Subgroups — C₁₃×#62102 #15748441

Order 3328.

1784 conjugacy classes of subgroups.

The subgroup lattice has 874 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×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3381	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3361	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3340	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3339	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3305	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3301	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3247	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3245	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3233	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3106	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3076	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2988	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#559	—	2	1	no	—
19	C₁₃×#559	C₂²	1	1	yes	characteristic
20	C₁₃×#557	C₂²	1	1	yes	characteristic
21	C₁₃×#556	—	2	1	no	—
22	C₁₃×#556	—	2	1	no	—
23	C₁₃×#556	C₂²	1	1	yes	characteristic
24	C₁₃×#555	C₂²	1	2	yes	—
25	C₁₃×#554	C₂²	1	2	yes	—
26	C₁₃×#553	—	2	2	no	—
27	C₁₃×#553	C₂²	1	4	yes	—
28	C₁₃×#553	C₂²	1	2	yes	—
29	C₁₃×#550	C₂²	1	1	yes	characteristic
30	C₁₃×#548	—	2	2	no	—
31	C₁₃×#548	C₂²	1	2	yes	—
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	C₂²	1	1	yes	characteristic
38	C₁₃×#532	C₂²	1	2	yes	—
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₁₃×#529	—	2	2	no	—
42	C₁₃×#529	C₂²	1	2	yes	—
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	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₁₃×#499	C₂²	1	4	yes	—
49	C₁₃×#498	C₂²	1	2	yes	—
50	C₁₃×#488	C₂²	1	4	yes	—
51	C₁₃×#486	C₂²	1	2	yes	—
52	C₁₃×#485	C₂²	1	4	yes	—
53	C₁₃×#482	C₂²	1	4	yes	—
54	C₁₃×#482	C₂²	1	4	yes	—
55	C₁₃×#481	C₂²	1	4	yes	—
56	C₁₃×#481	C₂²	1	2	yes	—
57	C₁₃×#479	C₂²	1	4	yes	—
58	C₁₃×#478	C₂²	1	4	yes	—
59	C₁₃×#478	C₂²	1	4	yes	—
60	C₁₃×#477	C₂²	1	2	yes	—
61	C₁₃×#477	C₂²	1	2	yes	—
62	C₁₃×#477	C₂²	1	2	yes	—
63	C₁₃×#477	C₂²	1	2	yes	—
64	C₁₃×#476	C₂²	1	2	yes	—
65	C₁₃×#476	C₂²	1	2	yes	—
66	C₁₃×#475	C₂²	1	1	yes	characteristic
67	C₁₃×#475	C₂²	1	1	yes	characteristic
68	C₁₃×#474	C₂²	1	2	yes	—
69	C₁₃×#474	C₂²	1	2	yes	—
70	C₁₃×#466	C₂²	1	4	yes	—
71	C₁₃×#466	C₂²	1	4	yes	—
72	C₁₃×#465	C₂²	1	4	yes	—
73	C₁₃×#463	C₂²	1	4	yes	—
74	C₁₃×#460	C₂²	1	1	yes	characteristic
75	C₁₃×#460	C₂²	1	1	yes	characteristic
76	C₁₃×#459	C₂²	1	2	yes	—
77	C₁₃×#459	C₂²	1	2	yes	—
78	C₁₃×#449	C₂²	1	4	yes	—
79	C₁₃×#448	C₂²	1	2	yes	—
80	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
81	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
82	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
83	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
84	C₄×C₁₃×D₈	C₂²	1	4	yes	—
85	C₈×D₄×C₁₃	C₂²	1	4	yes	—
86	C₈×D₄×C₁₃	C₂²	1	2	yes	—
87	C₁₃×#431	C₂²	1	1	yes	characteristic
88	C₁₃×#431	C₂²	1	2	yes	—
89	C₁₃×#427	C₂²	1	4	yes	—
90	C₂×C₁₃×#107	C₂²	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
93	C₁₃×#416	C₂²	1	4	yes	—
94	C₂×C₁₃×#103	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	1	no	—
97	C₂×C₁₃×#41	—	2	2	no	—
98	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
99	C₂×C₁₃×#41	C₂³	1	2	yes	—
100	C₂²×Q₈×C₁₃	—	2	1	no	—
101	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
103	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
104	C₂×C₁₃×D₈	C₂³	1	4	yes	—
105	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
106	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
107	C₁₃×C₄⋊Q₈	—	2	1	no	—
108	C₁₃×C₄⋊Q₈	—	2	1	no	—
109	C₁₃×C₄⋊Q₈	—	2	1	no	—
110	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₁₃×#127	—	2	1	no	—
115	C₁₃×#127	C₂³	1	1	yes	characteristic
116	C₁₃×#127	C₂³	1	1	yes	characteristic
117	C₁₃×#126	—	2	2	no	—
118	C₁₃×#126	—	2	4	no	—
119	C₁₃×#126	—	2	2	no	—
120	C₁₃×#126	—	2	2	no	—
121	C₁₃×#125	—	2	2	no	—
122	C₁₃×#125	C₂³	1	2	yes	—
123	C₁₃×#125	C₂³	1	4	yes	—
124	C₁₃×#124	—	2	1	no	—
125	C₁₃×#124	—	2	1	no	—
126	C₁₃×#124	—	2	2	no	—
127	C₁₃×#124	—	2	4	no	—
128	C₁₃×#124	—	2	1	no	—
129	C₁₃×#124	—	2	2	no	—
130	C₁₃×#124	—	2	1	no	—
131	C₁₃×#124	C₂³	1	2	yes	—
132	C₁₃×#123	—	2	2	no	—
133	C₁₃×#123	—	2	2	no	—
134	C₁₃×#123	—	2	2	no	—
135	C₁₃×#123	—	2	4	no	—
136	C₁₃×C₂²⋊Q₈	—	2	2	no	—
137	C₁₃×C₂²⋊Q₈	—	2	2	no	—
138	C₁₃×C₂²⋊Q₈	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	—	2	4	no	—
141	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₁₃×#121	—	2	2	no	—
143	C₁₃×#121	—	2	2	no	—
144	C₁₃×#121	—	2	2	no	—
145	C₁₃×#121	—	2	4	no	—
146	C₁₃×#121	—	2	2	no	—
147	C₁₃×#121	—	2	1	no	—
148	C₁₃×#121	—	2	1	no	—
149	C₁₃×#121	—	2	2	no	—
150	C₁₃×#121	C₂³	1	2	yes	—
151	C₁₃×#121	C₂³	1	4	yes	—
152	C₁₃×#121	C₂³	1	2	yes	—
153	C₁₃×#121	C₂³	1	2	yes	—
154	C₄×Q₈×C₁₃	—	2	1	no	—
155	C₄×Q₈×C₁₃	—	2	1	no	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	—	2	1	no	—
158	C₄×Q₈×C₁₃	—	2	2	no	—
159	C₄×Q₈×C₁₃	—	2	2	no	—
160	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
162	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
164	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₁₃	—	2	2	no	—
168	C₄×D₄×C₁₃	—	2	2	no	—
169	C₄×D₄×C₁₃	—	2	2	no	—
170	C₄×D₄×C₁₃	—	2	1	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	4	no	—
175	C₄×D₄×C₁₃	—	2	2	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
179	C₄×D₄×C₁₃	D₄	1	2	yes	—
180	C₄×D₄×C₁₃	C₂³	1	2	yes	—
181	C₄×D₄×C₁₃	C₂³	1	4	yes	—
182	C₄×D₄×C₁₃	C₂³	1	2	yes	—
183	C₄×D₄×C₁₃	C₂³	1	2	yes	—
184	C₄×D₄×C₁₃	C₂³	1	2	yes	—
185	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
186	C₁₃×#117	—	2	2	no	—
187	C₁₃×#117	—	2	2	no	—
188	C₁₃×#117	—	2	2	no	—
189	C₁₃×#117	D₄	1	1	yes	characteristic
190	C₁₃×#117	D₄	1	2	yes	—
191	C₁₃×#117	C₂³	1	4	yes	—
192	C₁₃×#117	C₂³	1	2	yes	—
193	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₁₃	—	2	1	no	—
199	C₂×C₄²×C₁₃	—	2	2	no	—
200	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
202	C₁₃×#107	C₂³	1	4	yes	—
203	C₁₃×#107	C₂³	1	4	yes	—
204	C₁₃×#107	C₂³	1	4	yes	—
205	C₁₃×#106	C₂³	1	2	yes	—
206	C₁₃×#106	C₂³	1	4	yes	—
207	C₁₃×#106	C₂³	1	2	yes	—
208	C₁₃×#106	C₂³	1	4	yes	—
209	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
210	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
211	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₁₃×#103	C₂³	1	4	yes	—
215	C₁₃×#103	C₂³	1	4	yes	—
216	C₁₃×#103	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	2	yes	—
218	C₁₃×#102	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	2	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	2	yes	—
224	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
225	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₄×C₈×C₁₃	C₂³	1	4	yes	—
227	C₄×C₈×C₁₃	C₂³	1	2	yes	—
228	#62102	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₁₃×#41	—	2	4	no	—
230	C₁₃×#41	—	2	4	no	—
231	C₁₃×#41	—	4	2	no	—
232	C₁₃×#41	—	4	4	no	—
233	C₁₃×#41	—	4	4	no	—
234	C₁₃×#41	—	8	4	no	—
235	C₂×Q₈×C₁₃	—	2	1	no	—
236	C₂×Q₈×C₁₃	—	2	1	no	—
237	C₂×Q₈×C₁₃	—	2	1	no	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×Q₈×C₁₃	—	4	1	no	—
242	C₂×Q₈×C₁₃	—	8	2	no	—
243	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	4	no	—
251	C₂×D₄×C₁₃	—	2	1	no	—
252	C₂×D₄×C₁₃	—	2	1	no	—
253	C₂×D₄×C₁₃	—	2	1	no	—
254	C₂×D₄×C₁₃	—	2	1	no	—
255	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
256	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
257	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃	—	2	1	no	—
260	C₂²×C₄×C₁₃	—	2	1	no	—
261	C₂²×C₄×C₁₃	—	2	2	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	—	2	2	no	—
264	C₂²×C₄×C₁₃	—	2	2	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	4	no	—
267	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
273	C₁₃×SD₁₆	—	2	4	no	—
274	C₁₃×SD₁₆	—	4	2	no	—
275	C₁₃×D₈	—	4	4	no	—
276	C₂×C₈×C₁₃	—	4	2	no	—
277	C₂×C₈×C₁₃	—	4	4	no	—
278	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
279	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
280	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	2	1	no	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	4	no	—
285	C₁₃×C₄⋊C₄	—	2	1	no	—
286	C₁₃×C₄⋊C₄	—	2	1	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	—	2	1	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	1	no	—
294	C₁₃×C₄⋊C₄	—	2	1	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	4	no	—
297	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
298	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
299	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
300	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
301	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
305	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
306	C₁₃×C₂²⋊C₄	—	2	2	no	—
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	—	2	2	no	—
309	C₁₃×C₂²⋊C₄	—	2	2	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	2	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	4	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
320	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
321	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
322	C₄²×C₁₃	—	2	1	no	—
323	C₄²×C₁₃	—	2	1	no	—
324	C₄²×C₁₃	—	2	2	no	—
325	C₄²×C₁₃	—	2	2	no	—
326	C₄²×C₁₃	—	2	1	no	—
327	C₄²×C₁₃	—	2	1	no	—
328	C₄²×C₁₃	—	2	4	no	—
329	C₄²×C₁₃	C₂×D₄	1	2	yes	—
330	C₄²×C₁₃	C₂×D₄	1	2	yes	—
331	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₁₃	C₂⁴	1	2	yes	—
334	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
335	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
336	#3511	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#3480	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#3381	C₂×C₁₃	1	2	yes	complemented
339	#3361	C₂×C₁₃	1	2	yes	complemented
340	#3340	C₂×C₁₃	1	2	yes	complemented
341	#3339	C₂×C₁₃	1	4	yes	complemented
342	#3305	C₂×C₁₃	1	2	yes	complemented
343	#3301	C₂×C₁₃	1	4	yes	complemented
344	#3247	C₂×C₁₃	1	2	yes	complemented
345	#3245	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#3233	C₂×C₁₃	1	2	yes	complemented
347	#3227	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3106	C₂×C₁₃	1	2	yes	complemented
349	#3103	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#3076	C₂×C₁₃	1	2	yes	complemented
351	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#2988	C₂×C₁₃	1	1	yes	characteristic, complemented
353	C₂³×C₁₃	—	2	2	no	—
354	C₂³×C₁₃	—	2	2	no	—
355	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
356	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
357	Q₈×C₁₃	—	2	2	no	—
358	Q₈×C₁₃	—	2	1	no	—
359	Q₈×C₁₃	—	2	1	no	—
360	Q₈×C₁₃	—	2	1	no	—
361	Q₈×C₁₃	—	4	2	no	—
362	Q₈×C₁₃	—	4	4	no	—
363	Q₈×C₁₃	—	4	2	no	—
364	Q₈×C₁₃	—	4	2	no	—
365	Q₈×C₁₃	—	8	2	no	—
366	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
367	D₄×C₁₃	—	2	4	no	—
368	D₄×C₁₃	—	2	2	no	—
369	D₄×C₁₃	—	2	2	no	—
370	D₄×C₁₃	—	2	2	no	—
371	D₄×C₁₃	—	2	2	no	—
372	D₄×C₁₃	—	2	2	no	—
373	D₄×C₁₃	—	4	4	no	—
374	D₄×C₁₃	—	4	2	no	—
375	D₄×C₁₃	—	4	4	no	—
376	D₄×C₁₃	—	4	4	no	—
377	D₄×C₁₃	—	4	2	no	—
378	D₄×C₁₃	—	4	2	no	—
379	D₄×C₁₃	—	8	1	no	—
380	D₄×C₁₃	—	8	2	no	—
381	D₄×C₁₃	—	8	4	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	2	4	no	—
384	C₂×C₄×C₁₃	—	2	1	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	2	1	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	1	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	1	no	—
393	C₂×C₄×C₁₃	—	2	4	no	—
394	C₂×C₄×C₁₃	—	4	1	no	—
395	C₂×C₄×C₁₃	—	4	2	no	—
396	C₂×C₄×C₁₃	—	4	4	no	—
397	C₂×C₄×C₁₃	—	4	2	no	—
398	C₂×C₄×C₁₃	—	4	4	no	—
399	C₂×C₄×C₁₃	—	4	4	no	—
400	C₂×C₄×C₁₃	—	8	2	no	—
401	C₂×C₄×C₁₃	—	8	4	no	—
402	C₂×C₄×C₁₃	—	8	1	no	—
403	C₂×C₄×C₁₃	—	8	2	no	—
404	C₂×C₄×C₁₃	#135	1	4	yes	—
405	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
407	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
410	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
414	C₈×C₁₃	—	2	2	no	—
415	C₈×C₁₃	—	2	4	no	—
416	C₈×C₁₃	—	2	2	no	—
417	#559	—	2	1	no	—
418	#559	C₂²×C₁₃	1	1	yes	characteristic
419	#557	C₂²×C₁₃	1	1	yes	characteristic
420	#556	—	2	1	no	—
421	#556	—	2	1	no	—
422	#556	C₂²×C₁₃	1	1	yes	characteristic
423	#555	C₂²×C₁₃	1	2	yes	—
424	#554	C₂²×C₁₃	1	2	yes	—
425	#553	—	2	2	no	—
426	#553	C₂²×C₁₃	1	2	yes	—
427	#553	C₂²×C₁₃	1	4	yes	—
428	#550	C₂²×C₁₃	1	1	yes	characteristic
429	#548	—	2	2	no	—
430	#548	C₂²×C₁₃	1	2	yes	—
431	#547	—	2	1	no	—
432	#542	—	2	2	no	—
433	#537	—	2	1	no	—
434	#533	C₂²×C₁₃	1	2	yes	—
435	#532	—	2	1	no	—
436	#532	C₂²×C₁₃	1	1	yes	characteristic
437	#532	C₂²×C₁₃	1	2	yes	—
438	#532	C₂²×C₁₃	1	1	yes	characteristic
439	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
440	#529	—	2	2	no	—
441	#529	C₂²×C₁₃	1	2	yes	—
442	#520	—	2	1	no	—
443	C₄×#41	—	2	1	no	—
444	C₄×#41	C₂²×C₁₃	1	2	yes	—
445	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
447	#499	C₂²×C₁₃	1	4	yes	—
448	#498	C₂²×C₁₃	1	2	yes	—
449	#488	C₂²×C₁₃	1	4	yes	—
450	#486	C₂²×C₁₃	1	2	yes	—
451	#485	C₂²×C₁₃	1	4	yes	—
452	#482	C₂²×C₁₃	1	4	yes	—
453	#482	C₂²×C₁₃	1	4	yes	—
454	#481	C₂²×C₁₃	1	2	yes	—
455	#481	C₂²×C₁₃	1	4	yes	—
456	#479	C₂²×C₁₃	1	4	yes	—
457	#478	C₂²×C₁₃	1	4	yes	—
458	#478	C₂²×C₁₃	1	4	yes	—
459	#477	C₂²×C₁₃	1	2	yes	—
460	#477	C₂²×C₁₃	1	2	yes	—
461	#477	C₂²×C₁₃	1	2	yes	—
462	#477	C₂²×C₁₃	1	2	yes	—
463	#476	C₂²×C₁₃	1	2	yes	—
464	#476	C₂²×C₁₃	1	2	yes	—
465	#475	C₂²×C₁₃	1	1	yes	characteristic
466	#475	C₂²×C₁₃	1	1	yes	characteristic
467	#474	C₂²×C₁₃	1	2	yes	—
468	#474	C₂²×C₁₃	1	2	yes	—
469	#466	C₂²×C₁₃	1	4	yes	—
470	#466	C₂²×C₁₃	1	4	yes	—
471	#465	C₂²×C₁₃	1	4	yes	—
472	#463	C₂²×C₁₃	1	4	yes	—
473	#460	C₂²×C₁₃	1	1	yes	characteristic
474	#460	C₂²×C₁₃	1	1	yes	characteristic
475	#459	C₂²×C₁₃	1	2	yes	—
476	#459	C₂²×C₁₃	1	2	yes	—
477	#449	C₂²×C₁₃	1	4	yes	—
478	#448	C₂²×C₁₃	1	2	yes	—
479	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
480	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
481	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
482	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
483	C₄×D₈	C₂²×C₁₃	1	4	yes	—
484	C₈×D₄	C₂²×C₁₃	1	4	yes	—
485	C₈×D₄	C₂²×C₁₃	1	2	yes	—
486	#431	C₂²×C₁₃	1	1	yes	characteristic
487	#431	C₂²×C₁₃	1	2	yes	—
488	#427	C₂²×C₁₃	1	4	yes	—
489	C₂×#107	C₂²×C₁₃	1	2	yes	—
490	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
491	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
492	#416	C₂²×C₁₃	1	4	yes	—
493	C₂×#103	C₂²×C₁₃	1	2	yes	—
494	C₂²×C₁₃	—	2	1	no	—
495	C₂²×C₁₃	—	2	1	no	—
496	C₂²×C₁₃	—	2	2	no	—
497	C₂²×C₁₃	—	2	2	no	—
498	C₂²×C₁₃	—	2	2	no	—
499	C₂²×C₁₃	—	4	2	no	—
500	C₂²×C₁₃	—	4	2	no	—
501	C₂²×C₁₃	—	4	2	no	—
502	C₂²×C₁₃	—	4	2	no	—
503	C₂²×C₁₃	—	4	2	no	—
504	C₂²×C₁₃	—	4	2	no	—
505	C₂²×C₁₃	C₂×#135	1	2	yes	—
506	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
507	C₄×C₁₃	—	2	1	no	—
508	C₄×C₁₃	—	2	2	no	—
509	C₄×C₁₃	—	2	1	no	—
510	C₄×C₁₃	—	2	2	no	—
511	C₄×C₁₃	—	2	1	no	—
512	C₄×C₁₃	—	2	2	no	—
513	C₄×C₁₃	—	2	2	no	—
514	C₄×C₁₃	—	4	1	no	—
515	C₄×C₁₃	—	4	4	no	—
516	C₄×C₁₃	—	4	1	no	—
517	C₄×C₁₃	—	4	1	no	—
518	C₄×C₁₃	—	4	2	no	—
519	C₄×C₁₃	—	4	2	no	—
520	C₄×C₁₃	C₂×#135	1	2	yes	—
521	C₄×C₁₃	C₂×#135	1	2	yes	—
522	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
523	C₄×C₁₃	#585	1	1	yes	characteristic
524	C₂×#41	—	2	1	no	—
525	C₂×#41	—	2	1	no	—
526	C₂×#41	—	2	2	no	—
527	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
528	C₂×#41	C₂³×C₁₃	1	2	yes	—
529	C₂²×Q₈	—	2	1	no	—
530	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
531	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
532	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
533	C₂×D₈	C₂³×C₁₃	1	4	yes	—
534	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
535	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
536	C₄⋊Q₈	—	2	1	no	—
537	C₄⋊Q₈	—	2	1	no	—
538	C₄⋊Q₈	—	2	1	no	—
539	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
540	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
541	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
542	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
543	#127	—	2	1	no	—
544	#127	C₂³×C₁₃	1	1	yes	characteristic
545	#127	C₂³×C₁₃	1	1	yes	characteristic
546	#126	—	2	2	no	—
547	#126	—	2	4	no	—
548	#126	—	2	2	no	—
549	#126	—	2	2	no	—
550	#125	—	2	2	no	—
551	#125	C₂³×C₁₃	1	2	yes	—
552	#125	C₂³×C₁₃	1	4	yes	—
553	#124	—	2	1	no	—
554	#124	—	2	1	no	—
555	#124	—	2	2	no	—
556	#124	—	2	4	no	—
557	#124	—	2	1	no	—
558	#124	—	2	2	no	—
559	#124	—	2	1	no	—
560	#124	C₂³×C₁₃	1	2	yes	—
561	#123	—	2	2	no	—
562	#123	—	2	2	no	—
563	#123	—	2	2	no	—
564	#123	—	2	4	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
571	#121	—	2	2	no	—
572	#121	—	2	2	no	—
573	#121	—	2	2	no	—
574	#121	—	2	4	no	—
575	#121	—	2	2	no	—
576	#121	—	2	1	no	—
577	#121	—	2	1	no	—
578	#121	—	2	2	no	—
579	#121	C₂³×C₁₃	1	2	yes	—
580	#121	C₂³×C₁₃	1	2	yes	—
581	#121	C₂³×C₁₃	1	2	yes	—
582	#121	C₂³×C₁₃	1	4	yes	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	—	2	1	no	—
585	C₄×Q₈	—	2	1	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	2	no	—
588	C₄×Q₈	—	2	2	no	—
589	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
590	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
591	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
593	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
594	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
595	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	1	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	4	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
608	C₄×D₄	D₄×C₁₃	1	2	yes	—
609	C₄×D₄	C₂³×C₁₃	1	2	yes	—
610	C₄×D₄	C₂³×C₁₃	1	2	yes	—
611	C₄×D₄	C₂³×C₁₃	1	4	yes	—
612	C₄×D₄	C₂³×C₁₃	1	2	yes	—
613	C₄×D₄	C₂³×C₁₃	1	2	yes	—
614	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
615	#117	—	2	2	no	—
616	#117	—	2	2	no	—
617	#117	—	2	2	no	—
618	#117	D₄×C₁₃	1	1	yes	characteristic
619	#117	D₄×C₁₃	1	2	yes	—
620	#117	C₂³×C₁₃	1	2	yes	—
621	#117	C₂³×C₁₃	1	4	yes	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	—	2	2	no	—
625	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
627	C₂×C₄²	—	2	1	no	—
628	C₂×C₄²	—	2	2	no	—
629	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
631	#107	C₂³×C₁₃	1	4	yes	—
632	#107	C₂³×C₁₃	1	4	yes	—
633	#107	C₂³×C₁₃	1	4	yes	—
634	#106	C₂³×C₁₃	1	2	yes	—
635	#106	C₂³×C₁₃	1	4	yes	—
636	#106	C₂³×C₁₃	1	2	yes	—
637	#106	C₂³×C₁₃	1	4	yes	—
638	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
639	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
640	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
641	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
642	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
643	#103	C₂³×C₁₃	1	4	yes	—
644	#103	C₂³×C₁₃	1	4	yes	—
645	#103	C₂³×C₁₃	1	2	yes	—
646	#103	C₂³×C₁₃	1	2	yes	—
647	#102	C₂³×C₁₃	1	4	yes	—
648	#102	C₂³×C₁₃	1	4	yes	—
649	#102	C₂³×C₁₃	1	2	yes	—
650	#102	C₂³×C₁₃	1	4	yes	—
651	#102	C₂³×C₁₃	1	4	yes	—
652	#102	C₂³×C₁₃	1	2	yes	—
653	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
654	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
655	C₄×C₈	C₂³×C₁₃	1	4	yes	—
656	C₄×C₈	C₂³×C₁₃	1	2	yes	—
657	C₂×C₁₃	—	2	2	no	—
658	C₂×C₁₃	—	4	2	no	—
659	C₂×C₁₃	—	8	2	no	—
660	C₂×C₁₃	—	8	2	no	—
661	C₂×C₁₃	#3489	1	1	yes	characteristic
662	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
663	C₂×C₁₃	#3585	1	1	yes	characteristic
664	#41	—	2	4	no	—
665	#41	—	2	4	no	—
666	#41	—	4	2	no	—
667	#41	—	4	4	no	—
668	#41	—	4	4	no	—
669	#41	—	8	4	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	4	1	no	—
677	C₂×Q₈	—	8	2	no	—
678	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
679	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
680	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
691	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
692	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
693	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	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	C₂×D₄×C₁₃	1	2	yes	—
703	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
704	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
705	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
708	SD₁₆	—	2	4	no	—
709	SD₁₆	—	4	2	no	—
710	D₈	—	4	4	no	—
711	C₂×C₈	—	4	2	no	—
712	C₂×C₈	—	4	4	no	—
713	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
714	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
715	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
733	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
734	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
735	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
736	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
737	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
739	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
740	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
755	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
756	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
757	C₄²	—	2	1	no	—
758	C₄²	—	2	1	no	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	1	no	—
762	C₄²	—	2	1	no	—
763	C₄²	—	2	4	no	—
764	C₄²	C₂×D₄×C₁₃	1	2	yes	—
765	C₄²	C₂×D₄×C₁₃	1	2	yes	—
766	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
767	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
768	C₄²	C₂⁴×C₁₃	1	2	yes	—
769	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
770	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
771	C₁₃	#62102	1	1	yes	characteristic, direct product factor, Sylow
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
775	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
776	Q₈	—	2	2	no	—
777	Q₈	—	2	1	no	—
778	Q₈	—	2	1	no	—
779	Q₈	—	2	1	no	—
780	Q₈	—	4	2	no	—
781	Q₈	—	4	4	no	—
782	Q₈	—	4	2	no	—
783	Q₈	—	4	2	no	—
784	Q₈	—	8	2	no	—
785	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
786	D₄	—	2	4	no	—
787	D₄	—	2	2	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	2	no	—
790	D₄	—	2	2	no	—
791	D₄	—	2	2	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	2	no	—
794	D₄	—	4	4	no	—
795	D₄	—	4	4	no	—
796	D₄	—	4	2	no	—
797	D₄	—	4	2	no	—
798	D₄	—	8	1	no	—
799	D₄	—	8	2	no	—
800	D₄	—	8	4	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	8	2	no	—
820	C₂×C₄	—	8	4	no	—
821	C₂×C₄	—	8	1	no	—
822	C₂×C₄	—	8	2	no	—
823	C₂×C₄	C₁₃×#135	1	4	yes	—
824	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
825	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
826	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
829	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
831	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
832	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
833	C₈	—	2	2	no	—
834	C₈	—	2	4	no	—
835	C₈	—	2	2	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	C₂×C₁₃×#135	1	2	yes	—
848	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
849	C₄	—	2	2	no	—
850	C₄	—	2	1	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	4	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	C₂×C₁₃×#135	1	2	yes	—
863	C₄	C₂×C₁₃×#135	1	2	yes	—
864	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
865	C₄	C₁₃×#585	1	1	yes	characteristic
866	C₂	—	2	2	no	—
867	C₂	—	4	2	no	—
868	C₂	—	8	2	no	—
869	C₂	—	8	2	no	—
870	C₂	C₁₃×#3489	1	1	yes	characteristic
871	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
872	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×#3511	C₂	semidirect
2. C₁₃×#3480	C₂	semidirect
3. C₁₃×#3381	C₂	semidirect
4. C₁₃×#3361	C₂	semidirect
5. C₁₃×#3340	C₂	semidirect
6. C₁₃×#3339	C₂	semidirect
7. C₁₃×#3305	C₂	semidirect
8. C₁₃×#3301	C₂	semidirect
9. C₁₃×#3247	C₂	semidirect
10. C₁₃×#3245	C₂	semidirect
11. C₁₃×#3233	C₂	semidirect
12. C₁₃×#3227	C₂	semidirect
13. C₁₃×#3106	C₂	semidirect
14. C₁₃×#3103	C₂	semidirect
15. C₁₃×#3076	C₂	semidirect
16. C₂×C₁₃×#477	C₂	semidirect
17. C₁₃×#2988	C₂	semidirect
228. #62102	C₁₃	direct (N × H)
336. #3511	C₂×C₁₃	semidirect
337. #3480	C₂×C₁₃	semidirect
338. #3381	C₂×C₁₃	semidirect
339. #3361	C₂×C₁₃	semidirect
340. #3340	C₂×C₁₃	semidirect
341. #3339	C₂×C₁₃	semidirect
342. #3305	C₂×C₁₃	semidirect
343. #3301	C₂×C₁₃	semidirect
344. #3247	C₂×C₁₃	semidirect
345. #3245	C₂×C₁₃	semidirect
346. #3233	C₂×C₁₃	semidirect
347. #3227	C₂×C₁₃	semidirect
348. #3106	C₂×C₁₃	semidirect
349. #3103	C₂×C₁₃	semidirect
350. #3076	C₂×C₁₃	semidirect
351. C₂×#477	C₂×C₁₃	semidirect
352. #2988	C₂×C₁₃	semidirect
771. C₁₃	#62102	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×#3480	2
C₁₃×#3381	2
C₁₃×#3361	2
C₁₃×#3340	2
C₁₃×#3339	2
C₁₃×#3305	2
C₁₃×#3301	2
C₁₃×#3247	2
C₁₃×#3245	2
C₁₃×#3233	2
C₁₃×#3227	2
C₁₃×#3106	2
C₁₃×#3103	2
C₁₃×#3076	2
C₂×C₁₃×#477	2
C₁₃×#2988	2
#62102	13

Subgroups — C13×#62102 #15748441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62102 #15748441