Subgroups — C₁₃×#62576 #15748915

Order 3328.

2050 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3368	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3366	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3318	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3310	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3295	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3294	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3234	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3217	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3180	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3171	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#490	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
19	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
20	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
21	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#553	C₂²	1	2	yes	complemented
23	C₁₃×#552	—	2	2	no	—
24	C₁₃×#552	—	2	1	no	—
25	C₁₃×#552	C₂²	1	2	yes	complemented
26	C₁₃×#550	—	2	1	no	—
27	C₁₃×#550	C₂²	1	2	yes	—
28	C₁₃×#547	—	2	1	no	—
29	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
30	D₄²×C₁₃	—	2	1	no	—
31	D₄²×C₁₃	—	2	2	no	—
32	D₄²×C₁₃	C₂²	1	2	yes	—
33	D₄²×C₁₃	C₂²	1	4	yes	—
34	C₁₃×#541	—	2	1	no	—
35	C₁₃×#539	—	2	2	no	—
36	C₁₃×#535	—	2	1	no	—
37	C₁₃×#535	—	2	2	no	—
38	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₁₃×#532	C₂²	1	2	yes	—
41	C₂×C₁₃×#127	C₂²	1	2	yes	—
42	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
43	C₁₃×#529	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#529	C₂²	1	2	yes	complemented
45	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
46	C₁₃×#520	—	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, complemented
51	C₁₃×#496	C₂²	1	2	yes	complemented
52	C₁₃×#490	C₂²	1	4	yes	complemented
53	C₁₃×#490	C₂²	1	4	yes	complemented
54	C₁₃×#490	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#490	C₂²	1	2	yes	complemented
56	C₁₃×#490	C₂²	1	2	yes	complemented
57	C₁₃×#490	C₂²	1	2	yes	complemented
58	C₁₃×#490	C₂²	1	2	yes	complemented
59	C₁₃×#489	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#486	C₂²	1	2	yes	complemented
61	C₁₃×#486	C₂²	1	2	yes	complemented
62	C₁₃×#482	C₂²	1	4	yes	complemented
63	C₁₃×#481	C₂²	1	4	yes	complemented
64	C₁₃×#480	C₂²	1	4	yes	complemented
65	C₁₃×#478	C₂²	1	4	yes	complemented
66	C₁₃×#478	C₂²	1	4	yes	complemented
67	C₁₃×#476	C₂²	1	2	yes	complemented
68	C₁₃×#474	C₂²	1	2	yes	complemented
69	C₁₃×#469	C₂²	1	2	yes	complemented
70	C₁₃×#468	C₂²	1	2	yes	complemented
71	C₁₃×#466	C₂²	1	4	yes	complemented
72	C₁₃×#465	C₂²	1	4	yes	complemented
73	C₁₃×#460	C₂²	1	2	yes	complemented
74	C₁₃×#460	C₂²	1	4	yes	complemented
75	C₁₃×#459	C₂²	1	2	yes	complemented
76	C₁₃×#459	C₂²	1	4	yes	complemented
77	C₁₃×#450	C₂²	1	4	yes	complemented
78	C₁₃×#450	C₂²	1	2	yes	complemented
79	C₁₃×#447	C₂²	1	4	yes	complemented
80	C₁₃×#447	C₂²	1	2	yes	complemented
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	complemented
86	C₁₃×#435	C₂²	1	4	yes	complemented
87	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
88	C₁₃×#432	C₂²	1	2	yes	complemented
89	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#418	C₂²	1	4	yes	complemented
91	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
92	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
93	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₁₃×#97	C₂²	1	2	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	C₂²×D₄×C₁₃	—	2	4	no	—
102	C₂²×D₄×C₁₃	—	2	2	no	—
103	C₂²×D₄×C₁₃	—	2	2	no	—
104	C₂²×D₄×C₁₃	—	2	1	no	—
105	C₂²×D₄×C₁₃	—	2	2	no	—
106	C₂²×D₄×C₁₃	—	2	1	no	—
107	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
108	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
109	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
110	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
111	C₂×C₁₃×D₈	C₂³	1	2	yes	—
112	C₂×C₁₃×D₈	C₂³	1	4	yes	—
113	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
114	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
115	C₁₃×C₄⋊Q₈	—	2	1	no	—
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₃×#127	—	2	2	no	—
120	C₁₃×#127	—	2	1	no	—
121	C₁₃×#127	—	2	1	no	—
122	C₁₃×#127	—	2	2	no	—
123	C₁₃×#127	C₂³	1	2	yes	—
124	C₁₃×#127	C₂³	1	4	yes	—
125	C₁₃×#127	C₂³	1	1	yes	characteristic
126	C₁₃×#127	C₂³	1	2	yes	—
127	C₁₃×#126	—	2	2	no	—
128	C₁₃×#126	—	2	2	no	—
129	C₁₃×#126	—	2	2	no	—
130	C₁₃×#126	—	2	1	no	—
131	C₁₃×#125	—	2	2	no	—
132	C₁₃×#125	—	2	2	no	—
133	C₁₃×#125	—	2	1	no	—
134	C₁₃×#125	—	2	2	no	—
135	C₁₃×#125	—	2	2	no	—
136	C₁₃×#125	C₂³	1	2	yes	—
137	C₁₃×#125	C₂³	1	2	yes	—
138	C₁₃×#125	C₂³	1	1	yes	characteristic
139	C₁₃×#125	C₂³	1	2	yes	—
140	C₁₃×#124	—	2	2	no	—
141	C₁₃×#124	—	2	1	no	—
142	C₁₃×#124	C₂³	1	1	yes	characteristic
143	C₁₃×#123	—	2	2	no	—
144	C₁₃×#123	—	2	1	no	—
145	C₁₃×#123	—	2	2	no	—
146	C₁₃×#123	—	2	2	no	—
147	C₁₃×#123	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	1	no	—
149	C₁₃×C₂²⋊Q₈	—	2	1	no	—
150	C₁₃×C₂²⋊Q₈	—	2	1	no	—
151	C₁₃×C₂²⋊Q₈	—	2	2	no	—
152	C₁₃×C₂²⋊Q₈	—	2	1	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	2	no	—
158	C₁₃×#121	—	2	1	no	—
159	C₁₃×#121	—	2	2	no	—
160	C₁₃×#121	—	2	4	no	—
161	C₁₃×#121	—	2	2	no	—
162	C₁₃×#121	—	2	4	no	—
163	C₁₃×#121	C₂³	1	2	yes	—
164	C₁₃×#121	C₂³	1	1	yes	characteristic
165	C₁₃×#121	C₂³	1	4	yes	—
166	C₁₃×#121	C₂³	1	2	yes	—
167	C₁₃×#120	—	2	4	no	—
168	C₁₃×#120	—	2	4	no	—
169	C₁₃×#120	—	2	4	no	—
170	C₄×Q₈×C₁₃	—	2	1	no	—
171	C₄×Q₈×C₁₃	—	2	1	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	1	yes	characteristic
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	—	2	1	no	—
180	C₄×D₄×C₁₃	—	2	2	no	—
181	C₄×D₄×C₁₃	—	2	1	no	—
182	C₄×D₄×C₁₃	—	2	2	no	—
183	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
184	C₄×D₄×C₁₃	D₄	1	2	yes	—
185	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₁₃	C₂³	1	2	yes	—
187	C₄×D₄×C₁₃	C₂³	1	4	yes	—
188	C₄×D₄×C₁₃	C₂³	1	2	yes	—
189	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₁₃	C₂³	1	2	yes	—
191	C₁₃×#117	—	2	2	no	—
192	C₁₃×#117	—	2	1	no	—
193	C₁₃×#117	—	2	2	no	—
194	C₁₃×#117	D₄	1	1	yes	characteristic
195	C₁₃×#117	D₄	1	2	yes	—
196	C₁₃×#117	C₂³	1	2	yes	—
197	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
198	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
199	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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×#102	C₂³	1	2	yes	—
212	C₁₃×#102	C₂³	1	2	yes	—
213	C₁₃×#102	C₂³	1	4	yes	—
214	C₁₃×#102	C₂³	1	4	yes	—
215	C₁₃×#102	C₂³	1	4	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	4	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	#62576	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂⁴×C₁₃	—	2	2	no	—
231	C₂⁴×C₁₃	—	2	4	no	—
232	C₁₃×#41	—	2	4	no	—
233	C₁₃×#41	—	4	8	no	—
234	C₁₃×#41	—	4	4	no	—
235	C₁₃×#41	—	4	8	no	—
236	C₁₃×#41	—	4	4	no	—
237	C₂×Q₈×C₁₃	—	2	1	no	—
238	C₂×Q₈×C₁₃	—	2	1	no	—
239	C₂×Q₈×C₁₃	—	2	1	no	—
240	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₁₃	—	2	2	no	—
243	C₂×D₄×C₁₃	—	2	2	no	—
244	C₂×D₄×C₁₃	—	2	4	no	—
245	C₂×D₄×C₁₃	—	2	1	no	—
246	C₂×D₄×C₁₃	—	2	1	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	2	no	—
251	C₂×D₄×C₁₃	—	2	1	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	4	no	—
254	C₂×D₄×C₁₃	—	2	4	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	4	4	no	—
257	C₂×D₄×C₁₃	—	4	4	no	—
258	C₂×D₄×C₁₃	—	4	4	no	—
259	C₂×D₄×C₁₃	—	4	8	no	—
260	C₂×D₄×C₁₃	—	4	4	no	—
261	C₂×D₄×C₁₃	—	4	16	no	—
262	C₂×D₄×C₁₃	—	4	8	no	—
263	C₂×D₄×C₁₃	—	8	4	no	—
264	C₂×D₄×C₁₃	—	8	2	no	—
265	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
266	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
268	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
269	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃	—	2	2	no	—
271	C₂²×C₄×C₁₃	—	2	2	no	—
272	C₂²×C₄×C₁₃	—	2	1	no	—
273	C₂²×C₄×C₁₃	—	2	4	no	—
274	C₂²×C₄×C₁₃	—	2	2	no	—
275	C₂²×C₄×C₁₃	—	2	2	no	—
276	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
279	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
282	C₁₃×SD₁₆	—	4	4	no	—
283	C₁₃×SD₁₆	—	4	2	no	—
284	C₁₃×D₈	—	4	4	no	—
285	C₁₃×D₈	—	4	2	no	—
286	C₁₃×M₁₆	—	4	2	no	—
287	C₂×C₈×C₁₃	—	4	4	no	—
288	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
289	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
290	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	1	no	—
293	C₁₃×C₄⋊C₄	—	2	1	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	1	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	2	2	no	—
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	—	2	1	no	—
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	—	2	1	no	—
305	C₁₃×C₄⋊C₄	—	2	1	no	—
306	C₁₃×C₄⋊C₄	—	2	1	no	—
307	C₁₃×C₄⋊C₄	—	2	2	no	—
308	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
309	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
310	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
311	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
312	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
313	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
314	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
315	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	1	no	—
320	C₁₃×C₂²⋊C₄	—	2	1	no	—
321	C₁₃×C₂²⋊C₄	—	2	1	no	—
322	C₁₃×C₂²⋊C₄	—	2	1	no	—
323	C₁₃×C₂²⋊C₄	—	2	2	no	—
324	C₁₃×C₂²⋊C₄	—	2	2	no	—
325	C₁₃×C₂²⋊C₄	—	2	4	no	—
326	C₁₃×C₂²⋊C₄	—	2	4	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	—	2	1	no	—
330	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
331	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
332	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
333	C₄²×C₁₃	—	2	2	no	—
334	C₄²×C₁₃	—	2	2	no	—
335	C₄²×C₁₃	—	2	1	no	—
336	C₄²×C₁₃	C₂×D₄	1	2	yes	—
337	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₁₃	C₂×D₄	1	2	yes	—
340	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
341	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
342	C₄²×C₁₃	C₂⁴	1	2	yes	—
343	#3515	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3368	C₂×C₁₃	1	2	yes	complemented
346	#3366	C₂×C₁₃	1	2	yes	complemented
347	#3318	C₂×C₁₃	1	4	yes	complemented
348	#3310	C₂×C₁₃	1	4	yes	complemented
349	#3295	C₂×C₁₃	1	2	yes	complemented
350	#3294	C₂×C₁₃	1	2	yes	complemented
351	#3235	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#3234	C₂×C₁₃	1	2	yes	complemented
353	#3217	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#3217	C₂×C₁₃	1	2	yes	complemented
355	#3180	C₂×C₁₃	1	2	yes	complemented
356	#3171	C₂×C₁₃	1	1	yes	characteristic, complemented
357	#3138	C₂×C₁₃	1	1	yes	characteristic, complemented
358	C₂×#490	C₂×C₁₃	1	2	yes	complemented
359	#2970	C₂×C₁₃	1	1	yes	characteristic, complemented
360	C₂³×C₁₃	—	2	1	no	—
361	C₂³×C₁₃	—	2	4	no	—
362	C₂³×C₁₃	—	2	2	no	—
363	C₂³×C₁₃	—	4	4	no	—
364	C₂³×C₁₃	—	4	8	no	—
365	C₂³×C₁₃	—	8	4	no	—
366	C₂³×C₁₃	—	8	2	no	—
367	C₂³×C₁₃	—	8	4	no	—
368	C₂³×C₁₃	—	8	2	no	—
369	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
370	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
371	Q₈×C₁₃	—	2	2	no	—
372	Q₈×C₁₃	—	2	2	no	—
373	Q₈×C₁₃	—	4	2	no	—
374	Q₈×C₁₃	—	4	2	no	—
375	Q₈×C₁₃	—	8	1	no	—
376	D₄×C₁₃	—	2	4	no	—
377	D₄×C₁₃	—	2	2	no	—
378	D₄×C₁₃	—	2	4	no	—
379	D₄×C₁₃	—	2	2	no	—
380	D₄×C₁₃	—	2	4	no	—
381	D₄×C₁₃	—	2	2	no	—
382	D₄×C₁₃	—	4	4	no	—
383	D₄×C₁₃	—	4	2	no	—
384	D₄×C₁₃	—	4	8	no	—
385	D₄×C₁₃	—	4	2	no	—
386	D₄×C₁₃	—	4	4	no	—
387	D₄×C₁₃	—	4	4	no	—
388	D₄×C₁₃	—	4	8	no	—
389	D₄×C₁₃	—	4	4	no	—
390	D₄×C₁₃	—	4	4	no	—
391	D₄×C₁₃	—	8	4	no	—
392	D₄×C₁₃	—	8	2	no	—
393	D₄×C₁₃	—	8	4	no	—
394	D₄×C₁₃	—	8	2	no	—
395	D₄×C₁₃	—	8	1	no	—
396	D₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
397	C₂×C₄×C₁₃	—	2	4	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	4	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	1	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	1	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	1	no	—
407	C₂×C₄×C₁₃	—	4	2	no	—
408	C₂×C₄×C₁₃	—	4	1	no	—
409	C₂×C₄×C₁₃	—	4	8	no	—
410	C₂×C₄×C₁₃	—	4	4	no	—
411	C₂×C₄×C₁₃	—	4	4	no	—
412	C₂×C₄×C₁₃	—	4	2	no	—
413	C₂×C₄×C₁₃	—	8	2	no	—
414	C₂×C₄×C₁₃	—	8	2	no	—
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	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
424	C₈×C₁₃	—	2	2	no	—
425	C₈×C₁₃	—	2	4	no	—
426	C₈×C₁₃	—	2	2	no	—
427	C₂×H(5,𝔽₂)	—	2	1	no	—
428	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
429	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
430	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	#553	C₂²×C₁₃	1	2	yes	complemented
432	#552	—	2	2	no	—
433	#552	—	2	1	no	—
434	#552	C₂²×C₁₃	1	2	yes	complemented
435	#550	—	2	1	no	—
436	#550	C₂²×C₁₃	1	2	yes	—
437	#547	—	2	1	no	—
438	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	D₄²	—	2	1	no	—
440	D₄²	—	2	2	no	—
441	D₄²	C₂²×C₁₃	1	2	yes	—
442	D₄²	C₂²×C₁₃	1	4	yes	—
443	#541	—	2	1	no	—
444	#539	—	2	2	no	—
445	#535	—	2	1	no	—
446	#535	—	2	2	no	—
447	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
448	#532	C₂²×C₁₃	1	1	yes	characteristic
449	#532	C₂²×C₁₃	1	2	yes	—
450	C₂×#127	C₂²×C₁₃	1	2	yes	—
451	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
452	#529	C₂²×C₁₃	1	1	yes	characteristic, complemented
453	#529	C₂²×C₁₃	1	2	yes	complemented
454	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
455	#520	—	2	1	no	—
456	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
457	#501	C₂²×C₁₃	1	1	yes	characteristic, complemented
458	#501	C₂²×C₁₃	1	2	yes	complemented
459	#496	C₂²×C₁₃	1	1	yes	characteristic, complemented
460	#496	C₂²×C₁₃	1	2	yes	complemented
461	#490	C₂²×C₁₃	1	4	yes	complemented
462	#490	C₂²×C₁₃	1	4	yes	complemented
463	#490	C₂²×C₁₃	1	1	yes	characteristic, complemented
464	#490	C₂²×C₁₃	1	2	yes	complemented
465	#490	C₂²×C₁₃	1	2	yes	complemented
466	#490	C₂²×C₁₃	1	2	yes	complemented
467	#490	C₂²×C₁₃	1	2	yes	complemented
468	#489	C₂²×C₁₃	1	1	yes	characteristic, complemented
469	#486	C₂²×C₁₃	1	2	yes	complemented
470	#486	C₂²×C₁₃	1	2	yes	complemented
471	#482	C₂²×C₁₃	1	4	yes	complemented
472	#481	C₂²×C₁₃	1	4	yes	complemented
473	#480	C₂²×C₁₃	1	4	yes	complemented
474	#478	C₂²×C₁₃	1	4	yes	complemented
475	#478	C₂²×C₁₃	1	4	yes	complemented
476	#476	C₂²×C₁₃	1	2	yes	complemented
477	#474	C₂²×C₁₃	1	2	yes	complemented
478	#469	C₂²×C₁₃	1	2	yes	complemented
479	#468	C₂²×C₁₃	1	2	yes	complemented
480	#466	C₂²×C₁₃	1	4	yes	complemented
481	#465	C₂²×C₁₃	1	4	yes	complemented
482	#460	C₂²×C₁₃	1	2	yes	complemented
483	#460	C₂²×C₁₃	1	4	yes	complemented
484	#459	C₂²×C₁₃	1	2	yes	complemented
485	#459	C₂²×C₁₃	1	4	yes	complemented
486	#450	C₂²×C₁₃	1	4	yes	complemented
487	#450	C₂²×C₁₃	1	2	yes	complemented
488	#447	C₂²×C₁₃	1	4	yes	complemented
489	#447	C₂²×C₁₃	1	2	yes	complemented
490	#446	C₂²×C₁₃	1	2	yes	complemented
491	#442	C₂²×C₁₃	1	4	yes	complemented
492	#440	C₂²×C₁₃	1	4	yes	complemented
493	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
494	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
495	#435	C₂²×C₁₃	1	4	yes	complemented
496	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
497	#432	C₂²×C₁₃	1	2	yes	complemented
498	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
499	#418	C₂²×C₁₃	1	4	yes	complemented
500	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
501	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
502	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
503	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
504	C₂²×C₁₃	—	2	2	no	—
505	C₂²×C₁₃	—	2	2	no	—
506	C₂²×C₁₃	—	2	1	no	—
507	C₂²×C₁₃	—	2	1	no	—
508	C₂²×C₁₃	—	2	1	no	—
509	C₂²×C₁₃	—	4	1	no	—
510	C₂²×C₁₃	—	4	2	no	—
511	C₂²×C₁₃	—	4	4	no	—
512	C₂²×C₁₃	—	4	2	no	—
513	C₂²×C₁₃	—	4	4	no	—
514	C₂²×C₁₃	—	4	1	no	—
515	C₂²×C₁₃	—	4	4	no	—
516	C₂²×C₁₃	—	4	2	no	—
517	C₂²×C₁₃	—	4	1	no	—
518	C₂²×C₁₃	—	16	8	no	—
519	C₂²×C₁₃	—	16	4	no	—
520	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
521	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
522	C₄×C₁₃	—	2	1	no	—
523	C₄×C₁₃	—	2	2	no	—
524	C₄×C₁₃	—	2	1	no	—
525	C₄×C₁₃	—	2	2	no	—
526	C₄×C₁₃	—	2	1	no	—
527	C₄×C₁₃	—	2	1	no	—
528	C₄×C₁₃	—	2	2	no	—
529	C₄×C₁₃	—	4	1	no	—
530	C₄×C₁₃	—	4	2	no	—
531	C₄×C₁₃	—	4	1	no	—
532	C₄×C₁₃	—	4	1	no	—
533	C₄×C₁₃	—	4	2	no	—
534	C₄×C₁₃	—	4	2	no	—
535	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
536	C₄×C₁₃	#585	1	2	yes	—
537	H(5,𝔽₂)	—	4	8	no	—
538	C₂×#41	—	2	2	no	—
539	C₂×#41	—	2	1	no	—
540	C₂×#41	—	2	2	no	—
541	C₂×#41	—	2	1	no	—
542	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
543	C₂²×D₄	—	2	4	no	—
544	C₂²×D₄	—	2	2	no	—
545	C₂²×D₄	—	2	2	no	—
546	C₂²×D₄	—	2	1	no	—
547	C₂²×D₄	—	2	2	no	—
548	C₂²×D₄	—	2	1	no	—
549	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
550	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
551	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
552	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
553	C₂×D₈	C₂³×C₁₃	1	2	yes	—
554	C₂×D₈	C₂³×C₁₃	1	4	yes	—
555	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
556	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
557	C₄⋊Q₈	—	2	1	no	—
558	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
559	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
560	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
561	#127	—	2	2	no	—
562	#127	—	2	1	no	—
563	#127	—	2	1	no	—
564	#127	—	2	2	no	—
565	#127	C₂³×C₁₃	1	1	yes	characteristic
566	#127	C₂³×C₁₃	1	2	yes	—
567	#127	C₂³×C₁₃	1	2	yes	—
568	#127	C₂³×C₁₃	1	4	yes	—
569	#126	—	2	2	no	—
570	#126	—	2	2	no	—
571	#126	—	2	2	no	—
572	#126	—	2	1	no	—
573	#125	—	2	2	no	—
574	#125	—	2	2	no	—
575	#125	—	2	1	no	—
576	#125	—	2	2	no	—
577	#125	—	2	2	no	—
578	#125	C₂³×C₁₃	1	1	yes	characteristic
579	#125	C₂³×C₁₃	1	2	yes	—
580	#125	C₂³×C₁₃	1	2	yes	—
581	#125	C₂³×C₁₃	1	2	yes	—
582	#124	—	2	2	no	—
583	#124	—	2	1	no	—
584	#124	C₂³×C₁₃	1	1	yes	characteristic
585	#123	—	2	2	no	—
586	#123	—	2	1	no	—
587	#123	—	2	2	no	—
588	#123	—	2	2	no	—
589	#123	—	2	2	no	—
590	C₂²⋊Q₈	—	2	1	no	—
591	C₂²⋊Q₈	—	2	1	no	—
592	C₂²⋊Q₈	—	2	1	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	—	2	1	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
597	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
598	#121	—	2	2	no	—
599	#121	—	2	2	no	—
600	#121	—	2	1	no	—
601	#121	—	2	2	no	—
602	#121	—	2	4	no	—
603	#121	—	2	2	no	—
604	#121	—	2	4	no	—
605	#121	C₂³×C₁₃	1	2	yes	—
606	#121	C₂³×C₁₃	1	1	yes	characteristic
607	#121	C₂³×C₁₃	1	4	yes	—
608	#121	C₂³×C₁₃	1	2	yes	—
609	#120	—	2	4	no	—
610	#120	—	2	4	no	—
611	#120	—	2	4	no	—
612	C₄×Q₈	—	2	1	no	—
613	C₄×Q₈	—	2	1	no	—
614	C₄×Q₈	—	2	1	no	—
615	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
616	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
617	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
618	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
626	C₄×D₄	D₄×C₁₃	1	2	yes	—
627	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
628	C₄×D₄	C₂³×C₁₃	1	2	yes	—
629	C₄×D₄	C₂³×C₁₃	1	2	yes	—
630	C₄×D₄	C₂³×C₁₃	1	4	yes	—
631	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
632	C₄×D₄	C₂³×C₁₃	1	2	yes	—
633	#117	—	2	2	no	—
634	#117	—	2	1	no	—
635	#117	—	2	2	no	—
636	#117	D₄×C₁₃	1	1	yes	characteristic
637	#117	D₄×C₁₃	1	2	yes	—
638	#117	C₂³×C₁₃	1	2	yes	—
639	C₂×C₄⋊C₄	—	2	2	no	—
640	C₂×C₄⋊C₄	—	2	2	no	—
641	C₂×C₄⋊C₄	—	2	1	no	—
642	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
644	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
645	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
646	#107	C₂³×C₁₃	1	2	yes	—
647	#107	C₂³×C₁₃	1	4	yes	—
648	#106	C₂³×C₁₃	1	2	yes	—
649	#106	C₂³×C₁₃	1	4	yes	—
650	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
651	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
652	#103	C₂³×C₁₃	1	2	yes	—
653	#102	C₂³×C₁₃	1	2	yes	—
654	#102	C₂³×C₁₃	1	2	yes	—
655	#102	C₂³×C₁₃	1	4	yes	—
656	#102	C₂³×C₁₃	1	4	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	4	yes	—
661	#102	C₂³×C₁₃	1	4	yes	—
662	#102	C₂³×C₁₃	1	4	yes	—
663	#102	C₂³×C₁₃	1	2	yes	—
664	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
665	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
666	#97	C₂³×C₁₃	1	1	yes	characteristic
667	#97	C₂³×C₁₃	1	2	yes	—
668	#97	C₂³×C₁₃	1	4	yes	—
669	#97	C₂³×C₁₃	1	1	yes	characteristic
670	C₄×C₈	C₂³×C₁₃	1	2	yes	—
671	C₂×C₁₃	—	2	4	no	—
672	C₂×C₁₃	—	4	1	no	—
673	C₂×C₁₃	—	8	1	no	—
674	C₂×C₁₃	—	8	2	no	—
675	C₂×C₁₃	—	8	4	no	—
676	C₂×C₁₃	#3500	1	1	yes	characteristic
677	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
678	C₂×C₁₃	#3585	1	1	yes	characteristic
679	C₂⁴	—	2	2	no	—
680	C₂⁴	—	2	4	no	—
681	#41	—	2	4	no	—
682	#41	—	4	8	no	—
683	#41	—	4	4	no	—
684	#41	—	4	8	no	—
685	#41	—	4	4	no	—
686	C₂×Q₈	—	2	1	no	—
687	C₂×Q₈	—	2	1	no	—
688	C₂×Q₈	—	2	1	no	—
689	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
690	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	4	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	4	no	—
703	C₂×D₄	—	2	4	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	4	4	no	—
706	C₂×D₄	—	4	4	no	—
707	C₂×D₄	—	4	4	no	—
708	C₂×D₄	—	4	8	no	—
709	C₂×D₄	—	4	4	no	—
710	C₂×D₄	—	4	16	no	—
711	C₂×D₄	—	4	8	no	—
712	C₂×D₄	—	8	4	no	—
713	C₂×D₄	—	8	2	no	—
714	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
715	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
716	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
717	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
718	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	4	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
726	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
727	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
728	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
731	SD₁₆	—	4	4	no	—
732	SD₁₆	—	4	2	no	—
733	D₈	—	4	4	no	—
734	D₈	—	4	2	no	—
735	M₁₆	—	4	2	no	—
736	C₂×C₈	—	4	4	no	—
737	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
738	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
739	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	1	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
758	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
759	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
760	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
761	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
762	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
763	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
764	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
765	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	1	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	1	no	—
771	C₂²⋊C₄	—	2	1	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	1	no	—
779	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
780	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
781	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	1	no	—
785	C₄²	C₂×D₄×C₁₃	1	2	yes	—
786	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
787	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
788	C₄²	C₂×D₄×C₁₃	1	2	yes	—
789	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
790	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
791	C₄²	C₂⁴×C₁₃	1	2	yes	—
792	C₁₃	#62576	1	1	yes	characteristic, direct product factor, Sylow
793	C₂³	—	2	1	no	—
794	C₂³	—	2	4	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	4	4	no	—
797	C₂³	—	4	8	no	—
798	C₂³	—	8	4	no	—
799	C₂³	—	8	2	no	—
800	C₂³	—	8	4	no	—
801	C₂³	—	8	2	no	—
802	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
803	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
804	Q₈	—	2	2	no	—
805	Q₈	—	2	2	no	—
806	Q₈	—	4	2	no	—
807	Q₈	—	4	2	no	—
808	Q₈	—	8	1	no	—
809	D₄	—	2	4	no	—
810	D₄	—	2	2	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	4	no	—
814	D₄	—	2	2	no	—
815	D₄	—	4	4	no	—
816	D₄	—	4	2	no	—
817	D₄	—	4	8	no	—
818	D₄	—	4	2	no	—
819	D₄	—	4	4	no	—
820	D₄	—	4	4	no	—
821	D₄	—	4	8	no	—
822	D₄	—	4	4	no	—
823	D₄	—	4	4	no	—
824	D₄	—	8	4	no	—
825	D₄	—	8	2	no	—
826	D₄	—	8	4	no	—
827	D₄	—	8	2	no	—
828	D₄	—	8	1	no	—
829	D₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	1	no	—
842	C₂×C₄	—	4	8	no	—
843	C₂×C₄	—	4	4	no	—
844	C₂×C₄	—	4	4	no	—
845	C₂×C₄	—	4	2	no	—
846	C₂×C₄	—	8	2	no	—
847	C₂×C₄	—	8	2	no	—
848	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
850	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
851	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
852	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
853	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
854	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
855	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
856	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
857	C₈	—	2	2	no	—
858	C₈	—	2	4	no	—
859	C₈	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	1	no	—
865	C₂²	—	4	4	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	4	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	4	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	16	8	no	—
875	C₂²	—	16	4	no	—
876	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
877	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
878	C₄	—	2	1	no	—
879	C₄	—	2	2	no	—
880	C₄	—	2	1	no	—
881	C₄	—	2	2	no	—
882	C₄	—	2	1	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	1	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	2	no	—
887	C₄	—	4	2	no	—
888	C₄	—	4	1	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	1	no	—
891	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
892	C₄	C₁₃×#585	1	2	yes	—
893	C₂	—	2	4	no	—
894	C₂	—	4	1	no	—
895	C₂	—	8	2	no	—
896	C₂	—	8	4	no	—
897	C₂	—	8	1	no	—
898	C₂	C₁₃×#3500	1	1	yes	characteristic
899	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
900	C₂	C₁₃×#3585	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×#3515	C₂	semidirect
2. C₁₃×#3498	C₂	semidirect
3. C₁₃×#3368	C₂	semidirect
4. C₁₃×#3366	C₂	semidirect
5. C₁₃×#3318	C₂	semidirect
6. C₁₃×#3310	C₂	semidirect
7. C₁₃×#3295	C₂	semidirect
8. C₁₃×#3294	C₂	semidirect
9. C₁₃×#3235	C₂	semidirect
10. C₁₃×#3234	C₂	semidirect
11. C₁₃×#3217	C₂	semidirect
12. C₁₃×#3217	C₂	semidirect
13. C₁₃×#3180	C₂	semidirect
14. C₁₃×#3171	C₂	semidirect
15. C₁₃×#3138	C₂	semidirect
16. C₂×C₁₃×#490	C₂	semidirect
17. C₁₃×#2970	C₂	semidirect
19. C₁₃×#557	C₂²	semidirect
20. C₁₃×#554	C₂²	semidirect
21. C₁₃×#554	C₂²	semidirect
22. C₁₃×#553	C₂²	semidirect
25. C₁₃×#552	C₂²	semidirect
29. C₁₃×#547	C₂²	semidirect
38. C₁₃×#533	C₂²	semidirect
43. C₁₃×#529	C₂²	semidirect
44. C₁₃×#529	C₂²	semidirect
45. C₂×C₁₃×#125	C₂²	semidirect
48. C₁₃×#501	C₂²	semidirect
49. C₁₃×#501	C₂²	semidirect
50. C₁₃×#496	C₂²	semidirect
51. C₁₃×#496	C₂²	semidirect
52. C₁₃×#490	C₂²	semidirect
53. C₁₃×#490	C₂²	semidirect
54. C₁₃×#490	C₂²	semidirect
55. C₁₃×#490	C₂²	semidirect
56. C₁₃×#490	C₂²	semidirect
57. C₁₃×#490	C₂²	semidirect
58. C₁₃×#490	C₂²	semidirect
59. C₁₃×#489	C₂²	semidirect
60. C₁₃×#486	C₂²	semidirect
61. C₁₃×#486	C₂²	semidirect
62. C₁₃×#482	C₂²	semidirect
63. C₁₃×#481	C₂²	semidirect
64. C₁₃×#480	C₂²	semidirect
65. C₁₃×#478	C₂²	semidirect
66. C₁₃×#478	C₂²	semidirect
67. C₁₃×#476	C₂²	semidirect
68. C₁₃×#474	C₂²	semidirect
69. C₁₃×#469	C₂²	semidirect
70. C₁₃×#468	C₂²	semidirect
71. C₁₃×#466	C₂²	semidirect
72. C₁₃×#465	C₂²	semidirect
73. C₁₃×#460	C₂²	semidirect
74. C₁₃×#460	C₂²	semidirect
75. C₁₃×#459	C₂²	semidirect
76. C₁₃×#459	C₂²	semidirect
77. C₁₃×#450	C₂²	semidirect
78. C₁₃×#450	C₂²	semidirect
79. C₁₃×#447	C₂²	semidirect
80. C₁₃×#447	C₂²	semidirect
81. C₁₃×#446	C₂²	semidirect
82. C₁₃×#442	C₂²	semidirect
83. C₁₃×#440	C₂²	semidirect
84. C₄×C₁₃×SD₁₆	C₂²	semidirect
85. C₄×C₁₃×D₈	C₂²	semidirect
86. C₁₃×#435	C₂²	semidirect
87. C₈×D₄×C₁₃	C₂²	semidirect
88. C₁₃×#432	C₂²	semidirect
89. C₁₃×#432	C₂²	semidirect
90. C₁₃×#418	C₂²	semidirect
91. C₂×C₁₃×#102	C₂²	semidirect
92. C₂×C₁₃×#102	C₂²	semidirect
93. C₄×C₁₃×M₁₆	C₂²	semidirect
94. C₂×C₁₃×#97	C₂²	semidirect
229. #62576	C₁₃	direct (N × H)
343. #3515	C₂×C₁₃	semidirect
344. #3498	C₂×C₁₃	semidirect
345. #3368	C₂×C₁₃	semidirect
346. #3366	C₂×C₁₃	semidirect
347. #3318	C₂×C₁₃	semidirect
348. #3310	C₂×C₁₃	semidirect
349. #3295	C₂×C₁₃	semidirect
350. #3294	C₂×C₁₃	semidirect
351. #3235	C₂×C₁₃	semidirect
352. #3234	C₂×C₁₃	semidirect
353. #3217	C₂×C₁₃	semidirect
354. #3217	C₂×C₁₃	semidirect
355. #3180	C₂×C₁₃	semidirect
356. #3171	C₂×C₁₃	semidirect
357. #3138	C₂×C₁₃	semidirect
358. C₂×#490	C₂×C₁₃	semidirect
359. #2970	C₂×C₁₃	semidirect
428. #557	C₂²×C₁₃	semidirect
429. #554	C₂²×C₁₃	semidirect
430. #554	C₂²×C₁₃	semidirect
431. #553	C₂²×C₁₃	semidirect
434. #552	C₂²×C₁₃	semidirect
438. #547	C₂²×C₁₃	semidirect
447. #533	C₂²×C₁₃	semidirect
452. #529	C₂²×C₁₃	semidirect
453. #529	C₂²×C₁₃	semidirect
454. C₂×#125	C₂²×C₁₃	semidirect
457. #501	C₂²×C₁₃	semidirect
458. #501	C₂²×C₁₃	semidirect
459. #496	C₂²×C₁₃	semidirect
460. #496	C₂²×C₁₃	semidirect
461. #490	C₂²×C₁₃	semidirect
462. #490	C₂²×C₁₃	semidirect
463. #490	C₂²×C₁₃	semidirect
464. #490	C₂²×C₁₃	semidirect
465. #490	C₂²×C₁₃	semidirect
466. #490	C₂²×C₁₃	semidirect
467. #490	C₂²×C₁₃	semidirect
468. #489	C₂²×C₁₃	semidirect
469. #486	C₂²×C₁₃	semidirect
470. #486	C₂²×C₁₃	semidirect
471. #482	C₂²×C₁₃	semidirect
472. #481	C₂²×C₁₃	semidirect
473. #480	C₂²×C₁₃	semidirect
474. #478	C₂²×C₁₃	semidirect
475. #478	C₂²×C₁₃	semidirect
476. #476	C₂²×C₁₃	semidirect
477. #474	C₂²×C₁₃	semidirect
478. #469	C₂²×C₁₃	semidirect
479. #468	C₂²×C₁₃	semidirect
480. #466	C₂²×C₁₃	semidirect
481. #465	C₂²×C₁₃	semidirect
482. #460	C₂²×C₁₃	semidirect
483. #460	C₂²×C₁₃	semidirect
484. #459	C₂²×C₁₃	semidirect
485. #459	C₂²×C₁₃	semidirect
486. #450	C₂²×C₁₃	semidirect
487. #450	C₂²×C₁₃	semidirect
488. #447	C₂²×C₁₃	semidirect
489. #447	C₂²×C₁₃	semidirect
490. #446	C₂²×C₁₃	semidirect
491. #442	C₂²×C₁₃	semidirect
492. #440	C₂²×C₁₃	semidirect
493. C₄×SD₁₆	C₂²×C₁₃	semidirect
494. C₄×D₈	C₂²×C₁₃	semidirect
495. #435	C₂²×C₁₃	semidirect
496. C₈×D₄	C₂²×C₁₃	semidirect
497. #432	C₂²×C₁₃	semidirect
498. #432	C₂²×C₁₃	semidirect
499. #418	C₂²×C₁₃	semidirect
500. C₂×#102	C₂²×C₁₃	semidirect
501. C₂×#102	C₂²×C₁₃	semidirect
502. C₄×M₁₆	C₂²×C₁₃	semidirect
503. C₂×#97	C₂²×C₁₃	semidirect
792. C₁₃	#62576	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×#3515	2
C₁₃×#3498	2
C₁₃×#3368	2
C₁₃×#3366	2
C₁₃×#3318	2
C₁₃×#3310	2
C₁₃×#3295	2
C₁₃×#3294	2
C₁₃×#3235	2
C₁₃×#3234	2
C₁₃×#3217	2
C₁₃×#3180	2
C₁₃×#3171	2
C₁₃×#3138	2
C₂×C₁₃×#490	2
C₁₃×#2970	2
#62576	13

Subgroups — C13×#62576 #15748915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62576 #15748915