Subgroups — C₁₃×#60949 #15747288

Order 3328.

2092 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3251	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3239	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3234	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3217	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3213	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3193	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3192	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3171	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3105	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3103	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3100	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	—	2	1	no	—
16	C₁₃×#532	—	2	1	no	—
17	C₁₃×#532	—	2	1	no	—
18	C₁₃×#532	—	2	1	no	—
19	C₁₃×#532	—	2	1	no	—
20	C₁₃×#532	C₂²	1	2	yes	—
21	C₁₃×#532	C₂²	1	2	yes	—
22	C₁₃×#532	C₂²	1	2	yes	complemented
23	C₁₃×#532	C₂²	1	2	yes	complemented
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#529	—	2	1	no	—
27	C₁₃×#529	—	2	1	no	—
28	C₁₃×#529	—	2	1	no	—
29	C₁₃×#529	—	2	1	no	—
30	C₁₃×#529	C₂²	1	2	yes	—
31	C₁₃×#529	C₂²	1	2	yes	—
32	C₁₃×#529	C₂²	1	2	yes	complemented
33	C₁₃×#529	C₂²	1	2	yes	complemented
34	C₂×C₁₃×#126	—	2	1	no	—
35	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₃×#124	—	2	1	no	—
37	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₃×#123	—	2	1	no	—
39	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#121	—	2	1	no	—
41	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#121	C₂²	1	2	yes	—
43	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄×D₄×C₁₃	—	2	1	no	—
45	C₂×C₄×D₄×C₁₃	—	2	1	no	—
46	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
48	C₂×C₁₃×#117	—	2	1	no	—
49	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
50	C₁₃×#501	C₂²	1	4	yes	complemented
51	C₁₃×#496	C₂²	1	4	yes	complemented
52	C₁₃×#490	C₂²	1	4	yes	complemented
53	C₁₃×#489	C₂²	1	4	yes	complemented
54	C₁₃×#484	C₂²	1	4	yes	complemented
55	C₁₃×#481	C₂²	1	4	yes	—
56	C₁₃×#481	C₂²	1	4	yes	complemented
57	C₁₃×#480	C₂²	1	4	yes	complemented
58	C₁₃×#478	C₂²	1	8	yes	complemented
59	C₁₃×#475	C₂²	1	4	yes	complemented
60	C₁₃×#474	C₂²	1	4	yes	complemented
61	C₁₃×#469	C₂²	1	8	yes	complemented
62	C₁₃×#468	C₂²	1	8	yes	complemented
63	C₁₃×#463	C₂²	1	8	yes	complemented
64	C₁₃×#460	C₂²	1	4	yes	complemented
65	C₁₃×#459	C₂²	1	4	yes	complemented
66	C₁₃×#450	C₂²	1	4	yes	complemented
67	C₁₃×#448	C₂²	1	4	yes	complemented
68	C₁₃×#447	C₂²	1	4	yes	—
69	C₁₃×#447	C₂²	1	4	yes	complemented
70	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
71	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
72	C₁₃×#432	C₂²	1	2	yes	complemented
73	C₁₃×#432	C₂²	1	2	yes	complemented
74	C₁₃×#431	C₂²	1	2	yes	complemented
75	C₁₃×#431	C₂²	1	2	yes	complemented
76	C₁₃×#423	C₂²	1	2	yes	complemented
77	C₁₃×#407	C₂²	1	2	yes	—
78	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
79	C₂×C₁₃×#41	—	2	2	no	—
80	C₂×C₁₃×#41	—	2	2	no	—
81	C₂×C₁₃×#41	—	2	2	no	—
82	C₂×C₁₃×#41	—	2	2	no	—
83	C₂×C₁₃×#41	—	4	8	no	—
84	C₂²×Q₈×C₁₃	—	2	1	no	—
85	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₃	—	2	1	no	—
87	C₂²×D₄×C₁₃	—	2	2	no	—
88	C₂²×D₄×C₁₃	—	2	1	no	—
89	C₂²×D₄×C₁₃	—	2	1	no	—
90	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃	—	2	1	no	—
93	C₂³×C₄×C₁₃	—	2	2	no	—
94	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
96	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
98	C₂×C₁₃×D₈	C₂³	1	8	yes	—
99	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
100	C₁₃×C₄⋊Q₈	—	2	1	no	—
101	C₁₃×C₄⋊Q₈	—	2	1	no	—
102	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
103	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
104	C₁₃×#127	—	2	1	no	—
105	C₁₃×#127	—	2	1	no	—
106	C₁₃×#127	C₂³	1	2	yes	—
107	C₁₃×#127	C₂³	1	2	yes	—
108	C₁₃×#126	—	2	2	no	—
109	C₁₃×#126	—	2	2	no	—
110	C₁₃×#126	—	2	2	no	—
111	C₁₃×#126	—	2	2	no	—
112	C₁₃×#125	—	2	1	no	—
113	C₁₃×#125	—	2	1	no	—
114	C₁₃×#125	C₂³	1	2	yes	—
115	C₁₃×#125	C₂³	1	2	yes	—
116	C₁₃×#124	—	2	2	no	—
117	C₁₃×#124	—	2	2	no	—
118	C₁₃×#124	—	2	2	no	—
119	C₁₃×#124	—	2	2	no	—
120	C₁₃×#124	—	2	1	no	—
121	C₁₃×#124	—	2	1	no	—
122	C₁₃×#124	C₂³	1	2	yes	—
123	C₁₃×#124	C₂³	1	2	yes	—
124	C₁₃×#123	—	2	2	no	—
125	C₁₃×#123	—	2	2	no	—
126	C₁₃×#123	—	2	2	no	—
127	C₁₃×#123	—	2	2	no	—
128	C₁₃×C₂²⋊Q₈	—	2	1	no	—
129	C₁₃×C₂²⋊Q₈	—	2	1	no	—
130	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
131	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
132	C₁₃×#121	—	2	2	no	—
133	C₁₃×#121	—	2	2	no	—
134	C₁₃×#121	—	2	2	no	—
135	C₁₃×#121	—	2	2	no	—
136	C₁₃×#121	—	2	1	no	—
137	C₁₃×#121	—	2	1	no	—
138	C₁₃×#121	—	2	2	no	—
139	C₁₃×#121	—	2	2	no	—
140	C₁₃×#121	C₂³	1	2	yes	—
141	C₁₃×#121	C₂³	1	4	yes	—
142	C₁₃×#121	C₂³	1	4	yes	—
143	C₁₃×#121	C₂³	1	2	yes	—
144	C₄×Q₈×C₁₃	—	2	1	no	—
145	C₄×Q₈×C₁₃	—	2	1	no	—
146	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
147	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
148	C₄×D₄×C₁₃	—	2	2	no	—
149	C₄×D₄×C₁₃	—	2	2	no	—
150	C₄×D₄×C₁₃	—	2	2	no	—
151	C₄×D₄×C₁₃	—	2	2	no	—
152	C₄×D₄×C₁₃	—	2	2	no	—
153	C₄×D₄×C₁₃	—	2	2	no	—
154	C₄×D₄×C₁₃	—	2	2	no	—
155	C₄×D₄×C₁₃	—	2	2	no	—
156	C₄×D₄×C₁₃	—	2	1	no	—
157	C₄×D₄×C₁₃	—	2	1	no	—
158	C₄×D₄×C₁₃	—	2	2	no	—
159	C₄×D₄×C₁₃	—	2	2	no	—
160	C₄×D₄×C₁₃	C₂³	1	2	yes	—
161	C₄×D₄×C₁₃	C₂³	1	4	yes	—
162	C₄×D₄×C₁₃	C₂³	1	2	yes	—
163	C₄×D₄×C₁₃	C₂³	1	4	yes	—
164	C₁₃×#117	—	2	2	no	—
165	C₁₃×#117	—	2	2	no	—
166	C₁₃×#117	—	2	2	no	—
167	C₁₃×#117	—	2	2	no	—
168	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
177	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
178	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
179	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
180	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
181	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
182	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
183	C₂×C₄²×C₁₃	—	2	1	no	—
184	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
185	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
196	C₁₃×#107	C₂³	1	8	yes	—
197	C₁₃×#106	C₂³	1	8	yes	—
198	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
199	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
200	C₁₃×#103	C₂³	1	8	yes	—
201	C₁₃×#102	C₂³	1	8	yes	—
202	C₁₃×#102	C₂³	1	8	yes	—
203	C₁₃×#102	C₂³	1	8	yes	—
204	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
205	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
206	C₁₃×#97	C₂³	1	4	yes	—
207	C₄×C₈×C₁₃	C₂³	1	4	yes	—
208	#60949	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂⁴×C₁₃	—	2	1	no	—
210	C₂⁴×C₁₃	—	2	2	no	—
211	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₁₃×#41	—	4	8	no	—
213	C₁₃×#41	—	4	8	no	—
214	C₁₃×#41	—	4	8	no	—
215	C₁₃×#41	—	4	8	no	—
216	C₂×Q₈×C₁₃	—	2	1	no	—
217	C₂×Q₈×C₁₃	—	2	2	no	—
218	C₂×Q₈×C₁₃	—	2	2	no	—
219	C₂×Q₈×C₁₃	—	4	2	no	—
220	C₂×Q₈×C₁₃	—	4	4	no	—
221	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
222	C₂×D₄×C₁₃	—	2	2	no	—
223	C₂×D₄×C₁₃	—	2	2	no	—
224	C₂×D₄×C₁₃	—	2	4	no	—
225	C₂×D₄×C₁₃	—	2	4	no	—
226	C₂×D₄×C₁₃	—	2	1	no	—
227	C₂×D₄×C₁₃	—	2	2	no	—
228	C₂×D₄×C₁₃	—	2	2	no	—
229	C₂×D₄×C₁₃	—	2	2	no	—
230	C₂×D₄×C₁₃	—	2	2	no	—
231	C₂×D₄×C₁₃	—	2	2	no	—
232	C₂×D₄×C₁₃	—	4	4	no	—
233	C₂×D₄×C₁₃	—	4	2	no	—
234	C₂×D₄×C₁₃	—	4	4	no	—
235	C₂×D₄×C₁₃	—	4	4	no	—
236	C₂×D₄×C₁₃	—	4	4	no	—
237	C₂×D₄×C₁₃	—	4	8	no	—
238	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
240	C₂²×C₄×C₁₃	—	2	4	no	—
241	C₂²×C₄×C₁₃	—	2	1	no	—
242	C₂²×C₄×C₁₃	—	2	1	no	—
243	C₂²×C₄×C₁₃	—	2	1	no	—
244	C₂²×C₄×C₁₃	—	2	2	no	—
245	C₂²×C₄×C₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₃	—	2	4	no	—
247	C₂²×C₄×C₁₃	—	2	2	no	—
248	C₂²×C₄×C₁₃	—	2	4	no	—
249	C₂²×C₄×C₁₃	—	4	2	no	—
250	C₂²×C₄×C₁₃	—	4	2	no	—
251	C₂²×C₄×C₁₃	—	4	8	no	—
252	C₂²×C₄×C₁₃	—	4	4	no	—
253	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₁₃×SD₁₆	—	4	8	no	—
272	C₁₃×D₈	—	4	8	no	—
273	C₁₃×M₁₆	—	4	4	no	—
274	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
275	C₁₃×C₄⋊C₄	—	2	2	no	—
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	—	2	2	no	—
279	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
285	C₁₃×C₄⋊C₄	—	2	2	no	—
286	C₁₃×C₄⋊C₄	—	2	1	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
289	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
290	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
291	C₁₃×C₂²⋊C₄	—	2	2	no	—
292	C₁₃×C₂²⋊C₄	—	2	2	no	—
293	C₁₃×C₂²⋊C₄	—	2	2	no	—
294	C₁₃×C₂²⋊C₄	—	2	2	no	—
295	C₁₃×C₂²⋊C₄	—	2	2	no	—
296	C₁₃×C₂²⋊C₄	—	2	2	no	—
297	C₁₃×C₂²⋊C₄	—	2	4	no	—
298	C₁₃×C₂²⋊C₄	—	2	4	no	—
299	C₁₃×C₂²⋊C₄	—	2	2	no	—
300	C₁₃×C₂²⋊C₄	—	2	2	no	—
301	C₁₃×C₂²⋊C₄	—	2	4	no	—
302	C₁₃×C₂²⋊C₄	—	2	4	no	—
303	C₁₃×C₂²⋊C₄	—	2	2	no	—
304	C₁₃×C₂²⋊C₄	—	2	2	no	—
305	C₄²×C₁₃	—	2	2	no	—
306	C₄²×C₁₃	—	2	2	no	—
307	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
320	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
321	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
322	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
323	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
324	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
325	#3251	C₂×C₁₃	1	4	yes	complemented
326	#3239	C₂×C₁₃	1	2	yes	complemented
327	#3234	C₂×C₁₃	1	2	yes	complemented
328	#3217	C₂×C₁₃	1	2	yes	complemented
329	#3213	C₂×C₁₃	1	2	yes	complemented
330	#3193	C₂×C₁₃	1	2	yes	complemented
331	#3192	C₂×C₁₃	1	2	yes	complemented
332	#3171	C₂×C₁₃	1	4	yes	complemented
333	#3105	C₂×C₁₃	1	4	yes	complemented
334	#3103	C₂×C₁₃	1	2	yes	complemented
335	#3100	C₂×C₁₃	1	2	yes	complemented
336	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
337	C₂³×C₁₃	—	2	2	no	—
338	C₂³×C₁₃	—	2	2	no	—
339	C₂³×C₁₃	—	2	2	no	—
340	C₂³×C₁₃	—	2	4	no	—
341	C₂³×C₁₃	—	4	1	no	—
342	C₂³×C₁₃	—	4	4	no	—
343	C₂³×C₁₃	—	4	2	no	—
344	C₂³×C₁₃	—	4	4	no	—
345	C₂³×C₁₃	—	4	2	no	—
346	C₂³×C₁₃	—	4	2	no	—
347	C₂³×C₁₃	—	4	4	no	—
348	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
349	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
350	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
351	Q₈×C₁₃	—	2	4	no	—
352	Q₈×C₁₃	—	4	2	no	—
353	Q₈×C₁₃	—	4	4	no	—
354	Q₈×C₁₃	—	4	4	no	—
355	D₄×C₁₃	—	2	4	no	—
356	D₄×C₁₃	—	2	8	no	—
357	D₄×C₁₃	—	4	4	no	—
358	D₄×C₁₃	—	4	2	no	—
359	D₄×C₁₃	—	4	4	no	—
360	D₄×C₁₃	—	4	4	no	—
361	D₄×C₁₃	—	4	4	no	—
362	D₄×C₁₃	—	4	4	no	—
363	D₄×C₁₃	—	4	8	no	—
364	D₄×C₁₃	—	4	8	no	—
365	D₄×C₁₃	—	4	4	no	—
366	D₄×C₁₃	—	4	4	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	2	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	4	no	—
381	C₂×C₄×C₁₃	—	4	1	no	—
382	C₂×C₄×C₁₃	—	4	1	no	—
383	C₂×C₄×C₁₃	—	4	1	no	—
384	C₂×C₄×C₁₃	—	4	1	no	—
385	C₂×C₄×C₁₃	—	4	1	no	—
386	C₂×C₄×C₁₃	—	4	1	no	—
387	C₂×C₄×C₁₃	—	4	1	no	—
388	C₂×C₄×C₁₃	—	4	8	no	—
389	C₂×C₄×C₁₃	—	4	4	no	—
390	C₂×C₄×C₁₃	—	4	2	no	—
391	C₂×C₄×C₁₃	—	4	2	no	—
392	C₂×C₄×C₁₃	—	4	2	no	—
393	C₂×C₄×C₁₃	—	4	4	no	—
394	C₂×C₄×C₁₃	—	4	4	no	—
395	C₂×C₄×C₁₃	—	4	8	no	—
396	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
397	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
409	C₈×C₁₃	—	2	8	no	—
410	C₂²×#41	—	2	1	no	—
411	#532	—	2	1	no	—
412	#532	—	2	1	no	—
413	#532	—	2	1	no	—
414	#532	—	2	1	no	—
415	#532	C₂²×C₁₃	1	2	yes	—
416	#532	C₂²×C₁₃	1	2	yes	—
417	#532	C₂²×C₁₃	1	2	yes	complemented
418	#532	C₂²×C₁₃	1	2	yes	complemented
419	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
420	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
421	#529	—	2	1	no	—
422	#529	—	2	1	no	—
423	#529	—	2	1	no	—
424	#529	—	2	1	no	—
425	#529	C₂²×C₁₃	1	2	yes	—
426	#529	C₂²×C₁₃	1	2	yes	—
427	#529	C₂²×C₁₃	1	2	yes	complemented
428	#529	C₂²×C₁₃	1	2	yes	complemented
429	C₂×#126	—	2	1	no	—
430	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	C₂×#124	—	2	1	no	—
432	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
433	C₂×#123	—	2	1	no	—
434	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
435	C₂×#121	—	2	1	no	—
436	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×#121	C₂²×C₁₃	1	2	yes	—
438	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	C₂×C₄×D₄	—	2	1	no	—
440	C₂×C₄×D₄	—	2	1	no	—
441	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
442	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
443	C₂×#117	—	2	1	no	—
444	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
445	#501	C₂²×C₁₃	1	4	yes	complemented
446	#496	C₂²×C₁₃	1	4	yes	complemented
447	#490	C₂²×C₁₃	1	4	yes	complemented
448	#489	C₂²×C₁₃	1	4	yes	complemented
449	#484	C₂²×C₁₃	1	4	yes	complemented
450	#481	C₂²×C₁₃	1	4	yes	—
451	#481	C₂²×C₁₃	1	4	yes	complemented
452	#480	C₂²×C₁₃	1	4	yes	complemented
453	#478	C₂²×C₁₃	1	8	yes	complemented
454	#475	C₂²×C₁₃	1	4	yes	complemented
455	#474	C₂²×C₁₃	1	4	yes	complemented
456	#469	C₂²×C₁₃	1	8	yes	complemented
457	#468	C₂²×C₁₃	1	8	yes	complemented
458	#463	C₂²×C₁₃	1	8	yes	complemented
459	#460	C₂²×C₁₃	1	4	yes	complemented
460	#459	C₂²×C₁₃	1	4	yes	complemented
461	#450	C₂²×C₁₃	1	4	yes	complemented
462	#448	C₂²×C₁₃	1	4	yes	complemented
463	#447	C₂²×C₁₃	1	4	yes	—
464	#447	C₂²×C₁₃	1	4	yes	complemented
465	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
466	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
467	#432	C₂²×C₁₃	1	2	yes	complemented
468	#432	C₂²×C₁₃	1	2	yes	complemented
469	#431	C₂²×C₁₃	1	2	yes	complemented
470	#431	C₂²×C₁₃	1	2	yes	complemented
471	#423	C₂²×C₁₃	1	2	yes	complemented
472	#407	C₂²×C₁₃	1	2	yes	—
473	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
474	C₂²×C₁₃	—	2	1	no	—
475	C₂²×C₁₃	—	2	1	no	—
476	C₂²×C₁₃	—	2	1	no	—
477	C₂²×C₁₃	—	2	1	no	—
478	C₂²×C₁₃	—	2	1	no	—
479	C₂²×C₁₃	—	2	1	no	—
480	C₂²×C₁₃	—	2	1	no	—
481	C₂²×C₁₃	—	4	4	no	—
482	C₂²×C₁₃	—	4	2	no	—
483	C₂²×C₁₃	—	4	4	no	—
484	C₂²×C₁₃	—	4	4	no	—
485	C₂²×C₁₃	—	4	2	no	—
486	C₂²×C₁₃	—	4	4	no	—
487	C₂²×C₁₃	—	4	2	no	—
488	C₂²×C₁₃	—	8	8	no	—
489	C₂²×C₁₃	—	8	4	no	—
490	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
491	C₂²×C₁₃	#575	1	2	yes	—
492	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
493	C₄×C₁₃	—	2	1	no	—
494	C₄×C₁₃	—	2	1	no	—
495	C₄×C₁₃	—	2	1	no	—
496	C₄×C₁₃	—	2	1	no	—
497	C₄×C₁₃	—	2	1	no	—
498	C₄×C₁₃	—	2	1	no	—
499	C₄×C₁₃	—	2	1	no	—
500	C₄×C₁₃	—	2	1	no	—
501	C₄×C₁₃	—	2	1	no	—
502	C₄×C₁₃	—	4	2	no	—
503	C₄×C₁₃	—	4	2	no	—
504	C₄×C₁₃	—	4	4	no	—
505	C₄×C₁₃	—	4	2	no	—
506	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
507	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
508	C₄×C₁₃	#585	1	2	yes	—
509	C₂×#41	—	2	2	no	—
510	C₂×#41	—	2	2	no	—
511	C₂×#41	—	2	2	no	—
512	C₂×#41	—	2	2	no	—
513	C₂×#41	—	4	8	no	—
514	C₂²×Q₈	—	2	1	no	—
515	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
516	C₂²×D₄	—	2	1	no	—
517	C₂²×D₄	—	2	2	no	—
518	C₂²×D₄	—	2	1	no	—
519	C₂²×D₄	—	2	1	no	—
520	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
521	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
522	C₂³×C₄	—	2	1	no	—
523	C₂³×C₄	—	2	2	no	—
524	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
525	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
526	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
527	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
528	C₂×D₈	C₂³×C₁₃	1	8	yes	—
529	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
530	C₄⋊Q₈	—	2	1	no	—
531	C₄⋊Q₈	—	2	1	no	—
532	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
533	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
534	#127	—	2	1	no	—
535	#127	—	2	1	no	—
536	#127	C₂³×C₁₃	1	2	yes	—
537	#127	C₂³×C₁₃	1	2	yes	—
538	#126	—	2	2	no	—
539	#126	—	2	2	no	—
540	#126	—	2	2	no	—
541	#126	—	2	2	no	—
542	#125	—	2	1	no	—
543	#125	—	2	1	no	—
544	#125	C₂³×C₁₃	1	2	yes	—
545	#125	C₂³×C₁₃	1	2	yes	—
546	#124	—	2	2	no	—
547	#124	—	2	2	no	—
548	#124	—	2	2	no	—
549	#124	—	2	2	no	—
550	#124	—	2	1	no	—
551	#124	—	2	1	no	—
552	#124	C₂³×C₁₃	1	2	yes	—
553	#124	C₂³×C₁₃	1	2	yes	—
554	#123	—	2	2	no	—
555	#123	—	2	2	no	—
556	#123	—	2	2	no	—
557	#123	—	2	2	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
561	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
562	#121	—	2	2	no	—
563	#121	—	2	2	no	—
564	#121	—	2	2	no	—
565	#121	—	2	2	no	—
566	#121	—	2	1	no	—
567	#121	—	2	1	no	—
568	#121	—	2	2	no	—
569	#121	—	2	2	no	—
570	#121	C₂³×C₁₃	1	2	yes	—
571	#121	C₂³×C₁₃	1	2	yes	—
572	#121	C₂³×C₁₃	1	4	yes	—
573	#121	C₂³×C₁₃	1	4	yes	—
574	C₄×Q₈	—	2	1	no	—
575	C₄×Q₈	—	2	1	no	—
576	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
577	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	—	2	2	no	—
585	C₄×D₄	—	2	2	no	—
586	C₄×D₄	—	2	1	no	—
587	C₄×D₄	—	2	1	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	—	2	2	no	—
590	C₄×D₄	C₂³×C₁₃	1	2	yes	—
591	C₄×D₄	C₂³×C₁₃	1	2	yes	—
592	C₄×D₄	C₂³×C₁₃	1	4	yes	—
593	C₄×D₄	C₂³×C₁₃	1	4	yes	—
594	#117	—	2	2	no	—
595	#117	—	2	2	no	—
596	#117	—	2	2	no	—
597	#117	—	2	2	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	—	2	2	no	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
611	C₂×C₂²⋊C₄	—	2	2	no	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₄²	—	2	1	no	—
614	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
615	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
616	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
617	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
618	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
619	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
626	#107	C₂³×C₁₃	1	8	yes	—
627	#106	C₂³×C₁₃	1	8	yes	—
628	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
629	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
630	#103	C₂³×C₁₃	1	8	yes	—
631	#102	C₂³×C₁₃	1	8	yes	—
632	#102	C₂³×C₁₃	1	8	yes	—
633	#102	C₂³×C₁₃	1	8	yes	—
634	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
635	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
636	#97	C₂³×C₁₃	1	4	yes	—
637	C₄×C₈	C₂³×C₁₃	1	4	yes	—
638	C₂×C₁₃	—	2	2	no	—
639	C₂×C₁₃	—	2	2	no	—
640	C₂×C₁₃	—	4	1	no	—
641	C₂×C₁₃	—	8	4	no	—
642	C₂×C₁₃	—	8	2	no	—
643	C₂×C₁₃	#3449	1	1	yes	characteristic
644	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
645	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
646	C₂⁴	—	2	1	no	—
647	C₂⁴	—	2	2	no	—
648	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
649	#41	—	4	8	no	—
650	#41	—	4	8	no	—
651	#41	—	4	8	no	—
652	#41	—	4	8	no	—
653	C₂×Q₈	—	2	1	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	4	2	no	—
657	C₂×Q₈	—	4	4	no	—
658	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	2	no	—
665	C₂×D₄	—	2	2	no	—
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	4	4	no	—
670	C₂×D₄	—	4	2	no	—
671	C₂×D₄	—	4	4	no	—
672	C₂×D₄	—	4	4	no	—
673	C₂×D₄	—	4	8	no	—
674	C₂×D₄	—	4	4	no	—
675	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
676	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	4	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	—	4	8	no	—
689	C₂²×C₄	—	4	4	no	—
690	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
691	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
694	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
696	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
702	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
703	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
704	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
708	SD₁₆	—	4	8	no	—
709	D₈	—	4	8	no	—
710	M₁₆	—	4	4	no	—
711	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	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	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
726	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
727	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	2	no	—
744	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
745	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
746	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
747	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
748	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
749	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
750	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
751	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
752	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
753	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
754	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
755	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
756	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
757	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
758	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
759	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
760	C₁₃	#60949	1	1	yes	characteristic, direct product factor, Sylow
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	4	no	—
765	C₂³	—	4	1	no	—
766	C₂³	—	4	4	no	—
767	C₂³	—	4	2	no	—
768	C₂³	—	4	2	no	—
769	C₂³	—	4	4	no	—
770	C₂³	—	4	2	no	—
771	C₂³	—	4	4	no	—
772	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
773	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
774	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
775	Q₈	—	2	4	no	—
776	Q₈	—	4	4	no	—
777	Q₈	—	4	2	no	—
778	Q₈	—	4	4	no	—
779	D₄	—	2	4	no	—
780	D₄	—	2	8	no	—
781	D₄	—	4	4	no	—
782	D₄	—	4	4	no	—
783	D₄	—	4	4	no	—
784	D₄	—	4	2	no	—
785	D₄	—	4	4	no	—
786	D₄	—	4	4	no	—
787	D₄	—	4	8	no	—
788	D₄	—	4	8	no	—
789	D₄	—	4	4	no	—
790	D₄	—	4	4	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	4	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	4	1	no	—
811	C₂×C₄	—	4	1	no	—
812	C₂×C₄	—	4	8	no	—
813	C₂×C₄	—	4	4	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	8	no	—
820	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
821	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
822	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
823	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
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	C₂²×D₄×C₁₃	1	1	yes	characteristic
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	C₂²×D₄×C₁₃	1	1	yes	characteristic
832	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
833	C₈	—	2	8	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	4	4	no	—
842	C₂²	—	4	4	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	4	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	4	no	—
848	C₂²	—	8	8	no	—
849	C₂²	—	8	4	no	—
850	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
851	C₂²	C₁₃×#575	1	2	yes	—
852	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
853	C₄	—	2	1	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	1	no	—
859	C₄	—	2	1	no	—
860	C₄	—	2	1	no	—
861	C₄	—	2	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	4	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
867	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
868	C₄	C₁₃×#585	1	2	yes	—
869	C₂	—	2	2	no	—
870	C₂	—	2	2	no	—
871	C₂	—	4	1	no	—
872	C₂	—	8	4	no	—
873	C₂	—	8	2	no	—
874	C₂	C₁₃×#3449	1	1	yes	characteristic
875	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
876	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#532	C₂	semidirect
2. C₂×C₁₃×#529	C₂	semidirect
3. C₁₃×#3251	C₂	semidirect
4. C₁₃×#3239	C₂	semidirect
5. C₁₃×#3234	C₂	semidirect
6. C₁₃×#3217	C₂	semidirect
7. C₁₃×#3213	C₂	semidirect
8. C₁₃×#3193	C₂	semidirect
9. C₁₃×#3192	C₂	semidirect
10. C₁₃×#3171	C₂	semidirect
11. C₁₃×#3105	C₂	semidirect
12. C₁₃×#3103	C₂	semidirect
13. C₁₃×#3100	C₂	semidirect
14. C₁₃×#2920	C₂	semidirect
22. C₁₃×#532	C₂²	semidirect
23. C₁₃×#532	C₂²	semidirect
24. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₁₃×#127	C₂²	semidirect
32. C₁₃×#529	C₂²	semidirect
33. C₁₃×#529	C₂²	semidirect
35. C₂×C₁₃×#125	C₂²	semidirect
37. C₂×C₁₃×#124	C₂²	semidirect
43. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
46. C₂×C₄×D₄×C₁₃	C₂²	semidirect
47. C₂×C₄×D₄×C₁₃	C₂²	semidirect
50. C₁₃×#501	C₂²	semidirect
51. C₁₃×#496	C₂²	semidirect
52. C₁₃×#490	C₂²	semidirect
53. C₁₃×#489	C₂²	semidirect
54. C₁₃×#484	C₂²	semidirect
56. C₁₃×#481	C₂²	semidirect
57. C₁₃×#480	C₂²	semidirect
58. C₁₃×#478	C₂²	semidirect
59. C₁₃×#475	C₂²	semidirect
60. C₁₃×#474	C₂²	semidirect
61. C₁₃×#469	C₂²	semidirect
62. C₁₃×#468	C₂²	semidirect
63. C₁₃×#463	C₂²	semidirect
64. C₁₃×#460	C₂²	semidirect
65. C₁₃×#459	C₂²	semidirect
66. C₁₃×#450	C₂²	semidirect
67. C₁₃×#448	C₂²	semidirect
69. C₁₃×#447	C₂²	semidirect
70. C₄×C₁₃×SD₁₆	C₂²	semidirect
71. C₄×C₁₃×D₈	C₂²	semidirect
72. C₁₃×#432	C₂²	semidirect
73. C₁₃×#432	C₂²	semidirect
74. C₁₃×#431	C₂²	semidirect
75. C₁₃×#431	C₂²	semidirect
76. C₁₃×#423	C₂²	semidirect
78. C₄×C₁₃×M₁₆	C₂²	semidirect
208. #60949	C₁₃	direct (N × H)
323. C₂×#532	C₂×C₁₃	semidirect
324. C₂×#529	C₂×C₁₃	semidirect
325. #3251	C₂×C₁₃	semidirect
326. #3239	C₂×C₁₃	semidirect
327. #3234	C₂×C₁₃	semidirect
328. #3217	C₂×C₁₃	semidirect
329. #3213	C₂×C₁₃	semidirect
330. #3193	C₂×C₁₃	semidirect
331. #3192	C₂×C₁₃	semidirect
332. #3171	C₂×C₁₃	semidirect
333. #3105	C₂×C₁₃	semidirect
334. #3103	C₂×C₁₃	semidirect
335. #3100	C₂×C₁₃	semidirect
336. #2920	C₂×C₁₃	semidirect
417. #532	C₂²×C₁₃	semidirect
418. #532	C₂²×C₁₃	semidirect
419. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
420. C₂×#127	C₂²×C₁₃	semidirect
427. #529	C₂²×C₁₃	semidirect
428. #529	C₂²×C₁₃	semidirect
430. C₂×#125	C₂²×C₁₃	semidirect
432. C₂×#124	C₂²×C₁₃	semidirect
438. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
441. C₂×C₄×D₄	C₂²×C₁₃	semidirect
442. C₂×C₄×D₄	C₂²×C₁₃	semidirect
445. #501	C₂²×C₁₃	semidirect
446. #496	C₂²×C₁₃	semidirect
447. #490	C₂²×C₁₃	semidirect
448. #489	C₂²×C₁₃	semidirect
449. #484	C₂²×C₁₃	semidirect
451. #481	C₂²×C₁₃	semidirect
452. #480	C₂²×C₁₃	semidirect
453. #478	C₂²×C₁₃	semidirect
454. #475	C₂²×C₁₃	semidirect
455. #474	C₂²×C₁₃	semidirect
456. #469	C₂²×C₁₃	semidirect
457. #468	C₂²×C₁₃	semidirect
458. #463	C₂²×C₁₃	semidirect
459. #460	C₂²×C₁₃	semidirect
460. #459	C₂²×C₁₃	semidirect
461. #450	C₂²×C₁₃	semidirect
462. #448	C₂²×C₁₃	semidirect
464. #447	C₂²×C₁₃	semidirect
465. C₄×SD₁₆	C₂²×C₁₃	semidirect
466. C₄×D₈	C₂²×C₁₃	semidirect
467. #432	C₂²×C₁₃	semidirect
468. #432	C₂²×C₁₃	semidirect
469. #431	C₂²×C₁₃	semidirect
470. #431	C₂²×C₁₃	semidirect
471. #423	C₂²×C₁₃	semidirect
473. C₄×M₁₆	C₂²×C₁₃	semidirect
760. C₁₃	#60949	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#532	2
C₂×C₁₃×#529	2
C₁₃×#3251	2
C₁₃×#3239	2
C₁₃×#3234	2
C₁₃×#3217	2
C₁₃×#3213	2
C₁₃×#3193	2
C₁₃×#3192	2
C₁₃×#3171	2
C₁₃×#3105	2
C₁₃×#3103	2
C₁₃×#3100	2
C₁₃×#2920	2
#60949	13

Subgroups — C13×#60949 #15747288

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60949 #15747288