Subgroups — C₁₃×#61871 #15748210

Order 3328.

1700 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3387	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3384	C₂	1	2	yes	maximal, complemented
5	Q₈×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
6	Q₈×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3373	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3369	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3365	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3360	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3244	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3125	C₂	1	4	yes	maximal, complemented
15	C₁₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic
17	C₁₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#563	—	2	2	no	—
19	C₁₃×#559	C₂²	1	2	yes	—
20	Q₈²×C₁₃	C₂²	1	2	yes	—
21	Q₈²×C₁₃	C₂²	1	2	yes	—
22	C₁₃×#557	C₂²	1	2	yes	—
23	C₁₃×#556	—	2	1	no	—
24	C₁₃×#556	C₂²	1	2	yes	—
25	C₁₃×#554	—	2	2	no	—
26	C₁₃×#554	C₂²	1	2	yes	—
27	D₄×Q₈×C₁₃	—	2	1	no	—
28	D₄×Q₈×C₁₃	—	2	2	no	—
29	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
30	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
31	C₁₃×#544	—	2	2	no	—
32	C₁₃×#544	C₂²	1	2	yes	—
33	C₁₃×#542	—	2	2	no	—
34	C₁₃×#542	C₂²	1	4	yes	—
35	C₁₃×#536	—	2	2	no	—
36	C₁₃×#533	—	2	1	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#533	C₂²	1	1	yes	characteristic
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
42	C₁₃×#520	C₂²	1	2	yes	—
43	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
44	C₁₃×#501	C₂²	1	4	yes	—
45	C₁₃×#498	C₂²	1	4	yes	—
46	C₁₃×#498	C₂²	1	2	yes	—
47	C₁₃×#498	C₂²	1	2	yes	—
48	C₁₃×#489	C₂²	1	4	yes	—
49	C₁₃×#488	C₂²	1	4	yes	—
50	C₁₃×#487	C₂²	1	2	yes	—
51	C₁₃×#486	C₂²	1	2	yes	—
52	C₁₃×#485	C₂²	1	2	yes	—
53	C₁₃×#483	C₂²	1	4	yes	—
54	C₁₃×#482	C₂²	1	2	yes	—
55	C₁₃×#481	C₂²	1	4	yes	—
56	C₁₃×#479	C₂²	1	4	yes	—
57	C₁₃×#478	C₂²	1	4	yes	—
58	C₁₃×#477	C₂²	1	1	yes	characteristic
59	C₁₃×#476	C₂²	1	2	yes	—
60	C₁₃×#476	C₂²	1	1	yes	characteristic
61	C₁₃×#476	C₂²	1	2	yes	—
62	C₁₃×#476	C₂²	1	4	yes	—
63	C₁₃×#476	C₂²	1	4	yes	—
64	C₁₃×#475	C₂²	1	1	yes	characteristic
65	C₁₃×#475	C₂²	1	2	yes	—
66	C₁₃×#475	C₂²	1	4	yes	—
67	C₁₃×#475	C₂²	1	2	yes	—
68	C₁₃×#475	C₂²	1	4	yes	—
69	C₁₃×#474	C₂²	1	1	yes	characteristic
70	C₁₃×#464	C₂²	1	4	yes	—
71	C₁₃×#463	C₂²	1	4	yes	—
72	C₁₃×#462	C₂²	1	1	yes	characteristic
73	C₁₃×#461	C₂²	1	1	yes	characteristic
74	C₁₃×#460	C₂²	1	1	yes	characteristic
75	C₁₃×#459	C₂²	1	1	yes	characteristic
76	C₁₃×#452	C₂²	1	2	yes	—
77	C₁₃×#449	C₂²	1	2	yes	—
78	C₁₃×#446	C₂²	1	2	yes	—
79	C₁₃×#446	C₂²	1	2	yes	—
80	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
81	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
82	C₁₃×#442	C₂²	1	4	yes	—
83	C₁₃×#441	C₂²	1	4	yes	—
84	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
85	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
86	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
87	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
88	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
89	C₄×C₁₃×D₈	C₂²	1	2	yes	—
90	C₁₃×#433	C₂²	1	4	yes	—
91	C₁₃×#431	C₂²	1	1	yes	characteristic
92	C₁₃×#431	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×#41	—	2	1	no	—
94	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₁₃	—	2	2	no	—
96	C₂²×Q₈×C₁₃	—	2	2	no	—
97	C₂²×Q₈×C₁₃	—	2	1	no	—
98	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
99	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
100	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
101	C₂×C₁₃×D₈	C₂³	1	2	yes	—
102	C₁₃×C₄⋊Q₈	—	2	2	no	—
103	C₁₃×C₄⋊Q₈	—	2	2	no	—
104	C₁₃×C₄⋊Q₈	—	2	2	no	—
105	C₁₃×C₄⋊Q₈	—	2	4	no	—
106	C₁₃×C₄⋊Q₈	—	2	2	no	—
107	C₁₃×C₄⋊Q₈	—	2	4	no	—
108	C₁₃×C₄⋊Q₈	—	2	1	no	—
109	C₁₃×C₄⋊Q₈	—	2	1	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	2	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₃×#127	C₂³	1	1	yes	characteristic
120	C₁₃×#126	—	2	4	no	—
121	C₁₃×#126	—	2	4	no	—
122	C₁₃×#125	—	2	2	no	—
123	C₁₃×#125	—	2	4	no	—
124	C₁₃×#125	—	2	1	no	—
125	C₁₃×#125	D₄	1	2	yes	—
126	C₁₃×#125	C₂³	1	4	yes	—
127	C₁₃×#124	—	2	2	no	—
128	C₁₃×#124	—	2	4	no	—
129	C₁₃×#124	—	2	1	no	—
130	C₁₃×#124	C₂³	1	4	yes	—
131	C₁₃×#123	—	2	4	no	—
132	C₁₃×#123	—	2	4	no	—
133	C₁₃×C₂²⋊Q₈	—	2	2	no	—
134	C₁₃×C₂²⋊Q₈	—	2	2	no	—
135	C₁₃×C₂²⋊Q₈	—	2	1	no	—
136	C₁₃×C₂²⋊Q₈	—	2	2	no	—
137	C₁₃×C₂²⋊Q₈	—	2	2	no	—
138	C₁₃×C₂²⋊Q₈	—	2	4	no	—
139	C₁₃×C₂²⋊Q₈	—	2	4	no	—
140	C₁₃×C₂²⋊Q₈	—	2	4	no	—
141	C₁₃×C₂²⋊Q₈	—	2	4	no	—
142	C₁₃×C₂²⋊Q₈	—	2	4	no	—
143	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
144	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₁₃×#121	—	2	1	no	—
147	C₁₃×#121	C₂³	1	2	yes	—
148	C₄×Q₈×C₁₃	—	2	2	no	—
149	C₄×Q₈×C₁₃	—	2	2	no	—
150	C₄×Q₈×C₁₃	—	2	2	no	—
151	C₄×Q₈×C₁₃	—	2	1	no	—
152	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
153	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
154	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
156	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
157	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
158	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
159	C₄×D₄×C₁₃	—	2	1	no	—
160	C₄×D₄×C₁₃	—	2	1	no	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	—	2	4	no	—
163	C₄×D₄×C₁₃	—	2	1	no	—
164	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
165	C₄×D₄×C₁₃	C₂³	1	2	yes	—
166	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₁₃	C₂³	1	4	yes	—
168	C₄×D₄×C₁₃	C₂³	1	4	yes	—
169	C₁₃×#117	—	2	1	no	—
170	C₁₃×#117	—	2	2	no	—
171	C₁₃×#117	—	2	2	no	—
172	C₁₃×#117	—	2	1	no	—
173	C₁₃×#117	C₂³	1	1	yes	characteristic
174	C₁₃×#117	C₂³	1	2	yes	—
175	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₃	—	2	1	no	—
180	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
181	C₁₃×#107	C₂³	1	2	yes	—
182	C₁₃×#107	C₂³	1	2	yes	—
183	C₁₃×#106	C₂³	1	2	yes	—
184	C₁₃×#106	C₂³	1	2	yes	—
185	C₁₃×#106	C₂³	1	4	yes	—
186	C₁₃×#106	C₂³	1	4	yes	—
187	C₁₃×#106	C₂³	1	4	yes	—
188	C₁₃×#106	C₂³	1	4	yes	—
189	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
190	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
191	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
192	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
194	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
195	C₁₃×#103	C₂³	1	2	yes	—
196	C₁₃×#103	C₂³	1	2	yes	—
197	C₁₃×#103	C₂³	1	2	yes	—
198	C₁₃×#103	C₂³	1	4	yes	—
199	C₁₃×#103	C₂³	1	2	yes	—
200	C₁₃×#103	C₂³	1	4	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	2	yes	—
205	C₁₃×#102	C₂³	1	4	yes	—
206	C₁₃×#102	C₂³	1	4	yes	—
207	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
209	C₁₃×#97	C₂³	1	4	yes	—
210	C₄×C₈×C₁₃	C₂³	1	2	yes	—
211	C₄×C₈×C₁₃	C₂³	1	2	yes	—
212	C₄×C₈×C₁₃	C₂³	1	4	yes	—
213	#61871	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₁₃×#41	—	2	2	no	—
215	C₁₃×#41	—	2	2	no	—
216	C₁₃×#41	—	8	2	no	—
217	C₂×Q₈×C₁₃	—	2	1	no	—
218	C₂×Q₈×C₁₃	—	2	2	no	—
219	C₂×Q₈×C₁₃	—	2	4	no	—
220	C₂×Q₈×C₁₃	—	2	4	no	—
221	C₂×Q₈×C₁₃	—	2	2	no	—
222	C₂×Q₈×C₁₃	—	2	1	no	—
223	C₂×Q₈×C₁₃	—	8	2	no	—
224	C₂×Q₈×C₁₃	—	8	4	no	—
225	C₂×Q₈×C₁₃	—	8	4	no	—
226	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
229	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	2	2	no	—
232	C₂×D₄×C₁₃	—	2	1	no	—
233	C₂×D₄×C₁₃	—	2	1	no	—
234	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
235	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₁₃	—	2	1	no	—
237	C₂²×C₄×C₁₃	—	2	2	no	—
238	C₂²×C₄×C₁₃	—	2	1	no	—
239	C₂²×C₄×C₁₃	—	2	1	no	—
240	C₂²×C₄×C₁₃	—	2	2	no	—
241	C₂²×C₄×C₁₃	—	2	4	no	—
242	C₂²×C₄×C₁₃	—	2	4	no	—
243	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₁₃×Q₁₆	—	2	4	no	—
247	C₁₃×SD₁₆	—	2	4	no	—
248	C₁₃×SD₁₆	—	2	4	no	—
249	C₁₃×D₈	—	2	4	no	—
250	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
251	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
252	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
253	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
254	C₁₃×C₄⋊C₄	—	2	2	no	—
255	C₁₃×C₄⋊C₄	—	2	2	no	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	—	2	2	no	—
258	C₁₃×C₄⋊C₄	—	2	4	no	—
259	C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₁₃×C₄⋊C₄	—	2	1	no	—
261	C₁₃×C₄⋊C₄	—	2	1	no	—
262	C₁₃×C₄⋊C₄	—	2	1	no	—
263	C₁₃×C₄⋊C₄	—	2	1	no	—
264	C₁₃×C₄⋊C₄	—	2	1	no	—
265	C₁₃×C₄⋊C₄	—	2	4	no	—
266	C₁₃×C₄⋊C₄	—	2	4	no	—
267	C₁₃×C₄⋊C₄	—	2	2	no	—
268	C₁₃×C₄⋊C₄	—	2	4	no	—
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	2	2	no	—
271	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
272	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
273	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
274	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
275	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
276	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
277	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
278	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
279	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
280	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
282	C₁₃×C₂²⋊C₄	—	2	2	no	—
283	C₁₃×C₂²⋊C₄	—	2	1	no	—
284	C₁₃×C₂²⋊C₄	—	2	1	no	—
285	C₁₃×C₂²⋊C₄	—	2	1	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	2	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	2	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
293	C₄²×C₁₃	—	2	1	no	—
294	C₄²×C₁₃	—	2	1	no	—
295	C₄²×C₁₃	—	2	1	no	—
296	C₄²×C₁₃	—	2	2	no	—
297	C₄²×C₁₃	—	2	4	no	—
298	C₄²×C₁₃	—	2	4	no	—
299	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
302	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
303	C₄²×C₁₃	C₂⁴	1	4	yes	—
304	#3550	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
306	#3387	C₂×C₁₃	1	2	yes	complemented
307	#3384	C₂×C₁₃	1	2	yes	complemented
308	Q₈×SD₁₆	C₂×C₁₃	1	2	yes	complemented
309	Q₈×SD₁₆	C₂×C₁₃	1	2	yes	complemented
310	#3373	C₂×C₁₃	1	2	yes	complemented
311	#3369	C₂×C₁₃	1	2	yes	complemented
312	#3365	C₂×C₁₃	1	2	yes	complemented
313	#3360	C₂×C₁₃	1	2	yes	complemented
314	#3244	C₂×C₁₃	1	4	yes	complemented
315	#3229	C₂×C₁₃	1	1	yes	characteristic, complemented
316	#3227	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#3125	C₂×C₁₃	1	4	yes	complemented
318	#3107	C₂×C₁₃	1	1	yes	characteristic, complemented
319	#3106	C₂×C₁₃	1	1	yes	characteristic
320	#2986	C₂×C₁₃	1	1	yes	characteristic, complemented
321	C₂³×C₁₃	—	2	1	no	—
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
324	Q₈×C₁₃	—	2	4	no	—
325	Q₈×C₁₃	—	2	4	no	—
326	Q₈×C₁₃	—	2	1	no	—
327	Q₈×C₁₃	—	2	2	no	—
328	Q₈×C₁₃	—	2	2	no	—
329	Q₈×C₁₃	—	4	2	no	—
330	Q₈×C₁₃	—	4	4	no	—
331	Q₈×C₁₃	—	8	2	no	—
332	Q₈×C₁₃	—	8	4	no	—
333	Q₈×C₁₃	—	8	4	no	—
334	Q₈×C₁₃	—	8	1	no	—
335	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
336	D₄×C₁₃	—	2	4	no	—
337	D₄×C₁₃	—	2	1	no	—
338	D₄×C₁₃	—	2	2	no	—
339	D₄×C₁₃	—	2	2	no	—
340	D₄×C₁₃	—	4	2	no	—
341	D₄×C₁₃	—	8	1	no	—
342	D₄×C₁₃	—	8	2	no	—
343	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
344	C₂×C₄×C₁₃	—	2	4	no	—
345	C₂×C₄×C₁₃	—	2	1	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	1	no	—
349	C₂×C₄×C₁₃	—	2	1	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	1	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	1	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	4	no	—
356	C₂×C₄×C₁₃	—	4	2	no	—
357	C₂×C₄×C₁₃	—	4	2	no	—
358	C₂×C₄×C₁₃	—	4	4	no	—
359	C₂×C₄×C₁₃	—	8	4	no	—
360	C₂×C₄×C₁₃	—	8	4	no	—
361	C₂×C₄×C₁₃	—	8	2	no	—
362	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
364	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
365	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
370	C₈×C₁₃	—	2	2	no	—
371	C₈×C₁₃	—	2	2	no	—
372	C₈×C₁₃	—	2	2	no	—
373	C₈×C₁₃	—	2	2	no	—
374	#563	—	2	2	no	—
375	#559	C₂²×C₁₃	1	2	yes	—
376	Q₈²	C₂²×C₁₃	1	2	yes	—
377	Q₈²	C₂²×C₁₃	1	2	yes	—
378	#557	C₂²×C₁₃	1	2	yes	—
379	#556	—	2	1	no	—
380	#556	C₂²×C₁₃	1	2	yes	—
381	#554	—	2	2	no	—
382	#554	C₂²×C₁₃	1	2	yes	—
383	D₄×Q₈	—	2	1	no	—
384	D₄×Q₈	—	2	2	no	—
385	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
386	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
387	#544	—	2	2	no	—
388	#544	C₂²×C₁₃	1	2	yes	—
389	#542	—	2	2	no	—
390	#542	C₂²×C₁₃	1	4	yes	—
391	#536	—	2	2	no	—
392	#533	—	2	1	no	—
393	#533	C₂²×C₁₃	1	1	yes	characteristic
394	#533	C₂²×C₁₃	1	1	yes	characteristic
395	#532	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×C₄⋊Q₈	—	2	1	no	—
397	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
398	#520	C₂²×C₁₃	1	2	yes	—
399	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
400	#501	C₂²×C₁₃	1	4	yes	—
401	#498	C₂²×C₁₃	1	4	yes	—
402	#498	C₂²×C₁₃	1	2	yes	—
403	#498	C₂²×C₁₃	1	2	yes	—
404	#489	C₂²×C₁₃	1	4	yes	—
405	#488	C₂²×C₁₃	1	4	yes	—
406	#487	C₂²×C₁₃	1	2	yes	—
407	#486	C₂²×C₁₃	1	2	yes	—
408	#485	C₂²×C₁₃	1	2	yes	—
409	#483	C₂²×C₁₃	1	4	yes	—
410	#482	C₂²×C₁₃	1	2	yes	—
411	#481	C₂²×C₁₃	1	4	yes	—
412	#479	C₂²×C₁₃	1	4	yes	—
413	#478	C₂²×C₁₃	1	4	yes	—
414	#477	C₂²×C₁₃	1	1	yes	characteristic
415	#476	C₂²×C₁₃	1	2	yes	—
416	#476	C₂²×C₁₃	1	1	yes	characteristic
417	#476	C₂²×C₁₃	1	2	yes	—
418	#476	C₂²×C₁₃	1	4	yes	—
419	#476	C₂²×C₁₃	1	4	yes	—
420	#475	C₂²×C₁₃	1	1	yes	characteristic
421	#475	C₂²×C₁₃	1	2	yes	—
422	#475	C₂²×C₁₃	1	4	yes	—
423	#475	C₂²×C₁₃	1	2	yes	—
424	#475	C₂²×C₁₃	1	4	yes	—
425	#474	C₂²×C₁₃	1	1	yes	characteristic
426	#464	C₂²×C₁₃	1	4	yes	—
427	#463	C₂²×C₁₃	1	4	yes	—
428	#462	C₂²×C₁₃	1	1	yes	characteristic
429	#461	C₂²×C₁₃	1	1	yes	characteristic
430	#460	C₂²×C₁₃	1	1	yes	characteristic
431	#459	C₂²×C₁₃	1	1	yes	characteristic
432	#452	C₂²×C₁₃	1	2	yes	—
433	#449	C₂²×C₁₃	1	2	yes	—
434	#446	C₂²×C₁₃	1	2	yes	—
435	#446	C₂²×C₁₃	1	2	yes	—
436	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
437	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
438	#442	C₂²×C₁₃	1	4	yes	—
439	#441	C₂²×C₁₃	1	4	yes	—
440	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
441	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
442	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
443	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
444	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
445	C₄×D₈	C₂²×C₁₃	1	2	yes	—
446	#433	C₂²×C₁₃	1	4	yes	—
447	#431	C₂²×C₁₃	1	1	yes	characteristic
448	#431	C₂²×C₁₃	1	1	yes	characteristic
449	C₂²×C₁₃	—	2	1	no	—
450	C₂²×C₁₃	—	2	2	no	—
451	C₂²×C₁₃	—	2	1	no	—
452	C₂²×C₁₃	—	2	1	no	—
453	C₂²×C₁₃	—	4	1	no	—
454	C₂²×C₁₃	—	4	1	no	—
455	C₂²×C₁₃	—	4	2	no	—
456	C₂²×C₁₃	—	4	2	no	—
457	C₂²×C₁₃	—	4	2	no	—
458	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
459	C₄×C₁₃	—	2	1	no	—
460	C₄×C₁₃	—	2	2	no	—
461	C₄×C₁₃	—	2	1	no	—
462	C₄×C₁₃	—	2	1	no	—
463	C₄×C₁₃	—	2	4	no	—
464	C₄×C₁₃	—	2	4	no	—
465	C₄×C₁₃	—	4	2	no	—
466	C₄×C₁₃	—	4	1	no	—
467	C₄×C₁₃	—	4	2	no	—
468	C₄×C₁₃	—	4	1	no	—
469	C₄×C₁₃	—	4	2	no	—
470	C₄×C₁₃	—	4	4	no	—
471	C₄×C₁₃	#577	1	2	yes	—
472	C₄×C₁₃	#577	1	2	yes	—
473	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
474	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
475	C₂×#41	—	2	1	no	—
476	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
477	C₂²×Q₈	—	2	2	no	—
478	C₂²×Q₈	—	2	2	no	—
479	C₂²×Q₈	—	2	1	no	—
480	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
481	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
482	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
483	C₂×D₈	C₂³×C₁₃	1	2	yes	—
484	C₄⋊Q₈	—	2	2	no	—
485	C₄⋊Q₈	—	2	2	no	—
486	C₄⋊Q₈	—	2	2	no	—
487	C₄⋊Q₈	—	2	4	no	—
488	C₄⋊Q₈	—	2	2	no	—
489	C₄⋊Q₈	—	2	4	no	—
490	C₄⋊Q₈	—	2	1	no	—
491	C₄⋊Q₈	—	2	1	no	—
492	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
493	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
494	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
495	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
496	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
497	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
498	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
499	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
500	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
501	#127	C₂³×C₁₃	1	1	yes	characteristic
502	#126	—	2	4	no	—
503	#126	—	2	4	no	—
504	#125	—	2	2	no	—
505	#125	—	2	4	no	—
506	#125	—	2	1	no	—
507	#125	D₄×C₁₃	1	2	yes	—
508	#125	C₂³×C₁₃	1	4	yes	—
509	#124	—	2	2	no	—
510	#124	—	2	4	no	—
511	#124	—	2	1	no	—
512	#124	C₂³×C₁₃	1	4	yes	—
513	#123	—	2	4	no	—
514	#123	—	2	4	no	—
515	C₂²⋊Q₈	—	2	2	no	—
516	C₂²⋊Q₈	—	2	2	no	—
517	C₂²⋊Q₈	—	2	1	no	—
518	C₂²⋊Q₈	—	2	2	no	—
519	C₂²⋊Q₈	—	2	2	no	—
520	C₂²⋊Q₈	—	2	4	no	—
521	C₂²⋊Q₈	—	2	4	no	—
522	C₂²⋊Q₈	—	2	4	no	—
523	C₂²⋊Q₈	—	2	4	no	—
524	C₂²⋊Q₈	—	2	4	no	—
525	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
526	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
527	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
528	#121	—	2	1	no	—
529	#121	C₂³×C₁₃	1	2	yes	—
530	C₄×Q₈	—	2	2	no	—
531	C₄×Q₈	—	2	2	no	—
532	C₄×Q₈	—	2	2	no	—
533	C₄×Q₈	—	2	1	no	—
534	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
535	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
536	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
537	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
538	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
539	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
540	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	—	2	1	no	—
543	C₄×D₄	—	2	2	no	—
544	C₄×D₄	—	2	4	no	—
545	C₄×D₄	—	2	1	no	—
546	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
547	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
548	C₄×D₄	C₂³×C₁₃	1	4	yes	—
549	C₄×D₄	C₂³×C₁₃	1	2	yes	—
550	C₄×D₄	C₂³×C₁₃	1	4	yes	—
551	#117	—	2	1	no	—
552	#117	—	2	2	no	—
553	#117	—	2	2	no	—
554	#117	—	2	1	no	—
555	#117	C₂³×C₁₃	1	1	yes	characteristic
556	#117	C₂³×C₁₃	1	2	yes	—
557	C₂×C₄⋊C₄	—	2	1	no	—
558	C₂×C₄⋊C₄	—	2	2	no	—
559	C₂×C₄⋊C₄	—	2	2	no	—
560	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
561	C₂×C₄²	—	2	1	no	—
562	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
563	#107	C₂³×C₁₃	1	2	yes	—
564	#107	C₂³×C₁₃	1	2	yes	—
565	#106	C₂³×C₁₃	1	2	yes	—
566	#106	C₂³×C₁₃	1	2	yes	—
567	#106	C₂³×C₁₃	1	4	yes	—
568	#106	C₂³×C₁₃	1	4	yes	—
569	#106	C₂³×C₁₃	1	4	yes	—
570	#106	C₂³×C₁₃	1	4	yes	—
571	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
572	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
573	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
574	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
575	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
576	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
577	#103	C₂³×C₁₃	1	2	yes	—
578	#103	C₂³×C₁₃	1	2	yes	—
579	#103	C₂³×C₁₃	1	2	yes	—
580	#103	C₂³×C₁₃	1	4	yes	—
581	#103	C₂³×C₁₃	1	2	yes	—
582	#103	C₂³×C₁₃	1	4	yes	—
583	#102	C₂³×C₁₃	1	2	yes	—
584	#102	C₂³×C₁₃	1	2	yes	—
585	#102	C₂³×C₁₃	1	2	yes	—
586	#102	C₂³×C₁₃	1	2	yes	—
587	#102	C₂³×C₁₃	1	4	yes	—
588	#102	C₂³×C₁₃	1	4	yes	—
589	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
590	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
591	#97	C₂³×C₁₃	1	4	yes	—
592	C₄×C₈	C₂³×C₁₃	1	2	yes	—
593	C₄×C₈	C₂³×C₁₃	1	2	yes	—
594	C₄×C₈	C₂³×C₁₃	1	4	yes	—
595	C₂×C₁₃	—	4	1	no	—
596	C₂×C₁₃	—	4	2	no	—
597	C₂×C₁₃	—	8	2	no	—
598	C₂×C₁₃	#3486	1	1	yes	characteristic
599	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
600	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
601	#41	—	2	2	no	—
602	#41	—	2	2	no	—
603	#41	—	8	2	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	—	2	4	no	—
607	C₂×Q₈	—	2	4	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	—	8	2	no	—
611	C₂×Q₈	—	8	4	no	—
612	C₂×Q₈	—	8	4	no	—
613	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
614	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
615	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
616	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
622	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
631	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
633	Q₁₆	—	2	4	no	—
634	SD₁₆	—	2	4	no	—
635	SD₁₆	—	2	4	no	—
636	D₈	—	2	4	no	—
637	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
638	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
639	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
640	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
659	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
660	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
661	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
662	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
663	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
664	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
665	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
666	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
667	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
668	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	2	1	no	—
671	C₂²⋊C₄	—	2	1	no	—
672	C₂²⋊C₄	—	2	1	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
680	C₄²	—	2	1	no	—
681	C₄²	—	2	1	no	—
682	C₄²	—	2	1	no	—
683	C₄²	—	2	2	no	—
684	C₄²	—	2	4	no	—
685	C₄²	—	2	4	no	—
686	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
687	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
688	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
689	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
690	C₄²	C₂⁴×C₁₃	1	4	yes	—
691	C₁₃	#61871	1	1	yes	characteristic, direct product factor, Sylow
692	C₂³	—	2	1	no	—
693	C₂³	—	2	2	no	—
694	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
695	Q₈	—	2	4	no	—
696	Q₈	—	2	4	no	—
697	Q₈	—	2	1	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	2	no	—
700	Q₈	—	4	2	no	—
701	Q₈	—	4	4	no	—
702	Q₈	—	8	2	no	—
703	Q₈	—	8	4	no	—
704	Q₈	—	8	4	no	—
705	Q₈	—	8	1	no	—
706	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
707	D₄	—	2	4	no	—
708	D₄	—	2	1	no	—
709	D₄	—	2	2	no	—
710	D₄	—	2	2	no	—
711	D₄	—	4	2	no	—
712	D₄	—	8	1	no	—
713	D₄	—	8	2	no	—
714	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	4	2	no	—
728	C₂×C₄	—	4	2	no	—
729	C₂×C₄	—	4	4	no	—
730	C₂×C₄	—	8	4	no	—
731	C₂×C₄	—	8	4	no	—
732	C₂×C₄	—	8	2	no	—
733	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
734	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
735	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
736	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
737	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
738	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
739	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
740	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
741	C₈	—	2	2	no	—
742	C₈	—	2	2	no	—
743	C₈	—	2	2	no	—
744	C₈	—	2	2	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
755	C₄	—	2	1	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	4	no	—
758	C₄	—	2	4	no	—
759	C₄	—	2	1	no	—
760	C₄	—	2	2	no	—
761	C₄	—	4	1	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	1	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	4	no	—
766	C₄	—	4	2	no	—
767	C₄	C₁₃×#577	1	2	yes	—
768	C₄	C₁₃×#577	1	2	yes	—
769	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
770	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
771	C₂	—	4	1	no	—
772	C₂	—	4	2	no	—
773	C₂	—	8	2	no	—
774	C₂	C₁₃×#3486	1	1	yes	characteristic
775	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
776	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3106	C₂
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×#3550	C₂	semidirect
2. C₁₃×#3503	C₂	semidirect
3. C₁₃×#3387	C₂	semidirect
4. C₁₃×#3384	C₂	semidirect
5. Q₈×C₁₃×SD₁₆	C₂	semidirect
6. Q₈×C₁₃×SD₁₆	C₂	semidirect
7. C₁₃×#3373	C₂	semidirect
8. C₁₃×#3369	C₂	semidirect
9. C₁₃×#3365	C₂	semidirect
10. C₁₃×#3360	C₂	semidirect
11. C₁₃×#3244	C₂	semidirect
12. C₁₃×#3229	C₂	semidirect
13. C₁₃×#3227	C₂	semidirect
14. C₁₃×#3125	C₂	semidirect
15. C₁₃×#3107	C₂	semidirect
17. C₁₃×#2986	C₂	semidirect
213. #61871	C₁₃	direct (N × H)
304. #3550	C₂×C₁₃	semidirect
305. #3503	C₂×C₁₃	semidirect
306. #3387	C₂×C₁₃	semidirect
307. #3384	C₂×C₁₃	semidirect
308. Q₈×SD₁₆	C₂×C₁₃	semidirect
309. Q₈×SD₁₆	C₂×C₁₃	semidirect
310. #3373	C₂×C₁₃	semidirect
311. #3369	C₂×C₁₃	semidirect
312. #3365	C₂×C₁₃	semidirect
313. #3360	C₂×C₁₃	semidirect
314. #3244	C₂×C₁₃	semidirect
315. #3229	C₂×C₁₃	semidirect
316. #3227	C₂×C₁₃	semidirect
317. #3125	C₂×C₁₃	semidirect
318. #3107	C₂×C₁₃	semidirect
320. #2986	C₂×C₁₃	semidirect
691. C₁₃	#61871	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×#3550	2
C₁₃×#3503	2
C₁₃×#3387	2
C₁₃×#3384	2
Q₈×C₁₃×SD₁₆	2
C₁₃×#3373	2
C₁₃×#3369	2
C₁₃×#3365	2
C₁₃×#3360	2
C₁₃×#3244	2
C₁₃×#3229	2
C₁₃×#3227	2
C₁₃×#3125	2
C₁₃×#3107	2
C₁₃×#3106	2
C₁₃×#2986	2
#61871	13

Subgroups — C13×#61871 #15748210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61871 #15748210