Subgroups — C₁₃×#60952 #15747291

Order 3328.

1802 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3255	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3254	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3239	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3237	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3218	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3216	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3196	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3172	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3107	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3104	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3103	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#533	—	2	1	no	—
16	C₁₃×#533	—	2	1	no	—
17	C₁₃×#533	—	2	1	no	—
18	C₁₃×#533	—	2	1	no	—
19	C₁₃×#533	C₂²	1	1	yes	characteristic
20	C₁₃×#533	C₂²	1	2	yes	—
21	C₁₃×#533	C₂²	1	2	yes	—
22	C₁₃×#533	C₂²	1	2	yes	—
23	C₁₃×#533	C₂²	1	2	yes	—
24	C₁₃×#533	C₂²	1	1	yes	characteristic
25	C₁₃×#533	C₂²	1	1	yes	characteristic
26	C₁₃×#532	C₂²	1	1	yes	characteristic
27	C₁₃×#532	C₂²	1	1	yes	characteristic
28	C₁₃×#532	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₁₃×#529	—	2	1	no	—
32	C₁₃×#529	—	2	1	no	—
33	C₁₃×#529	—	2	1	no	—
34	C₁₃×#529	—	2	1	no	—
35	C₁₃×#529	C₂²	1	2	yes	—
36	C₁₃×#529	C₂²	1	2	yes	—
37	C₂×C₁₃×#125	—	2	1	no	—
38	C₁₃×#525	—	2	1	no	—
39	C₁₃×#525	—	2	1	no	—
40	C₁₃×#525	C₂²	1	2	yes	—
41	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
42	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₄×C₁₃×#41	—	2	1	no	—
44	C₄×C₁₃×#41	—	2	1	no	—
45	C₄×C₁₃×#41	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
47	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
48	C₂×C₁₃×#117	—	2	1	no	—
49	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
50	C₁₃×#501	C₂²	1	4	yes	complemented
51	C₁₃×#497	C₂²	1	4	yes	complemented
52	C₁₃×#491	C₂²	1	4	yes	complemented
53	C₁₃×#489	C₂²	1	4	yes	complemented
54	C₁₃×#485	C₂²	1	8	yes	—
55	C₁₃×#484	C₂²	1	4	yes	—
56	C₁₃×#481	C₂²	1	4	yes	—
57	C₁₃×#477	C₂²	1	4	yes	complemented
58	C₁₃×#475	C₂²	1	4	yes	complemented
59	C₁₃×#475	C₂²	1	4	yes	complemented
60	C₁₃×#474	C₂²	1	4	yes	complemented
61	C₁₃×#470	C₂²	1	8	yes	—
62	C₁₃×#468	C₂²	1	8	yes	—
63	C₁₃×#462	C₂²	1	4	yes	complemented
64	C₁₃×#462	C₂²	1	4	yes	complemented
65	C₁₃×#461	C₂²	1	4	yes	complemented
66	C₁₃×#460	C₂²	1	4	yes	complemented
67	C₁₃×#452	C₂²	1	8	yes	—
68	C₁₃×#451	C₂²	1	4	yes	—
69	C₁₃×#448	C₂²	1	4	yes	—
70	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
71	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
72	C₁₃×#432	C₂²	1	2	yes	—
73	C₁₃×#432	C₂²	1	2	yes	—
74	C₁₃×#431	C₂²	1	2	yes	—
75	C₁₃×#431	C₂²	1	2	yes	—
76	C₁₃×#423	C₂²	1	2	yes	—
77	C₁₃×#407	C₂²	1	2	yes	—
78	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
79	C₂×C₁₃×#41	—	2	1	no	—
80	C₂×C₁₃×#41	—	2	1	no	—
81	C₂×C₁₃×#41	C₂³	1	2	yes	—
82	C₂²×Q₈×C₁₃	—	2	1	no	—
83	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
88	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
89	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
90	C₁₃×C₄⋊Q₈	—	2	1	no	—
91	C₁₃×C₄⋊Q₈	—	2	1	no	—
92	C₁₃×C₄⋊Q₈	—	2	1	no	—
93	C₁₃×C₄⋊Q₈	—	2	1	no	—
94	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
95	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
96	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
101	C₁₃×#127	C₂³	1	1	yes	characteristic
102	C₁₃×#126	—	2	2	no	—
103	C₁₃×#126	—	2	2	no	—
104	C₁₃×#125	—	2	2	no	—
105	C₁₃×#125	—	2	2	no	—
106	C₁₃×#125	—	2	2	no	—
107	C₁₃×#125	—	2	2	no	—
108	C₁₃×#125	—	2	1	no	—
109	C₁₃×#125	—	2	1	no	—
110	C₁₃×#125	C₂³	1	2	yes	—
111	C₁₃×#124	—	2	1	no	—
112	C₁₃×#124	—	2	1	no	—
113	C₁₃×#124	C₂³	1	2	yes	—
114	C₁₃×#123	—	2	2	no	—
115	C₁₃×#123	—	2	2	no	—
116	C₁₃×#123	—	2	2	no	—
117	C₁₃×C₂²⋊Q₈	—	2	2	no	—
118	C₁₃×C₂²⋊Q₈	—	2	2	no	—
119	C₁₃×C₂²⋊Q₈	—	2	2	no	—
120	C₁₃×C₂²⋊Q₈	—	2	2	no	—
121	C₁₃×C₂²⋊Q₈	—	2	2	no	—
122	C₁₃×C₂²⋊Q₈	—	2	2	no	—
123	C₁₃×C₂²⋊Q₈	—	2	1	no	—
124	C₁₃×C₂²⋊Q₈	—	2	1	no	—
125	C₁₃×C₂²⋊Q₈	—	2	1	no	—
126	C₁₃×C₂²⋊Q₈	—	2	1	no	—
127	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
128	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
129	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
130	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
131	C₁₃×#121	—	2	1	no	—
132	C₁₃×#121	—	2	1	no	—
133	C₁₃×#121	—	2	1	no	—
134	C₁₃×#121	—	2	1	no	—
135	C₁₃×#121	C₂³	1	2	yes	—
136	C₁₃×#121	C₂³	1	2	yes	—
137	C₁₃×#120	—	2	2	no	—
138	C₄×Q₈×C₁₃	—	2	2	no	—
139	C₄×Q₈×C₁₃	—	2	2	no	—
140	C₄×Q₈×C₁₃	—	2	2	no	—
141	C₄×Q₈×C₁₃	—	2	2	no	—
142	C₄×Q₈×C₁₃	—	2	2	no	—
143	C₄×Q₈×C₁₃	—	2	2	no	—
144	C₄×Q₈×C₁₃	—	2	1	no	—
145	C₄×Q₈×C₁₃	—	2	1	no	—
146	C₄×Q₈×C₁₃	—	2	1	no	—
147	C₄×Q₈×C₁₃	—	2	1	no	—
148	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
149	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
150	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
151	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
152	C₄×D₄×C₁₃	—	2	2	no	—
153	C₄×D₄×C₁₃	—	2	2	no	—
154	C₄×D₄×C₁₃	—	2	2	no	—
155	C₄×D₄×C₁₃	—	2	2	no	—
156	C₄×D₄×C₁₃	—	2	2	no	—
157	C₄×D₄×C₁₃	—	2	2	no	—
158	C₄×D₄×C₁₃	—	2	1	no	—
159	C₄×D₄×C₁₃	—	2	1	no	—
160	C₄×D₄×C₁₃	—	2	1	no	—
161	C₄×D₄×C₁₃	—	2	1	no	—
162	C₄×D₄×C₁₃	C₂³	1	2	yes	—
163	C₄×D₄×C₁₃	C₂³	1	2	yes	—
164	C₁₃×#117	—	2	2	no	—
165	C₁₃×#117	—	2	2	no	—
166	C₁₃×#117	—	2	2	no	—
167	C₁₃×#117	—	2	2	no	—
168	C₁₃×#117	—	2	1	no	—
169	C₁₃×#117	—	2	1	no	—
170	C₁₃×#117	—	2	2	no	—
171	C₁₃×#117	—	2	2	no	—
172	C₁₃×#117	—	2	2	no	—
173	C₁₃×#117	C₂³	1	2	yes	—
174	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
179	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
181	C₂×C₄²×C₁₃	—	2	2	no	—
182	C₂×C₄²×C₁₃	—	2	2	no	—
183	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
184	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
185	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
195	C₁₃×#107	C₂³	1	8	yes	—
196	C₁₃×#106	C₂³	1	8	yes	—
197	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
198	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
199	C₁₃×#103	C₂³	1	8	yes	—
200	C₁₃×#103	C₂³	1	8	yes	—
201	C₁₃×#103	C₂³	1	8	yes	—
202	C₁₃×#102	C₂³	1	8	yes	—
203	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
204	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
205	C₁₃×#97	C₂³	1	4	yes	—
206	C₄×C₈×C₁₃	C₂³	1	4	yes	—
207	#60952	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₁₃×#41	—	4	4	no	—
210	C₁₃×#41	—	4	4	no	—
211	C₁₃×#41	—	4	4	no	—
212	C₂×Q₈×C₁₃	—	2	1	no	—
213	C₂×Q₈×C₁₃	—	2	1	no	—
214	C₂×Q₈×C₁₃	—	2	2	no	—
215	C₂×Q₈×C₁₃	—	2	2	no	—
216	C₂×Q₈×C₁₃	—	2	2	no	—
217	C₂×Q₈×C₁₃	—	4	4	no	—
218	C₂×Q₈×C₁₃	—	4	4	no	—
219	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
220	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
221	C₂×D₄×C₁₃	—	2	2	no	—
222	C₂×D₄×C₁₃	—	2	2	no	—
223	C₂×D₄×C₁₃	—	2	2	no	—
224	C₂×D₄×C₁₃	—	2	1	no	—
225	C₂×D₄×C₁₃	—	2	1	no	—
226	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃	—	2	4	no	—
228	C₂²×C₄×C₁₃	—	2	2	no	—
229	C₂²×C₄×C₁₃	—	2	2	no	—
230	C₂²×C₄×C₁₃	—	2	2	no	—
231	C₂²×C₄×C₁₃	—	2	2	no	—
232	C₂²×C₄×C₁₃	—	2	2	no	—
233	C₂²×C₄×C₁₃	—	4	2	no	—
234	C₂²×C₄×C₁₃	—	4	2	no	—
235	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₁₃×Q₁₆	—	4	8	no	—
254	C₁₃×SD₁₆	—	4	8	no	—
255	C₁₃×M₁₆	—	4	4	no	—
256	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
257	C₁₃×C₄⋊C₄	—	2	2	no	—
258	C₁₃×C₄⋊C₄	—	2	2	no	—
259	C₁₃×C₄⋊C₄	—	2	2	no	—
260	C₁₃×C₄⋊C₄	—	2	2	no	—
261	C₁₃×C₄⋊C₄	—	2	2	no	—
262	C₁₃×C₄⋊C₄	—	2	2	no	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	2	4	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	1	no	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	2	no	—
273	C₁₃×C₄⋊C₄	—	2	2	no	—
274	C₁₃×C₄⋊C₄	—	2	2	no	—
275	C₁₃×C₄⋊C₄	—	2	2	no	—
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
281	C₁₃×C₂²⋊C₄	—	2	4	no	—
282	C₁₃×C₂²⋊C₄	—	2	4	no	—
283	C₁₃×C₂²⋊C₄	—	2	2	no	—
284	C₁₃×C₂²⋊C₄	—	2	2	no	—
285	C₁₃×C₂²⋊C₄	—	2	2	no	—
286	C₁₃×C₂²⋊C₄	—	2	2	no	—
287	C₁₃×C₂²⋊C₄	—	2	2	no	—
288	C₁₃×C₂²⋊C₄	—	2	2	no	—
289	C₁₃×C₂²⋊C₄	—	2	2	no	—
290	C₁₃×C₂²⋊C₄	—	2	2	no	—
291	C₁₃×C₂²⋊C₄	—	2	2	no	—
292	C₄²×C₁₃	—	2	2	no	—
293	C₄²×C₁₃	—	2	4	no	—
294	C₄²×C₁₃	—	2	2	no	—
295	C₄²×C₁₃	—	2	2	no	—
296	C₄²×C₁₃	—	2	4	no	—
297	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
310	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
311	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
312	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
313	#3444	C₂×C₁₃	1	1	yes	characteristic
314	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
315	#3255	C₂×C₁₃	1	2	yes	complemented
316	#3254	C₂×C₁₃	1	2	yes	complemented
317	#3239	C₂×C₁₃	1	2	yes	complemented
318	#3237	C₂×C₁₃	1	2	yes	complemented
319	#3218	C₂×C₁₃	1	2	yes	complemented
320	#3216	C₂×C₁₃	1	2	yes	complemented
321	#3196	C₂×C₁₃	1	4	yes	complemented
322	#3172	C₂×C₁₃	1	4	yes	complemented
323	#3107	C₂×C₁₃	1	4	yes	complemented
324	#3104	C₂×C₁₃	1	2	yes	complemented
325	#3103	C₂×C₁₃	1	2	yes	complemented
326	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
327	C₂³×C₁₃	—	2	2	no	—
328	C₂³×C₁₃	—	2	2	no	—
329	C₂³×C₁₃	—	4	1	no	—
330	C₂³×C₁₃	—	4	1	no	—
331	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
332	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
333	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
334	Q₈×C₁₃	—	2	4	no	—
335	Q₈×C₁₃	—	2	4	no	—
336	Q₈×C₁₃	—	2	4	no	—
337	Q₈×C₁₃	—	4	4	no	—
338	Q₈×C₁₃	—	4	4	no	—
339	Q₈×C₁₃	—	4	2	no	—
340	Q₈×C₁₃	—	4	2	no	—
341	Q₈×C₁₃	—	4	4	no	—
342	D₄×C₁₃	—	2	4	no	—
343	D₄×C₁₃	—	4	2	no	—
344	D₄×C₁₃	—	4	4	no	—
345	D₄×C₁₃	—	4	4	no	—
346	D₄×C₁₃	—	4	4	no	—
347	D₄×C₁₃	—	4	2	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	4	no	—
363	C₂×C₄×C₁₃	—	2	4	no	—
364	C₂×C₄×C₁₃	—	4	1	no	—
365	C₂×C₄×C₁₃	—	4	1	no	—
366	C₂×C₄×C₁₃	—	4	1	no	—
367	C₂×C₄×C₁₃	—	4	1	no	—
368	C₂×C₄×C₁₃	—	4	1	no	—
369	C₂×C₄×C₁₃	—	4	1	no	—
370	C₂×C₄×C₁₃	—	4	4	no	—
371	C₂×C₄×C₁₃	—	4	4	no	—
372	C₂×C₄×C₁₃	—	4	4	no	—
373	C₂×C₄×C₁₃	—	4	4	no	—
374	C₂×C₄×C₁₃	—	4	4	no	—
375	C₂×C₄×C₁₃	#137	1	4	yes	—
376	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
388	C₈×C₁₃	—	2	8	no	—
389	#533	—	2	1	no	—
390	#533	—	2	1	no	—
391	#533	—	2	1	no	—
392	#533	—	2	1	no	—
393	#533	C₂²×C₁₃	1	1	yes	characteristic
394	#533	C₂²×C₁₃	1	2	yes	—
395	#533	C₂²×C₁₃	1	2	yes	—
396	#533	C₂²×C₁₃	1	2	yes	—
397	#533	C₂²×C₁₃	1	2	yes	—
398	#533	C₂²×C₁₃	1	1	yes	characteristic
399	#533	C₂²×C₁₃	1	1	yes	characteristic
400	#532	C₂²×C₁₃	1	1	yes	characteristic
401	#532	C₂²×C₁₃	1	1	yes	characteristic
402	#532	C₂²×C₁₃	1	1	yes	characteristic
403	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
405	#529	—	2	1	no	—
406	#529	—	2	1	no	—
407	#529	—	2	1	no	—
408	#529	—	2	1	no	—
409	#529	C₂²×C₁₃	1	2	yes	—
410	#529	C₂²×C₁₃	1	2	yes	—
411	C₂×#125	—	2	1	no	—
412	#525	—	2	1	no	—
413	#525	—	2	1	no	—
414	#525	C₂²×C₁₃	1	2	yes	—
415	C₂×C₂²⋊Q₈	—	2	1	no	—
416	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
417	C₄×#41	—	2	1	no	—
418	C₄×#41	—	2	1	no	—
419	C₄×#41	C₂²×C₁₃	1	2	yes	—
420	C₂×C₄×Q₈	—	2	1	no	—
421	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
422	C₂×#117	—	2	1	no	—
423	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
424	#501	C₂²×C₁₃	1	4	yes	complemented
425	#497	C₂²×C₁₃	1	4	yes	complemented
426	#491	C₂²×C₁₃	1	4	yes	complemented
427	#489	C₂²×C₁₃	1	4	yes	complemented
428	#485	C₂²×C₁₃	1	8	yes	—
429	#484	C₂²×C₁₃	1	4	yes	—
430	#481	C₂²×C₁₃	1	4	yes	—
431	#477	C₂²×C₁₃	1	4	yes	complemented
432	#475	C₂²×C₁₃	1	4	yes	complemented
433	#475	C₂²×C₁₃	1	4	yes	complemented
434	#474	C₂²×C₁₃	1	4	yes	complemented
435	#470	C₂²×C₁₃	1	8	yes	—
436	#468	C₂²×C₁₃	1	8	yes	—
437	#462	C₂²×C₁₃	1	4	yes	complemented
438	#462	C₂²×C₁₃	1	4	yes	complemented
439	#461	C₂²×C₁₃	1	4	yes	complemented
440	#460	C₂²×C₁₃	1	4	yes	complemented
441	#452	C₂²×C₁₃	1	8	yes	—
442	#451	C₂²×C₁₃	1	4	yes	—
443	#448	C₂²×C₁₃	1	4	yes	—
444	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
445	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
446	#432	C₂²×C₁₃	1	2	yes	—
447	#432	C₂²×C₁₃	1	2	yes	—
448	#431	C₂²×C₁₃	1	2	yes	—
449	#431	C₂²×C₁₃	1	2	yes	—
450	#423	C₂²×C₁₃	1	2	yes	—
451	#407	C₂²×C₁₃	1	2	yes	—
452	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
453	C₂²×C₁₃	—	2	1	no	—
454	C₂²×C₁₃	—	2	1	no	—
455	C₂²×C₁₃	—	2	1	no	—
456	C₂²×C₁₃	—	2	1	no	—
457	C₂²×C₁₃	—	2	1	no	—
458	C₂²×C₁₃	—	2	1	no	—
459	C₂²×C₁₃	—	2	1	no	—
460	C₂²×C₁₃	—	2	1	no	—
461	C₂²×C₁₃	—	4	4	no	—
462	C₂²×C₁₃	—	4	2	no	—
463	C₂²×C₁₃	—	4	2	no	—
464	C₂²×C₁₃	—	4	2	no	—
465	C₂²×C₁₃	C₂×#137	1	2	yes	—
466	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
467	C₄×C₁₃	—	2	1	no	—
468	C₄×C₁₃	—	2	1	no	—
469	C₄×C₁₃	—	2	1	no	—
470	C₄×C₁₃	—	2	1	no	—
471	C₄×C₁₃	—	2	1	no	—
472	C₄×C₁₃	—	2	1	no	—
473	C₄×C₁₃	—	2	1	no	—
474	C₄×C₁₃	—	2	1	no	—
475	C₄×C₁₃	—	4	2	no	—
476	C₄×C₁₃	—	4	4	no	—
477	C₄×C₁₃	—	4	2	no	—
478	C₄×C₁₃	—	4	2	no	—
479	C₄×C₁₃	—	4	4	no	—
480	C₄×C₁₃	C₂×#137	1	2	yes	—
481	C₄×C₁₃	C₂×#137	1	2	yes	—
482	C₄×C₁₃	#575	1	2	yes	—
483	C₄×C₁₃	#585	1	2	yes	—
484	C₂×#41	—	2	1	no	—
485	C₂×#41	—	2	1	no	—
486	C₂×#41	C₂³×C₁₃	1	2	yes	—
487	C₂²×Q₈	—	2	1	no	—
488	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
489	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
490	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
492	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
493	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
494	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
495	C₄⋊Q₈	—	2	1	no	—
496	C₄⋊Q₈	—	2	1	no	—
497	C₄⋊Q₈	—	2	1	no	—
498	C₄⋊Q₈	—	2	1	no	—
499	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
500	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
501	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
502	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
503	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
504	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
506	#127	C₂³×C₁₃	1	1	yes	characteristic
507	#126	—	2	2	no	—
508	#126	—	2	2	no	—
509	#125	—	2	2	no	—
510	#125	—	2	2	no	—
511	#125	—	2	2	no	—
512	#125	—	2	2	no	—
513	#125	—	2	1	no	—
514	#125	—	2	1	no	—
515	#125	C₂³×C₁₃	1	2	yes	—
516	#124	—	2	1	no	—
517	#124	—	2	1	no	—
518	#124	C₂³×C₁₃	1	2	yes	—
519	#123	—	2	2	no	—
520	#123	—	2	2	no	—
521	#123	—	2	2	no	—
522	C₂²⋊Q₈	—	2	2	no	—
523	C₂²⋊Q₈	—	2	2	no	—
524	C₂²⋊Q₈	—	2	2	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	2	no	—
528	C₂²⋊Q₈	—	2	1	no	—
529	C₂²⋊Q₈	—	2	1	no	—
530	C₂²⋊Q₈	—	2	1	no	—
531	C₂²⋊Q₈	—	2	1	no	—
532	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
533	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
534	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
535	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
536	#121	—	2	1	no	—
537	#121	—	2	1	no	—
538	#121	—	2	1	no	—
539	#121	—	2	1	no	—
540	#121	C₂³×C₁₃	1	2	yes	—
541	#121	C₂³×C₁₃	1	2	yes	—
542	#120	—	2	2	no	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	—	2	2	no	—
547	C₄×Q₈	—	2	2	no	—
548	C₄×Q₈	—	2	2	no	—
549	C₄×Q₈	—	2	1	no	—
550	C₄×Q₈	—	2	1	no	—
551	C₄×Q₈	—	2	1	no	—
552	C₄×Q₈	—	2	1	no	—
553	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
554	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
555	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
556	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
557	C₄×D₄	—	2	2	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	C₂³×C₁₃	1	2	yes	—
568	C₄×D₄	C₂³×C₁₃	1	2	yes	—
569	#117	—	2	2	no	—
570	#117	—	2	2	no	—
571	#117	—	2	2	no	—
572	#117	—	2	2	no	—
573	#117	—	2	1	no	—
574	#117	—	2	1	no	—
575	#117	—	2	2	no	—
576	#117	—	2	2	no	—
577	#117	—	2	2	no	—
578	#117	C₂³×C₁₃	1	2	yes	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	2	no	—
583	C₂×C₄⋊C₄	—	2	2	no	—
584	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
585	C₂×C₂²⋊C₄	—	2	2	no	—
586	C₂×C₄²	—	2	2	no	—
587	C₂×C₄²	—	2	2	no	—
588	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
589	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
590	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
591	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
592	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
593	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
594	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
600	#107	C₂³×C₁₃	1	8	yes	—
601	#106	C₂³×C₁₃	1	8	yes	—
602	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
603	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
604	#103	C₂³×C₁₃	1	8	yes	—
605	#103	C₂³×C₁₃	1	8	yes	—
606	#103	C₂³×C₁₃	1	8	yes	—
607	#102	C₂³×C₁₃	1	8	yes	—
608	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
609	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
610	#97	C₂³×C₁₃	1	4	yes	—
611	C₄×C₈	C₂³×C₁₃	1	4	yes	—
612	C₂×C₁₃	—	2	2	no	—
613	C₂×C₁₃	—	4	1	no	—
614	C₂×C₁₃	—	4	1	no	—
615	C₂×C₁₃	—	8	2	no	—
616	C₂×C₁₃	#3449	1	1	yes	characteristic
617	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
618	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
619	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
620	#41	—	4	4	no	—
621	#41	—	4	4	no	—
622	#41	—	4	4	no	—
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	2	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	2	2	no	—
628	C₂×Q₈	—	4	4	no	—
629	C₂×Q₈	—	4	4	no	—
630	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
631	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	4	2	no	—
645	C₂²×C₄	—	4	2	no	—
646	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
649	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
654	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
660	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
664	Q₁₆	—	4	8	no	—
665	SD₁₆	—	4	8	no	—
666	M₁₆	—	4	4	no	—
667	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
690	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
691	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	2	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	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₄²	—	2	2	no	—
704	C₄²	—	2	2	no	—
705	C₄²	—	2	4	no	—
706	C₄²	—	2	4	no	—
707	C₄²	—	2	2	no	—
708	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
709	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
710	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
711	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
712	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
713	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
714	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
715	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
716	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
717	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
718	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
719	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
720	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
721	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
722	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
723	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
724	C₁₃	#60952	1	1	yes	characteristic, direct product factor, Sylow
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	4	1	no	—
728	C₂³	—	4	1	no	—
729	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
730	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
731	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
732	Q₈	—	2	4	no	—
733	Q₈	—	2	4	no	—
734	Q₈	—	2	4	no	—
735	Q₈	—	4	4	no	—
736	Q₈	—	4	4	no	—
737	Q₈	—	4	2	no	—
738	Q₈	—	4	2	no	—
739	Q₈	—	4	4	no	—
740	D₄	—	2	4	no	—
741	D₄	—	4	2	no	—
742	D₄	—	4	4	no	—
743	D₄	—	4	4	no	—
744	D₄	—	4	4	no	—
745	D₄	—	4	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	4	no	—
769	C₂×C₄	—	4	4	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	4	no	—
772	C₂×C₄	—	4	4	no	—
773	C₂×C₄	C₁₃×#137	1	4	yes	—
774	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
775	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
776	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
777	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
778	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
779	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
784	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
785	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
786	C₈	—	2	8	no	—
787	C₂²	—	2	1	no	—
788	C₂²	—	2	1	no	—
789	C₂²	—	2	1	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	1	no	—
793	C₂²	—	2	1	no	—
794	C₂²	—	2	1	no	—
795	C₂²	—	4	4	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	C₂×C₁₃×#137	1	2	yes	—
800	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
801	C₄	—	2	1	no	—
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	2	1	no	—
805	C₄	—	2	1	no	—
806	C₄	—	2	1	no	—
807	C₄	—	2	1	no	—
808	C₄	—	2	1	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	4	no	—
812	C₄	—	4	2	no	—
813	C₄	—	4	4	no	—
814	C₄	C₂×C₁₃×#137	1	2	yes	—
815	C₄	C₂×C₁₃×#137	1	2	yes	—
816	C₄	C₁₃×#575	1	2	yes	—
817	C₄	C₁₃×#585	1	2	yes	—
818	C₂	—	2	2	no	—
819	C₂	—	4	1	no	—
820	C₂	—	4	1	no	—
821	C₂	—	8	2	no	—
822	C₂	C₁₃×#3449	1	1	yes	characteristic
823	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
824	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
prime radical	C₁₃×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#533	C₂	semidirect
3. C₁₃×#3255	C₂	semidirect
4. C₁₃×#3254	C₂	semidirect
5. C₁₃×#3239	C₂	semidirect
6. C₁₃×#3237	C₂	semidirect
7. C₁₃×#3218	C₂	semidirect
8. C₁₃×#3216	C₂	semidirect
9. C₁₃×#3196	C₂	semidirect
10. C₁₃×#3172	C₂	semidirect
11. C₁₃×#3107	C₂	semidirect
12. C₁₃×#3104	C₂	semidirect
13. C₁₃×#3103	C₂	semidirect
14. C₁₃×#2920	C₂	semidirect
50. C₁₃×#501	C₂²	semidirect
51. C₁₃×#497	C₂²	semidirect
52. C₁₃×#491	C₂²	semidirect
53. C₁₃×#489	C₂²	semidirect
57. C₁₃×#477	C₂²	semidirect
58. C₁₃×#475	C₂²	semidirect
59. C₁₃×#475	C₂²	semidirect
60. C₁₃×#474	C₂²	semidirect
63. C₁₃×#462	C₂²	semidirect
64. C₁₃×#462	C₂²	semidirect
65. C₁₃×#461	C₂²	semidirect
66. C₁₃×#460	C₂²	semidirect
70. C₄×C₁₃×Q₁₆	C₂²	semidirect
71. C₄×C₁₃×SD₁₆	C₂²	semidirect
207. #60952	C₁₃	direct (N × H)
314. C₂×#533	C₂×C₁₃	semidirect
315. #3255	C₂×C₁₃	semidirect
316. #3254	C₂×C₁₃	semidirect
317. #3239	C₂×C₁₃	semidirect
318. #3237	C₂×C₁₃	semidirect
319. #3218	C₂×C₁₃	semidirect
320. #3216	C₂×C₁₃	semidirect
321. #3196	C₂×C₁₃	semidirect
322. #3172	C₂×C₁₃	semidirect
323. #3107	C₂×C₁₃	semidirect
324. #3104	C₂×C₁₃	semidirect
325. #3103	C₂×C₁₃	semidirect
326. #2920	C₂×C₁₃	semidirect
424. #501	C₂²×C₁₃	semidirect
425. #497	C₂²×C₁₃	semidirect
426. #491	C₂²×C₁₃	semidirect
427. #489	C₂²×C₁₃	semidirect
431. #477	C₂²×C₁₃	semidirect
432. #475	C₂²×C₁₃	semidirect
433. #475	C₂²×C₁₃	semidirect
434. #474	C₂²×C₁₃	semidirect
437. #462	C₂²×C₁₃	semidirect
438. #462	C₂²×C₁₃	semidirect
439. #461	C₂²×C₁₃	semidirect
440. #460	C₂²×C₁₃	semidirect
444. C₄×Q₁₆	C₂²×C₁₃	semidirect
445. C₄×SD₁₆	C₂²×C₁₃	semidirect
724. C₁₃	#60952	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×#3444	2
C₂×C₁₃×#533	2
C₁₃×#3255	2
C₁₃×#3254	2
C₁₃×#3239	2
C₁₃×#3237	2
C₁₃×#3218	2
C₁₃×#3216	2
C₁₃×#3196	2
C₁₃×#3172	2
C₁₃×#3107	2
C₁₃×#3104	2
C₁₃×#3103	2
C₁₃×#2920	2
#60952	13

Subgroups — C13×#60952 #15747291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60952 #15747291