Subgroups — C₁₃×#61983 #15748322

Order 3328.

2164 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3397	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3368	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3310	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3294	C₂	1	2	yes	maximal, complemented
7	D₄×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3265	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3247	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3217	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3112	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#460	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
20	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
21	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#556	—	2	1	no	—
23	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#552	—	2	2	no	—
25	C₁₃×#552	C₂²	1	2	yes	complemented
26	C₁₃×#550	—	2	1	no	—
27	C₁₃×#550	C₂²	1	2	yes	—
28	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#548	C₂²	1	2	yes	complemented
30	C₁₃×#547	—	2	1	no	—
31	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
32	D₄²×C₁₃	—	2	1	no	—
33	D₄²×C₁₃	—	2	2	no	—
34	D₄²×C₁₃	C₂²	1	4	yes	—
35	D₄²×C₁₃	C₂²	1	2	yes	—
36	C₁₃×#535	—	2	2	no	—
37	C₁₃×#535	—	2	1	no	—
38	C₁₃×#533	—	2	1	no	—
39	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#532	C₂²	1	1	yes	characteristic
41	C₁₃×#532	C₂²	1	2	yes	—
42	C₂×C₁₃×#127	C₂²	1	2	yes	—
43	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
44	C₁₃×#529	—	2	2	no	—
45	C₁₃×#529	C₂²	1	2	yes	complemented
46	C₄×C₁₃×#41	—	2	1	no	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
50	C₁₃×#496	C₂²	1	4	yes	complemented
51	C₁₃×#492	C₂²	1	2	yes	complemented
52	C₁₃×#490	C₂²	1	4	yes	complemented
53	C₁₃×#486	C₂²	1	2	yes	complemented
54	C₁₃×#482	C₂²	1	2	yes	complemented
55	C₁₃×#480	C₂²	1	4	yes	complemented
56	C₁₃×#478	C₂²	1	4	yes	complemented
57	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#477	C₂²	1	2	yes	complemented
59	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#474	C₂²	1	2	yes	complemented
61	C₁₃×#468	C₂²	1	4	yes	complemented
62	C₁₃×#466	C₂²	1	4	yes	complemented
63	C₁₃×#465	C₂²	1	4	yes	complemented
64	C₁₃×#463	C₂²	1	4	yes	complemented
65	C₁₃×#461	C₂²	1	2	yes	complemented
66	C₁₃×#460	C₂²	1	4	yes	complemented
67	C₁₃×#460	C₂²	1	2	yes	complemented
68	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#460	C₂²	1	2	yes	complemented
70	C₁₃×#460	C₂²	1	4	yes	complemented
71	C₁₃×#460	C₂²	1	2	yes	complemented
72	C₁₃×#460	C₂²	1	2	yes	complemented
73	C₁₃×#460	C₂²	1	2	yes	complemented
74	C₁₃×#459	C₂²	1	2	yes	complemented
75	C₁₃×#459	C₂²	1	2	yes	complemented
76	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#450	C₂²	1	4	yes	complemented
78	C₁₃×#450	C₂²	1	4	yes	complemented
79	C₁₃×#449	C₂²	1	2	yes	complemented
80	C₁₃×#448	C₂²	1	4	yes	complemented
81	C₁₃×#447	C₂²	1	4	yes	complemented
82	C₁₃×#446	C₂²	1	2	yes	complemented
83	C₁₃×#440	C₂²	1	4	yes	complemented
84	C₁₃×#440	C₂²	1	4	yes	complemented
85	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
86	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
87	C₁₃×#435	C₂²	1	4	yes	complemented
88	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
89	C₁₃×#432	C₂²	1	2	yes	complemented
90	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
93	C₁₃×#418	C₂²	1	2	yes	complemented
94	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
95	C₁₃×H(5,𝔽₂)	—	4	8	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	—	2	1	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	1	yes	characteristic
102	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
103	C₂²×D₄×C₁₃	—	2	4	no	—
104	C₂²×D₄×C₁₃	—	2	2	no	—
105	C₂²×D₄×C₁₃	—	2	2	no	—
106	C₂²×D₄×C₁₃	—	2	1	no	—
107	C₂²×D₄×C₁₃	—	2	2	no	—
108	C₂²×D₄×C₁₃	—	2	1	no	—
109	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
112	C₂×C₁₃×SD₁₆	—	4	8	no	—
113	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
114	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
115	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
116	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
117	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
118	C₂×C₁₃×D₈	C₂³	1	2	yes	—
119	C₂×C₁₃×D₈	C₂³	1	4	yes	—
120	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
121	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
122	C₁₃×C₄⋊Q₈	—	2	1	no	—
123	C₁₃×C₄⋊Q₈	—	2	1	no	—
124	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₁₃×#127	—	2	1	no	—
128	C₁₃×#127	—	2	2	no	—
129	C₁₃×#127	—	2	1	no	—
130	C₁₃×#127	—	2	2	no	—
131	C₁₃×#127	C₂³	1	2	yes	—
132	C₁₃×#127	C₂³	1	1	yes	characteristic
133	C₁₃×#127	C₂³	1	2	yes	—
134	C₁₃×#127	C₂³	1	4	yes	—
135	C₁₃×#126	—	2	2	no	—
136	C₁₃×#126	—	2	2	no	—
137	C₁₃×#126	—	2	2	no	—
138	C₁₃×#125	—	2	2	no	—
139	C₁₃×#125	—	2	2	no	—
140	C₁₃×#125	—	2	1	no	—
141	C₁₃×#125	C₂³	1	2	yes	—
142	C₁₃×#124	—	2	2	no	—
143	C₁₃×#124	—	2	1	no	—
144	C₁₃×#124	—	2	2	no	—
145	C₁₃×#124	C₂³	1	2	yes	—
146	C₁₃×#123	—	2	2	no	—
147	C₁₃×#123	—	2	2	no	—
148	C₁₃×#123	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	—	2	1	no	—
150	C₁₃×C₂²⋊Q₈	—	2	1	no	—
151	C₁₃×C₂²⋊Q₈	—	2	1	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	2	yes	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	2	no	—
158	C₁₃×#121	—	2	1	no	—
159	C₁₃×#121	—	2	2	no	—
160	C₁₃×#121	—	2	4	no	—
161	C₁₃×#121	—	2	4	no	—
162	C₁₃×#121	—	2	2	no	—
163	C₁₃×#121	C₂³	1	2	yes	—
164	C₁₃×#121	C₂³	1	4	yes	—
165	C₁₃×#121	C₂³	1	2	yes	—
166	C₁₃×#120	—	2	4	no	—
167	C₁₃×#120	—	2	4	no	—
168	C₁₃×#120	—	2	4	no	—
169	C₄×Q₈×C₁₃	—	2	1	no	—
170	C₄×Q₈×C₁₃	—	2	2	no	—
171	C₄×Q₈×C₁₃	—	2	2	no	—
172	C₄×Q₈×C₁₃	—	2	1	no	—
173	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
174	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
175	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
176	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
177	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
178	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
179	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₁₃	—	2	1	no	—
181	C₄×D₄×C₁₃	—	2	2	no	—
182	C₄×D₄×C₁₃	—	2	1	no	—
183	C₄×D₄×C₁₃	—	2	1	no	—
184	C₄×D₄×C₁₃	—	2	2	no	—
185	C₄×D₄×C₁₃	—	2	1	no	—
186	C₄×D₄×C₁₃	—	2	2	no	—
187	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
188	C₄×D₄×C₁₃	D₄	1	2	yes	—
189	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₁₃	C₂³	1	2	yes	—
191	C₄×D₄×C₁₃	C₂³	1	4	yes	—
192	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
193	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
194	C₄×D₄×C₁₃	C₂³	1	2	yes	—
195	C₁₃×#117	—	2	1	no	—
196	C₁₃×#117	—	2	1	no	—
197	C₁₃×#117	—	2	2	no	—
198	C₁₃×#117	—	2	1	no	—
199	C₁₃×#117	—	2	2	no	—
200	C₁₃×#117	D₄	1	2	yes	—
201	C₁₃×#117	D₄	1	1	yes	characteristic
202	C₁₃×#117	C₂³	1	1	yes	characteristic
203	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₄²×C₁₃	—	2	2	no	—
206	C₂×C₄²×C₁₃	—	2	1	no	—
207	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
208	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
209	C₁₃×#107	C₂³	1	2	yes	—
210	C₁₃×#107	C₂³	1	4	yes	—
211	C₁₃×#106	C₂³	1	2	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
213	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
216	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
217	C₁₃×#103	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	2	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	2	yes	—
225	C₁₃×#102	C₂³	1	2	yes	—
226	C₁₃×#102	C₂³	1	4	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
228	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₁₃×#97	C₂³	1	4	yes	—
230	C₄×C₈×C₁₃	C₂³	1	2	yes	—
231	#61983	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂⁴×C₁₃	—	2	2	no	—
233	C₂⁴×C₁₃	—	2	4	no	—
234	C₁₃×#41	—	2	4	no	—
235	C₁₃×#41	—	2	2	no	—
236	C₁₃×#41	—	4	1	no	—
237	C₁₃×#41	—	4	8	no	—
238	C₁₃×#41	—	4	4	no	—
239	C₁₃×#41	—	4	8	no	—
240	C₁₃×#41	—	4	4	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	2	1	no	—
243	C₂×Q₈×C₁₃	—	2	1	no	—
244	C₂×Q₈×C₁₃	—	2	4	no	—
245	C₂×Q₈×C₁₃	—	4	2	no	—
246	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
248	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×D₄×C₁₃	—	2	1	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	4	no	—
253	C₂×D₄×C₁₃	—	2	1	no	—
254	C₂×D₄×C₁₃	—	2	2	no	—
255	C₂×D₄×C₁₃	—	2	4	no	—
256	C₂×D₄×C₁₃	—	2	2	no	—
257	C₂×D₄×C₁₃	—	2	1	no	—
258	C₂×D₄×C₁₃	—	2	2	no	—
259	C₂×D₄×C₁₃	—	2	2	no	—
260	C₂×D₄×C₁₃	—	2	4	no	—
261	C₂×D₄×C₁₃	—	2	4	no	—
262	C₂×D₄×C₁₃	—	2	2	no	—
263	C₂×D₄×C₁₃	—	4	4	no	—
264	C₂×D₄×C₁₃	—	4	2	no	—
265	C₂×D₄×C₁₃	—	4	4	no	—
266	C₂×D₄×C₁₃	—	4	2	no	—
267	C₂×D₄×C₁₃	—	4	8	no	—
268	C₂×D₄×C₁₃	—	4	4	no	—
269	C₂×D₄×C₁₃	—	4	16	no	—
270	C₂×D₄×C₁₃	—	4	8	no	—
271	C₂×D₄×C₁₃	—	8	4	no	—
272	C₂×D₄×C₁₃	—	8	2	no	—
273	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
274	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
276	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
277	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	—	2	2	no	—
279	C₂²×C₄×C₁₃	—	2	2	no	—
280	C₂²×C₄×C₁₃	—	2	1	no	—
281	C₂²×C₄×C₁₃	—	2	1	no	—
282	C₂²×C₄×C₁₃	—	2	1	no	—
283	C₂²×C₄×C₁₃	—	2	4	no	—
284	C₂²×C₄×C₁₃	—	2	2	no	—
285	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₁₃×SD₁₆	—	2	4	no	—
292	C₁₃×SD₁₆	—	2	8	no	—
293	C₁₃×SD₁₆	—	4	4	no	—
294	C₁₃×SD₁₆	—	4	4	no	—
295	C₁₃×SD₁₆	—	4	4	no	—
296	C₁₃×D₈	—	4	2	no	—
297	C₁₃×D₈	—	4	4	no	—
298	C₁₃×M₁₆	—	4	2	no	—
299	C₂×C₈×C₁₃	—	4	4	no	—
300	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
301	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
302	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
303	C₁₃×C₄⋊C₄	—	2	1	no	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	2	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	—	2	2	no	—
308	C₁₃×C₄⋊C₄	—	2	1	no	—
309	C₁₃×C₄⋊C₄	—	2	2	no	—
310	C₁₃×C₄⋊C₄	—	2	2	no	—
311	C₁₃×C₄⋊C₄	—	2	1	no	—
312	C₁₃×C₄⋊C₄	—	2	1	no	—
313	C₁₃×C₄⋊C₄	—	2	2	no	—
314	C₁₃×C₄⋊C₄	—	2	1	no	—
315	C₁₃×C₄⋊C₄	—	2	2	no	—
316	C₁₃×C₄⋊C₄	—	2	1	no	—
317	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
318	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
319	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
320	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
321	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
322	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
323	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
324	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
325	C₁₃×C₂²⋊C₄	—	2	2	no	—
326	C₁₃×C₂²⋊C₄	—	2	2	no	—
327	C₁₃×C₂²⋊C₄	—	2	1	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	—	2	1	no	—
330	C₁₃×C₂²⋊C₄	—	2	1	no	—
331	C₁₃×C₂²⋊C₄	—	2	2	no	—
332	C₁₃×C₂²⋊C₄	—	2	2	no	—
333	C₁₃×C₂²⋊C₄	—	2	2	no	—
334	C₁₃×C₂²⋊C₄	—	2	4	no	—
335	C₁₃×C₂²⋊C₄	—	2	4	no	—
336	C₁₃×C₂²⋊C₄	—	2	2	no	—
337	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
338	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
339	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
340	C₄²×C₁₃	—	2	1	no	—
341	C₄²×C₁₃	—	2	1	no	—
342	C₄²×C₁₃	—	2	2	no	—
343	C₄²×C₁₃	—	2	2	no	—
344	C₄²×C₁₃	—	2	1	no	—
345	C₄²×C₁₃	—	2	2	no	—
346	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₁₃	C₂×D₄	1	2	yes	—
349	C₄²×C₁₃	C₂×D₄	1	2	yes	—
350	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
351	C₄²×C₁₃	C₂⁴	1	2	yes	—
352	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
353	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#3482	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#3397	C₂×C₁₃	1	2	yes	complemented
356	#3368	C₂×C₁₃	1	2	yes	complemented
357	#3310	C₂×C₁₃	1	4	yes	complemented
358	#3294	C₂×C₁₃	1	2	yes	complemented
359	D₄×SD₁₆	C₂×C₁₃	1	2	yes	complemented
360	#3265	C₂×C₁₃	1	4	yes	complemented
361	#3254	C₂×C₁₃	1	1	yes	characteristic, complemented
362	#3247	C₂×C₁₃	1	2	yes	complemented
363	#3217	C₂×C₁₃	1	2	yes	complemented
364	#3208	C₂×C₁₃	1	1	yes	characteristic, complemented
365	#3112	C₂×C₁₃	1	2	yes	complemented
366	#3106	C₂×C₁₃	1	1	yes	characteristic, complemented
367	#3038	C₂×C₁₃	1	1	yes	characteristic, complemented
368	C₂×#460	C₂×C₁₃	1	2	yes	complemented
369	#2990	C₂×C₁₃	1	1	yes	characteristic, complemented
370	C₂³×C₁₃	—	2	1	no	—
371	C₂³×C₁₃	—	2	4	no	—
372	C₂³×C₁₃	—	2	2	no	—
373	C₂³×C₁₃	—	4	4	no	—
374	C₂³×C₁₃	—	4	8	no	—
375	C₂³×C₁₃	—	8	4	no	—
376	C₂³×C₁₃	—	8	2	no	—
377	C₂³×C₁₃	—	8	4	no	—
378	C₂³×C₁₃	—	8	2	no	—
379	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
380	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
381	Q₈×C₁₃	—	2	2	no	—
382	Q₈×C₁₃	—	2	1	no	—
383	Q₈×C₁₃	—	2	2	no	—
384	Q₈×C₁₃	—	2	2	no	—
385	Q₈×C₁₃	—	4	4	no	—
386	Q₈×C₁₃	—	4	2	no	—
387	Q₈×C₁₃	—	4	2	no	—
388	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	complemented
389	D₄×C₁₃	—	2	4	no	—
390	D₄×C₁₃	—	2	1	no	—
391	D₄×C₁₃	—	2	4	no	—
392	D₄×C₁₃	—	2	2	no	—
393	D₄×C₁₃	—	2	1	no	—
394	D₄×C₁₃	—	2	2	no	—
395	D₄×C₁₃	—	2	4	no	—
396	D₄×C₁₃	—	4	2	no	—
397	D₄×C₁₃	—	4	4	no	—
398	D₄×C₁₃	—	4	2	no	—
399	D₄×C₁₃	—	4	8	no	—
400	D₄×C₁₃	—	4	4	no	—
401	D₄×C₁₃	—	4	8	no	—
402	D₄×C₁₃	—	4	4	no	—
403	D₄×C₁₃	—	4	4	no	—
404	D₄×C₁₃	—	4	2	no	—
405	D₄×C₁₃	—	4	4	no	—
406	D₄×C₁₃	—	8	2	no	—
407	D₄×C₁₃	—	8	4	no	—
408	D₄×C₁₃	—	8	4	no	—
409	D₄×C₁₃	—	8	2	no	—
410	D₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
411	C₂×C₄×C₁₃	—	2	4	no	—
412	C₂×C₄×C₁₃	—	2	1	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	4	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	2	1	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	1	no	—
420	C₂×C₄×C₁₃	—	2	1	no	—
421	C₂×C₄×C₁₃	—	2	1	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	4	2	no	—
426	C₂×C₄×C₁₃	—	4	4	no	—
427	C₂×C₄×C₁₃	—	4	8	no	—
428	C₂×C₄×C₁₃	—	4	4	no	—
429	C₂×C₄×C₁₃	—	4	4	no	—
430	C₂×C₄×C₁₃	—	4	2	no	—
431	C₂×C₄×C₁₃	—	4	2	no	—
432	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
438	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
441	C₈×C₁₃	—	2	2	no	—
442	C₈×C₁₃	—	2	4	no	—
443	C₈×C₁₃	—	2	2	no	—
444	C₂×H(5,𝔽₂)	—	2	1	no	—
445	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
446	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
447	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
448	#556	—	2	1	no	—
449	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
450	#552	—	2	2	no	—
451	#552	C₂²×C₁₃	1	2	yes	complemented
452	#550	—	2	1	no	—
453	#550	C₂²×C₁₃	1	2	yes	—
454	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
455	#548	C₂²×C₁₃	1	2	yes	complemented
456	#547	—	2	1	no	—
457	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
458	D₄²	—	2	1	no	—
459	D₄²	—	2	2	no	—
460	D₄²	C₂²×C₁₃	1	4	yes	—
461	D₄²	C₂²×C₁₃	1	2	yes	—
462	#535	—	2	2	no	—
463	#535	—	2	1	no	—
464	#533	—	2	1	no	—
465	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
466	#532	C₂²×C₁₃	1	1	yes	characteristic
467	#532	C₂²×C₁₃	1	2	yes	—
468	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
469	C₂×#127	C₂²×C₁₃	1	2	yes	—
470	#529	—	2	2	no	—
471	#529	C₂²×C₁₃	1	2	yes	complemented
472	C₄×#41	—	2	1	no	—
473	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
474	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
475	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
476	#496	C₂²×C₁₃	1	4	yes	complemented
477	#492	C₂²×C₁₃	1	2	yes	complemented
478	#490	C₂²×C₁₃	1	4	yes	complemented
479	#486	C₂²×C₁₃	1	2	yes	complemented
480	#482	C₂²×C₁₃	1	2	yes	complemented
481	#480	C₂²×C₁₃	1	4	yes	complemented
482	#478	C₂²×C₁₃	1	4	yes	complemented
483	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
484	#477	C₂²×C₁₃	1	2	yes	complemented
485	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
486	#474	C₂²×C₁₃	1	2	yes	complemented
487	#468	C₂²×C₁₃	1	4	yes	complemented
488	#466	C₂²×C₁₃	1	4	yes	complemented
489	#465	C₂²×C₁₃	1	4	yes	complemented
490	#463	C₂²×C₁₃	1	4	yes	complemented
491	#461	C₂²×C₁₃	1	2	yes	complemented
492	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
493	#460	C₂²×C₁₃	1	2	yes	complemented
494	#460	C₂²×C₁₃	1	2	yes	complemented
495	#460	C₂²×C₁₃	1	4	yes	complemented
496	#460	C₂²×C₁₃	1	2	yes	complemented
497	#460	C₂²×C₁₃	1	4	yes	complemented
498	#460	C₂²×C₁₃	1	2	yes	complemented
499	#460	C₂²×C₁₃	1	2	yes	complemented
500	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
501	#459	C₂²×C₁₃	1	2	yes	complemented
502	#459	C₂²×C₁₃	1	2	yes	complemented
503	#450	C₂²×C₁₃	1	4	yes	complemented
504	#450	C₂²×C₁₃	1	4	yes	complemented
505	#449	C₂²×C₁₃	1	2	yes	complemented
506	#448	C₂²×C₁₃	1	4	yes	complemented
507	#447	C₂²×C₁₃	1	4	yes	complemented
508	#446	C₂²×C₁₃	1	2	yes	complemented
509	#440	C₂²×C₁₃	1	4	yes	complemented
510	#440	C₂²×C₁₃	1	4	yes	complemented
511	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
512	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
513	#435	C₂²×C₁₃	1	4	yes	complemented
514	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
515	#432	C₂²×C₁₃	1	2	yes	complemented
516	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
517	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
518	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
519	#418	C₂²×C₁₃	1	2	yes	complemented
520	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
521	C₂²×C₁₃	—	2	2	no	—
522	C₂²×C₁₃	—	2	2	no	—
523	C₂²×C₁₃	—	2	1	no	—
524	C₂²×C₁₃	—	2	1	no	—
525	C₂²×C₁₃	—	2	1	no	—
526	C₂²×C₁₃	—	4	1	no	—
527	C₂²×C₁₃	—	4	4	no	—
528	C₂²×C₁₃	—	4	2	no	—
529	C₂²×C₁₃	—	4	4	no	—
530	C₂²×C₁₃	—	4	2	no	—
531	C₂²×C₁₃	—	4	1	no	—
532	C₂²×C₁₃	—	4	1	no	—
533	C₂²×C₁₃	—	4	2	no	—
534	C₂²×C₁₃	—	4	4	no	—
535	C₂²×C₁₃	—	16	8	no	—
536	C₂²×C₁₃	—	16	4	no	—
537	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
538	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
539	C₄×C₁₃	—	2	1	no	—
540	C₄×C₁₃	—	2	2	no	—
541	C₄×C₁₃	—	2	2	no	—
542	C₄×C₁₃	—	2	1	no	—
543	C₄×C₁₃	—	2	2	no	—
544	C₄×C₁₃	—	2	2	no	—
545	C₄×C₁₃	—	2	1	no	—
546	C₄×C₁₃	—	4	2	no	—
547	C₄×C₁₃	—	4	1	no	—
548	C₄×C₁₃	—	4	2	no	—
549	C₄×C₁₃	—	4	2	no	—
550	C₄×C₁₃	—	4	1	no	—
551	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
552	C₄×C₁₃	#577	1	2	yes	—
553	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
554	C₄×C₁₃	#585	1	1	yes	characteristic
555	H(5,𝔽₂)	—	4	8	no	—
556	C₂×#41	—	2	2	no	—
557	C₂×#41	—	2	1	no	—
558	C₂×#41	—	2	2	no	—
559	C₂×#41	—	2	1	no	—
560	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
561	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
562	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
563	C₂²×D₄	—	2	4	no	—
564	C₂²×D₄	—	2	2	no	—
565	C₂²×D₄	—	2	2	no	—
566	C₂²×D₄	—	2	1	no	—
567	C₂²×D₄	—	2	2	no	—
568	C₂²×D₄	—	2	1	no	—
569	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
570	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
571	AGL(1,ℤ/8)	—	4	4	no	—
572	C₂×SD₁₆	—	4	8	no	—
573	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
574	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
575	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
576	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
577	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
578	C₂×D₈	C₂³×C₁₃	1	4	yes	—
579	C₂×D₈	C₂³×C₁₃	1	2	yes	—
580	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
581	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
582	C₄⋊Q₈	—	2	1	no	—
583	C₄⋊Q₈	—	2	1	no	—
584	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
585	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
586	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
587	#127	—	2	1	no	—
588	#127	—	2	2	no	—
589	#127	—	2	1	no	—
590	#127	—	2	2	no	—
591	#127	C₂³×C₁₃	1	2	yes	—
592	#127	C₂³×C₁₃	1	1	yes	characteristic
593	#127	C₂³×C₁₃	1	2	yes	—
594	#127	C₂³×C₁₃	1	4	yes	—
595	#126	—	2	2	no	—
596	#126	—	2	2	no	—
597	#126	—	2	2	no	—
598	#125	—	2	2	no	—
599	#125	—	2	2	no	—
600	#125	—	2	1	no	—
601	#125	C₂³×C₁₃	1	2	yes	—
602	#124	—	2	2	no	—
603	#124	—	2	1	no	—
604	#124	—	2	2	no	—
605	#124	C₂³×C₁₃	1	2	yes	—
606	#123	—	2	2	no	—
607	#123	—	2	2	no	—
608	#123	—	2	2	no	—
609	C₂²⋊Q₈	—	2	1	no	—
610	C₂²⋊Q₈	—	2	1	no	—
611	C₂²⋊Q₈	—	2	1	no	—
612	C₂²⋊Q₈	—	2	2	no	—
613	C₂²⋊Q₈	—	2	2	no	—
614	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
615	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
616	#121	—	2	2	no	—
617	#121	—	2	2	no	—
618	#121	—	2	1	no	—
619	#121	—	2	2	no	—
620	#121	—	2	4	no	—
621	#121	—	2	4	no	—
622	#121	—	2	2	no	—
623	#121	C₂³×C₁₃	1	2	yes	—
624	#121	C₂³×C₁₃	1	4	yes	—
625	#121	C₂³×C₁₃	1	2	yes	—
626	#120	—	2	4	no	—
627	#120	—	2	4	no	—
628	#120	—	2	4	no	—
629	C₄×Q₈	—	2	1	no	—
630	C₄×Q₈	—	2	2	no	—
631	C₄×Q₈	—	2	2	no	—
632	C₄×Q₈	—	2	1	no	—
633	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
634	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
635	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
636	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
637	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
638	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
639	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
640	C₄×D₄	—	2	1	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	1	no	—
643	C₄×D₄	—	2	1	no	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	1	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
648	C₄×D₄	D₄×C₁₃	1	2	yes	—
649	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
650	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
651	C₄×D₄	C₂³×C₁₃	1	2	yes	—
652	C₄×D₄	C₂³×C₁₃	1	4	yes	—
653	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
654	C₄×D₄	C₂³×C₁₃	1	2	yes	—
655	#117	—	2	1	no	—
656	#117	—	2	1	no	—
657	#117	—	2	2	no	—
658	#117	—	2	1	no	—
659	#117	—	2	2	no	—
660	#117	D₄×C₁₃	1	2	yes	—
661	#117	D₄×C₁₃	1	1	yes	characteristic
662	#117	C₂³×C₁₃	1	1	yes	characteristic
663	C₂×C₄⋊C₄	—	2	2	no	—
664	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
665	C₂×C₄²	—	2	2	no	—
666	C₂×C₄²	—	2	1	no	—
667	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
668	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
669	#107	C₂³×C₁₃	1	2	yes	—
670	#107	C₂³×C₁₃	1	4	yes	—
671	#106	C₂³×C₁₃	1	2	yes	—
672	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
673	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
674	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
675	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
676	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
677	#103	C₂³×C₁₃	1	2	yes	—
678	#103	C₂³×C₁₃	1	4	yes	—
679	#102	C₂³×C₁₃	1	2	yes	—
680	#102	C₂³×C₁₃	1	4	yes	—
681	#102	C₂³×C₁₃	1	4	yes	—
682	#102	C₂³×C₁₃	1	4	yes	—
683	#102	C₂³×C₁₃	1	4	yes	—
684	#102	C₂³×C₁₃	1	2	yes	—
685	#102	C₂³×C₁₃	1	2	yes	—
686	#102	C₂³×C₁₃	1	4	yes	—
687	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
688	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
689	#97	C₂³×C₁₃	1	4	yes	—
690	C₄×C₈	C₂³×C₁₃	1	2	yes	—
691	C₂×C₁₃	—	2	4	no	—
692	C₂×C₁₃	—	4	1	no	—
693	C₂×C₁₃	—	8	1	no	—
694	C₂×C₁₃	—	8	2	no	—
695	C₂×C₁₃	—	8	4	no	—
696	C₂×C₁₃	#3488	1	1	yes	characteristic
697	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
698	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
699	C₂⁴	—	2	2	no	—
700	C₂⁴	—	2	4	no	—
701	#41	—	2	4	no	—
702	#41	—	2	2	no	—
703	#41	—	4	1	no	—
704	#41	—	4	8	no	—
705	#41	—	4	4	no	—
706	#41	—	4	8	no	—
707	#41	—	4	4	no	—
708	C₂×Q₈	—	2	2	no	—
709	C₂×Q₈	—	2	1	no	—
710	C₂×Q₈	—	2	1	no	—
711	C₂×Q₈	—	2	4	no	—
712	C₂×Q₈	—	4	2	no	—
713	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
714	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
715	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
716	C₂×D₄	—	2	1	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	2	1	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	4	4	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	4	no	—
733	C₂×D₄	—	4	2	no	—
734	C₂×D₄	—	4	8	no	—
735	C₂×D₄	—	4	4	no	—
736	C₂×D₄	—	4	16	no	—
737	C₂×D₄	—	4	8	no	—
738	C₂×D₄	—	8	4	no	—
739	C₂×D₄	—	8	2	no	—
740	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
741	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
742	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
743	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
744	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	4	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
753	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
754	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
755	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
758	SD₁₆	—	2	4	no	—
759	SD₁₆	—	2	8	no	—
760	SD₁₆	—	4	4	no	—
761	SD₁₆	—	4	4	no	—
762	SD₁₆	—	4	4	no	—
763	D₈	—	4	4	no	—
764	D₈	—	4	2	no	—
765	M₁₆	—	4	2	no	—
766	C₂×C₈	—	4	4	no	—
767	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
768	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
769	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	1	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	1	no	—
779	C₄⋊C₄	—	2	1	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
785	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
786	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
787	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
788	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
789	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
790	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
791	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	1	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	1	no	—
797	C₂²⋊C₄	—	2	1	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
805	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
806	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
807	C₄²	—	2	1	no	—
808	C₄²	—	2	1	no	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	1	no	—
812	C₄²	—	2	2	no	—
813	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
814	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
815	C₄²	C₂×D₄×C₁₃	1	2	yes	—
816	C₄²	C₂×D₄×C₁₃	1	2	yes	—
817	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
818	C₄²	C₂⁴×C₁₃	1	2	yes	—
819	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
820	C₁₃	#61983	1	1	yes	characteristic, direct product factor, Sylow
821	C₂³	—	2	1	no	—
822	C₂³	—	2	4	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	4	4	no	—
825	C₂³	—	4	8	no	—
826	C₂³	—	8	4	no	—
827	C₂³	—	8	2	no	—
828	C₂³	—	8	4	no	—
829	C₂³	—	8	2	no	—
830	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
831	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
832	Q₈	—	2	2	no	—
833	Q₈	—	2	1	no	—
834	Q₈	—	2	2	no	—
835	Q₈	—	2	2	no	—
836	Q₈	—	4	4	no	—
837	Q₈	—	4	2	no	—
838	Q₈	—	4	2	no	—
839	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	complemented
840	D₄	—	2	4	no	—
841	D₄	—	2	1	no	—
842	D₄	—	2	4	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	1	no	—
845	D₄	—	2	2	no	—
846	D₄	—	2	4	no	—
847	D₄	—	4	2	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	2	no	—
850	D₄	—	4	8	no	—
851	D₄	—	4	4	no	—
852	D₄	—	4	8	no	—
853	D₄	—	4	4	no	—
854	D₄	—	4	4	no	—
855	D₄	—	4	2	no	—
856	D₄	—	4	4	no	—
857	D₄	—	8	2	no	—
858	D₄	—	8	4	no	—
859	D₄	—	8	4	no	—
860	D₄	—	8	2	no	—
861	D₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
862	C₂×C₄	—	2	4	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	4	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	4	2	no	—
877	C₂×C₄	—	4	4	no	—
878	C₂×C₄	—	4	8	no	—
879	C₂×C₄	—	4	4	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	4	2	no	—
882	C₂×C₄	—	4	2	no	—
883	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
884	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
885	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
886	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
887	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
888	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
889	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
890	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
891	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
892	C₈	—	2	2	no	—
893	C₈	—	2	4	no	—
894	C₈	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	4	4	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	4	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	4	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	16	8	no	—
910	C₂²	—	16	4	no	—
911	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
912	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
913	C₄	—	2	1	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	4	1	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	2	no	—
925	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
926	C₄	C₁₃×#577	1	2	yes	—
927	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
928	C₄	C₁₃×#585	1	1	yes	characteristic
929	C₂	—	2	4	no	—
930	C₂	—	4	1	no	—
931	C₂	—	8	2	no	—
932	C₂	—	8	4	no	—
933	C₂	—	8	1	no	—
934	C₂	C₁₃×#3488	1	1	yes	characteristic
935	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
936	C₂	C₂×C₁₃×#577	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×#3498	C₂	semidirect
2. C₁₃×#3482	C₂	semidirect
3. C₁₃×#3397	C₂	semidirect
4. C₁₃×#3368	C₂	semidirect
5. C₁₃×#3310	C₂	semidirect
6. C₁₃×#3294	C₂	semidirect
7. D₄×C₁₃×SD₁₆	C₂	semidirect
8. C₁₃×#3265	C₂	semidirect
9. C₁₃×#3254	C₂	semidirect
10. C₁₃×#3247	C₂	semidirect
11. C₁₃×#3217	C₂	semidirect
12. C₁₃×#3208	C₂	semidirect
13. C₁₃×#3112	C₂	semidirect
14. C₁₃×#3106	C₂	semidirect
15. C₁₃×#3038	C₂	semidirect
16. C₂×C₁₃×#460	C₂	semidirect
17. C₁₃×#2990	C₂	semidirect
19. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂²×C₁₃×SD₁₆	C₂²	semidirect
21. C₁₃×#557	C₂²	semidirect
23. C₁₃×#556	C₂²	semidirect
25. C₁₃×#552	C₂²	semidirect
28. D₄×Q₈×C₁₃	C₂²	semidirect
29. C₁₃×#548	C₂²	semidirect
31. C₁₃×#547	C₂²	semidirect
39. C₁₃×#533	C₂²	semidirect
45. C₁₃×#529	C₂²	semidirect
48. C₄×C₁₃×#41	C₂²	semidirect
49. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
50. C₁₃×#496	C₂²	semidirect
51. C₁₃×#492	C₂²	semidirect
52. C₁₃×#490	C₂²	semidirect
53. C₁₃×#486	C₂²	semidirect
54. C₁₃×#482	C₂²	semidirect
55. C₁₃×#480	C₂²	semidirect
56. C₁₃×#478	C₂²	semidirect
57. C₁₃×#477	C₂²	semidirect
58. C₁₃×#477	C₂²	semidirect
59. C₁₃×#476	C₂²	semidirect
60. C₁₃×#474	C₂²	semidirect
61. C₁₃×#468	C₂²	semidirect
62. C₁₃×#466	C₂²	semidirect
63. C₁₃×#465	C₂²	semidirect
64. C₁₃×#463	C₂²	semidirect
65. C₁₃×#461	C₂²	semidirect
66. C₁₃×#460	C₂²	semidirect
67. C₁₃×#460	C₂²	semidirect
68. C₁₃×#460	C₂²	semidirect
69. C₁₃×#460	C₂²	semidirect
70. C₁₃×#460	C₂²	semidirect
71. C₁₃×#460	C₂²	semidirect
72. C₁₃×#460	C₂²	semidirect
73. C₁₃×#460	C₂²	semidirect
74. C₁₃×#459	C₂²	semidirect
75. C₁₃×#459	C₂²	semidirect
76. C₁₃×#459	C₂²	semidirect
77. C₁₃×#450	C₂²	semidirect
78. C₁₃×#450	C₂²	semidirect
79. C₁₃×#449	C₂²	semidirect
80. C₁₃×#448	C₂²	semidirect
81. C₁₃×#447	C₂²	semidirect
82. C₁₃×#446	C₂²	semidirect
83. C₁₃×#440	C₂²	semidirect
84. C₁₃×#440	C₂²	semidirect
85. C₄×C₁₃×SD₁₆	C₂²	semidirect
86. C₄×C₁₃×D₈	C₂²	semidirect
87. C₁₃×#435	C₂²	semidirect
88. C₈×D₄×C₁₃	C₂²	semidirect
89. C₁₃×#432	C₂²	semidirect
90. C₁₃×#431	C₂²	semidirect
91. C₁₃×#423	C₂²	semidirect
92. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
93. C₁₃×#418	C₂²	semidirect
94. C₂×C₁₃×#102	C₂²	semidirect
231. #61983	C₁₃	direct (N × H)
353. #3498	C₂×C₁₃	semidirect
354. #3482	C₂×C₁₃	semidirect
355. #3397	C₂×C₁₃	semidirect
356. #3368	C₂×C₁₃	semidirect
357. #3310	C₂×C₁₃	semidirect
358. #3294	C₂×C₁₃	semidirect
359. D₄×SD₁₆	C₂×C₁₃	semidirect
360. #3265	C₂×C₁₃	semidirect
361. #3254	C₂×C₁₃	semidirect
362. #3247	C₂×C₁₃	semidirect
363. #3217	C₂×C₁₃	semidirect
364. #3208	C₂×C₁₃	semidirect
365. #3112	C₂×C₁₃	semidirect
366. #3106	C₂×C₁₃	semidirect
367. #3038	C₂×C₁₃	semidirect
368. C₂×#460	C₂×C₁₃	semidirect
369. #2990	C₂×C₁₃	semidirect
388. Q₈×C₁₃	H(5,𝔽₂)	semidirect
410. D₄×C₁₃	AGL(1,ℤ/8)	semidirect
445. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
446. C₂²×SD₁₆	C₂²×C₁₃	semidirect
447. #557	C₂²×C₁₃	semidirect
449. #556	C₂²×C₁₃	semidirect
451. #552	C₂²×C₁₃	semidirect
454. D₄×Q₈	C₂²×C₁₃	semidirect
455. #548	C₂²×C₁₃	semidirect
457. #547	C₂²×C₁₃	semidirect
465. #533	C₂²×C₁₃	semidirect
471. #529	C₂²×C₁₃	semidirect
474. C₄×#41	C₂²×C₁₃	semidirect
475. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
476. #496	C₂²×C₁₃	semidirect
477. #492	C₂²×C₁₃	semidirect
478. #490	C₂²×C₁₃	semidirect
479. #486	C₂²×C₁₃	semidirect
480. #482	C₂²×C₁₃	semidirect
481. #480	C₂²×C₁₃	semidirect
482. #478	C₂²×C₁₃	semidirect
483. #477	C₂²×C₁₃	semidirect
484. #477	C₂²×C₁₃	semidirect
485. #476	C₂²×C₁₃	semidirect
486. #474	C₂²×C₁₃	semidirect
487. #468	C₂²×C₁₃	semidirect
488. #466	C₂²×C₁₃	semidirect
489. #465	C₂²×C₁₃	semidirect
490. #463	C₂²×C₁₃	semidirect
491. #461	C₂²×C₁₃	semidirect
492. #460	C₂²×C₁₃	semidirect
493. #460	C₂²×C₁₃	semidirect
494. #460	C₂²×C₁₃	semidirect
495. #460	C₂²×C₁₃	semidirect
496. #460	C₂²×C₁₃	semidirect
497. #460	C₂²×C₁₃	semidirect
498. #460	C₂²×C₁₃	semidirect
499. #460	C₂²×C₁₃	semidirect
500. #459	C₂²×C₁₃	semidirect
501. #459	C₂²×C₁₃	semidirect
502. #459	C₂²×C₁₃	semidirect
503. #450	C₂²×C₁₃	semidirect
504. #450	C₂²×C₁₃	semidirect
505. #449	C₂²×C₁₃	semidirect
506. #448	C₂²×C₁₃	semidirect
507. #447	C₂²×C₁₃	semidirect
508. #446	C₂²×C₁₃	semidirect
509. #440	C₂²×C₁₃	semidirect
510. #440	C₂²×C₁₃	semidirect
511. C₄×SD₁₆	C₂²×C₁₃	semidirect
512. C₄×D₈	C₂²×C₁₃	semidirect
513. #435	C₂²×C₁₃	semidirect
514. C₈×D₄	C₂²×C₁₃	semidirect
515. #432	C₂²×C₁₃	semidirect
516. #431	C₂²×C₁₃	semidirect
517. #423	C₂²×C₁₃	semidirect
518. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
519. #418	C₂²×C₁₃	semidirect
520. C₂×#102	C₂²×C₁₃	semidirect
820. C₁₃	#61983	direct (N × H)
839. Q₈	C₁₃×H(5,𝔽₂)	semidirect
861. D₄	C₁₃×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3498	2
C₁₃×#3482	2
C₁₃×#3397	2
C₁₃×#3368	2
C₁₃×#3310	2
C₁₃×#3294	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3265	2
C₁₃×#3254	2
C₁₃×#3247	2
C₁₃×#3217	2
C₁₃×#3208	2
C₁₃×#3112	2
C₁₃×#3106	2
C₁₃×#3038	2
C₂×C₁₃×#460	2
C₁₃×#2990	2
#61983	13

Subgroups — C13×#61983 #15748322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61983 #15748322