Subgroups — C₁₃×#61986 #15748325

Order 3328.

1906 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3400	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3373	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3311	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3304	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3284	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3267	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3255	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3246	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3216	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3115	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3035	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
20	C₁₃×#559	—	2	1	no	—
21	C₁₃×#559	C₂²	1	2	yes	—
22	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#556	C₂²	1	2	yes	—
24	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#552	—	2	2	no	—
26	C₁₃×#552	—	2	1	no	—
27	C₁₃×#550	—	2	1	no	—
28	C₁₃×#550	C₂²	1	2	yes	—
29	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#548	—	2	1	no	—
31	C₁₃×#547	C₂²	1	2	yes	—
32	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#546	—	2	2	no	—
34	C₁₃×#546	C₂²	1	4	yes	—
35	C₁₃×#540	—	2	2	no	—
36	C₁₃×#535	—	2	1	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#533	C₂²	1	1	yes	characteristic
39	C₁₃×#533	C₂²	1	2	yes	complemented
40	C₁₃×#532	C₂²	1	2	yes	—
41	C₁₃×#532	C₂²	1	2	yes	—
42	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
43	C₁₃×#529	—	2	1	no	—
44	C₁₃×#529	—	2	2	no	—
45	C₁₃×#518	—	2	1	no	—
46	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
49	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
50	C₁₃×#497	C₂²	1	4	yes	complemented
51	C₁₃×#492	C₂²	1	2	yes	—
52	C₁₃×#489	C₂²	1	4	yes	complemented
53	C₁₃×#486	C₂²	1	2	yes	—
54	C₁₃×#485	C₂²	1	2	yes	—
55	C₁₃×#482	C₂²	1	4	yes	complemented
56	C₁₃×#476	C₂²	1	4	yes	complemented
57	C₁₃×#475	C₂²	1	2	yes	complemented
58	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#475	C₂²	1	2	yes	complemented
60	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#470	C₂²	1	4	yes	—
62	C₁₃×#465	C₂²	1	4	yes	complemented
63	C₁₃×#465	C₂²	1	4	yes	complemented
64	C₁₃×#464	C₂²	1	4	yes	complemented
65	C₁₃×#463	C₂²	1	4	yes	complemented
66	C₁₃×#462	C₂²	1	2	yes	complemented
67	C₁₃×#462	C₂²	1	2	yes	complemented
68	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#461	C₂²	1	4	yes	complemented
70	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×#460	C₂²	1	2	yes	—
72	C₁₃×#460	C₂²	1	2	yes	—
73	C₁₃×#460	C₂²	1	2	yes	—
74	C₁₃×#460	C₂²	1	2	yes	—
75	C₁₃×#459	C₂²	1	2	yes	—
76	C₁₃×#459	C₂²	1	2	yes	—
77	C₁₃×#452	C₂²	1	2	yes	—
78	C₁₃×#452	C₂²	1	4	yes	complemented
79	C₁₃×#452	C₂²	1	4	yes	complemented
80	C₁₃×#450	C₂²	1	4	yes	—
81	C₁₃×#449	C₂²	1	4	yes	complemented
82	C₁₃×#446	C₂²	1	2	yes	complemented
83	C₁₃×#442	C₂²	1	4	yes	complemented
84	C₁₃×#440	C₂²	1	4	yes	complemented
85	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
86	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
87	C₁₃×#435	C₂²	1	4	yes	—
88	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
89	C₁₃×#432	C₂²	1	2	yes	complemented
90	C₁₃×#431	C₂²	1	1	yes	characteristic
91	C₁₃×#423	C₂²	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
93	C₁₃×#418	C₂²	1	2	yes	—
94	C₁₃×#416	C₂²	1	4	yes	complemented
95	C₂×C₁₃×#41	—	2	2	no	—
96	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
97	C₂×C₁₃×#41	C₂³	1	2	yes	—
98	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×#41	C₂³	1	4	yes	—
100	C₂²×Q₈×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	—	2	1	no	—
102	C₂²×D₄×C₁₃	—	2	1	no	—
103	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
104	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
105	C₁₃×#135	—	4	8	no	—
106	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
107	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
108	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
109	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
111	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
112	C₂×C₁₃×D₈	C₂³	1	4	yes	—
113	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
114	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₁₃×#127	—	2	2	no	—
122	C₁₃×#127	—	2	1	no	—
123	C₁₃×#127	—	2	1	no	—
124	C₁₃×#127	C₂³	1	2	yes	—
125	C₁₃×#127	C₂³	1	2	yes	—
126	C₁₃×#126	—	2	2	no	—
127	C₁₃×#126	—	2	2	no	—
128	C₁₃×#126	—	2	2	no	—
129	C₁₃×#125	—	2	1	no	—
130	C₁₃×#125	—	2	2	no	—
131	C₁₃×#125	—	2	1	no	—
132	C₁₃×#125	—	2	1	no	—
133	C₁₃×#125	—	2	2	no	—
134	C₁₃×#124	—	2	2	no	—
135	C₁₃×#124	—	2	2	no	—
136	C₁₃×#124	—	2	1	no	—
137	C₁₃×#124	—	2	2	no	—
138	C₁₃×#124	C₂³	1	4	yes	—
139	C₁₃×#123	—	2	4	no	—
140	C₁₃×#123	—	2	4	no	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×#123	—	2	2	no	—
143	C₁₃×#123	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	1	no	—
145	C₁₃×C₂²⋊Q₈	—	2	1	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	1	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	1	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	2	no	—
158	C₁₃×#121	—	2	4	no	—
159	C₁₃×#121	—	2	4	no	—
160	C₁₃×#121	C₂³	1	4	yes	—
161	C₁₃×#120	—	2	4	no	—
162	C₄×Q₈×C₁₃	—	2	1	no	—
163	C₄×Q₈×C₁₃	—	2	2	no	—
164	C₄×Q₈×C₁₃	—	2	1	no	—
165	C₄×Q₈×C₁₃	—	2	1	no	—
166	C₄×Q₈×C₁₃	—	2	2	no	—
167	C₄×Q₈×C₁₃	—	2	1	no	—
168	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
169	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
172	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
173	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
174	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	2	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	—	2	2	no	—
180	C₄×D₄×C₁₃	—	2	2	no	—
181	C₄×D₄×C₁₃	—	2	2	no	—
182	C₄×D₄×C₁₃	—	2	2	no	—
183	C₄×D₄×C₁₃	—	2	2	no	—
184	C₄×D₄×C₁₃	D₄	1	2	yes	—
185	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
186	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₁₃	C₂³	1	4	yes	—
188	C₄×D₄×C₁₃	C₂³	1	2	yes	—
189	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₁₃	C₂³	1	2	yes	—
192	C₁₃×#117	—	2	1	no	—
193	C₁₃×#117	—	2	1	no	—
194	C₁₃×#117	—	2	2	no	—
195	C₁₃×#117	—	2	1	no	—
196	C₁₃×#117	—	2	2	no	—
197	C₁₃×#117	D₄	1	1	yes	characteristic
198	C₁₃×#117	D₄	1	2	yes	—
199	C₁₃×#117	C₂³	1	2	yes	—
200	C₁₃×#117	C₂³	1	1	yes	characteristic
201	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
202	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₂×C₄²×C₁₃	—	2	1	no	—
205	C₂×C₄²×C₁₃	—	2	2	no	—
206	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
207	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
208	C₁₃×#107	C₂³	1	2	yes	—
209	C₁₃×#106	C₂³	1	2	yes	—
210	C₁₃×#106	C₂³	1	4	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
212	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
214	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₁₃×#103	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	2	yes	—
219	C₁₃×#103	C₂³	1	2	yes	—
220	C₁₃×#103	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	2	yes	—
225	C₁₃×#102	C₂³	1	4	yes	—
226	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₁₃×#97	C₂³	1	4	yes	—
229	C₄×C₈×C₁₃	C₂³	1	2	yes	—
230	#61986	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂⁴×C₁₃	—	2	2	no	—
232	C₁₃×#41	—	2	4	no	—
233	C₁₃×#41	—	2	2	no	—
234	C₁₃×#41	—	4	2	no	—
235	C₁₃×#41	—	4	1	no	—
236	C₁₃×#41	—	4	2	no	—
237	C₁₃×#41	—	4	4	no	—
238	C₁₃×#41	—	4	4	no	—
239	C₁₃×#41	—	8	4	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×Q₈×C₁₃	—	2	1	no	—
242	C₂×Q₈×C₁₃	—	2	1	no	—
243	C₂×Q₈×C₁₃	—	4	4	no	—
244	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
248	C₂×D₄×C₁₃	—	2	1	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	4	no	—
251	C₂×D₄×C₁₃	—	2	4	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	2	no	—
254	C₂×D₄×C₁₃	—	2	2	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	2	2	no	—
257	C₂×D₄×C₁₃	—	4	2	no	—
258	C₂×D₄×C₁₃	—	4	2	no	—
259	C₂×D₄×C₁₃	—	4	4	no	—
260	C₂×D₄×C₁₃	—	8	2	no	—
261	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
262	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
263	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
264	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	—	2	1	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	4	no	—
271	C₂²×C₄×C₁₃	—	2	4	no	—
272	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₁₃×Q₁₆	—	4	2	no	—
279	C₁₃×Q₁₆	—	4	4	no	—
280	C₁₃×SD₁₆	—	2	4	no	—
281	C₁₃×SD₁₆	—	4	4	no	—
282	C₁₃×SD₁₆	—	4	4	no	—
283	C₁₃×SD₁₆	—	4	4	no	—
284	C₁₃×D₈	—	2	8	no	—
285	C₁₃×M₁₆	—	4	2	no	—
286	C₂×C₈×C₁₃	—	4	4	no	—
287	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
288	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
289	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	1	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	1	no	—
296	C₁₃×C₄⋊C₄	—	2	1	no	—
297	C₁₃×C₄⋊C₄	—	2	1	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	2	1	no	—
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	—	2	1	no	—
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	—	2	1	no	—
305	C₁₃×C₄⋊C₄	—	2	1	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	—	2	2	no	—
308	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
309	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
310	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
311	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
312	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
313	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
314	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
315	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	1	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	—	2	4	no	—
323	C₁₃×C₂²⋊C₄	—	2	4	no	—
324	C₁₃×C₂²⋊C₄	—	2	1	no	—
325	C₁₃×C₂²⋊C₄	—	2	2	no	—
326	C₁₃×C₂²⋊C₄	—	2	1	no	—
327	C₁₃×C₂²⋊C₄	—	2	4	no	—
328	C₁₃×C₂²⋊C₄	—	2	4	no	—
329	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
330	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
331	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
332	C₄²×C₁₃	—	2	1	no	—
333	C₄²×C₁₃	—	2	2	no	—
334	C₄²×C₁₃	—	2	2	no	—
335	C₄²×C₁₃	—	2	1	no	—
336	C₄²×C₁₃	—	2	2	no	—
337	C₄²×C₁₃	—	2	1	no	—
338	C₄²×C₁₃	—	2	2	no	—
339	C₄²×C₁₃	C₂×D₄	1	2	yes	—
340	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₁₃	C₂×D₄	1	2	yes	—
342	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
343	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
344	C₄²×C₁₃	C₂⁴	1	2	yes	—
345	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
346	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#3482	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3400	C₂×C₁₃	1	2	yes	complemented
349	#3373	C₂×C₁₃	1	2	yes	complemented
350	#3311	C₂×C₁₃	1	4	yes	complemented
351	#3304	C₂×C₁₃	1	2	yes	complemented
352	#3284	C₂×C₁₃	1	2	yes	complemented
353	#3267	C₂×C₁₃	1	4	yes	complemented
354	#3255	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#3246	C₂×C₁₃	1	2	yes	complemented
356	#3216	C₂×C₁₃	1	2	yes	complemented
357	#3208	C₂×C₁₃	1	1	yes	characteristic, complemented
358	#3115	C₂×C₁₃	1	2	yes	complemented
359	#3107	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#3038	C₂×C₁₃	1	1	yes	characteristic, complemented
361	#3035	C₂×C₁₃	1	2	yes	complemented
362	#2990	C₂×C₁₃	1	1	yes	characteristic, complemented
363	C₂³×C₁₃	—	2	1	no	—
364	C₂³×C₁₃	—	2	4	no	—
365	C₂³×C₁₃	—	4	4	no	—
366	C₂³×C₁₃	—	8	2	no	—
367	C₂³×C₁₃	—	8	2	no	—
368	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
369	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
370	Q₈×C₁₃	—	2	2	no	—
371	Q₈×C₁₃	—	2	2	no	—
372	Q₈×C₁₃	—	2	1	no	—
373	Q₈×C₁₃	—	2	2	no	—
374	Q₈×C₁₃	—	2	2	no	—
375	Q₈×C₁₃	—	2	1	no	—
376	Q₈×C₁₃	—	2	2	no	—
377	Q₈×C₁₃	—	4	4	no	—
378	Q₈×C₁₃	—	4	2	no	—
379	Q₈×C₁₃	—	4	2	no	—
380	D₄×C₁₃	—	2	2	no	—
381	D₄×C₁₃	—	2	4	no	—
382	D₄×C₁₃	—	2	1	no	—
383	D₄×C₁₃	—	2	4	no	—
384	D₄×C₁₃	—	4	2	no	—
385	D₄×C₁₃	—	4	4	no	—
386	D₄×C₁₃	—	4	4	no	—
387	D₄×C₁₃	—	4	2	no	—
388	D₄×C₁₃	—	4	4	no	—
389	D₄×C₁₃	—	4	4	no	—
390	D₄×C₁₃	—	8	2	no	—
391	D₄×C₁₃	—	8	2	no	—
392	D₄×C₁₃	—	8	4	no	—
393	D₄×C₁₃	—	8	4	no	—
394	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	4	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	1	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	1	no	—
405	C₂×C₄×C₁₃	—	2	1	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	4	2	no	—
410	C₂×C₄×C₁₃	—	4	4	no	—
411	C₂×C₄×C₁₃	—	4	2	no	—
412	C₂×C₄×C₁₃	—	4	4	no	—
413	C₂×C₄×C₁₃	—	4	2	no	—
414	C₂×C₄×C₁₃	—	4	2	no	—
415	C₂×C₄×C₁₃	—	8	4	no	—
416	C₂×C₄×C₁₃	—	8	4	no	—
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	2	yes	—
420	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
426	C₈×C₁₃	—	2	2	no	—
427	C₈×C₁₃	—	2	4	no	—
428	C₈×C₁₃	—	2	2	no	—
429	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
430	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
431	#559	—	2	1	no	—
432	#559	C₂²×C₁₃	1	2	yes	—
433	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
434	#556	C₂²×C₁₃	1	2	yes	—
435	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
436	#552	—	2	2	no	—
437	#552	—	2	1	no	—
438	#550	—	2	1	no	—
439	#550	C₂²×C₁₃	1	2	yes	—
440	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
441	#548	—	2	1	no	—
442	#547	C₂²×C₁₃	1	2	yes	—
443	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
444	#546	—	2	2	no	—
445	#546	C₂²×C₁₃	1	4	yes	—
446	#540	—	2	2	no	—
447	#535	—	2	1	no	—
448	#533	C₂²×C₁₃	1	1	yes	characteristic
449	#533	C₂²×C₁₃	1	1	yes	characteristic
450	#533	C₂²×C₁₃	1	2	yes	complemented
451	#532	C₂²×C₁₃	1	2	yes	—
452	#532	C₂²×C₁₃	1	2	yes	—
453	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
454	#529	—	2	1	no	—
455	#529	—	2	2	no	—
456	#518	—	2	1	no	—
457	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
458	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
459	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
460	C₂×C₄×Q₈	—	2	1	no	—
461	#497	C₂²×C₁₃	1	4	yes	complemented
462	#492	C₂²×C₁₃	1	2	yes	—
463	#489	C₂²×C₁₃	1	4	yes	complemented
464	#486	C₂²×C₁₃	1	2	yes	—
465	#485	C₂²×C₁₃	1	2	yes	—
466	#482	C₂²×C₁₃	1	4	yes	complemented
467	#476	C₂²×C₁₃	1	4	yes	complemented
468	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
469	#475	C₂²×C₁₃	1	2	yes	complemented
470	#475	C₂²×C₁₃	1	2	yes	complemented
471	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
472	#470	C₂²×C₁₃	1	4	yes	—
473	#465	C₂²×C₁₃	1	4	yes	complemented
474	#465	C₂²×C₁₃	1	4	yes	complemented
475	#464	C₂²×C₁₃	1	4	yes	complemented
476	#463	C₂²×C₁₃	1	4	yes	complemented
477	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
478	#462	C₂²×C₁₃	1	2	yes	complemented
479	#462	C₂²×C₁₃	1	2	yes	complemented
480	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
481	#461	C₂²×C₁₃	1	4	yes	complemented
482	#460	C₂²×C₁₃	1	2	yes	—
483	#460	C₂²×C₁₃	1	2	yes	—
484	#460	C₂²×C₁₃	1	2	yes	—
485	#460	C₂²×C₁₃	1	2	yes	—
486	#459	C₂²×C₁₃	1	2	yes	—
487	#459	C₂²×C₁₃	1	2	yes	—
488	#452	C₂²×C₁₃	1	2	yes	—
489	#452	C₂²×C₁₃	1	4	yes	complemented
490	#452	C₂²×C₁₃	1	4	yes	complemented
491	#450	C₂²×C₁₃	1	4	yes	—
492	#449	C₂²×C₁₃	1	4	yes	complemented
493	#446	C₂²×C₁₃	1	2	yes	complemented
494	#442	C₂²×C₁₃	1	4	yes	complemented
495	#440	C₂²×C₁₃	1	4	yes	complemented
496	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
497	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
498	#435	C₂²×C₁₃	1	4	yes	—
499	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
500	#432	C₂²×C₁₃	1	2	yes	complemented
501	#431	C₂²×C₁₃	1	1	yes	characteristic
502	#423	C₂²×C₁₃	1	1	yes	characteristic
503	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
504	#418	C₂²×C₁₃	1	2	yes	—
505	#416	C₂²×C₁₃	1	4	yes	complemented
506	C₂²×C₁₃	—	2	2	no	—
507	C₂²×C₁₃	—	2	1	no	—
508	C₂²×C₁₃	—	2	2	no	—
509	C₂²×C₁₃	—	2	1	no	—
510	C₂²×C₁₃	—	2	2	no	—
511	C₂²×C₁₃	—	2	2	no	—
512	C₂²×C₁₃	—	2	1	no	—
513	C₂²×C₁₃	—	4	1	no	—
514	C₂²×C₁₃	—	4	1	no	—
515	C₂²×C₁₃	—	4	4	no	—
516	C₂²×C₁₃	—	4	4	no	—
517	C₂²×C₁₃	—	4	4	no	—
518	C₂²×C₁₃	—	16	4	no	—
519	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
520	C₄×C₁₃	—	2	2	no	—
521	C₄×C₁₃	—	2	1	no	—
522	C₄×C₁₃	—	2	1	no	—
523	C₄×C₁₃	—	2	2	no	—
524	C₄×C₁₃	—	2	2	no	—
525	C₄×C₁₃	—	2	1	no	—
526	C₄×C₁₃	—	4	1	no	—
527	C₄×C₁₃	—	4	2	no	—
528	C₄×C₁₃	—	4	2	no	—
529	C₄×C₁₃	—	4	2	no	—
530	C₄×C₁₃	—	4	1	no	—
531	C₄×C₁₃	—	4	1	no	—
532	C₄×C₁₃	—	4	2	no	—
533	C₄×C₁₃	#575	1	2	yes	—
534	C₄×C₁₃	#577	1	2	yes	—
535	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
536	C₄×C₁₃	#585	1	1	yes	characteristic
537	C₂×#41	—	2	2	no	—
538	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
539	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
540	C₂×#41	C₂³×C₁₃	1	2	yes	—
541	C₂×#41	C₂³×C₁₃	1	4	yes	—
542	C₂²×Q₈	—	2	1	no	—
543	C₂²×D₄	—	2	1	no	—
544	C₂²×D₄	—	2	1	no	—
545	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
546	AGL(1,ℤ/8)	—	4	4	no	—
547	#135	—	4	8	no	—
548	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
549	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
550	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
551	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
552	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
553	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
554	C₂×D₈	C₂³×C₁₃	1	4	yes	—
555	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
556	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
557	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
558	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
559	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
560	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
561	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
562	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
563	#127	—	2	2	no	—
564	#127	—	2	1	no	—
565	#127	—	2	1	no	—
566	#127	C₂³×C₁₃	1	2	yes	—
567	#127	C₂³×C₁₃	1	2	yes	—
568	#126	—	2	2	no	—
569	#126	—	2	2	no	—
570	#126	—	2	2	no	—
571	#125	—	2	1	no	—
572	#125	—	2	2	no	—
573	#125	—	2	1	no	—
574	#125	—	2	1	no	—
575	#125	—	2	2	no	—
576	#124	—	2	2	no	—
577	#124	—	2	2	no	—
578	#124	—	2	1	no	—
579	#124	—	2	2	no	—
580	#124	C₂³×C₁₃	1	4	yes	—
581	#123	—	2	4	no	—
582	#123	—	2	4	no	—
583	#123	—	2	2	no	—
584	#123	—	2	2	no	—
585	#123	—	2	2	no	—
586	C₂²⋊Q₈	—	2	1	no	—
587	C₂²⋊Q₈	—	2	1	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	—	2	1	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
592	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
593	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
594	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
595	#121	—	2	2	no	—
596	#121	—	2	1	no	—
597	#121	—	2	2	no	—
598	#121	—	2	2	no	—
599	#121	—	2	2	no	—
600	#121	—	2	4	no	—
601	#121	—	2	4	no	—
602	#121	C₂³×C₁₃	1	4	yes	—
603	#120	—	2	4	no	—
604	C₄×Q₈	—	2	1	no	—
605	C₄×Q₈	—	2	2	no	—
606	C₄×Q₈	—	2	1	no	—
607	C₄×Q₈	—	2	1	no	—
608	C₄×Q₈	—	2	2	no	—
609	C₄×Q₈	—	2	1	no	—
610	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
611	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
612	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
613	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
614	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
615	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
616	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	D₄×C₁₃	1	2	yes	—
627	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
628	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
629	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
630	C₄×D₄	C₂³×C₁₃	1	2	yes	—
631	C₄×D₄	C₂³×C₁₃	1	4	yes	—
632	C₄×D₄	C₂³×C₁₃	1	2	yes	—
633	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
634	#117	—	2	1	no	—
635	#117	—	2	1	no	—
636	#117	—	2	2	no	—
637	#117	—	2	1	no	—
638	#117	—	2	2	no	—
639	#117	D₄×C₁₃	1	1	yes	characteristic
640	#117	D₄×C₁₃	1	2	yes	—
641	#117	C₂³×C₁₃	1	1	yes	characteristic
642	#117	C₂³×C₁₃	1	2	yes	—
643	C₂×C₄⋊C₄	—	2	2	no	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₂²⋊C₄	—	2	4	no	—
646	C₂×C₄²	—	2	1	no	—
647	C₂×C₄²	—	2	2	no	—
648	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
650	#107	C₂³×C₁₃	1	2	yes	—
651	#106	C₂³×C₁₃	1	2	yes	—
652	#106	C₂³×C₁₃	1	4	yes	—
653	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
654	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
655	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
656	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
657	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
658	#103	C₂³×C₁₃	1	2	yes	—
659	#103	C₂³×C₁₃	1	4	yes	—
660	#103	C₂³×C₁₃	1	2	yes	—
661	#103	C₂³×C₁₃	1	2	yes	—
662	#103	C₂³×C₁₃	1	4	yes	—
663	#102	C₂³×C₁₃	1	4	yes	—
664	#102	C₂³×C₁₃	1	4	yes	—
665	#102	C₂³×C₁₃	1	4	yes	—
666	#102	C₂³×C₁₃	1	2	yes	—
667	#102	C₂³×C₁₃	1	4	yes	—
668	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
669	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
670	#97	C₂³×C₁₃	1	4	yes	—
671	C₄×C₈	C₂³×C₁₃	1	2	yes	—
672	C₂×C₁₃	—	4	2	no	—
673	C₂×C₁₃	—	4	1	no	—
674	C₂×C₁₃	—	4	2	no	—
675	C₂×C₁₃	—	8	4	no	—
676	C₂×C₁₃	#3488	1	1	yes	characteristic
677	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
678	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
679	C₂⁴	—	2	2	no	—
680	#41	—	2	4	no	—
681	#41	—	2	2	no	—
682	#41	—	4	2	no	—
683	#41	—	4	1	no	—
684	#41	—	4	2	no	—
685	#41	—	4	4	no	—
686	#41	—	4	4	no	—
687	#41	—	8	4	no	—
688	C₂×Q₈	—	2	2	no	—
689	C₂×Q₈	—	2	1	no	—
690	C₂×Q₈	—	2	1	no	—
691	C₂×Q₈	—	4	4	no	—
692	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
693	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
694	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
695	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	4	2	no	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	4	4	no	—
708	C₂×D₄	—	8	2	no	—
709	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
710	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
711	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
712	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	4	no	—
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	1	yes	characteristic
723	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
726	Q₁₆	—	4	4	no	—
727	Q₁₆	—	4	2	no	—
728	SD₁₆	—	2	4	no	—
729	SD₁₆	—	4	4	no	—
730	SD₁₆	—	4	4	no	—
731	SD₁₆	—	4	4	no	—
732	D₈	—	2	8	no	—
733	M₁₆	—	4	2	no	—
734	C₂×C₈	—	4	4	no	—
735	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
736	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
737	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	1	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
757	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
758	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
759	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
760	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
761	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
762	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
763	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	1	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	1	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	1	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
778	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
779	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
780	C₄²	—	2	1	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	1	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	1	no	—
786	C₄²	—	2	2	no	—
787	C₄²	C₂×D₄×C₁₃	1	2	yes	—
788	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
789	C₄²	C₂×D₄×C₁₃	1	2	yes	—
790	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
791	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
792	C₄²	C₂⁴×C₁₃	1	2	yes	—
793	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
794	C₁₃	#61986	1	1	yes	characteristic, direct product factor, Sylow
795	C₂³	—	2	1	no	—
796	C₂³	—	2	4	no	—
797	C₂³	—	4	4	no	—
798	C₂³	—	8	2	no	—
799	C₂³	—	8	2	no	—
800	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
801	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
802	Q₈	—	2	2	no	—
803	Q₈	—	2	2	no	—
804	Q₈	—	2	1	no	—
805	Q₈	—	2	2	no	—
806	Q₈	—	2	2	no	—
807	Q₈	—	2	1	no	—
808	Q₈	—	2	2	no	—
809	Q₈	—	4	4	no	—
810	Q₈	—	4	2	no	—
811	Q₈	—	4	2	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	4	no	—
814	D₄	—	2	1	no	—
815	D₄	—	2	4	no	—
816	D₄	—	4	2	no	—
817	D₄	—	4	4	no	—
818	D₄	—	4	4	no	—
819	D₄	—	4	2	no	—
820	D₄	—	4	4	no	—
821	D₄	—	4	4	no	—
822	D₄	—	8	2	no	—
823	D₄	—	8	2	no	—
824	D₄	—	8	4	no	—
825	D₄	—	8	4	no	—
826	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	4	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	4	2	no	—
842	C₂×C₄	—	4	4	no	—
843	C₂×C₄	—	4	2	no	—
844	C₂×C₄	—	4	4	no	—
845	C₂×C₄	—	4	2	no	—
846	C₂×C₄	—	4	2	no	—
847	C₂×C₄	—	8	4	no	—
848	C₂×C₄	—	8	4	no	—
849	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
850	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
851	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
852	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
853	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
854	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
855	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
856	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
857	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
858	C₈	—	2	2	no	—
859	C₈	—	2	4	no	—
860	C₈	—	2	2	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	1	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	1	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	4	no	—
871	C₂²	—	4	4	no	—
872	C₂²	—	4	4	no	—
873	C₂²	—	16	4	no	—
874	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
875	C₄	—	2	1	no	—
876	C₄	—	2	2	no	—
877	C₄	—	2	2	no	—
878	C₄	—	2	1	no	—
879	C₄	—	2	2	no	—
880	C₄	—	2	1	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	1	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	2	no	—
887	C₄	—	4	2	no	—
888	C₄	C₁₃×#575	1	2	yes	—
889	C₄	C₁₃×#577	1	2	yes	—
890	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
891	C₄	C₁₃×#585	1	1	yes	characteristic
892	C₂	—	4	1	no	—
893	C₂	—	4	2	no	—
894	C₂	—	4	2	no	—
895	C₂	—	8	4	no	—
896	C₂	C₁₃×#3488	1	1	yes	characteristic
897	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
898	C₂	C₂×C₁₃×#577	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×#3508	C₂	semidirect
2. C₁₃×#3482	C₂	semidirect
3. C₁₃×#3400	C₂	semidirect
4. C₁₃×#3373	C₂	semidirect
5. C₁₃×#3311	C₂	semidirect
6. C₁₃×#3304	C₂	semidirect
7. C₁₃×#3284	C₂	semidirect
8. C₁₃×#3267	C₂	semidirect
9. C₁₃×#3255	C₂	semidirect
10. C₁₃×#3246	C₂	semidirect
11. C₁₃×#3216	C₂	semidirect
12. C₁₃×#3208	C₂	semidirect
13. C₁₃×#3115	C₂	semidirect
14. C₁₃×#3107	C₂	semidirect
15. C₁₃×#3038	C₂	semidirect
16. C₁₃×#3035	C₂	semidirect
17. C₁₃×#2990	C₂	semidirect
19. C₂×C₁₃×#135	C₂²	semidirect
22. C₁₃×#557	C₂²	semidirect
24. C₁₃×#556	C₂²	semidirect
29. D₄×Q₈×C₁₃	C₂²	semidirect
32. C₁₃×#547	C₂²	semidirect
39. C₁₃×#533	C₂²	semidirect
48. C₄×C₁₃×#41	C₂²	semidirect
50. C₁₃×#497	C₂²	semidirect
52. C₁₃×#489	C₂²	semidirect
55. C₁₃×#482	C₂²	semidirect
56. C₁₃×#476	C₂²	semidirect
57. C₁₃×#475	C₂²	semidirect
58. C₁₃×#475	C₂²	semidirect
59. C₁₃×#475	C₂²	semidirect
60. C₁₃×#474	C₂²	semidirect
62. C₁₃×#465	C₂²	semidirect
63. C₁₃×#465	C₂²	semidirect
64. C₁₃×#464	C₂²	semidirect
65. C₁₃×#463	C₂²	semidirect
66. C₁₃×#462	C₂²	semidirect
67. C₁₃×#462	C₂²	semidirect
68. C₁₃×#462	C₂²	semidirect
69. C₁₃×#461	C₂²	semidirect
70. C₁₃×#461	C₂²	semidirect
78. C₁₃×#452	C₂²	semidirect
79. C₁₃×#452	C₂²	semidirect
81. C₁₃×#449	C₂²	semidirect
82. C₁₃×#446	C₂²	semidirect
83. C₁₃×#442	C₂²	semidirect
84. C₁₃×#440	C₂²	semidirect
85. C₄×C₁₃×Q₁₆	C₂²	semidirect
86. C₄×C₁₃×SD₁₆	C₂²	semidirect
88. C₈×D₄×C₁₃	C₂²	semidirect
89. C₁₃×#432	C₂²	semidirect
92. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
94. C₁₃×#416	C₂²	semidirect
230. #61986	C₁₃	direct (N × H)
346. #3508	C₂×C₁₃	semidirect
347. #3482	C₂×C₁₃	semidirect
348. #3400	C₂×C₁₃	semidirect
349. #3373	C₂×C₁₃	semidirect
350. #3311	C₂×C₁₃	semidirect
351. #3304	C₂×C₁₃	semidirect
352. #3284	C₂×C₁₃	semidirect
353. #3267	C₂×C₁₃	semidirect
354. #3255	C₂×C₁₃	semidirect
355. #3246	C₂×C₁₃	semidirect
356. #3216	C₂×C₁₃	semidirect
357. #3208	C₂×C₁₃	semidirect
358. #3115	C₂×C₁₃	semidirect
359. #3107	C₂×C₁₃	semidirect
360. #3038	C₂×C₁₃	semidirect
361. #3035	C₂×C₁₃	semidirect
362. #2990	C₂×C₁₃	semidirect
430. C₂×#135	C₂²×C₁₃	semidirect
433. #557	C₂²×C₁₃	semidirect
435. #556	C₂²×C₁₃	semidirect
440. D₄×Q₈	C₂²×C₁₃	semidirect
443. #547	C₂²×C₁₃	semidirect
450. #533	C₂²×C₁₃	semidirect
459. C₄×#41	C₂²×C₁₃	semidirect
461. #497	C₂²×C₁₃	semidirect
463. #489	C₂²×C₁₃	semidirect
466. #482	C₂²×C₁₃	semidirect
467. #476	C₂²×C₁₃	semidirect
468. #475	C₂²×C₁₃	semidirect
469. #475	C₂²×C₁₃	semidirect
470. #475	C₂²×C₁₃	semidirect
471. #474	C₂²×C₁₃	semidirect
473. #465	C₂²×C₁₃	semidirect
474. #465	C₂²×C₁₃	semidirect
475. #464	C₂²×C₁₃	semidirect
476. #463	C₂²×C₁₃	semidirect
477. #462	C₂²×C₁₃	semidirect
478. #462	C₂²×C₁₃	semidirect
479. #462	C₂²×C₁₃	semidirect
480. #461	C₂²×C₁₃	semidirect
481. #461	C₂²×C₁₃	semidirect
489. #452	C₂²×C₁₃	semidirect
490. #452	C₂²×C₁₃	semidirect
492. #449	C₂²×C₁₃	semidirect
493. #446	C₂²×C₁₃	semidirect
494. #442	C₂²×C₁₃	semidirect
495. #440	C₂²×C₁₃	semidirect
496. C₄×Q₁₆	C₂²×C₁₃	semidirect
497. C₄×SD₁₆	C₂²×C₁₃	semidirect
499. C₈×D₄	C₂²×C₁₃	semidirect
500. #432	C₂²×C₁₃	semidirect
503. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
505. #416	C₂²×C₁₃	semidirect
794. C₁₃	#61986	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×#3508	2
C₁₃×#3482	2
C₁₃×#3400	2
C₁₃×#3373	2
C₁₃×#3311	2
C₁₃×#3304	2
C₁₃×#3284	2
C₁₃×#3267	2
C₁₃×#3255	2
C₁₃×#3246	2
C₁₃×#3216	2
C₁₃×#3208	2
C₁₃×#3115	2
C₁₃×#3107	2
C₁₃×#3038	2
C₁₃×#3035	2
C₁₃×#2990	2
#61986	13

Subgroups — C13×#61986 #15748325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61986 #15748325