Subgroups — C₁₃×#61325 #15747664

Order 3328.

1870 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3370	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3367	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3366	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3361	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3360	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3358	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3136	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3083	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3041	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2946	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
20	C₁₃×#559	C₂²	1	4	yes	complemented
21	C₁₃×#556	C₂²	1	2	yes	complemented
22	C₁₃×#555	—	2	1	no	—
23	C₁₃×#554	—	2	1	no	—
24	C₁₃×#554	—	2	2	no	—
25	C₁₃×#554	C₂²	1	2	yes	complemented
26	C₁₃×#554	C₂²	1	4	yes	complemented
27	C₁₃×#553	—	2	2	no	—
28	C₁₃×#550	C₂²	1	2	yes	complemented
29	D₄×Q₈×C₁₃	—	2	1	no	—
30	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
31	C₁₃×#547	—	2	1	no	—
32	C₁₃×#544	C₂²	1	2	yes	—
33	C₁₃×#543	—	2	2	no	—
34	C₁₃×#538	—	2	2	no	—
35	C₁₃×#535	C₂²	1	2	yes	—
36	C₁₃×#533	C₂²	1	1	yes	characteristic
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₁₃×#525	—	2	2	no	—
40	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
41	C₁₃×#520	C₂²	1	2	yes	—
42	C₁₃×#518	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#490	C₂²	1	4	yes	complemented
46	C₁₃×#489	C₂²	1	4	yes	complemented
47	C₁₃×#488	C₂²	1	4	yes	complemented
48	C₁₃×#488	C₂²	1	2	yes	complemented
49	C₁₃×#488	C₂²	1	2	yes	complemented
50	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#486	C₂²	1	4	yes	complemented
54	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#479	C₂²	1	4	yes	complemented
56	C₁₃×#478	C₂²	1	4	yes	complemented
57	C₁₃×#478	C₂²	1	4	yes	complemented
58	C₁₃×#477	C₂²	1	4	yes	complemented
59	C₁₃×#476	C₂²	1	2	yes	complemented
60	C₁₃×#474	C₂²	1	2	yes	complemented
61	C₁₃×#474	C₂²	1	4	yes	complemented
62	C₁₃×#463	C₂²	1	4	yes	—
63	C₁₃×#463	C₂²	1	4	yes	—
64	C₁₃×#463	C₂²	1	4	yes	complemented
65	C₁₃×#461	C₂²	1	2	yes	complemented
66	C₁₃×#459	C₂²	1	4	yes	—
67	C₁₃×#459	C₂²	1	4	yes	—
68	C₁₃×#459	C₂²	1	2	yes	complemented
69	C₁₃×#446	C₂²	1	2	yes	complemented
70	C₁₃×#446	C₂²	1	2	yes	complemented
71	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
72	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
73	C₁₃×#442	C₂²	1	4	yes	complemented
74	C₁₃×#440	C₂²	1	4	yes	complemented
75	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
76	C₄×C₁₃×D₈	C₂²	1	2	yes	—
77	C₄×C₁₃×D₈	C₂²	1	2	yes	—
78	C₄×C₁₃×D₈	C₂²	1	2	yes	—
79	C₄×C₁₃×D₈	C₂²	1	2	yes	—
80	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
81	C₁₃×#428	C₂²	1	2	yes	—
82	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
83	C₁₃×#424	C₂²	1	2	yes	—
84	C₁₃×#423	C₂²	1	1	yes	characteristic
85	C₁₃×#418	C₂²	1	2	yes	—
86	C₁₃×#417	C₂²	1	2	yes	—
87	C₁₃×#416	C₂²	1	2	yes	—
88	C₁₃×#416	C₂²	1	2	yes	—
89	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
90	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
91	C₁₃×#405	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×#41	—	2	2	no	—
94	C₂×C₁₃×#41	C₂³	1	2	yes	—
95	C₂²×Q₈×C₁₃	—	2	2	no	—
96	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃	—	2	1	no	—
99	C₂³×C₄×C₁₃	—	2	1	no	—
100	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
101	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
102	C₂×C₁₃×D₈	—	2	4	no	—
103	C₂×C₁₃×D₈	C₂³	1	2	yes	—
104	C₂×C₁₃×D₈	C₂³	1	2	yes	—
105	C₂×C₁₃×D₈	C₂³	1	4	yes	—
106	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
107	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×C₄⋊Q₈	—	2	2	no	—
110	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
111	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×#127	C₂³	1	4	yes	—
117	C₁₃×#127	C₂³	1	1	yes	characteristic
118	C₁₃×#126	—	2	4	no	—
119	C₁₃×#125	—	2	2	no	—
120	C₁₃×#125	D₄	1	2	yes	—
121	C₁₃×#125	C₂³	1	2	yes	—
122	C₁₃×#125	C₂³	1	4	yes	—
123	C₁₃×#124	—	2	4	no	—
124	C₁₃×#124	C₂³	1	4	yes	—
125	C₁₃×#124	C₂³	1	2	yes	—
126	C₁₃×#123	—	2	4	no	—
127	C₁₃×#123	—	2	4	no	—
128	C₁₃×C₂²⋊Q₈	—	2	2	no	—
129	C₁₃×C₂²⋊Q₈	—	2	2	no	—
130	C₁₃×C₂²⋊Q₈	—	2	4	no	—
131	C₁₃×C₂²⋊Q₈	—	2	1	no	—
132	C₁₃×C₂²⋊Q₈	—	2	1	no	—
133	C₁₃×C₂²⋊Q₈	—	2	2	no	—
134	C₁₃×C₂²⋊Q₈	—	2	4	no	—
135	C₁₃×C₂²⋊Q₈	—	2	4	no	—
136	C₁₃×C₂²⋊Q₈	—	2	4	no	—
137	C₁₃×C₂²⋊Q₈	—	2	4	no	—
138	C₁₃×C₂²⋊Q₈	—	2	4	no	—
139	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
140	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
141	C₁₃×#121	—	2	1	no	—
142	C₁₃×#121	—	2	1	no	—
143	C₁₃×#121	—	2	2	no	—
144	C₁₃×#121	—	2	2	no	—
145	C₁₃×#121	—	2	2	no	—
146	C₁₃×#121	—	2	4	no	—
147	C₁₃×#120	—	2	4	no	—
148	C₄×Q₈×C₁₃	—	2	1	no	—
149	C₄×Q₈×C₁₃	—	2	1	no	—
150	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
151	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
152	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
153	C₄×D₄×C₁₃	—	2	2	no	—
154	C₄×D₄×C₁₃	—	2	2	no	—
155	C₄×D₄×C₁₃	—	2	4	no	—
156	C₄×D₄×C₁₃	—	2	4	no	—
157	C₄×D₄×C₁₃	—	2	1	no	—
158	C₄×D₄×C₁₃	—	2	1	no	—
159	C₄×D₄×C₁₃	—	2	1	no	—
160	C₄×D₄×C₁₃	—	2	1	no	—
161	C₄×D₄×C₁₃	—	2	1	no	—
162	C₄×D₄×C₁₃	—	2	1	no	—
163	C₄×D₄×C₁₃	C₂³	1	2	yes	—
164	C₄×D₄×C₁₃	C₂³	1	2	yes	—
165	C₄×D₄×C₁₃	C₂³	1	2	yes	—
166	C₄×D₄×C₁₃	C₂³	1	2	yes	—
167	C₄×D₄×C₁₃	C₂³	1	4	yes	—
168	C₄×D₄×C₁₃	C₂³	1	4	yes	—
169	C₄×D₄×C₁₃	C₂³	1	4	yes	—
170	C₁₃×#117	—	2	2	no	—
171	C₁₃×#117	—	2	2	no	—
172	C₁₃×#117	C₂³	1	2	yes	—
173	C₁₃×#117	C₂³	1	2	yes	—
174	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
175	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
176	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
180	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
181	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
182	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
183	C₁₃×#107	C₂³	1	2	yes	—
184	C₁₃×#107	C₂³	1	2	yes	—
185	C₁₃×#107	C₂³	1	4	yes	—
186	C₁₃×#106	C₂³	1	4	yes	—
187	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
188	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
189	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
190	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
191	C₁₃×#103	C₂³	1	2	yes	—
192	C₁₃×#103	C₂³	1	2	yes	—
193	C₁₃×#103	C₂³	1	2	yes	—
194	C₁₃×#103	C₂³	1	2	yes	—
195	C₁₃×#103	C₂³	1	4	yes	—
196	C₁₃×#102	C₂³	1	2	yes	—
197	C₁₃×#102	C₂³	1	2	yes	—
198	C₁₃×#102	C₂³	1	2	yes	—
199	C₁₃×#102	C₂³	1	2	yes	—
200	C₁₃×#102	C₂³	1	2	yes	—
201	C₁₃×#102	C₂³	1	2	yes	—
202	C₁₃×#102	C₂³	1	2	yes	—
203	C₁₃×#102	C₂³	1	2	yes	—
204	C₁₃×#102	C₂³	1	4	yes	—
205	C₁₃×#102	C₂³	1	4	yes	—
206	C₁₃×#102	C₂³	1	4	yes	—
207	C₁₃×#97	C₂³	1	4	yes	—
208	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
209	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
211	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
212	C₄×C₈×C₁₃	C₂³	1	4	yes	—
213	#61325	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂⁴×C₁₃	—	2	1	no	—
215	C₂⁴×C₁₃	—	2	1	no	—
216	C₁₃×#41	—	2	4	no	—
217	C₁₃×#41	—	2	4	no	—
218	C₁₃×#41	—	8	4	no	—
219	C₂×Q₈×C₁₃	—	2	1	no	—
220	C₂×Q₈×C₁₃	—	2	1	no	—
221	C₂×Q₈×C₁₃	—	2	4	no	—
222	C₂×Q₈×C₁₃	—	8	4	no	—
223	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
224	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
225	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
226	C₂×D₄×C₁₃	—	2	2	no	—
227	C₂×D₄×C₁₃	—	2	1	no	—
228	C₂×D₄×C₁₃	—	2	1	no	—
229	C₂×D₄×C₁₃	—	2	1	no	—
230	C₂×D₄×C₁₃	—	2	4	no	—
231	C₂×D₄×C₁₃	—	2	1	no	—
232	C₂×D₄×C₁₃	—	2	4	no	—
233	C₂×D₄×C₁₃	—	2	2	no	—
234	C₂×D₄×C₁₃	—	2	2	no	—
235	C₂×D₄×C₁₃	—	2	2	no	—
236	C₂×D₄×C₁₃	#41	1	4	yes	complemented
237	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃	—	2	1	no	—
241	C₂²×C₄×C₁₃	—	2	1	no	—
242	C₂²×C₄×C₁₃	—	2	2	no	—
243	C₂²×C₄×C₁₃	—	2	2	no	—
244	C₂²×C₄×C₁₃	—	2	2	no	—
245	C₂²×C₄×C₁₃	—	2	4	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	—	2	2	no	—
250	C₂²×C₄×C₁₃	—	8	2	no	—
251	C₂²×C₄×C₁₃	—	8	2	no	—
252	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₁₃×SD₁₆	—	2	8	no	—
256	C₁₃×D₈	—	2	4	no	—
257	C₁₃×D₈	—	2	4	no	—
258	C₁₃×D₈	—	2	8	no	—
259	C₁₃×M₁₆	—	2	4	no	—
260	C₂×C₈×C₁₃	—	2	2	no	—
261	C₂×C₈×C₁₃	—	2	2	no	—
262	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
267	C₁₃×C₄⋊C₄	—	2	1	no	—
268	C₁₃×C₄⋊C₄	—	2	2	no	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	4	no	—
271	C₁₃×C₄⋊C₄	—	2	4	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	4	no	—
274	C₁₃×C₄⋊C₄	—	2	1	no	—
275	C₁₃×C₄⋊C₄	—	2	1	no	—
276	C₁₃×C₄⋊C₄	—	2	1	no	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	—	2	1	no	—
279	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
280	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
281	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
282	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
283	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
284	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
285	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
286	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
287	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
288	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
289	C₁₃×C₂²⋊C₄	—	2	2	no	—
290	C₁₃×C₂²⋊C₄	—	2	2	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	4	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	4	no	—
297	C₁₃×C₂²⋊C₄	—	2	4	no	—
298	C₁₃×C₂²⋊C₄	—	2	2	no	—
299	C₁₃×C₂²⋊C₄	—	2	4	no	—
300	C₁₃×C₂²⋊C₄	—	2	2	no	—
301	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
302	C₄²×C₁₃	—	2	4	no	—
303	C₄²×C₁₃	—	2	2	no	—
304	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
307	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
308	C₄²×C₁₃	C₂⁴	1	4	yes	—
309	#3506	C₂×C₁₃	1	1	yes	characteristic, complemented
310	#3501	C₂×C₁₃	1	1	yes	characteristic, complemented
311	#3370	C₂×C₁₃	1	4	yes	complemented
312	#3367	C₂×C₁₃	1	2	yes	complemented
313	#3366	C₂×C₁₃	1	2	yes	complemented
314	#3361	C₂×C₁₃	1	4	yes	complemented
315	#3360	C₂×C₁₃	1	2	yes	complemented
316	#3358	C₂×C₁₃	1	2	yes	complemented
317	#3136	C₂×C₁₃	1	2	yes	complemented
318	#3131	C₂×C₁₃	1	1	yes	characteristic, complemented
319	#3083	C₂×C₁₃	1	2	yes	complemented
320	#3077	C₂×C₁₃	1	1	yes	characteristic, complemented
321	#3041	C₂×C₁₃	1	2	yes	complemented
322	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
323	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
324	#2946	C₂×C₁₃	1	2	yes	complemented
325	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
326	C₂³×C₁₃	—	2	2	no	—
327	C₂³×C₁₃	—	2	4	no	—
328	C₂³×C₁₃	—	2	2	no	—
329	C₂³×C₁₃	—	2	2	no	—
330	C₂³×C₁₃	—	4	2	no	—
331	C₂³×C₁₃	—	8	1	no	—
332	C₂³×C₁₃	—	8	1	no	—
333	C₂³×C₁₃	—	8	1	no	—
334	C₂³×C₁₃	—	8	1	no	—
335	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
336	Q₈×C₁₃	—	2	4	no	—
337	Q₈×C₁₃	—	2	2	no	—
338	Q₈×C₁₃	—	2	2	no	—
339	Q₈×C₁₃	—	4	2	no	—
340	Q₈×C₁₃	—	4	2	no	—
341	Q₈×C₁₃	—	8	1	no	—
342	Q₈×C₁₃	—	8	4	no	—
343	D₄×C₁₃	—	2	4	no	—
344	D₄×C₁₃	—	2	2	no	—
345	D₄×C₁₃	—	2	2	no	—
346	D₄×C₁₃	—	2	2	no	—
347	D₄×C₁₃	—	2	2	no	—
348	D₄×C₁₃	—	2	2	no	—
349	D₄×C₁₃	—	4	4	no	—
350	D₄×C₁₃	—	4	2	no	—
351	D₄×C₁₃	—	4	2	no	—
352	D₄×C₁₃	—	8	1	no	—
353	D₄×C₁₃	—	8	4	no	—
354	D₄×C₁₃	—	8	4	no	—
355	D₄×C₁₃	C₂×#41	1	4	yes	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	4	1	no	—
363	C₂×C₄×C₁₃	—	4	4	no	—
364	C₂×C₄×C₁₃	—	4	4	no	—
365	C₂×C₄×C₁₃	—	4	4	no	—
366	C₂×C₄×C₁₃	—	8	4	no	—
367	C₂×C₄×C₁₃	—	8	2	no	—
368	C₂×C₄×C₁₃	—	8	2	no	—
369	C₂×C₄×C₁₃	—	8	4	no	—
370	C₂×C₄×C₁₃	—	8	4	no	—
371	C₂×C₄×C₁₃	—	8	1	no	—
372	C₂×C₄×C₁₃	—	8	1	no	—
373	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
374	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
378	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
381	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
382	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
383	C₈×C₁₃	—	2	1	no	—
384	C₈×C₁₃	—	2	1	no	—
385	C₈×C₁₃	—	2	4	no	—
386	C₈×C₁₃	—	2	1	no	—
387	C₈×C₁₃	—	2	1	no	—
388	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
389	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
390	#559	C₂²×C₁₃	1	4	yes	complemented
391	#556	C₂²×C₁₃	1	2	yes	complemented
392	#555	—	2	1	no	—
393	#554	—	2	1	no	—
394	#554	—	2	2	no	—
395	#554	C₂²×C₁₃	1	2	yes	complemented
396	#554	C₂²×C₁₃	1	4	yes	complemented
397	#553	—	2	2	no	—
398	#550	C₂²×C₁₃	1	2	yes	complemented
399	D₄×Q₈	—	2	1	no	—
400	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
401	#547	—	2	1	no	—
402	#544	C₂²×C₁₃	1	2	yes	—
403	#543	—	2	2	no	—
404	#538	—	2	2	no	—
405	#535	C₂²×C₁₃	1	2	yes	—
406	#533	C₂²×C₁₃	1	1	yes	characteristic
407	#533	C₂²×C₁₃	1	1	yes	characteristic
408	#532	C₂²×C₁₃	1	1	yes	characteristic
409	#525	—	2	2	no	—
410	C₂×C₂²⋊Q₈	—	2	2	no	—
411	#520	C₂²×C₁₃	1	2	yes	—
412	#518	C₂²×C₁₃	1	2	yes	—
413	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
415	#490	C₂²×C₁₃	1	4	yes	complemented
416	#489	C₂²×C₁₃	1	4	yes	complemented
417	#488	C₂²×C₁₃	1	4	yes	complemented
418	#488	C₂²×C₁₃	1	2	yes	complemented
419	#488	C₂²×C₁₃	1	2	yes	complemented
420	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
421	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
422	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
423	#486	C₂²×C₁₃	1	4	yes	complemented
424	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
425	#479	C₂²×C₁₃	1	4	yes	complemented
426	#478	C₂²×C₁₃	1	4	yes	complemented
427	#478	C₂²×C₁₃	1	4	yes	complemented
428	#477	C₂²×C₁₃	1	4	yes	complemented
429	#476	C₂²×C₁₃	1	2	yes	complemented
430	#474	C₂²×C₁₃	1	2	yes	complemented
431	#474	C₂²×C₁₃	1	4	yes	complemented
432	#463	C₂²×C₁₃	1	4	yes	—
433	#463	C₂²×C₁₃	1	4	yes	—
434	#463	C₂²×C₁₃	1	4	yes	complemented
435	#461	C₂²×C₁₃	1	2	yes	complemented
436	#459	C₂²×C₁₃	1	4	yes	—
437	#459	C₂²×C₁₃	1	4	yes	—
438	#459	C₂²×C₁₃	1	2	yes	complemented
439	#446	C₂²×C₁₃	1	2	yes	complemented
440	#446	C₂²×C₁₃	1	2	yes	complemented
441	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
442	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
443	#442	C₂²×C₁₃	1	4	yes	complemented
444	#440	C₂²×C₁₃	1	4	yes	complemented
445	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
446	C₄×D₈	C₂²×C₁₃	1	2	yes	—
447	C₄×D₈	C₂²×C₁₃	1	2	yes	—
448	C₄×D₈	C₂²×C₁₃	1	2	yes	—
449	C₄×D₈	C₂²×C₁₃	1	2	yes	—
450	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
451	#428	C₂²×C₁₃	1	2	yes	—
452	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
453	#424	C₂²×C₁₃	1	2	yes	—
454	#423	C₂²×C₁₃	1	1	yes	characteristic
455	#418	C₂²×C₁₃	1	2	yes	—
456	#417	C₂²×C₁₃	1	2	yes	—
457	#416	C₂²×C₁₃	1	2	yes	—
458	#416	C₂²×C₁₃	1	2	yes	—
459	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
460	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
461	#405	C₂²×C₁₃	1	2	yes	—
462	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
463	C₂²×C₁₃	—	2	1	no	—
464	C₂²×C₁₃	—	2	1	no	—
465	C₂²×C₁₃	—	2	4	no	—
466	C₂²×C₁₃	—	4	2	no	—
467	C₂²×C₁₃	—	4	2	no	—
468	C₂²×C₁₃	—	4	2	no	—
469	C₂²×C₁₃	—	4	2	no	—
470	C₂²×C₁₃	—	4	2	no	—
471	C₂²×C₁₃	—	4	2	no	—
472	C₂²×C₁₃	—	4	2	no	—
473	C₂²×C₁₃	—	4	2	no	—
474	C₂²×C₁₃	—	8	4	no	—
475	C₂²×C₁₃	—	8	4	no	—
476	C₂²×C₁₃	#548	1	2	yes	—
477	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
478	C₄×C₁₃	—	2	1	no	—
479	C₄×C₁₃	—	2	1	no	—
480	C₄×C₁₃	—	2	4	no	—
481	C₄×C₁₃	—	2	1	no	—
482	C₄×C₁₃	—	2	4	no	—
483	C₄×C₁₃	—	4	2	no	—
484	C₄×C₁₃	—	4	2	no	—
485	C₄×C₁₃	—	4	2	no	—
486	C₄×C₁₃	—	4	2	no	—
487	C₄×C₁₃	—	4	2	no	—
488	C₄×C₁₃	#548	1	2	yes	—
489	C₄×C₁₃	#576	1	2	yes	—
490	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
491	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
492	C₂×#41	—	2	2	no	—
493	C₂×#41	C₂³×C₁₃	1	2	yes	—
494	C₂²×Q₈	—	2	2	no	—
495	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
496	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
497	C₂³×C₄	—	2	1	no	—
498	C₂³×C₄	—	2	1	no	—
499	AGL(1,ℤ/8)	—	2	8	no	—
500	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
501	C₂×D₈	—	2	4	no	—
502	C₂×D₈	C₂³×C₁₃	1	2	yes	—
503	C₂×D₈	C₂³×C₁₃	1	2	yes	—
504	C₂×D₈	C₂³×C₁₃	1	4	yes	—
505	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
506	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
507	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
508	C₄⋊Q₈	—	2	2	no	—
509	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
510	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
511	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
512	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
513	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
515	#127	C₂³×C₁₃	1	1	yes	characteristic
516	#127	C₂³×C₁₃	1	4	yes	—
517	#126	—	2	4	no	—
518	#125	—	2	2	no	—
519	#125	D₄×C₁₃	1	2	yes	—
520	#125	C₂³×C₁₃	1	2	yes	—
521	#125	C₂³×C₁₃	1	4	yes	—
522	#124	—	2	4	no	—
523	#124	C₂³×C₁₃	1	2	yes	—
524	#124	C₂³×C₁₃	1	4	yes	—
525	#123	—	2	4	no	—
526	#123	—	2	4	no	—
527	C₂²⋊Q₈	—	2	2	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	—	2	1	no	—
531	C₂²⋊Q₈	—	2	1	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	4	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	C₂²⋊Q₈	—	2	4	no	—
536	C₂²⋊Q₈	—	2	4	no	—
537	C₂²⋊Q₈	—	2	4	no	—
538	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
539	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
540	#121	—	2	1	no	—
541	#121	—	2	1	no	—
542	#121	—	2	2	no	—
543	#121	—	2	2	no	—
544	#121	—	2	2	no	—
545	#121	—	2	4	no	—
546	#120	—	2	4	no	—
547	C₄×Q₈	—	2	1	no	—
548	C₄×Q₈	—	2	1	no	—
549	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
550	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
551	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	4	no	—
555	C₄×D₄	—	2	4	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	—	2	1	no	—
562	C₄×D₄	C₂³×C₁₃	1	2	yes	—
563	C₄×D₄	C₂³×C₁₃	1	2	yes	—
564	C₄×D₄	C₂³×C₁₃	1	2	yes	—
565	C₄×D₄	C₂³×C₁₃	1	2	yes	—
566	C₄×D₄	C₂³×C₁₃	1	4	yes	—
567	C₄×D₄	C₂³×C₁₃	1	4	yes	—
568	C₄×D₄	C₂³×C₁₃	1	4	yes	—
569	#117	—	2	2	no	—
570	#117	—	2	2	no	—
571	#117	C₂³×C₁₃	1	2	yes	—
572	#117	C₂³×C₁₃	1	2	yes	—
573	C₂×C₄⋊C₄	—	2	2	no	—
574	C₂×C₄⋊C₄	—	2	4	no	—
575	C₂×C₄⋊C₄	—	2	2	no	—
576	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
578	C₂×C₂²⋊C₄	—	2	1	no	—
579	C₂×C₂²⋊C₄	—	2	1	no	—
580	C₂×C₂²⋊C₄	—	2	4	no	—
581	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
582	#107	C₂³×C₁₃	1	2	yes	—
583	#107	C₂³×C₁₃	1	2	yes	—
584	#107	C₂³×C₁₃	1	4	yes	—
585	#106	C₂³×C₁₃	1	4	yes	—
586	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
587	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
588	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
589	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
590	#103	C₂³×C₁₃	1	2	yes	—
591	#103	C₂³×C₁₃	1	2	yes	—
592	#103	C₂³×C₁₃	1	2	yes	—
593	#103	C₂³×C₁₃	1	2	yes	—
594	#103	C₂³×C₁₃	1	4	yes	—
595	#102	C₂³×C₁₃	1	2	yes	—
596	#102	C₂³×C₁₃	1	2	yes	—
597	#102	C₂³×C₁₃	1	2	yes	—
598	#102	C₂³×C₁₃	1	2	yes	—
599	#102	C₂³×C₁₃	1	2	yes	—
600	#102	C₂³×C₁₃	1	2	yes	—
601	#102	C₂³×C₁₃	1	2	yes	—
602	#102	C₂³×C₁₃	1	2	yes	—
603	#102	C₂³×C₁₃	1	4	yes	—
604	#102	C₂³×C₁₃	1	4	yes	—
605	#102	C₂³×C₁₃	1	4	yes	—
606	#97	C₂³×C₁₃	1	4	yes	—
607	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
608	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
609	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
610	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
611	C₄×C₈	C₂³×C₁₃	1	4	yes	—
612	C₂×C₁₃	—	2	2	no	—
613	C₂×C₁₃	—	4	4	no	—
614	C₂×C₁₃	—	8	2	no	—
615	C₂×C₁₃	—	8	2	no	—
616	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
617	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
618	C₂×C₁₃	#3584	1	1	yes	characteristic
619	C₂⁴	—	2	1	no	—
620	C₂⁴	—	2	1	no	—
621	#41	—	2	4	no	—
622	#41	—	2	4	no	—
623	#41	—	8	4	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	4	no	—
627	C₂×Q₈	—	8	4	no	—
628	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
629	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
630	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	2	no	—
641	C₂×D₄	C₁₃×#41	1	4	yes	complemented
642	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
643	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
644	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	8	2	no	—
656	C₂²×C₄	—	8	2	no	—
657	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
660	SD₁₆	—	2	8	no	—
661	D₈	—	2	4	no	—
662	D₈	—	2	4	no	—
663	D₈	—	2	8	no	—
664	M₁₆	—	2	4	no	—
665	C₂×C₈	—	2	2	no	—
666	C₂×C₈	—	2	2	no	—
667	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
668	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
669	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
670	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
671	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
685	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
686	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
687	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
688	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
689	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
690	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
691	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
692	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
693	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
707	C₄²	—	2	4	no	—
708	C₄²	—	2	2	no	—
709	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
710	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
711	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
712	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
713	C₄²	C₂⁴×C₁₃	1	4	yes	—
714	C₁₃	#61325	1	1	yes	characteristic, direct product factor, Sylow
715	C₂³	—	2	2	no	—
716	C₂³	—	2	4	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	4	2	no	—
720	C₂³	—	8	1	no	—
721	C₂³	—	8	1	no	—
722	C₂³	—	8	1	no	—
723	C₂³	—	8	1	no	—
724	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
725	Q₈	—	2	4	no	—
726	Q₈	—	2	2	no	—
727	Q₈	—	2	2	no	—
728	Q₈	—	4	2	no	—
729	Q₈	—	4	2	no	—
730	Q₈	—	8	4	no	—
731	Q₈	—	8	1	no	—
732	D₄	—	2	4	no	—
733	D₄	—	2	2	no	—
734	D₄	—	2	2	no	—
735	D₄	—	2	2	no	—
736	D₄	—	2	2	no	—
737	D₄	—	2	2	no	—
738	D₄	—	4	4	no	—
739	D₄	—	4	2	no	—
740	D₄	—	4	2	no	—
741	D₄	—	8	1	no	—
742	D₄	—	8	4	no	—
743	D₄	—	8	4	no	—
744	D₄	C₂×C₁₃×#41	1	4	yes	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	4	no	—
753	C₂×C₄	—	4	4	no	—
754	C₂×C₄	—	4	4	no	—
755	C₂×C₄	—	8	2	no	—
756	C₂×C₄	—	8	2	no	—
757	C₂×C₄	—	8	4	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	—	8	4	no	—
760	C₂×C₄	—	8	1	no	—
761	C₂×C₄	—	8	1	no	—
762	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
763	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
764	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
765	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
766	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
767	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
768	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
769	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
770	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
771	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
772	C₈	—	2	1	no	—
773	C₈	—	2	1	no	—
774	C₈	—	2	4	no	—
775	C₈	—	2	1	no	—
776	C₈	—	2	1	no	—
777	C₂²	—	2	1	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	8	4	no	—
789	C₂²	—	8	4	no	—
790	C₂²	C₁₃×#548	1	2	yes	—
791	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
792	C₄	—	2	1	no	—
793	C₄	—	2	4	no	—
794	C₄	—	2	1	no	—
795	C₄	—	2	1	no	—
796	C₄	—	2	4	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	2	no	—
802	C₄	C₁₃×#548	1	2	yes	—
803	C₄	C₁₃×#576	1	2	yes	—
804	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
805	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
806	C₂	—	2	2	no	—
807	C₂	—	4	4	no	—
808	C₂	—	8	2	no	—
809	C₂	—	8	2	no	—
810	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
811	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
812	C₂	C₁₃×#3584	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 ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3506	C₂	semidirect
2. C₁₃×#3501	C₂	semidirect
3. C₁₃×#3370	C₂	semidirect
4. C₁₃×#3367	C₂	semidirect
5. C₁₃×#3366	C₂	semidirect
6. C₁₃×#3361	C₂	semidirect
7. C₁₃×#3360	C₂	semidirect
8. C₁₃×#3358	C₂	semidirect
9. C₁₃×#3136	C₂	semidirect
10. C₁₃×#3131	C₂	semidirect
11. C₁₃×#3083	C₂	semidirect
12. C₁₃×#3077	C₂	semidirect
13. C₁₃×#3041	C₂	semidirect
14. C₁₃×#3036	C₂	semidirect
15. C₁₃×#2960	C₂	semidirect
16. C₁₃×#2946	C₂	semidirect
17. C₂×C₄×C₁₃×D₈	C₂	semidirect
20. C₁₃×#559	C₂²	semidirect
21. C₁₃×#556	C₂²	semidirect
25. C₁₃×#554	C₂²	semidirect
26. C₁₃×#554	C₂²	semidirect
28. C₁₃×#550	C₂²	semidirect
30. D₄×Q₈×C₁₃	C₂²	semidirect
45. C₁₃×#490	C₂²	semidirect
46. C₁₃×#489	C₂²	semidirect
47. C₁₃×#488	C₂²	semidirect
48. C₁₃×#488	C₂²	semidirect
49. C₁₃×#488	C₂²	semidirect
50. C₁₃×#487	C₂²	semidirect
51. C₁₃×#487	C₂²	semidirect
52. C₁₃×#486	C₂²	semidirect
53. C₁₃×#486	C₂²	semidirect
54. C₁₃×#486	C₂²	semidirect
55. C₁₃×#479	C₂²	semidirect
56. C₁₃×#478	C₂²	semidirect
57. C₁₃×#478	C₂²	semidirect
58. C₁₃×#477	C₂²	semidirect
59. C₁₃×#476	C₂²	semidirect
60. C₁₃×#474	C₂²	semidirect
61. C₁₃×#474	C₂²	semidirect
64. C₁₃×#463	C₂²	semidirect
65. C₁₃×#461	C₂²	semidirect
68. C₁₃×#459	C₂²	semidirect
69. C₁₃×#446	C₂²	semidirect
70. C₁₃×#446	C₂²	semidirect
71. C₈×Q₈×C₁₃	C₂²	semidirect
72. C₈×Q₈×C₁₃	C₂²	semidirect
73. C₁₃×#442	C₂²	semidirect
74. C₁₃×#440	C₂²	semidirect
75. C₄×C₁₃×SD₁₆	C₂²	semidirect
80. C₄×C₁₃×D₈	C₂²	semidirect
213. #61325	C₁₃	direct (N × H)
236. C₂×D₄×C₁₃	#41	semidirect
309. #3506	C₂×C₁₃	semidirect
310. #3501	C₂×C₁₃	semidirect
311. #3370	C₂×C₁₃	semidirect
312. #3367	C₂×C₁₃	semidirect
313. #3366	C₂×C₁₃	semidirect
314. #3361	C₂×C₁₃	semidirect
315. #3360	C₂×C₁₃	semidirect
316. #3358	C₂×C₁₃	semidirect
317. #3136	C₂×C₁₃	semidirect
318. #3131	C₂×C₁₃	semidirect
319. #3083	C₂×C₁₃	semidirect
320. #3077	C₂×C₁₃	semidirect
321. #3041	C₂×C₁₃	semidirect
322. #3036	C₂×C₁₃	semidirect
323. #2960	C₂×C₁₃	semidirect
324. #2946	C₂×C₁₃	semidirect
325. C₂×C₄×D₈	C₂×C₁₃	semidirect
390. #559	C₂²×C₁₃	semidirect
391. #556	C₂²×C₁₃	semidirect
395. #554	C₂²×C₁₃	semidirect
396. #554	C₂²×C₁₃	semidirect
398. #550	C₂²×C₁₃	semidirect
400. D₄×Q₈	C₂²×C₁₃	semidirect
415. #490	C₂²×C₁₃	semidirect
416. #489	C₂²×C₁₃	semidirect
417. #488	C₂²×C₁₃	semidirect
418. #488	C₂²×C₁₃	semidirect
419. #488	C₂²×C₁₃	semidirect
420. #487	C₂²×C₁₃	semidirect
421. #487	C₂²×C₁₃	semidirect
422. #486	C₂²×C₁₃	semidirect
423. #486	C₂²×C₁₃	semidirect
424. #486	C₂²×C₁₃	semidirect
425. #479	C₂²×C₁₃	semidirect
426. #478	C₂²×C₁₃	semidirect
427. #478	C₂²×C₁₃	semidirect
428. #477	C₂²×C₁₃	semidirect
429. #476	C₂²×C₁₃	semidirect
430. #474	C₂²×C₁₃	semidirect
431. #474	C₂²×C₁₃	semidirect
434. #463	C₂²×C₁₃	semidirect
435. #461	C₂²×C₁₃	semidirect
438. #459	C₂²×C₁₃	semidirect
439. #446	C₂²×C₁₃	semidirect
440. #446	C₂²×C₁₃	semidirect
441. C₈×Q₈	C₂²×C₁₃	semidirect
442. C₈×Q₈	C₂²×C₁₃	semidirect
443. #442	C₂²×C₁₃	semidirect
444. #440	C₂²×C₁₃	semidirect
445. C₄×SD₁₆	C₂²×C₁₃	semidirect
450. C₄×D₈	C₂²×C₁₃	semidirect
641. C₂×D₄	C₁₃×#41	semidirect
714. C₁₃	#61325	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×#3506	2
C₁₃×#3501	2
C₁₃×#3370	2
C₁₃×#3367	2
C₁₃×#3366	2
C₁₃×#3361	2
C₁₃×#3360	2
C₁₃×#3358	2
C₁₃×#3136	2
C₁₃×#3131	2
C₁₃×#3083	2
C₁₃×#3077	2
C₁₃×#3041	2
C₁₃×#3036	2
C₁₃×#2960	2
C₁₃×#2946	2
C₂×C₄×C₁₃×D₈	2
#61325	13

Subgroups — C13×#61325 #15747664

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61325 #15747664