Subgroups — C₁₃×#60790 #15747129

Order 3328.

2188 conjugacy classes of subgroups.

The subgroup lattice has 876 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, complemented
2	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3219	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3218	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3217	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3216	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3215	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3214	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3213	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3150	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3135	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3035	C₂	1	4	yes	maximal, complemented
13	C₁₃×#3002	C₂	1	4	yes	maximal, complemented
14	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	C₂²	1	2	yes	—
16	C₂×C₁₃×#135	C₂²	1	8	yes	complemented
17	C₁₃×#533	C₂²	1	1	yes	characteristic
18	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
20	C₁₃×#532	—	2	1	no	—
21	C₁₃×#532	—	2	1	no	—
22	C₁₃×#532	—	2	1	no	—
23	C₁₃×#532	—	2	1	no	—
24	C₁₃×#532	C₂²	1	2	yes	—
25	C₁₃×#532	C₂²	1	2	yes	—
26	C₁₃×#532	C₂²	1	2	yes	—
27	C₁₃×#532	C₂²	1	2	yes	—
28	C₁₃×#532	C₂²	1	1	yes	characteristic
29	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
33	C₁₃×#529	—	2	1	no	—
34	C₁₃×#529	—	2	1	no	—
35	C₁₃×#529	—	2	1	no	—
36	C₁₃×#529	—	2	1	no	—
37	C₁₃×#529	C₂²	1	2	yes	—
38	C₁₃×#529	C₂²	1	2	yes	complemented
39	C₂×C₁₃×#124	C₂²	1	2	yes	—
40	C₁₃×#525	—	2	1	no	—
41	C₁₃×#525	—	2	1	no	—
42	C₁₃×#525	C₂²	1	2	yes	—
43	C₂×C₁₃×#121	—	2	1	no	—
44	C₂×C₁₃×#121	—	2	1	no	—
45	C₄×C₁₃×#41	—	2	1	no	—
46	C₄×C₁₃×#41	—	2	1	no	—
47	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
48	C₂×C₄×D₄×C₁₃	—	2	1	no	—
49	C₂×C₄×D₄×C₁₃	—	2	1	no	—
50	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#497	C₂²	1	4	yes	complemented
52	C₁₃×#497	C₂²	1	4	yes	complemented
53	C₁₃×#496	C₂²	1	4	yes	complemented
54	C₁₃×#496	C₂²	1	4	yes	complemented
55	C₁₃×#491	C₂²	1	4	yes	complemented
56	C₁₃×#490	C₂²	1	4	yes	complemented
57	C₁₃×#489	C₂²	1	4	yes	complemented
58	C₁₃×#489	C₂²	1	4	yes	complemented
59	C₁₃×#464	C₂²	1	8	yes	complemented
60	C₁₃×#463	C₂²	1	8	yes	complemented
61	C₁₃×#462	C₂²	1	4	yes	complemented
62	C₁₃×#461	C₂²	1	4	yes	complemented
63	C₁₃×#460	C₂²	1	4	yes	complemented
64	C₁₃×#459	C₂²	1	4	yes	complemented
65	C₁₃×#452	C₂²	1	8	yes	complemented
66	C₁₃×#451	C₂²	1	4	yes	—
67	C₁₃×#450	C₂²	1	4	yes	—
68	C₁₃×#449	C₂²	1	8	yes	complemented
69	C₁₃×#448	C₂²	1	4	yes	—
70	C₁₃×#447	C₂²	1	4	yes	—
71	C₁₃×#432	C₂²	1	2	yes	—
72	C₁₃×#432	C₂²	1	2	yes	—
73	C₁₃×#432	C₂²	1	2	yes	complemented
74	C₁₃×#432	C₂²	1	2	yes	complemented
75	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
76	C₁₃×#416	C₂²	1	8	yes	complemented
77	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
78	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
79	C₂×C₁₃×#41	—	2	1	no	—
80	C₂×C₁₃×#41	—	2	1	no	—
81	C₂×C₁₃×#41	—	2	2	no	—
82	C₂×C₁₃×#41	—	2	2	no	—
83	C₂×C₁₃×#41	—	4	8	no	—
84	C₂×C₁₃×#41	C₂³	1	4	yes	—
85	C₂×C₁₃×#41	C₂³	1	2	yes	—
86	C₂×C₁₃×#41	C₂³	1	4	yes	—
87	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃	—	2	2	no	—
89	C₂²×D₄×C₁₃	—	2	1	no	—
90	C₂²×D₄×C₁₃	—	2	1	no	—
91	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃	—	2	2	no	—
93	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
94	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×#135	—	4	16	no	—
97	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
98	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
99	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
100	C₂×C₁₃×D₈	C₂³	1	8	yes	—
101	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
102	C₁₃×C₄⋊Q₈	—	2	1	no	—
103	C₁₃×C₄⋊Q₈	—	2	1	no	—
104	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
105	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
106	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
107	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
108	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
109	C₁₃×#127	—	2	1	no	—
110	C₁₃×#127	—	2	1	no	—
111	C₁₃×#127	C₂³	1	2	yes	—
112	C₁₃×#127	C₂³	1	2	yes	—
113	C₁₃×#127	C₂³	1	1	yes	characteristic
114	C₁₃×#126	—	2	2	no	—
115	C₁₃×#126	—	2	2	no	—
116	C₁₃×#125	—	2	1	no	—
117	C₁₃×#125	—	2	1	no	—
118	C₁₃×#125	C₂³	1	2	yes	—
119	C₁₃×#124	—	2	2	no	—
120	C₁₃×#124	—	2	2	no	—
121	C₁₃×#124	—	2	1	no	—
122	C₁₃×#124	—	2	1	no	—
123	C₁₃×#124	C₂³	1	4	yes	—
124	C₁₃×#124	C₂³	1	4	yes	—
125	C₁₃×#124	C₂³	1	2	yes	—
126	C₁₃×#123	—	2	2	no	—
127	C₁₃×#123	—	2	2	no	—
128	C₁₃×#123	—	2	2	no	—
129	C₁₃×C₂²⋊Q₈	—	2	1	no	—
130	C₁₃×C₂²⋊Q₈	—	2	1	no	—
131	C₁₃×C₂²⋊Q₈	—	2	1	no	—
132	C₁₃×C₂²⋊Q₈	—	2	1	no	—
133	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
134	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₁₃×#121	—	2	2	no	—
136	C₁₃×#121	—	2	2	no	—
137	C₁₃×#121	—	2	2	no	—
138	C₁₃×#121	—	2	2	no	—
139	C₁₃×#121	—	2	2	no	—
140	C₁₃×#121	—	2	2	no	—
141	C₁₃×#121	—	2	2	no	—
142	C₁₃×#121	—	2	2	no	—
143	C₁₃×#121	—	2	1	no	—
144	C₁₃×#121	—	2	1	no	—
145	C₁₃×#121	—	2	1	no	—
146	C₁₃×#121	—	2	1	no	—
147	C₁₃×#121	C₂³	1	2	yes	—
148	C₁₃×#121	C₂³	1	2	yes	—
149	C₁₃×#120	—	2	2	no	—
150	C₄×Q₈×C₁₃	—	2	1	no	—
151	C₄×Q₈×C₁₃	—	2	1	no	—
152	C₄×Q₈×C₁₃	—	2	1	no	—
153	C₄×Q₈×C₁₃	—	2	1	no	—
154	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
156	C₄×D₄×C₁₃	—	2	2	no	—
157	C₄×D₄×C₁₃	—	2	2	no	—
158	C₄×D₄×C₁₃	—	2	2	no	—
159	C₄×D₄×C₁₃	—	2	2	no	—
160	C₄×D₄×C₁₃	—	2	2	no	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	—	2	2	no	—
163	C₄×D₄×C₁₃	—	2	2	no	—
164	C₄×D₄×C₁₃	—	2	2	no	—
165	C₄×D₄×C₁₃	—	2	2	no	—
166	C₄×D₄×C₁₃	—	2	2	no	—
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	1	no	—
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	C₂³	1	2	yes	—
175	C₄×D₄×C₁₃	C₂³	1	2	yes	—
176	C₁₃×#117	—	2	1	no	—
177	C₁₃×#117	—	2	1	no	—
178	C₁₃×#117	—	2	2	no	—
179	C₁₃×#117	—	2	2	no	—
180	C₁₃×#117	—	2	2	no	—
181	C₁₃×#117	C₂³	1	2	yes	—
182	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
185	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
186	C₂×C₄²×C₁₃	—	2	2	no	—
187	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
199	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
200	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
201	C₁₃×#103	C₂³	1	8	yes	—
202	C₁₃×#103	C₂³	1	8	yes	—
203	C₁₃×#102	C₂³	1	8	yes	—
204	C₁₃×#102	C₂³	1	8	yes	—
205	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
206	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
207	C₁₃×#97	C₂³	1	4	yes	—
208	C₁₃×#97	C₂³	1	4	yes	—
209	#60790	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂⁴×C₁₃	—	2	2	no	—
211	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₁₃×#41	—	2	8	no	—
213	C₁₃×#41	—	2	16	no	—
214	C₁₃×#41	—	4	8	no	—
215	C₁₃×#41	—	4	4	no	—
216	C₁₃×#41	—	4	4	no	—
217	C₁₃×#41	—	4	8	no	—
218	C₁₃×#41	—	4	8	no	—
219	C₂×Q₈×C₁₃	—	2	1	no	—
220	C₂×Q₈×C₁₃	—	2	1	no	—
221	C₂×Q₈×C₁₃	—	2	2	no	—
222	C₂×Q₈×C₁₃	—	4	4	no	—
223	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
224	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
225	C₂×D₄×C₁₃	—	2	2	no	—
226	C₂×D₄×C₁₃	—	2	2	no	—
227	C₂×D₄×C₁₃	—	2	2	no	—
228	C₂×D₄×C₁₃	—	2	4	no	—
229	C₂×D₄×C₁₃	—	2	4	no	—
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	2	1	no	—
232	C₂×D₄×C₁₃	—	2	2	no	—
233	C₂×D₄×C₁₃	—	2	2	no	—
234	C₂×D₄×C₁₃	—	2	2	no	—
235	C₂×D₄×C₁₃	—	2	2	no	—
236	C₂×D₄×C₁₃	—	2	2	no	—
237	C₂×D₄×C₁₃	—	4	4	no	—
238	C₂×D₄×C₁₃	—	4	4	no	—
239	C₂×D₄×C₁₃	—	4	4	no	—
240	C₂×D₄×C₁₃	—	4	8	no	—
241	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
242	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃	—	2	4	no	—
244	C₂²×C₄×C₁₃	—	2	2	no	—
245	C₂²×C₄×C₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₃	—	2	2	no	—
247	C₂²×C₄×C₁₃	—	2	4	no	—
248	C₂²×C₄×C₁₃	—	2	2	no	—
249	C₂²×C₄×C₁₃	—	2	4	no	—
250	C₂²×C₄×C₁₃	—	4	2	no	—
251	C₂²×C₄×C₁₃	—	4	2	no	—
252	C₂²×C₄×C₁₃	—	4	8	no	—
253	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₁₃×Q₁₆	—	4	8	no	—
272	C₁₃×SD₁₆	—	4	8	no	—
273	C₁₃×SD₁₆	—	4	8	no	—
274	C₁₃×D₈	—	4	8	no	—
275	C₂×C₈×C₁₃	—	2	8	no	—
276	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	—	2	2	no	—
279	C₁₃×C₄⋊C₄	—	2	2	no	—
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	1	no	—
282	C₁₃×C₄⋊C₄	—	2	1	no	—
283	C₁₃×C₄⋊C₄	—	2	1	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	—	2	2	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
292	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
293	C₁₃×C₂²⋊C₄	—	2	2	no	—
294	C₁₃×C₂²⋊C₄	—	2	2	no	—
295	C₁₃×C₂²⋊C₄	—	2	2	no	—
296	C₁₃×C₂²⋊C₄	—	2	4	no	—
297	C₁₃×C₂²⋊C₄	—	2	4	no	—
298	C₁₃×C₂²⋊C₄	—	2	4	no	—
299	C₁₃×C₂²⋊C₄	—	2	4	no	—
300	C₁₃×C₂²⋊C₄	—	2	2	no	—
301	C₁₃×C₂²⋊C₄	—	2	2	no	—
302	C₁₃×C₂²⋊C₄	—	2	2	no	—
303	C₁₃×C₂²⋊C₄	—	2	2	no	—
304	C₁₃×C₂²⋊C₄	—	2	2	no	—
305	C₁₃×C₂²⋊C₄	—	2	2	no	—
306	C₄²×C₁₃	—	2	2	no	—
307	C₄²×C₁₃	—	2	2	no	—
308	C₄²×C₁₃	—	2	2	no	—
309	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
322	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
323	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
324	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
325	#3444	C₂×C₁₃	1	1	yes	characteristic, complemented
326	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
327	#3219	C₂×C₁₃	1	4	yes	complemented
328	#3218	C₂×C₁₃	1	2	yes	complemented
329	#3217	C₂×C₁₃	1	2	yes	complemented
330	#3216	C₂×C₁₃	1	2	yes	complemented
331	#3215	C₂×C₁₃	1	2	yes	complemented
332	#3214	C₂×C₁₃	1	2	yes	complemented
333	#3213	C₂×C₁₃	1	2	yes	complemented
334	#3150	C₂×C₁₃	1	2	yes	complemented
335	#3135	C₂×C₁₃	1	2	yes	complemented
336	#3035	C₂×C₁₃	1	4	yes	complemented
337	#3002	C₂×C₁₃	1	4	yes	complemented
338	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
339	C₂³×C₁₃	—	2	2	no	—
340	C₂³×C₁₃	—	2	2	no	—
341	C₂³×C₁₃	—	2	2	no	—
342	C₂³×C₁₃	—	2	4	no	—
343	C₂³×C₁₃	—	4	1	no	—
344	C₂³×C₁₃	—	4	4	no	—
345	C₂³×C₁₃	—	4	4	no	—
346	C₂³×C₁₃	—	4	4	no	—
347	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
348	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
349	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
350	Q₈×C₁₃	—	2	4	no	—
351	Q₈×C₁₃	—	2	8	no	—
352	Q₈×C₁₃	—	4	4	no	—
353	Q₈×C₁₃	—	4	2	no	—
354	Q₈×C₁₃	—	4	2	no	—
355	D₄×C₁₃	—	2	4	no	—
356	D₄×C₁₃	—	2	8	no	—
357	D₄×C₁₃	—	4	4	no	—
358	D₄×C₁₃	—	4	4	no	—
359	D₄×C₁₃	—	4	4	no	—
360	D₄×C₁₃	—	4	4	no	—
361	D₄×C₁₃	—	4	2	no	—
362	D₄×C₁₃	—	4	2	no	—
363	D₄×C₁₃	—	4	8	no	—
364	D₄×C₁₃	—	4	4	no	—
365	D₄×C₁₃	—	4	8	no	—
366	D₄×C₁₃	—	4	4	no	—
367	D₄×C₁₃	—	4	4	no	—
368	D₄×C₁₃	—	4	4	no	—
369	C₂×C₄×C₁₃	—	2	2	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	4	no	—
383	C₂×C₄×C₁₃	—	4	1	no	—
384	C₂×C₄×C₁₃	—	4	1	no	—
385	C₂×C₄×C₁₃	—	4	1	no	—
386	C₂×C₄×C₁₃	—	4	1	no	—
387	C₂×C₄×C₁₃	—	4	1	no	—
388	C₂×C₄×C₁₃	—	4	1	no	—
389	C₂×C₄×C₁₃	—	4	1	no	—
390	C₂×C₄×C₁₃	—	4	8	no	—
391	C₂×C₄×C₁₃	—	4	4	no	—
392	C₂×C₄×C₁₃	—	4	4	no	—
393	C₂×C₄×C₁₃	—	4	8	no	—
394	C₂×C₄×C₁₃	—	4	4	no	—
395	C₂×C₄×C₁₃	—	4	4	no	—
396	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
408	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
409	C₈×C₁₃	—	2	8	no	—
410	C₂²×#41	C₂²×C₁₃	1	2	yes	—
411	C₂×#135	C₂²×C₁₃	1	8	yes	complemented
412	#533	C₂²×C₁₃	1	1	yes	characteristic
413	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
414	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
415	#532	—	2	1	no	—
416	#532	—	2	1	no	—
417	#532	—	2	1	no	—
418	#532	—	2	1	no	—
419	#532	C₂²×C₁₃	1	2	yes	—
420	#532	C₂²×C₁₃	1	2	yes	—
421	#532	C₂²×C₁₃	1	2	yes	—
422	#532	C₂²×C₁₃	1	2	yes	—
423	#532	C₂²×C₁₃	1	1	yes	characteristic
424	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
425	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
426	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
428	#529	—	2	1	no	—
429	#529	—	2	1	no	—
430	#529	—	2	1	no	—
431	#529	—	2	1	no	—
432	#529	C₂²×C₁₃	1	2	yes	—
433	#529	C₂²×C₁₃	1	2	yes	complemented
434	C₂×#124	C₂²×C₁₃	1	2	yes	—
435	#525	—	2	1	no	—
436	#525	—	2	1	no	—
437	#525	C₂²×C₁₃	1	2	yes	—
438	C₂×#121	—	2	1	no	—
439	C₂×#121	—	2	1	no	—
440	C₄×#41	—	2	1	no	—
441	C₄×#41	—	2	1	no	—
442	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
443	C₂×C₄×D₄	—	2	1	no	—
444	C₂×C₄×D₄	—	2	1	no	—
445	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
446	#497	C₂²×C₁₃	1	4	yes	complemented
447	#497	C₂²×C₁₃	1	4	yes	complemented
448	#496	C₂²×C₁₃	1	4	yes	complemented
449	#496	C₂²×C₁₃	1	4	yes	complemented
450	#491	C₂²×C₁₃	1	4	yes	complemented
451	#490	C₂²×C₁₃	1	4	yes	complemented
452	#489	C₂²×C₁₃	1	4	yes	complemented
453	#489	C₂²×C₁₃	1	4	yes	complemented
454	#464	C₂²×C₁₃	1	8	yes	complemented
455	#463	C₂²×C₁₃	1	8	yes	complemented
456	#462	C₂²×C₁₃	1	4	yes	complemented
457	#461	C₂²×C₁₃	1	4	yes	complemented
458	#460	C₂²×C₁₃	1	4	yes	complemented
459	#459	C₂²×C₁₃	1	4	yes	complemented
460	#452	C₂²×C₁₃	1	8	yes	complemented
461	#451	C₂²×C₁₃	1	4	yes	—
462	#450	C₂²×C₁₃	1	4	yes	—
463	#449	C₂²×C₁₃	1	8	yes	complemented
464	#448	C₂²×C₁₃	1	4	yes	—
465	#447	C₂²×C₁₃	1	4	yes	—
466	#432	C₂²×C₁₃	1	2	yes	—
467	#432	C₂²×C₁₃	1	2	yes	—
468	#432	C₂²×C₁₃	1	2	yes	complemented
469	#432	C₂²×C₁₃	1	2	yes	complemented
470	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
471	#416	C₂²×C₁₃	1	8	yes	complemented
472	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
473	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
474	C₂²×C₁₃	—	2	1	no	—
475	C₂²×C₁₃	—	2	1	no	—
476	C₂²×C₁₃	—	2	1	no	—
477	C₂²×C₁₃	—	2	1	no	—
478	C₂²×C₁₃	—	2	1	no	—
479	C₂²×C₁₃	—	2	1	no	—
480	C₂²×C₁₃	—	2	1	no	—
481	C₂²×C₁₃	—	4	4	no	—
482	C₂²×C₁₃	—	4	4	no	—
483	C₂²×C₁₃	—	4	2	no	—
484	C₂²×C₁₃	—	4	2	no	—
485	C₂²×C₁₃	—	4	2	no	—
486	C₂²×C₁₃	—	4	4	no	—
487	C₂²×C₁₃	—	4	4	no	—
488	C₂²×C₁₃	—	8	8	no	—
489	C₂²×C₁₃	#535	1	2	yes	—
490	C₂²×C₁₃	#575	1	2	yes	—
491	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
492	C₄×C₁₃	—	2	1	no	—
493	C₄×C₁₃	—	2	1	no	—
494	C₄×C₁₃	—	2	1	no	—
495	C₄×C₁₃	—	2	1	no	—
496	C₄×C₁₃	—	2	1	no	—
497	C₄×C₁₃	—	2	1	no	—
498	C₄×C₁₃	—	2	1	no	—
499	C₄×C₁₃	—	2	1	no	—
500	C₄×C₁₃	—	2	1	no	—
501	C₄×C₁₃	—	4	4	no	—
502	C₄×C₁₃	—	4	2	no	—
503	C₄×C₁₃	—	4	2	no	—
504	C₄×C₁₃	—	4	2	no	—
505	C₄×C₁₃	#535	1	2	yes	—
506	C₄×C₁₃	#575	1	2	yes	—
507	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
508	C₂×#41	—	2	1	no	—
509	C₂×#41	—	2	1	no	—
510	C₂×#41	—	2	2	no	—
511	C₂×#41	—	2	2	no	—
512	C₂×#41	—	4	8	no	—
513	C₂×#41	C₂³×C₁₃	1	2	yes	—
514	C₂×#41	C₂³×C₁₃	1	4	yes	—
515	C₂×#41	C₂³×C₁₃	1	4	yes	—
516	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
517	C₂²×D₄	—	2	2	no	—
518	C₂²×D₄	—	2	1	no	—
519	C₂²×D₄	—	2	1	no	—
520	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
521	C₂³×C₄	—	2	2	no	—
522	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
523	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
525	#135	—	4	16	no	—
526	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
527	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
528	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
529	C₂×D₈	C₂³×C₁₃	1	8	yes	—
530	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
531	C₄⋊Q₈	—	2	1	no	—
532	C₄⋊Q₈	—	2	1	no	—
533	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
534	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
535	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
536	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
537	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
538	#127	—	2	1	no	—
539	#127	—	2	1	no	—
540	#127	C₂³×C₁₃	1	2	yes	—
541	#127	C₂³×C₁₃	1	2	yes	—
542	#127	C₂³×C₁₃	1	1	yes	characteristic
543	#126	—	2	2	no	—
544	#126	—	2	2	no	—
545	#125	—	2	1	no	—
546	#125	—	2	1	no	—
547	#125	C₂³×C₁₃	1	2	yes	—
548	#124	—	2	2	no	—
549	#124	—	2	2	no	—
550	#124	—	2	1	no	—
551	#124	—	2	1	no	—
552	#124	C₂³×C₁₃	1	4	yes	—
553	#124	C₂³×C₁₃	1	4	yes	—
554	#124	C₂³×C₁₃	1	2	yes	—
555	#123	—	2	2	no	—
556	#123	—	2	2	no	—
557	#123	—	2	2	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	—	2	1	no	—
561	C₂²⋊Q₈	—	2	1	no	—
562	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
563	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
564	#121	—	2	2	no	—
565	#121	—	2	2	no	—
566	#121	—	2	2	no	—
567	#121	—	2	2	no	—
568	#121	—	2	2	no	—
569	#121	—	2	2	no	—
570	#121	—	2	2	no	—
571	#121	—	2	2	no	—
572	#121	—	2	1	no	—
573	#121	—	2	1	no	—
574	#121	—	2	1	no	—
575	#121	—	2	1	no	—
576	#121	C₂³×C₁₃	1	2	yes	—
577	#121	C₂³×C₁₃	1	2	yes	—
578	#120	—	2	2	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	—	2	1	no	—
582	C₄×Q₈	—	2	1	no	—
583	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
584	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
585	C₄×D₄	—	2	2	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	—	2	2	no	—
590	C₄×D₄	—	2	2	no	—
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	2	no	—
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	1	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	C₂³×C₁₃	1	2	yes	—
604	C₄×D₄	C₂³×C₁₃	1	2	yes	—
605	#117	—	2	1	no	—
606	#117	—	2	1	no	—
607	#117	—	2	2	no	—
608	#117	—	2	2	no	—
609	#117	—	2	2	no	—
610	#117	C₂³×C₁₃	1	2	yes	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	2	no	—
614	C₂×C₂²⋊C₄	—	2	2	no	—
615	C₂×C₄²	—	2	2	no	—
616	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
617	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
618	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
619	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
620	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
621	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
628	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
629	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
630	#103	C₂³×C₁₃	1	8	yes	—
631	#103	C₂³×C₁₃	1	8	yes	—
632	#102	C₂³×C₁₃	1	8	yes	—
633	#102	C₂³×C₁₃	1	8	yes	—
634	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
635	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
636	#97	C₂³×C₁₃	1	4	yes	—
637	#97	C₂³×C₁₃	1	4	yes	—
638	C₂×C₁₃	—	2	2	no	—
639	C₂×C₁₃	—	2	2	no	—
640	C₂×C₁₃	—	4	1	no	—
641	C₂×C₁₃	—	8	2	no	—
642	C₂×C₁₃	—	8	4	no	—
643	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
644	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
645	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
646	C₂⁴	—	2	2	no	—
647	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
648	#41	—	2	8	no	—
649	#41	—	2	16	no	—
650	#41	—	4	8	no	—
651	#41	—	4	8	no	—
652	#41	—	4	8	no	—
653	#41	—	4	4	no	—
654	#41	—	4	4	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	4	4	no	—
659	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
660	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
661	C₂×D₄	—	2	2	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	2	4	no	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	4	4	no	—
674	C₂×D₄	—	4	4	no	—
675	C₂×D₄	—	4	4	no	—
676	C₂×D₄	—	4	8	no	—
677	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
678	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	4	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	—	4	8	no	—
689	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
690	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
691	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
694	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
696	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
699	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
700	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
701	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
702	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
703	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
707	Q₁₆	—	4	8	no	—
708	SD₁₆	—	4	8	no	—
709	SD₁₆	—	4	8	no	—
710	D₈	—	4	8	no	—
711	C₂×C₈	—	2	8	no	—
712	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
728	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	2	no	—
745	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
746	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
747	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
748	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
749	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
750	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
751	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
752	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
753	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
754	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
755	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
756	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
757	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
758	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
759	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
760	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
761	C₁₃	#60790	1	1	yes	characteristic, direct product factor, Sylow
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	4	no	—
766	C₂³	—	4	1	no	—
767	C₂³	—	4	4	no	—
768	C₂³	—	4	4	no	—
769	C₂³	—	4	4	no	—
770	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
771	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
772	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
773	Q₈	—	2	4	no	—
774	Q₈	—	2	8	no	—
775	Q₈	—	4	4	no	—
776	Q₈	—	4	2	no	—
777	Q₈	—	4	2	no	—
778	D₄	—	2	4	no	—
779	D₄	—	2	8	no	—
780	D₄	—	4	4	no	—
781	D₄	—	4	4	no	—
782	D₄	—	4	4	no	—
783	D₄	—	4	4	no	—
784	D₄	—	4	2	no	—
785	D₄	—	4	2	no	—
786	D₄	—	4	8	no	—
787	D₄	—	4	4	no	—
788	D₄	—	4	8	no	—
789	D₄	—	4	4	no	—
790	D₄	—	4	4	no	—
791	D₄	—	4	4	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	4	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	4	1	no	—
811	C₂×C₄	—	4	1	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	8	no	—
814	C₂×C₄	—	4	4	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	4	8	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
820	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
821	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
822	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
823	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
824	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
829	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
830	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
831	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
832	C₈	—	2	8	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	4	4	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	4	no	—
844	C₂²	—	4	4	no	—
845	C₂²	—	4	4	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	8	8	no	—
848	C₂²	C₁₃×#535	1	2	yes	—
849	C₂²	C₁₃×#575	1	2	yes	—
850	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
851	C₄	—	2	1	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	1	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	1	no	—
859	C₄	—	2	1	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	4	no	—
863	C₄	—	4	2	no	—
864	C₄	C₁₃×#535	1	2	yes	—
865	C₄	C₁₃×#575	1	2	yes	—
866	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
867	C₂	—	2	2	no	—
868	C₂	—	2	2	no	—
869	C₂	—	4	1	no	—
870	C₂	—	8	4	no	—
871	C₂	—	8	2	no	—
872	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
873	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
874	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
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
1. C₁₃×#3444	C₂	semidirect
2. C₂×C₁₃×#532	C₂	semidirect
3. C₁₃×#3219	C₂	semidirect
4. C₁₃×#3218	C₂	semidirect
5. C₁₃×#3217	C₂	semidirect
6. C₁₃×#3216	C₂	semidirect
7. C₁₃×#3215	C₂	semidirect
8. C₁₃×#3214	C₂	semidirect
9. C₁₃×#3213	C₂	semidirect
10. C₁₃×#3150	C₂	semidirect
11. C₁₃×#3135	C₂	semidirect
12. C₁₃×#3035	C₂	semidirect
13. C₁₃×#3002	C₂	semidirect
14. C₂×C₁₃×#432	C₂	semidirect
16. C₂×C₁₃×#135	C₂²	semidirect
18. C₁₃×#533	C₂²	semidirect
19. C₁₃×#533	C₂²	semidirect
29. C₁₃×#532	C₂²	semidirect
30. C₁₃×#532	C₂²	semidirect
38. C₁₃×#529	C₂²	semidirect
47. C₄×C₁₃×#41	C₂²	semidirect
51. C₁₃×#497	C₂²	semidirect
52. C₁₃×#497	C₂²	semidirect
53. C₁₃×#496	C₂²	semidirect
54. C₁₃×#496	C₂²	semidirect
55. C₁₃×#491	C₂²	semidirect
56. C₁₃×#490	C₂²	semidirect
57. C₁₃×#489	C₂²	semidirect
58. C₁₃×#489	C₂²	semidirect
59. C₁₃×#464	C₂²	semidirect
60. C₁₃×#463	C₂²	semidirect
61. C₁₃×#462	C₂²	semidirect
62. C₁₃×#461	C₂²	semidirect
63. C₁₃×#460	C₂²	semidirect
64. C₁₃×#459	C₂²	semidirect
65. C₁₃×#452	C₂²	semidirect
68. C₁₃×#449	C₂²	semidirect
73. C₁₃×#432	C₂²	semidirect
74. C₁₃×#432	C₂²	semidirect
75. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
76. C₁₃×#416	C₂²	semidirect
78. C₂×C₁₃×#97	C₂²	semidirect
209. #60790	C₁₃	direct (N × H)
325. #3444	C₂×C₁₃	semidirect
326. C₂×#532	C₂×C₁₃	semidirect
327. #3219	C₂×C₁₃	semidirect
328. #3218	C₂×C₁₃	semidirect
329. #3217	C₂×C₁₃	semidirect
330. #3216	C₂×C₁₃	semidirect
331. #3215	C₂×C₁₃	semidirect
332. #3214	C₂×C₁₃	semidirect
333. #3213	C₂×C₁₃	semidirect
334. #3150	C₂×C₁₃	semidirect
335. #3135	C₂×C₁₃	semidirect
336. #3035	C₂×C₁₃	semidirect
337. #3002	C₂×C₁₃	semidirect
338. C₂×#432	C₂×C₁₃	semidirect
411. C₂×#135	C₂²×C₁₃	semidirect
413. #533	C₂²×C₁₃	semidirect
414. #533	C₂²×C₁₃	semidirect
424. #532	C₂²×C₁₃	semidirect
425. #532	C₂²×C₁₃	semidirect
433. #529	C₂²×C₁₃	semidirect
442. C₄×#41	C₂²×C₁₃	semidirect
446. #497	C₂²×C₁₃	semidirect
447. #497	C₂²×C₁₃	semidirect
448. #496	C₂²×C₁₃	semidirect
449. #496	C₂²×C₁₃	semidirect
450. #491	C₂²×C₁₃	semidirect
451. #490	C₂²×C₁₃	semidirect
452. #489	C₂²×C₁₃	semidirect
453. #489	C₂²×C₁₃	semidirect
454. #464	C₂²×C₁₃	semidirect
455. #463	C₂²×C₁₃	semidirect
456. #462	C₂²×C₁₃	semidirect
457. #461	C₂²×C₁₃	semidirect
458. #460	C₂²×C₁₃	semidirect
459. #459	C₂²×C₁₃	semidirect
460. #452	C₂²×C₁₃	semidirect
463. #449	C₂²×C₁₃	semidirect
468. #432	C₂²×C₁₃	semidirect
469. #432	C₂²×C₁₃	semidirect
470. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
471. #416	C₂²×C₁₃	semidirect
473. C₂×#97	C₂²×C₁₃	semidirect
761. C₁₃	#60790	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×#532	2
C₁₃×#3219	2
C₁₃×#3218	2
C₁₃×#3217	2
C₁₃×#3216	2
C₁₃×#3215	2
C₁₃×#3214	2
C₁₃×#3213	2
C₁₃×#3150	2
C₁₃×#3135	2
C₁₃×#3035	2
C₁₃×#3002	2
C₂×C₁₃×#432	2
#60790	13

Subgroups — C13×#60790 #15747129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60790 #15747129