Subgroups — C₁₃×#62136 #15748475

Order 3328.

1812 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3483	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3385	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3366	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3347	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3341	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3309	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3305	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3253	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3245	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3235	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3115	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3076	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#556	—	2	1	no	—
20	C₁₃×#555	—	2	1	no	—
21	C₁₃×#555	—	2	2	no	—
22	C₁₃×#555	C₂²	1	2	yes	—
23	C₁₃×#555	C₂²	1	1	yes	characteristic
24	C₁₃×#555	C₂²	1	2	yes	—
25	C₁₃×#554	C₂²	1	2	yes	—
26	C₁₃×#553	C₂²	1	4	yes	—
27	C₁₃×#550	—	2	1	no	—
28	C₁₃×#550	C₂²	1	1	yes	characteristic
29	C₁₃×#550	C₂²	1	2	yes	—
30	C₁₃×#550	C₂²	1	1	yes	characteristic
31	C₁₃×#548	—	2	2	no	—
32	C₁₃×#547	—	2	1	no	—
33	C₁₃×#542	—	2	2	no	—
34	C₁₃×#537	—	2	1	no	—
35	C₁₃×#533	C₂²	1	2	yes	—
36	C₁₃×#532	—	2	1	no	—
37	C₁₃×#532	—	2	2	no	—
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₁₃×#532	C₂²	1	2	yes	—
40	C₁₃×#532	C₂²	1	1	yes	characteristic
41	C₁₃×#532	C₂²	1	2	yes	—
42	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
43	C₁₃×#520	—	2	1	no	—
44	C₄×C₁₃×#41	—	2	1	no	—
45	C₄×C₁₃×#41	C₂²	1	2	yes	—
46	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₁₃×#501	C₂²	1	4	yes	—
49	C₁₃×#500	C₂²	1	2	yes	—
50	C₁₃×#490	C₂²	1	4	yes	—
51	C₁₃×#486	C₂²	1	2	yes	—
52	C₁₃×#482	C₂²	1	4	yes	—
53	C₁₃×#482	C₂²	1	4	yes	—
54	C₁₃×#482	C₂²	1	4	yes	—
55	C₁₃×#482	C₂²	1	2	yes	—
56	C₁₃×#480	C₂²	1	4	yes	—
57	C₁₃×#479	C₂²	1	4	yes	—
58	C₁₃×#478	C₂²	1	4	yes	—
59	C₁₃×#477	C₂²	1	2	yes	—
60	C₁₃×#477	C₂²	1	1	yes	characteristic
61	C₁₃×#476	C₂²	1	2	yes	—
62	C₁₃×#476	C₂²	1	2	yes	—
63	C₁₃×#476	C₂²	1	2	yes	—
64	C₁₃×#476	C₂²	1	1	yes	characteristic
65	C₁₃×#475	C₂²	1	2	yes	—
66	C₁₃×#474	C₂²	1	2	yes	—
67	C₁₃×#474	C₂²	1	2	yes	—
68	C₁₃×#474	C₂²	1	4	yes	—
69	C₁₃×#474	C₂²	1	2	yes	—
70	C₁₃×#469	C₂²	1	4	yes	—
71	C₁₃×#466	C₂²	1	4	yes	—
72	C₁₃×#466	C₂²	1	4	yes	—
73	C₁₃×#460	C₂²	1	1	yes	characteristic
74	C₁₃×#459	C₂²	1	2	yes	—
75	C₁₃×#459	C₂²	1	4	yes	—
76	C₁₃×#459	C₂²	1	1	yes	characteristic
77	C₁₃×#459	C₂²	1	2	yes	—
78	C₁₃×#449	C₂²	1	4	yes	—
79	C₁₃×#449	C₂²	1	2	yes	—
80	C₁₃×#446	C₂²	1	2	yes	—
81	C₁₃×#442	C₂²	1	4	yes	—
82	C₁₃×#440	C₂²	1	4	yes	—
83	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
84	C₄×C₁₃×D₈	C₂²	1	2	yes	—
85	C₁₃×#435	C₂²	1	4	yes	—
86	C₈×D₄×C₁₃	C₂²	1	2	yes	—
87	C₁₃×#432	C₂²	1	2	yes	—
88	C₁₃×#431	C₂²	1	1	yes	characteristic
89	C₁₃×#428	C₂²	1	2	yes	—
90	C₁₃×#427	C₂²	1	4	yes	—
91	C₁₃×#423	C₂²	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
93	C₁₃×#417	C₂²	1	2	yes	—
94	C₁₃×#416	C₂²	1	4	yes	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	1	no	—
97	C₂×C₁₃×#41	—	2	1	no	—
98	C₂×C₁₃×#41	—	2	2	no	—
99	C₂×C₁₃×#41	—	2	2	no	—
100	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
101	C₂×C₁₃×#41	C₂³	1	2	yes	—
102	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₁₃	—	2	1	no	—
104	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
105	C₂×C₁₃×D₈	C₂³	1	2	yes	—
106	C₂×C₁₃×D₈	C₂³	1	4	yes	—
107	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
108	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
109	C₁₃×C₄⋊Q₈	—	2	1	no	—
110	C₁₃×C₄⋊Q₈	—	2	2	no	—
111	C₁₃×C₄⋊Q₈	—	2	1	no	—
112	C₁₃×C₄⋊Q₈	—	2	1	no	—
113	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×#127	—	2	1	no	—
119	C₁₃×#127	—	2	2	no	—
120	C₁₃×#127	C₂³	1	1	yes	characteristic
121	C₁₃×#127	C₂³	1	1	yes	characteristic
122	C₁₃×#127	C₂³	1	2	yes	—
123	C₁₃×#126	—	2	4	no	—
124	C₁₃×#125	C₂³	1	4	yes	—
125	C₁₃×#124	—	2	2	no	—
126	C₁₃×#124	—	2	2	no	—
127	C₁₃×#124	—	2	2	no	—
128	C₁₃×#124	—	2	4	no	—
129	C₁₃×#124	—	2	1	no	—
130	C₁₃×#124	—	2	2	no	—
131	C₁₃×#124	—	2	2	no	—
132	C₁₃×#124	—	2	1	no	—
133	C₁₃×#123	—	2	4	no	—
134	C₁₃×C₂²⋊Q₈	—	2	2	no	—
135	C₁₃×C₂²⋊Q₈	—	2	2	no	—
136	C₁₃×C₂²⋊Q₈	—	2	2	no	—
137	C₁₃×C₂²⋊Q₈	—	2	4	no	—
138	C₁₃×#121	—	2	1	no	—
139	C₁₃×#121	—	2	2	no	—
140	C₁₃×#121	—	2	2	no	—
141	C₁₃×#121	—	2	4	no	—
142	C₁₃×#121	—	2	2	no	—
143	C₁₃×#121	—	2	1	no	—
144	C₁₃×#121	—	2	1	no	—
145	C₁₃×#121	—	2	2	no	—
146	C₁₃×#121	—	2	1	no	—
147	C₁₃×#121	—	2	2	no	—
148	C₁₃×#121	—	2	2	no	—
149	C₁₃×#121	—	2	2	no	—
150	C₁₃×#121	—	2	2	no	—
151	C₁₃×#121	C₂³	1	4	yes	—
152	C₁₃×#121	C₂³	1	2	yes	—
153	C₁₃×#121	C₂³	1	2	yes	—
154	C₁₃×#121	C₂³	1	2	yes	—
155	C₁₃×#121	C₂³	1	2	yes	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	—	2	2	no	—
158	C₄×Q₈×C₁₃	—	2	2	no	—
159	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
160	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
162	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
164	C₄×D₄×C₁₃	—	2	1	no	—
165	C₄×D₄×C₁₃	—	2	2	no	—
166	C₄×D₄×C₁₃	—	2	1	no	—
167	C₄×D₄×C₁₃	—	2	2	no	—
168	C₄×D₄×C₁₃	—	2	1	no	—
169	C₄×D₄×C₁₃	—	2	2	no	—
170	C₄×D₄×C₁₃	—	2	4	no	—
171	C₄×D₄×C₁₃	—	2	1	no	—
172	C₄×D₄×C₁₃	—	2	2	no	—
173	C₄×D₄×C₁₃	—	2	2	no	—
174	C₄×D₄×C₁₃	—	2	1	no	—
175	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
176	C₄×D₄×C₁₃	D₄	1	2	yes	—
177	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₁₃	C₂³	1	2	yes	—
179	C₄×D₄×C₁₃	C₂³	1	4	yes	—
180	C₄×D₄×C₁₃	C₂³	1	2	yes	—
181	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₁₃	C₂³	1	2	yes	—
183	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₁₃	C₂³	1	2	yes	—
185	C₁₃×#117	—	2	1	no	—
186	C₁₃×#117	—	2	2	no	—
187	C₁₃×#117	—	2	2	no	—
188	C₁₃×#117	—	2	2	no	—
189	C₁₃×#117	—	2	1	no	—
190	C₁₃×#117	D₄	1	1	yes	characteristic
191	C₁₃×#117	D₄	1	2	yes	—
192	C₁₃×#117	C₂³	1	4	yes	—
193	C₁₃×#117	C₂³	1	2	yes	—
194	C₁₃×#117	C₂³	1	1	yes	characteristic
195	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₄²×C₁₃	—	2	1	no	—
199	C₂×C₄²×C₁₃	—	2	2	no	—
200	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₁₃×#107	C₂³	1	2	yes	—
203	C₁₃×#107	C₂³	1	4	yes	—
204	C₁₃×#107	C₂³	1	4	yes	—
205	C₁₃×#107	C₂³	1	4	yes	—
206	C₁₃×#106	C₂³	1	4	yes	—
207	C₁₃×#106	C₂³	1	4	yes	—
208	C₁₃×#106	C₂³	1	2	yes	—
209	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
210	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₁₃×#103	C₂³	1	2	yes	—
215	C₁₃×#103	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	2	yes	—
220	C₁₃×#102	C₂³	1	2	yes	—
221	C₁₃×#102	C₂³	1	2	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
225	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₁₃×#97	C₂³	1	4	yes	—
227	C₄×C₈×C₁₃	C₂³	1	2	yes	—
228	#62136	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₁₃×#41	—	2	4	no	—
230	C₁₃×#41	—	2	2	no	—
231	C₁₃×#41	—	4	2	no	—
232	C₁₃×#41	—	4	2	no	—
233	C₁₃×#41	—	4	1	no	—
234	C₁₃×#41	—	4	4	no	—
235	C₁₃×#41	—	4	4	no	—
236	C₁₃×#41	—	8	2	no	—
237	C₁₃×#41	—	8	4	no	—
238	C₁₃×#41	—	8	4	no	—
239	C₂×Q₈×C₁₃	—	2	1	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	2	1	no	—
243	C₂×Q₈×C₁₃	—	2	2	no	—
244	C₂×Q₈×C₁₃	—	8	2	no	—
245	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	—	2	1	no	—
250	C₂×D₄×C₁₃	—	2	4	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	2	no	—
254	C₂×D₄×C₁₃	—	2	1	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	2	1	no	—
257	C₂×D₄×C₁₃	—	2	1	no	—
258	C₂×D₄×C₁₃	—	2	1	no	—
259	C₂×D₄×C₁₃	—	2	2	no	—
260	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
262	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	1	no	—
268	C₂²×C₄×C₁₃	—	2	2	no	—
269	C₂²×C₄×C₁₃	—	2	1	no	—
270	C₂²×C₄×C₁₃	—	2	1	no	—
271	C₂²×C₄×C₁₃	—	2	2	no	—
272	C₂²×C₄×C₁₃	—	2	2	no	—
273	C₂²×C₄×C₁₃	—	2	4	no	—
274	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
278	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
280	C₁₃×SD₁₆	—	2	4	no	—
281	C₁₃×D₈	—	4	2	no	—
282	C₁₃×D₈	—	4	4	no	—
283	C₁₃×M₁₆	—	4	2	no	—
284	C₂×C₈×C₁₃	—	4	4	no	—
285	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
286	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
287	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	4	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	1	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	1	no	—
295	C₁₃×C₄⋊C₄	—	2	1	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	—	2	1	no	—
298	C₁₃×C₄⋊C₄	—	2	4	no	—
299	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
300	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
301	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
306	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
307	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
308	C₁₃×C₂²⋊C₄	—	2	2	no	—
309	C₁₃×C₂²⋊C₄	—	2	1	no	—
310	C₁₃×C₂²⋊C₄	—	2	4	no	—
311	C₁₃×C₂²⋊C₄	—	2	2	no	—
312	C₁₃×C₂²⋊C₄	—	2	2	no	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	4	no	—
315	C₁₃×C₂²⋊C₄	—	2	1	no	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	1	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	4	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
323	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
324	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
325	C₄²×C₁₃	—	2	1	no	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	—	2	1	no	—
328	C₄²×C₁₃	—	2	2	no	—
329	C₄²×C₁₃	—	2	1	no	—
330	C₄²×C₁₃	—	2	4	no	—
331	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₁₃	C₂×D₄	1	2	yes	—
333	C₄²×C₁₃	C₂×D₄	1	2	yes	—
334	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
336	C₄²×C₁₃	C₂⁴	1	2	yes	—
337	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
338	#3511	C₂×C₁₃	1	1	yes	characteristic, complemented
339	#3483	C₂×C₁₃	1	1	yes	characteristic, complemented
340	#3385	C₂×C₁₃	1	2	yes	complemented
341	#3366	C₂×C₁₃	1	2	yes	complemented
342	#3347	C₂×C₁₃	1	4	yes	complemented
343	#3341	C₂×C₁₃	1	2	yes	complemented
344	#3309	C₂×C₁₃	1	4	yes	complemented
345	#3305	C₂×C₁₃	1	2	yes	complemented
346	#3253	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#3245	C₂×C₁₃	1	2	yes	complemented
348	#3235	C₂×C₁₃	1	2	yes	complemented
349	#3226	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#3115	C₂×C₁₃	1	2	yes	complemented
351	#3106	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3076	C₂×C₁₃	1	2	yes	complemented
354	#2990	C₂×C₁₃	1	1	yes	characteristic, complemented
355	C₂³×C₁₃	—	2	2	no	—
356	C₂³×C₁₃	—	2	2	no	—
357	C₂³×C₁₃	—	2	1	no	—
358	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
359	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
360	Q₈×C₁₃	—	2	2	no	—
361	Q₈×C₁₃	—	2	1	no	—
362	Q₈×C₁₃	—	4	2	no	—
363	Q₈×C₁₃	—	4	4	no	—
364	Q₈×C₁₃	—	8	2	no	—
365	Q₈×C₁₃	—	8	2	no	—
366	Q₈×C₁₃	—	8	1	no	—
367	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
368	D₄×C₁₃	—	2	2	no	—
369	D₄×C₁₃	—	2	2	no	—
370	D₄×C₁₃	—	2	2	no	—
371	D₄×C₁₃	—	2	1	no	—
372	D₄×C₁₃	—	2	2	no	—
373	D₄×C₁₃	—	2	1	no	—
374	D₄×C₁₃	—	2	2	no	—
375	D₄×C₁₃	—	4	2	no	—
376	D₄×C₁₃	—	4	4	no	—
377	D₄×C₁₃	—	4	2	no	—
378	D₄×C₁₃	—	4	2	no	—
379	D₄×C₁₃	—	4	4	no	—
380	D₄×C₁₃	—	4	4	no	—
381	D₄×C₁₃	—	4	2	no	—
382	D₄×C₁₃	—	4	2	no	—
383	D₄×C₁₃	—	8	2	no	—
384	D₄×C₁₃	—	8	1	no	—
385	D₄×C₁₃	—	8	2	no	—
386	D₄×C₁₃	—	8	2	no	—
387	D₄×C₁₃	—	8	2	no	—
388	D₄×C₁₃	—	8	4	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	4	no	—
393	C₂×C₄×C₁₃	—	2	1	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	4	no	—
402	C₂×C₄×C₁₃	—	4	2	no	—
403	C₂×C₄×C₁₃	—	4	4	no	—
404	C₂×C₄×C₁₃	—	4	2	no	—
405	C₂×C₄×C₁₃	—	4	4	no	—
406	C₂×C₄×C₁₃	—	4	2	no	—
407	C₂×C₄×C₁₃	—	4	4	no	—
408	C₂×C₄×C₁₃	—	4	4	no	—
409	C₂×C₄×C₁₃	—	4	2	no	—
410	C₂×C₄×C₁₃	—	8	4	no	—
411	C₂×C₄×C₁₃	—	8	2	no	—
412	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
421	C₈×C₁₃	—	2	2	no	—
422	C₈×C₁₃	—	2	2	no	—
423	C₈×C₁₃	—	2	4	no	—
424	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
425	#556	—	2	1	no	—
426	#555	—	2	1	no	—
427	#555	—	2	2	no	—
428	#555	C₂²×C₁₃	1	1	yes	characteristic
429	#555	C₂²×C₁₃	1	2	yes	—
430	#555	C₂²×C₁₃	1	2	yes	—
431	#554	C₂²×C₁₃	1	2	yes	—
432	#553	C₂²×C₁₃	1	4	yes	—
433	#550	—	2	1	no	—
434	#550	C₂²×C₁₃	1	1	yes	characteristic
435	#550	C₂²×C₁₃	1	2	yes	—
436	#550	C₂²×C₁₃	1	1	yes	characteristic
437	#548	—	2	2	no	—
438	#547	—	2	1	no	—
439	#542	—	2	2	no	—
440	#537	—	2	1	no	—
441	#533	C₂²×C₁₃	1	2	yes	—
442	#532	—	2	1	no	—
443	#532	—	2	2	no	—
444	#532	C₂²×C₁₃	1	1	yes	characteristic
445	#532	C₂²×C₁₃	1	2	yes	—
446	#532	C₂²×C₁₃	1	1	yes	characteristic
447	#532	C₂²×C₁₃	1	2	yes	—
448	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
449	#520	—	2	1	no	—
450	C₄×#41	—	2	1	no	—
451	C₄×#41	C₂²×C₁₃	1	2	yes	—
452	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
453	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
454	#501	C₂²×C₁₃	1	4	yes	—
455	#500	C₂²×C₁₃	1	2	yes	—
456	#490	C₂²×C₁₃	1	4	yes	—
457	#486	C₂²×C₁₃	1	2	yes	—
458	#482	C₂²×C₁₃	1	4	yes	—
459	#482	C₂²×C₁₃	1	4	yes	—
460	#482	C₂²×C₁₃	1	2	yes	—
461	#482	C₂²×C₁₃	1	4	yes	—
462	#480	C₂²×C₁₃	1	4	yes	—
463	#479	C₂²×C₁₃	1	4	yes	—
464	#478	C₂²×C₁₃	1	4	yes	—
465	#477	C₂²×C₁₃	1	1	yes	characteristic
466	#477	C₂²×C₁₃	1	2	yes	—
467	#476	C₂²×C₁₃	1	2	yes	—
468	#476	C₂²×C₁₃	1	2	yes	—
469	#476	C₂²×C₁₃	1	2	yes	—
470	#476	C₂²×C₁₃	1	1	yes	characteristic
471	#475	C₂²×C₁₃	1	2	yes	—
472	#474	C₂²×C₁₃	1	2	yes	—
473	#474	C₂²×C₁₃	1	2	yes	—
474	#474	C₂²×C₁₃	1	4	yes	—
475	#474	C₂²×C₁₃	1	2	yes	—
476	#469	C₂²×C₁₃	1	4	yes	—
477	#466	C₂²×C₁₃	1	4	yes	—
478	#466	C₂²×C₁₃	1	4	yes	—
479	#460	C₂²×C₁₃	1	1	yes	characteristic
480	#459	C₂²×C₁₃	1	1	yes	characteristic
481	#459	C₂²×C₁₃	1	4	yes	—
482	#459	C₂²×C₁₃	1	2	yes	—
483	#459	C₂²×C₁₃	1	2	yes	—
484	#449	C₂²×C₁₃	1	2	yes	—
485	#449	C₂²×C₁₃	1	4	yes	—
486	#446	C₂²×C₁₃	1	2	yes	—
487	#442	C₂²×C₁₃	1	4	yes	—
488	#440	C₂²×C₁₃	1	4	yes	—
489	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
490	C₄×D₈	C₂²×C₁₃	1	2	yes	—
491	#435	C₂²×C₁₃	1	4	yes	—
492	C₈×D₄	C₂²×C₁₃	1	2	yes	—
493	#432	C₂²×C₁₃	1	2	yes	—
494	#431	C₂²×C₁₃	1	1	yes	characteristic
495	#428	C₂²×C₁₃	1	2	yes	—
496	#427	C₂²×C₁₃	1	4	yes	—
497	#423	C₂²×C₁₃	1	1	yes	characteristic
498	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
499	#417	C₂²×C₁₃	1	2	yes	—
500	#416	C₂²×C₁₃	1	4	yes	—
501	C₂²×C₁₃	—	2	2	no	—
502	C₂²×C₁₃	—	2	1	no	—
503	C₂²×C₁₃	—	2	1	no	—
504	C₂²×C₁₃	—	2	2	no	—
505	C₂²×C₁₃	—	2	1	no	—
506	C₂²×C₁₃	—	2	2	no	—
507	C₂²×C₁₃	—	4	2	no	—
508	C₂²×C₁₃	—	4	1	no	—
509	C₂²×C₁₃	—	4	2	no	—
510	C₂²×C₁₃	—	4	2	no	—
511	C₂²×C₁₃	—	4	1	no	—
512	C₂²×C₁₃	—	4	2	no	—
513	C₂²×C₁₃	—	4	1	no	—
514	C₂²×C₁₃	—	4	2	no	—
515	C₂²×C₁₃	—	4	2	no	—
516	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
517	C₄×C₁₃	—	2	2	no	—
518	C₄×C₁₃	—	2	1	no	—
519	C₄×C₁₃	—	2	2	no	—
520	C₄×C₁₃	—	2	1	no	—
521	C₄×C₁₃	—	2	2	no	—
522	C₄×C₁₃	—	2	2	no	—
523	C₄×C₁₃	—	2	1	no	—
524	C₄×C₁₃	—	4	1	no	—
525	C₄×C₁₃	—	4	2	no	—
526	C₄×C₁₃	—	4	2	no	—
527	C₄×C₁₃	—	4	1	no	—
528	C₄×C₁₃	—	4	4	no	—
529	C₄×C₁₃	#575	1	2	yes	—
530	C₄×C₁₃	#576	1	2	yes	—
531	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
532	C₄×C₁₃	#585	1	1	yes	characteristic
533	C₂×#41	—	2	1	no	—
534	C₂×#41	—	2	1	no	—
535	C₂×#41	—	2	1	no	—
536	C₂×#41	—	2	2	no	—
537	C₂×#41	—	2	2	no	—
538	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
539	C₂×#41	C₂³×C₁₃	1	2	yes	—
540	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
541	C₂²×Q₈	—	2	1	no	—
542	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
543	C₂×D₈	C₂³×C₁₃	1	2	yes	—
544	C₂×D₈	C₂³×C₁₃	1	4	yes	—
545	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
546	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
547	C₄⋊Q₈	—	2	1	no	—
548	C₄⋊Q₈	—	2	2	no	—
549	C₄⋊Q₈	—	2	1	no	—
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
552	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
553	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
554	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
555	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
556	#127	—	2	1	no	—
557	#127	—	2	2	no	—
558	#127	C₂³×C₁₃	1	1	yes	characteristic
559	#127	C₂³×C₁₃	1	1	yes	characteristic
560	#127	C₂³×C₁₃	1	2	yes	—
561	#126	—	2	4	no	—
562	#125	C₂³×C₁₃	1	4	yes	—
563	#124	—	2	2	no	—
564	#124	—	2	2	no	—
565	#124	—	2	2	no	—
566	#124	—	2	4	no	—
567	#124	—	2	1	no	—
568	#124	—	2	2	no	—
569	#124	—	2	2	no	—
570	#124	—	2	1	no	—
571	#123	—	2	4	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	4	no	—
576	#121	—	2	1	no	—
577	#121	—	2	2	no	—
578	#121	—	2	2	no	—
579	#121	—	2	4	no	—
580	#121	—	2	2	no	—
581	#121	—	2	1	no	—
582	#121	—	2	1	no	—
583	#121	—	2	2	no	—
584	#121	—	2	1	no	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	2	no	—
589	#121	C₂³×C₁₃	1	2	yes	—
590	#121	C₂³×C₁₃	1	2	yes	—
591	#121	C₂³×C₁₃	1	2	yes	—
592	#121	C₂³×C₁₃	1	2	yes	—
593	#121	C₂³×C₁₃	1	4	yes	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	—	2	2	no	—
597	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
598	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
601	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	4	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
614	C₄×D₄	D₄×C₁₃	1	2	yes	—
615	C₄×D₄	C₂³×C₁₃	1	2	yes	—
616	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
617	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
618	C₄×D₄	C₂³×C₁₃	1	2	yes	—
619	C₄×D₄	C₂³×C₁₃	1	4	yes	—
620	C₄×D₄	C₂³×C₁₃	1	2	yes	—
621	C₄×D₄	C₂³×C₁₃	1	2	yes	—
622	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
623	#117	—	2	1	no	—
624	#117	—	2	2	no	—
625	#117	—	2	2	no	—
626	#117	—	2	2	no	—
627	#117	—	2	1	no	—
628	#117	D₄×C₁₃	1	1	yes	characteristic
629	#117	D₄×C₁₃	1	2	yes	—
630	#117	C₂³×C₁₃	1	2	yes	—
631	#117	C₂³×C₁₃	1	1	yes	characteristic
632	#117	C₂³×C₁₃	1	4	yes	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	—	2	2	no	—
635	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
636	C₂×C₄²	—	2	1	no	—
637	C₂×C₄²	—	2	2	no	—
638	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
640	#107	C₂³×C₁₃	1	2	yes	—
641	#107	C₂³×C₁₃	1	4	yes	—
642	#107	C₂³×C₁₃	1	4	yes	—
643	#107	C₂³×C₁₃	1	4	yes	—
644	#106	C₂³×C₁₃	1	4	yes	—
645	#106	C₂³×C₁₃	1	4	yes	—
646	#106	C₂³×C₁₃	1	2	yes	—
647	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
648	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
649	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
650	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
651	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
652	#103	C₂³×C₁₃	1	2	yes	—
653	#103	C₂³×C₁₃	1	4	yes	—
654	#102	C₂³×C₁₃	1	4	yes	—
655	#102	C₂³×C₁₃	1	4	yes	—
656	#102	C₂³×C₁₃	1	4	yes	—
657	#102	C₂³×C₁₃	1	2	yes	—
658	#102	C₂³×C₁₃	1	2	yes	—
659	#102	C₂³×C₁₃	1	2	yes	—
660	#102	C₂³×C₁₃	1	4	yes	—
661	#102	C₂³×C₁₃	1	4	yes	—
662	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
663	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
664	#97	C₂³×C₁₃	1	4	yes	—
665	C₄×C₈	C₂³×C₁₃	1	2	yes	—
666	C₂×C₁₃	—	4	1	no	—
667	C₂×C₁₃	—	4	2	no	—
668	C₂×C₁₃	—	8	2	no	—
669	C₂×C₁₃	—	8	1	no	—
670	C₂×C₁₃	—	8	2	no	—
671	C₂×C₁₃	#3489	1	1	yes	characteristic
672	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
673	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
674	#41	—	2	4	no	—
675	#41	—	2	2	no	—
676	#41	—	4	2	no	—
677	#41	—	4	2	no	—
678	#41	—	4	1	no	—
679	#41	—	4	4	no	—
680	#41	—	4	4	no	—
681	#41	—	8	2	no	—
682	#41	—	8	4	no	—
683	#41	—	8	4	no	—
684	C₂×Q₈	—	2	1	no	—
685	C₂×Q₈	—	2	2	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	2	1	no	—
688	C₂×Q₈	—	2	2	no	—
689	C₂×Q₈	—	8	2	no	—
690	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
691	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
706	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
707	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
708	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
709	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
721	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
722	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
725	SD₁₆	—	2	4	no	—
726	D₈	—	4	2	no	—
727	D₈	—	4	4	no	—
728	M₁₆	—	4	2	no	—
729	C₂×C₈	—	4	4	no	—
730	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
731	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
732	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
745	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
746	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
747	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
748	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
749	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
750	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
751	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
752	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	1	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	1	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
768	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
769	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
770	C₄²	—	2	1	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	1	no	—
773	C₄²	—	2	2	no	—
774	C₄²	—	2	1	no	—
775	C₄²	—	2	4	no	—
776	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
777	C₄²	C₂×D₄×C₁₃	1	2	yes	—
778	C₄²	C₂×D₄×C₁₃	1	2	yes	—
779	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
780	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
781	C₄²	C₂⁴×C₁₃	1	2	yes	—
782	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
783	C₁₃	#62136	1	1	yes	characteristic, direct product factor, Sylow
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	1	no	—
787	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
788	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
789	Q₈	—	2	2	no	—
790	Q₈	—	2	1	no	—
791	Q₈	—	4	2	no	—
792	Q₈	—	4	4	no	—
793	Q₈	—	8	2	no	—
794	Q₈	—	8	2	no	—
795	Q₈	—	8	1	no	—
796	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
797	D₄	—	2	2	no	—
798	D₄	—	2	2	no	—
799	D₄	—	2	2	no	—
800	D₄	—	2	1	no	—
801	D₄	—	2	2	no	—
802	D₄	—	2	1	no	—
803	D₄	—	2	2	no	—
804	D₄	—	4	2	no	—
805	D₄	—	4	4	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	2	no	—
808	D₄	—	4	4	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	2	no	—
811	D₄	—	4	2	no	—
812	D₄	—	8	2	no	—
813	D₄	—	8	1	no	—
814	D₄	—	8	2	no	—
815	D₄	—	8	2	no	—
816	D₄	—	8	2	no	—
817	D₄	—	8	4	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	4	4	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	8	4	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
842	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
844	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
849	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
850	C₈	—	2	2	no	—
851	C₈	—	2	2	no	—
852	C₈	—	2	4	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	2	no	—
868	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
869	C₄	—	2	1	no	—
870	C₄	—	2	2	no	—
871	C₄	—	2	2	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	2	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	2	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	4	no	—
881	C₄	C₁₃×#575	1	2	yes	—
882	C₄	C₁₃×#576	1	2	yes	—
883	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
884	C₄	C₁₃×#585	1	1	yes	characteristic
885	C₂	—	4	1	no	—
886	C₂	—	4	2	no	—
887	C₂	—	8	2	no	—
888	C₂	—	8	1	no	—
889	C₂	—	8	2	no	—
890	C₂	C₁₃×#3489	1	1	yes	characteristic
891	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
892	C₂	C₂×C₁₃×#576	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×#3511	C₂	semidirect
2. C₁₃×#3483	C₂	semidirect
3. C₁₃×#3385	C₂	semidirect
4. C₁₃×#3366	C₂	semidirect
5. C₁₃×#3347	C₂	semidirect
6. C₁₃×#3341	C₂	semidirect
7. C₁₃×#3309	C₂	semidirect
8. C₁₃×#3305	C₂	semidirect
9. C₁₃×#3253	C₂	semidirect
10. C₁₃×#3245	C₂	semidirect
11. C₁₃×#3235	C₂	semidirect
12. C₁₃×#3226	C₂	semidirect
13. C₁₃×#3115	C₂	semidirect
14. C₁₃×#3106	C₂	semidirect
15. C₁₃×#3079	C₂	semidirect
16. C₁₃×#3076	C₂	semidirect
17. C₁₃×#2990	C₂	semidirect
228. #62136	C₁₃	direct (N × H)
338. #3511	C₂×C₁₃	semidirect
339. #3483	C₂×C₁₃	semidirect
340. #3385	C₂×C₁₃	semidirect
341. #3366	C₂×C₁₃	semidirect
342. #3347	C₂×C₁₃	semidirect
343. #3341	C₂×C₁₃	semidirect
344. #3309	C₂×C₁₃	semidirect
345. #3305	C₂×C₁₃	semidirect
346. #3253	C₂×C₁₃	semidirect
347. #3245	C₂×C₁₃	semidirect
348. #3235	C₂×C₁₃	semidirect
349. #3226	C₂×C₁₃	semidirect
350. #3115	C₂×C₁₃	semidirect
351. #3106	C₂×C₁₃	semidirect
352. #3079	C₂×C₁₃	semidirect
353. #3076	C₂×C₁₃	semidirect
354. #2990	C₂×C₁₃	semidirect
783. C₁₃	#62136	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×#3511	2
C₁₃×#3483	2
C₁₃×#3385	2
C₁₃×#3366	2
C₁₃×#3347	2
C₁₃×#3341	2
C₁₃×#3309	2
C₁₃×#3305	2
C₁₃×#3253	2
C₁₃×#3245	2
C₁₃×#3235	2
C₁₃×#3226	2
C₁₃×#3115	2
C₁₃×#3106	2
C₁₃×#3079	2
C₁₃×#3076	2
C₁₃×#2990	2
#62136	13

Subgroups — C13×#62136 #15748475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62136 #15748475