁₃×C₂²⋊C₄	—	2	1	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	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	C₁₃×C₂²⋊C₄	—	2	2	no	—
324	C₁₃×C₂²⋊C₄	—	2	4	no	—
325	C₁₃×C₂²⋊C₄	—	2	1	no	—
326	C₁₃×C₂²⋊C₄	—	2	2	no	—
327	C₁₃×C₂²⋊C₄	—	2	4	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
330	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
331	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
332	C₄²×C₁₃	—	2	2	no	—
333	C₄²×C₁₃	—	2	1	no	—
334	C₄²×C₁₃	C₂×D₄	1	2	yes	—
335	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₁₃	C₂×D₄	1	2	yes	—
338	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
339	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
340	C₄²×C₁₃	C₂⁴	1	2	yes	—
341	#3514	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#3373	C₂×C₁₃	1	2	yes	complemented
344	#3367	C₂×C₁₃	1	2	yes	complemented
345	#3308	C₂×C₁₃	1	4	yes	complemented
346	#3306	C₂×C₁₃	1	4	yes	complemented
347	#3298	C₂×C₁₃	1	2	yes	complemented
348	#3294	C₂×C₁₃	1	2	yes	complemented
349	#3239	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#3238	C₂×C₁₃	1	2	yes	complemented
351	#3214	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#3213	C₂×C₁₃	1	2	yes	complemented
353	#3180	C₂×C₁₃	1	2	yes	complemented
354	#3171	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
356	C₂×#489	C₂×C₁₃	1	2	yes	complemented
357	#2970	C₂×C₁₃	1	1	yes	characteristic, complemented
358	C₂³×C₁₃	—	2	1	no	—
359	C₂³×C₁₃	—	2	2	no	—
360	C₂³×C₁₃	—	2	2	no	—
361	C₂³×C₁₃	—	4	4	no	—
362	C₂³×C₁₃	—	8	2	no	—
363	C₂³×C₁₃	—	8	2	no	—
364	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
365	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
366	Q₈×C₁₃	—	2	2	no	—
367	Q₈×C₁₃	—	2	2	no	—
368	Q₈×C₁₃	—	2	4	no	—
369	Q₈×C₁₃	—	4	4	no	—
370	Q₈×C₁₃	—	4	2	no	—
371	Q₈×C₁₃	—	4	8	no	—
372	Q₈×C₁₃	—	4	4	no	—
373	Q₈×C₁₃	—	8	2	no	—
374	D₄×C₁₃	—	2	4	no	—
375	D₄×C₁₃	—	2	2	no	—
376	D₄×C₁₃	—	2	2	no	—
377	D₄×C₁₃	—	2	2	no	—
378	D₄×C₁₃	—	2	4	no	—
379	D₄×C₁₃	—	4	2	no	—
380	D₄×C₁₃	—	4	2	no	—
381	D₄×C₁₃	—	4	4	no	—
382	D₄×C₁₃	—	4	4	no	—
383	D₄×C₁₃	—	4	8	no	—
384	D₄×C₁₃	—	4	2	no	—
385	D₄×C₁₃	—	8	1	no	—
386	D₄×C₁₃	—	8	2	no	—
387	D₄×C₁₃	—	8	1	no	—
388	D₄×C₁₃	—	8	2	no	—
389	D₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
390	C₂×C₄×C₁₃	—	2	4	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	4	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	4	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	4	2	no	—
401	C₂×C₄×C₁₃	—	4	1	no	—
402	C₂×C₄×C₁₃	—	4	8	no	—
403	C₂×C₄×C₁₃	—	4	4	no	—
404	C₂×C₄×C₁₃	—	4	8	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	2	no	—
410	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
419	C₈×C₁₃	—	2	2	no	—
420	C₈×C₁₃	—	2	4	no	—
421	C₈×C₁₃	—	2	2	no	—
422	C₂×2₋¹⁺⁴	—	2	1	no	—
423	#559	C₂²×C₁₃	1	1	yes	characteristic
424	#556	C₂²×C₁₃	1	1	yes	characteristic
425	#555	—	2	1	no	—
426	#551	—	2	2	no	—
427	D₄×Q₈	—	2	1	no	—
428	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
429	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
430	#548	C₂²×C₁₃	1	2	yes	—
431	#547	—	2	1	no	—
432	#547	—	2	2	no	—
433	#547	C₂²×C₁₃	1	2	yes	—
434	#547	C₂²×C₁₃	1	4	yes	complemented
435	#546	—	2	1	no	—
436	#546	C₂²×C₁₃	1	2	yes	—
437	D₄²	C₂²×C₁₃	1	1	yes	characteristic
438	#542	—	2	1	no	—
439	#538	—	2	2	no	—
440	#536	—	2	2	no	—
441	#536	—	2	1	no	—
442	#532	C₂²×C₁₃	1	1	yes	characteristic
443	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
444	#532	C₂²×C₁₃	1	2	yes	complemented
445	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
446	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
447	#529	C₂²×C₁₃	1	1	yes	characteristic
448	#529	C₂²×C₁₃	1	2	yes	—
449	C₂×#124	C₂²×C₁₃	1	2	yes	—
450	#518	—	2	1	no	—
451	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
452	#501	C₂²×C₁₃	1	1	yes	characteristic, complemented
453	#501	C₂²×C₁₃	1	2	yes	complemented
454	#496	C₂²×C₁₃	1	1	yes	characteristic
455	#496	C₂²×C₁₃	1	2	yes	complemented
456	#490	C₂²×C₁₃	1	1	yes	characteristic, complemented
457	#489	C₂²×C₁₃	1	4	yes	—
458	#489	C₂²×C₁₃	1	1	yes	characteristic
459	#489	C₂²×C₁₃	1	2	yes	—
460	#489	C₂²×C₁₃	1	4	yes	complemented
461	#489	C₂²×C₁₃	1	2	yes	complemented
462	#489	C₂²×C₁₃	1	2	yes	complemented
463	#489	C₂²×C₁₃	1	2	yes	complemented
464	#487	C₂²×C₁₃	1	2	yes	complemented
465	#486	C₂²×C₁₃	1	2	yes	—
466	#484	C₂²×C₁₃	1	2	yes	complemented
467	#483	C₂²×C₁₃	1	4	yes	complemented
468	#481	C₂²×C₁₃	1	2	yes	—
469	#480	C₂²×C₁₃	1	4	yes	—
470	#477	C₂²×C₁₃	1	4	yes	complemented
471	#476	C₂²×C₁₃	1	4	yes	complemented
472	#475	C₂²×C₁₃	1	2	yes	complemented
473	#474	C₂²×C₁₃	1	2	yes	—
474	#469	C₂²×C₁₃	1	2	yes	—
475	#468	C₂²×C₁₃	1	2	yes	complemented
476	#466	C₂²×C₁₃	1	4	yes	—
477	#465	C₂²×C₁₃	1	4	yes	complemented
478	#463	C₂²×C₁₃	1	4	yes	—
479	#463	C₂²×C₁₃	1	4	yes	complemented
480	#461	C₂²×C₁₃	1	2	yes	complemented
481	#459	C₂²×C₁₃	1	2	yes	—
482	#449	C₂²×C₁₃	1	4	yes	complemented
483	#448	C₂²×C₁₃	1	4	yes	complemented
484	#447	C₂²×C₁₃	1	4	yes	—
485	#446	C₂²×C₁₃	1	2	yes	complemented
486	#442	C₂²×C₁₃	1	4	yes	complemented
487	#440	C₂²×C₁₃	1	4	yes	complemented
488	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
489	C₄×D₈	C₂²×C₁₃	1	2	yes	—
490	#435	C₂²×C₁₃	1	4	yes	complemented
491	C₈×D₄	C₂²×C₁₃	1	2	yes	—
492	#432	C₂²×C₁₃	1	2	yes	complemented
493	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
494	#417	C₂²×C₁₃	1	4	yes	complemented
495	C₂×#103	C₂²×C₁₃	1	4	yes	complemented
496	C₂×#102	C₂²×C₁₃	1	4	yes	—
497	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
498	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
499	C₂²×C₁₃	—	2	2	no	—
500	C₂²×C₁₃	—	2	2	no	—
501	C₂²×C₁₃	—	2	1	no	—
502	C₂²×C₁₃	—	2	1	no	—
503	C₂²×C₁₃	—	2	1	no	—
504	C₂²×C₁₃	—	4	2	no	—
505	C₂²×C₁₃	—	4	2	no	—
506	C₂²×C₁₃	—	4	1	no	—
507	C₂²×C₁₃	—	4	2	no	—
508	C₂²×C₁₃	—	4	1	no	—
509	C₂²×C₁₃	—	4	2	no	—
510	C₂²×C₁₃	—	4	2	no	—
511	C₂²×C₁₃	—	4	1	no	—
512	C₂²×C₁₃	—	4	2	no	—
513	C₂²×C₁₃	—	16	4	no	—
514	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
515	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
516	C₄×C₁₃	—	2	1	no	—
517	C₄×C₁₃	—	2	2	no	—
518	C₄×C₁₃	—	2	1	no	—
519	C₄×C₁₃	—	2	1	no	—
520	C₄×C₁₃	—	2	2	no	—
521	C₄×C₁₃	—	2	1	no	—
522	C₄×C₁₃	—	2	2	no	—
523	C₄×C₁₃	—	4	1	no	—
524	C₄×C₁₃	—	4	2	no	—
525	C₄×C₁₃	—	4	1	no	—
526	C₄×C₁₃	—	4	4	no	—
527	C₄×C₁₃	—	4	2	no	—
528	C₄×C₁₃	—	4	1	no	—
529	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
530	C₄×C₁₃	#585	1	2	yes	—
531	2₋¹⁺⁴	—	4	8	no	—
532	C₂×#41	—	2	2	no	—
533	C₂×#41	—	2	4	no	—
534	C₂×#41	—	2	2	no	—
535	C₂×#41	—	2	1	no	—
536	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
537	C₂×#41	C₂³×C₁₃	1	2	yes	—
538	C₂²×Q₈	—	2	2	no	—
539	C₂²×Q₈	—	2	2	no	—
540	C₂²×Q₈	—	2	1	no	—
541	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
542	C₂²×D₄	—	2	1	no	—
543	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
544	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
545	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
546	C₂×D₈	C₂³×C₁₃	1	2	yes	—
547	C₂×D₈	C₂³×C₁₃	1	4	yes	—
548	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
549	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	—	2	2	no	—
552	C₄⋊Q₈	—	2	1	no	—
553	C₄⋊Q₈	—	2	1	no	—
554	C₄⋊Q₈	—	2	2	no	—
555	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
556	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
557	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
558	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
559	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
560	#127	C₂³×C₁₃	1	1	yes	characteristic
561	#127	C₂³×C₁₃	1	1	yes	characteristic
562	#126	—	2	2	no	—
563	#126	—	2	2	no	—
564	#126	—	2	1	no	—
565	#125	C₂³×C₁₃	1	1	yes	characteristic
566	#124	—	2	1	no	—
567	#124	—	2	2	no	—
568	#124	—	2	2	no	—
569	#124	—	2	2	no	—
570	#124	—	2	2	no	—
571	#124	—	2	1	no	—
572	#124	C₂³×C₁₃	1	1	yes	characteristic
573	#124	C₂³×C₁₃	1	2	yes	—
574	#124	C₂³×C₁₃	1	2	yes	—
575	#124	C₂³×C₁₃	1	2	yes	—
576	#123	—	2	1	no	—
577	#123	—	2	2	no	—
578	#123	—	2	2	no	—
579	#123	—	2	2	no	—
580	#123	—	2	4	no	—
581	#123	—	2	4	no	—
582	#123	—	2	4	no	—
583	C₂²⋊Q₈	—	2	1	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	4	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	4	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
591	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
592	#121	—	2	2	no	—
593	#121	—	2	1	no	—
594	#121	—	2	1	no	—
595	#121	—	2	2	no	—
596	#121	—	2	1	no	—
597	#121	—	2	1	no	—
598	#121	—	2	2	no	—
599	#121	C₂³×C₁₃	1	2	yes	—
600	#121	C₂³×C₁₃	1	1	yes	characteristic
601	#121	C₂³×C₁₃	1	4	yes	—
602	#121	C₂³×C₁₃	1	2	yes	—
603	#120	—	2	2	no	—
604	#120	—	2	2	no	—
605	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
606	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
607	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
619	C₄×D₄	D₄×C₁₃	1	2	yes	—
620	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
621	C₄×D₄	C₂³×C₁₃	1	2	yes	—
622	C₄×D₄	C₂³×C₁₃	1	2	yes	—
623	C₄×D₄	C₂³×C₁₃	1	4	yes	—
624	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
625	C₄×D₄	C₂³×C₁₃	1	2	yes	—
626	#117	—	2	1	no	—
627	#117	—	2	1	no	—
628	#117	—	2	2	no	—
629	#117	D₄×C₁₃	1	2	yes	—
630	#117	D₄×C₁₃	1	1	yes	characteristic
631	C₂×C₄⋊C₄	—	2	2	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
634	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
635	C₂×C₂²⋊C₄	—	2	2	no	—
636	C₂×C₂²⋊C₄	—	2	2	no	—
637	C₂×C₂²⋊C₄	—	2	2	no	—
638	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
639	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
640	#107	C₂³×C₁₃	1	2	yes	—
641	#107	C₂³×C₁₃	1	4	yes	—
642	#106	C₂³×C₁₃	1	2	yes	—
643	#106	C₂³×C₁₃	1	4	yes	—
644	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
645	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
646	#103	C₂³×C₁₃	1	2	yes	—
647	#103	C₂³×C₁₃	1	4	yes	—
648	#103	C₂³×C₁₃	1	4	yes	—
649	#103	C₂³×C₁₃	1	4	yes	—
650	#103	C₂³×C₁₃	1	4	yes	—
651	#102	C₂³×C₁₃	1	2	yes	—
652	#102	C₂³×C₁₃	1	4	yes	—
653	#102	C₂³×C₁₃	1	4	yes	—
654	#102	C₂³×C₁₃	1	4	yes	—
655	#102	C₂³×C₁₃	1	4	yes	—
656	#102	C₂³×C₁₃	1	2	yes	—
657	#102	C₂³×C₁₃	1	2	yes	—
658	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
659	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
660	#97	C₂³×C₁₃	1	1	yes	characteristic
661	#97	C₂³×C₁₃	1	2	yes	—
662	#97	C₂³×C₁₃	1	4	yes	—
663	#97	C₂³×C₁₃	1	1	yes	characteristic
664	C₄×C₈	C₂³×C₁₃	1	2	yes	—
665	C₂×C₁₃	—	2	4	no	—
666	C₂×C₁₃	—	4	1	no	—
667	C₂×C₁₃	—	8	2	no	—
668	C₂×C₁₃	—	8	2	no	—
669	C₂×C₁₃	—	8	1	no	—
670	C₂×C₁₃	#3500	1	1	yes	characteristic
671	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
672	C₂×C₁₃	#3586	1	1	yes	characteristic
673	C₂⁴	—	2	2	no	—
674	#41	—	2	4	no	—
675	#41	—	4	8	no	—
676	#41	—	4	4	no	—
677	#41	—	4	4	no	—
678	#41	—	4	16	no	—
679	#41	—	4	8	no	—
680	C₂×Q₈	—	2	4	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×Q₈	—	2	2	no	—
683	C₂×Q₈	—	2	1	no	—
684	C₂×Q₈	—	2	2	no	—
685	C₂×Q₈	—	4	8	no	—
686	C₂×Q₈	—	4	4	no	—
687	C₂×Q₈	—	4	4	no	—
688	C₂×Q₈	—	4	8	no	—
689	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
690	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
691	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	4	4	no	—
703	C₂×D₄	—	4	4	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	1	yes	characteristic
707	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
708	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
718	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
719	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
720	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
723	SD₁₆	—	4	4	no	—
724	SD₁₆	—	4	2	no	—
725	D₈	—	4	4	no	—
726	D₈	—	4	2	no	—
727	M₁₆	—	4	2	no	—
728	C₂×C₈	—	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	1	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	1	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	C₂×D₄×C₁₃	1	1	yes	characteristic
747	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
748	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
749	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
750	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
751	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
752	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
753	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	1	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
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	2	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	1	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
773	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
774	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	1	no	—
777	C₄²	C₂×D₄×C₁₃	1	2	yes	—
778	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
779	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
780	C₄²	C₂×D₄×C₁₃	1	2	yes	—
781	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
782	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
783	C₄²	C₂⁴×C₁₃	1	2	yes	—
784	C₁₃	#62583	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	—	8	2	no	—
790	C₂³	—	8	2	no	—
791	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
792	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
793	Q₈	—	2	2	no	—
794	Q₈	—	2	2	no	—
795	Q₈	—	2	4	no	—
796	Q₈	—	4	4	no	—
797	Q₈	—	4	2	no	—
798	Q₈	—	4	8	no	—
799	Q₈	—	4	4	no	—
800	Q₈	—	8	2	no	—
801	D₄	—	2	4	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	2	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	4	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	2	no	—
808	D₄	—	4	4	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	8	no	—
811	D₄	—	4	2	no	—
812	D₄	—	8	2	no	—
813	D₄	—	8	1	no	—
814	D₄	—	8	1	no	—
815	D₄	—	8	2	no	—
816	D₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
817	C₂×C₄	—	2	4	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	8	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	8	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	8	2	no	—
835	C₂×C₄	—	8	2	no	—
836	C₂×C₄	—	8	2	no	—
837	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
838	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
842	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
844	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
845	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
846	C₈	—	2	2	no	—
847	C₈	—	2	4	no	—
848	C₈	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	16	4	no	—
864	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
865	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
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	1	no	—
872	C₄	—	2	2	no	—
873	C₄	—	4	4	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	1	no	—
879	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
880	C₄	C₁₃×#585	1	2	yes	—
881	C₂	—	2	4	no	—
882	C₂	—	4	1	no	—
883	C₂	—	8	1	no	—
884	C₂	—	8	2	no	—
885	C₂	—	8	2	no	—
886	C₂	C₁₃×#3500	1	1	yes	characteristic
887	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
888	C₂	C₁₃×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3514	C₂	semidirect
2. C₁₃×#3499	C₂	semidirect
3. C₁₃×#3373	C₂	semidirect
4. C₁₃×#3367	C₂	semidirect
5. C₁₃×#3308	C₂	semidirect
6. C₁₃×#3306	C₂	semidirect
7. C₁₃×#3298	C₂	semidirect
8. C₁₃×#3294	C₂	semidirect
9. C₁₃×#3239	C₂	semidirect
10. C₁₃×#3238	C₂	semidirect
11. C₁₃×#3214	C₂	semidirect
12. C₁₃×#3213	C₂	semidirect
13. C₁₃×#3180	C₂	semidirect
14. C₁₃×#3171	C₂	semidirect
15. C₁₃×#3141	C₂	semidirect
16. C₂×C₁₃×#489	C₂	semidirect
17. C₁₃×#2970	C₂	semidirect
25. D₄×Q₈×C₁₃	C₂²	semidirect
30. C₁₃×#547	C₂²	semidirect
39. C₁₃×#532	C₂²	semidirect
40. C₁₃×#532	C₂²	semidirect
41. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
42. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
48. C₁₃×#501	C₂²	semidirect
49. C₁₃×#501	C₂²	semidirect
51. C₁₃×#496	C₂²	semidirect
52. C₁₃×#490	C₂²	semidirect
56. C₁₃×#489	C₂²	semidirect
57. C₁₃×#489	C₂²	semidirect
58. C₁₃×#489	C₂²	semidirect
59. C₁₃×#489	C₂²	semidirect
60. C₁₃×#487	C₂²	semidirect
62. C₁₃×#484	C₂²	semidirect
63. C₁₃×#483	C₂²	semidirect
66. C₁₃×#477	C₂²	semidirect
67. C₁₃×#476	C₂²	semidirect
68. C₁₃×#475	C₂²	semidirect
71. C₁₃×#468	C₂²	semidirect
73. C₁₃×#465	C₂²	semidirect
75. C₁₃×#463	C₂²	semidirect
76. C₁₃×#461	C₂²	semidirect
78. C₁₃×#449	C₂²	semidirect
79. C₁₃×#448	C₂²	semidirect
81. C₁₃×#446	C₂²	semidirect
82. C₁₃×#442	C₂²	semidirect
83. C₁₃×#440	C₂²	semidirect
84. C₄×C₁₃×SD₁₆	C₂²	semidirect
86. C₁₃×#435	C₂²	semidirect
88. C₁₃×#432	C₂²	semidirect
89. C₁₃×#432	C₂²	semidirect
90. C₁₃×#417	C₂²	semidirect
91. C₂×C₁₃×#103	C₂²	semidirect
93. C₄×C₁₃×M₁₆	C₂²	semidirect
94. C₂×C₁₃×#97	C₂²	semidirect
229. #62583	C₁₃	direct (N × H)
341. #3514	C₂×C₁₃	semidirect
342. #3499	C₂×C₁₃	semidirect
343. #3373	C₂×C₁₃	semidirect
344. #3367	C₂×C₁₃	semidirect
345. #3308	C₂×C₁₃	semidirect
346. #3306	C₂×C₁₃	semidirect
347. #3298	C₂×C₁₃	semidirect
348. #3294	C₂×C₁₃	semidirect
349. #3239	C₂×C₁₃	semidirect
350. #3238	C₂×C₁₃	semidirect
351. #3214	C₂×C₁₃	semidirect
352. #3213	C₂×C₁₃	semidirect
353. #3180	C₂×C₁₃	semidirect
354. #3171	C₂×C₁₃	semidirect
355. #3141	C₂×C₁₃	semidirect
356. C₂×#489	C₂×C₁₃	semidirect
357. #2970	C₂×C₁₃	semidirect
429. D₄×Q₈	C₂²×C₁₃	semidirect
434. #547	C₂²×C₁₃	semidirect
443. #532	C₂²×C₁₃	semidirect
444. #532	C₂²×C₁₃	semidirect
445. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
446. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
452. #501	C₂²×C₁₃	semidirect
453. #501	C₂²×C₁₃	semidirect
455. #496	C₂²×C₁₃	semidirect
456. #490	C₂²×C₁₃	semidirect
460. #489	C₂²×C₁₃	semidirect
461. #489	C₂²×C₁₃	semidirect
462. #489	C₂²×C₁₃	semidirect
463. #489	C₂²×C₁₃	semidirect
464. #487	C₂²×C₁₃	semidirect
466. #484	C₂²×C₁₃	semidirect
467. #483	C₂²×C₁₃	semidirect
470. #477	C₂²×C₁₃	semidirect
471. #476	C₂²×C₁₃	semidirect
472. #475	C₂²×C₁₃	semidirect
475. #468	C₂²×C₁₃	semidirect
477. #465	C₂²×C₁₃	semidirect
479. #463	C₂²×C₁₃	semidirect
480. #461	C₂²×C₁₃	semidirect
482. #449	C₂²×C₁₃	semidirect
483. #448	C₂²×C₁₃	semidirect
485. #446	C₂²×C₁₃	semidirect
486. #442	C₂²×C₁₃	semidirect
487. #440	C₂²×C₁₃	semidirect
488. C₄×SD₁₆	C₂²×C₁₃	semidirect
490. #435	C₂²×C₁₃	semidirect
492. #432	C₂²×C₁₃	semidirect
493. #432	C₂²×C₁₃	semidirect
494. #417	C₂²×C₁₃	semidirect
495. C₂×#103	C₂²×C₁₃	semidirect
497. C₄×M₁₆	C₂²×C₁₃	semidirect
498. C₂×#97	C₂²×C₁₃	semidirect
784. C₁₃	#62583	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×#3514	2
C₁₃×#3499	2
C₁₃×#3373	2
C₁₃×#3367	2
C₁₃×#3308	2
C₁₃×#3306	2
C₁₃×#3298	2
C₁₃×#3294	2
C₁₃×#3239	2
C₁₃×#3238	2
C₁₃×#3214	2
C₁₃×#3213	2
C₁₃×#3180	2
C₁₃×#3171	2
C₁₃×#3141	2
C₂×C₁₃×#489	2
C₁₃×#2970	2
#62583	13

Subgroups — C13×#62583 #15748922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62583 #15748922