Subgroups — C₁₃×#61905 #15748244

Order 3328.

1724 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3402	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3398	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3393	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3377	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3367	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3364	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3215	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3211	C₂	1	2	yes	maximal
12	C₁₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3117	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3105	C₂	1	1	yes	maximal, characteristic
16	C₁₃×#3104	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
20	C₁₃×#557	C₂²	1	2	yes	complemented
21	C₁₃×#556	—	2	1	no	—
22	C₁₃×#556	—	2	1	no	—
23	C₁₃×#556	—	2	2	no	—
24	C₁₃×#556	C₂²	1	2	yes	—
25	C₁₃×#556	C₂²	1	2	yes	—
26	C₁₃×#556	C₂²	1	4	yes	—
27	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#556	C₂²	1	2	yes	complemented
29	C₁₃×#552	—	2	1	no	—
30	C₁₃×#552	—	2	2	no	—
31	D₄×Q₈×C₁₃	—	2	1	no	—
32	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#541	—	2	1	no	—
34	C₁₃×#541	—	2	2	no	—
35	C₁₃×#533	C₂²	1	2	yes	—
36	C₁₃×#533	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
38	C₁₃×#529	C₂²	1	1	yes	characteristic
39	C₁₃×#529	C₂²	1	2	yes	—
40	C₂×C₁₃×#126	—	2	2	no	—
41	C₂×C₁₃×#124	C₂²	1	2	yes	—
42	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
43	C₁₃×#519	—	2	1	no	—
44	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#117	—	2	1	no	—
48	C₁₃×#497	C₂²	1	4	yes	—
49	C₁₃×#497	C₂²	1	2	yes	complemented
50	C₁₃×#495	C₂²	1	4	yes	—
51	C₁₃×#494	C₂²	1	2	yes	complemented
52	C₁₃×#491	C₂²	1	2	yes	complemented
53	C₁₃×#489	C₂²	1	4	yes	—
54	C₁₃×#488	C₂²	1	4	yes	—
55	C₁₃×#487	C₂²	1	2	yes	complemented
56	C₁₃×#484	C₂²	1	1	yes	characteristic
57	C₁₃×#484	C₂²	1	2	yes	—
58	C₁₃×#481	C₂²	1	1	yes	characteristic
59	C₁₃×#479	C₂²	1	4	yes	complemented
60	C₁₃×#478	C₂²	1	2	yes	—
61	C₁₃×#477	C₂²	1	4	yes	complemented
62	C₁₃×#474	C₂²	1	2	yes	—
63	C₁₃×#464	C₂²	1	4	yes	—
64	C₁₃×#464	C₂²	1	4	yes	—
65	C₁₃×#464	C₂²	1	4	yes	—
66	C₁₃×#464	C₂²	1	4	yes	complemented
67	C₁₃×#463	C₂²	1	2	yes	—
68	C₁₃×#463	C₂²	1	4	yes	—
69	C₁₃×#462	C₂²	1	4	yes	complemented
70	C₁₃×#462	C₂²	1	2	yes	complemented
71	C₁₃×#462	C₂²	1	4	yes	complemented
72	C₁₃×#461	C₂²	1	2	yes	—
73	C₁₃×#461	C₂²	1	2	yes	complemented
74	C₁₃×#451	C₂²	1	2	yes	—
75	C₁₃×#451	C₂²	1	2	yes	—
76	C₁₃×#451	C₂²	1	2	yes	—
77	C₁₃×#450	C₂²	1	1	yes	characteristic
78	C₁₃×#450	C₂²	1	2	yes	—
79	C₁₃×#448	C₂²	1	2	yes	—
80	C₁₃×#447	C₂²	1	1	yes	characteristic
81	C₁₃×#446	C₂²	1	2	yes	complemented
82	C₁₃×#446	C₂²	1	4	yes	complemented
83	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
84	C₁₃×#441	C₂²	1	4	yes	complemented
85	C₁₃×#440	C₂²	1	4	yes	—
86	C₁₃×#440	C₂²	1	4	yes	complemented
87	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
88	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
89	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
90	C₄×C₁₃×D₈	C₂²	1	2	yes	—
91	C₁₃×#432	C₂²	1	1	yes	characteristic
92	C₁₃×#432	C₂²	1	2	yes	—
93	C₁₃×#431	C₂²	1	2	yes	—
94	C₁₃×#431	C₂²	1	1	yes	characteristic
95	C₂²×Q₈×C₁₃	—	2	1	no	—
96	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
98	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	—	2	1	no	—
100	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
101	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
102	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
103	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×D₈	C₂³	1	2	yes	—
107	C₁₃×C₄⋊Q₈	—	2	1	no	—
108	C₁₃×C₄⋊Q₈	—	2	2	no	—
109	C₁₃×C₄⋊Q₈	—	2	1	no	—
110	C₁₃×C₄⋊Q₈	—	2	1	no	—
111	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₃×#126	—	2	4	no	—
118	C₁₃×#126	—	2	4	no	—
119	C₁₃×#126	—	2	4	no	—
120	C₁₃×#126	—	2	4	no	—
121	C₁₃×#126	—	2	2	no	—
122	C₁₃×#126	—	2	2	no	—
123	C₁₃×#126	—	2	2	no	—
124	C₁₃×#126	—	2	1	no	—
125	C₁₃×#126	—	2	2	no	—
126	C₁₃×#125	—	2	2	no	—
127	C₁₃×#125	—	2	2	no	—
128	C₁₃×#125	—	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	2	no	—
133	C₁₃×#125	C₂³	1	1	yes	characteristic
134	C₁₃×#125	C₂³	1	2	yes	—
135	C₁₃×#124	—	2	2	no	—
136	C₁₃×#124	—	2	2	no	—
137	C₁₃×#124	C₂³	1	1	yes	characteristic
138	C₁₃×#124	C₂³	1	4	yes	—
139	C₁₃×#124	C₂³	1	4	yes	—
140	C₁₃×#124	C₂³	1	2	yes	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×#123	—	2	1	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	—	2	4	no	—
146	C₁₃×C₂²⋊Q₈	—	2	1	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	1	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	—	2	1	no	—
151	C₁₃×C₂²⋊Q₈	—	2	2	no	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
153	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₁₃×#121	C₂³	1	1	yes	characteristic
155	C₄×Q₈×C₁₃	—	2	1	no	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	—	2	2	no	—
158	C₄×Q₈×C₁₃	—	2	2	no	—
159	C₄×Q₈×C₁₃	—	2	2	no	—
160	C₄×Q₈×C₁₃	—	2	1	no	—
161	C₄×Q₈×C₁₃	—	2	2	no	—
162	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
164	C₄×Q₈×C₁₃	D₄	1	2	yes	—
165	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
167	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
171	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
172	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
173	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
174	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	—	2	2	no	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	—	2	1	no	—
179	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₁₃	C₂³	1	2	yes	—
181	C₄×D₄×C₁₃	C₂³	1	2	yes	—
182	C₄×D₄×C₁₃	C₂³	1	2	yes	—
183	C₁₃×#117	—	2	2	no	—
184	C₁₃×#117	—	2	1	no	—
185	C₁₃×#117	—	2	2	no	—
186	C₁₃×#117	—	2	2	no	—
187	C₁₃×#117	—	2	4	no	—
188	C₁₃×#117	—	2	1	no	—
189	C₁₃×#117	—	2	2	no	—
190	C₁₃×#117	—	2	1	no	—
191	C₁₃×#117	—	2	2	no	—
192	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
194	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
196	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
200	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₄²×C₁₃	—	2	2	no	—
202	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
204	C₁₃×#107	C₂³	1	2	yes	—
205	C₁₃×#107	C₂³	1	4	yes	—
206	C₁₃×#106	C₂³	1	2	yes	—
207	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
208	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
209	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
210	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
211	C₁₃×#103	C₂³	1	2	yes	—
212	C₁₃×#103	C₂³	1	4	yes	—
213	C₁₃×#103	C₂³	1	4	yes	—
214	C₁₃×#103	C₂³	1	4	yes	—
215	C₁₃×#103	C₂³	1	4	yes	—
216	C₁₃×#103	C₂³	1	4	yes	—
217	C₁₃×#102	C₂³	1	2	yes	—
218	C₁₃×#102	C₂³	1	2	yes	—
219	C₁₃×#102	C₂³	1	2	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
222	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
224	C₁₃×#97	C₂³	1	2	yes	—
225	C₁₃×#97	C₂³	1	4	yes	—
226	C₄×C₈×C₁₃	C₂³	1	2	yes	—
227	C₄×C₈×C₁₃	C₂³	1	4	yes	—
228	#61905	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂⁴×C₁₃	—	2	1	no	—
230	C₂×Q₈×C₁₃	—	2	2	no	—
231	C₂×Q₈×C₁₃	—	2	1	no	—
232	C₂×Q₈×C₁₃	—	2	2	no	—
233	C₂×Q₈×C₁₃	—	4	2	no	—
234	C₂×Q₈×C₁₃	—	4	4	no	—
235	C₂×Q₈×C₁₃	—	4	4	no	—
236	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
238	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
239	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
240	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
242	C₂×D₄×C₁₃	—	2	1	no	—
243	C₂×D₄×C₁₃	—	2	1	no	—
244	C₂×D₄×C₁₃	—	4	2	no	—
245	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
246	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	—	2	1	no	—
248	C₂²×C₄×C₁₃	—	2	2	no	—
249	C₂²×C₄×C₁₃	—	2	2	no	—
250	C₂²×C₄×C₁₃	—	2	2	no	—
251	C₂²×C₄×C₁₃	—	2	2	no	—
252	C₂²×C₄×C₁₃	—	2	1	no	—
253	C₂²×C₄×C₁₃	—	4	4	no	—
254	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
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	2	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₁₃×Q₁₆	—	4	4	no	—
260	C₁₃×Q₁₆	—	4	4	no	—
261	C₁₃×Q₁₆	—	4	4	no	—
262	C₁₃×SD₁₆	—	4	4	no	—
263	C₁₃×SD₁₆	—	4	4	no	—
264	C₁₃×SD₁₆	—	4	2	no	—
265	C₁₃×D₈	—	4	2	no	—
266	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
267	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
268	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
269	C₁₃×C₄⋊C₄	—	2	2	no	—
270	C₁₃×C₄⋊C₄	—	2	2	no	—
271	C₁₃×C₄⋊C₄	—	2	4	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	2	no	—
274	C₁₃×C₄⋊C₄	—	2	2	no	—
275	C₁₃×C₄⋊C₄	—	2	1	no	—
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	—	2	1	no	—
278	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
283	C₁₃×C₄⋊C₄	—	2	1	no	—
284	C₁₃×C₄⋊C₄	—	2	2	no	—
285	C₁₃×C₄⋊C₄	—	2	1	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	1	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	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	1	no	—
293	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
294	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
295	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
296	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
297	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
298	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
299	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
300	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
301	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
302	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₁₃×C₂²⋊C₄	—	2	1	no	—
305	C₁₃×C₂²⋊C₄	—	2	2	no	—
306	C₁₃×C₂²⋊C₄	—	2	4	no	—
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	—	2	2	no	—
309	C₁₃×C₂²⋊C₄	—	2	2	no	—
310	C₁₃×C₂²⋊C₄	—	2	4	no	—
311	C₁₃×C₂²⋊C₄	—	2	4	no	—
312	C₁₃×C₂²⋊C₄	—	2	1	no	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	1	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	1	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	1	no	—
319	C₄²×C₁₃	—	2	4	no	—
320	C₄²×C₁₃	—	2	4	no	—
321	C₄²×C₁₃	—	2	2	no	—
322	C₄²×C₁₃	—	2	2	no	—
323	C₄²×C₁₃	—	2	2	no	—
324	C₄²×C₁₃	—	2	2	no	—
325	C₄²×C₁₃	—	2	1	no	—
326	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₁₃	C₂×D₄	1	2	yes	—
328	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₁₃	C₂×D₄	1	2	yes	—
330	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
331	C₄²×C₁₃	C₂⁴	1	2	yes	—
332	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
333	C₄²×C₁₃	C₂⁴	1	2	yes	—
334	#3523	C₂×C₁₃	1	1	yes	characteristic, complemented
335	C₂×#556	C₂×C₁₃	1	1	yes	characteristic, complemented
336	#3402	C₂×C₁₃	1	4	yes	complemented
337	#3398	C₂×C₁₃	1	2	yes	complemented
338	#3393	C₂×C₁₃	1	2	yes	complemented
339	#3377	C₂×C₁₃	1	4	yes	complemented
340	#3367	C₂×C₁₃	1	2	yes	complemented
341	#3364	C₂×C₁₃	1	2	yes	complemented
342	#3218	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#3215	C₂×C₁₃	1	2	yes	complemented
344	#3211	C₂×C₁₃	1	2	yes	—
345	#3209	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#3117	C₂×C₁₃	1	2	yes	complemented
347	#3110	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3105	C₂×C₁₃	1	1	yes	characteristic
349	#3104	C₂×C₁₃	1	2	yes	complemented
350	#2984	C₂×C₁₃	1	1	yes	characteristic, complemented
351	C₂³×C₁₃	—	2	1	no	—
352	C₂³×C₁₃	—	2	2	no	—
353	C₂³×C₁₃	—	4	2	no	—
354	C₂³×C₁₃	—	4	2	no	—
355	C₂³×C₁₃	—	4	2	no	—
356	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
357	Q₈×C₁₃	—	2	2	no	—
358	Q₈×C₁₃	—	2	2	no	—
359	Q₈×C₁₃	—	2	4	no	—
360	Q₈×C₁₃	—	2	2	no	—
361	Q₈×C₁₃	—	2	4	no	—
362	Q₈×C₁₃	—	2	4	no	—
363	Q₈×C₁₃	—	4	2	no	—
364	Q₈×C₁₃	—	4	4	no	—
365	Q₈×C₁₃	—	4	4	no	—
366	Q₈×C₁₃	—	4	2	no	—
367	D₄×C₁₃	—	2	2	no	—
368	D₄×C₁₃	—	2	2	no	—
369	D₄×C₁₃	—	2	2	no	—
370	D₄×C₁₃	—	4	2	no	—
371	D₄×C₁₃	—	4	2	no	—
372	C₂×C₄×C₁₃	—	2	4	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	1	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	4	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	4	2	no	—
384	C₂×C₄×C₁₃	—	4	4	no	—
385	C₂×C₄×C₁₃	—	4	4	no	—
386	C₂×C₄×C₁₃	—	4	2	no	—
387	C₂×C₄×C₁₃	—	4	4	no	—
388	C₂×C₄×C₁₃	—	4	4	no	—
389	C₂×C₄×C₁₃	—	4	2	no	—
390	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
400	C₈×C₁₃	—	2	2	no	—
401	C₈×C₁₃	—	2	4	no	—
402	C₈×C₁₃	—	2	2	no	—
403	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
404	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
405	#557	C₂²×C₁₃	1	2	yes	complemented
406	#556	—	2	1	no	—
407	#556	—	2	1	no	—
408	#556	—	2	2	no	—
409	#556	C₂²×C₁₃	1	2	yes	—
410	#556	C₂²×C₁₃	1	2	yes	—
411	#556	C₂²×C₁₃	1	4	yes	—
412	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
413	#556	C₂²×C₁₃	1	2	yes	complemented
414	#552	—	2	1	no	—
415	#552	—	2	2	no	—
416	D₄×Q₈	—	2	1	no	—
417	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
418	#541	—	2	1	no	—
419	#541	—	2	2	no	—
420	#533	C₂²×C₁₃	1	2	yes	—
421	#533	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
423	#529	C₂²×C₁₃	1	1	yes	characteristic
424	#529	C₂²×C₁₃	1	2	yes	—
425	C₂×#126	—	2	2	no	—
426	C₂×#124	C₂²×C₁₃	1	2	yes	—
427	C₂×C₂²⋊Q₈	—	2	1	no	—
428	#519	—	2	1	no	—
429	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
430	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×#117	—	2	1	no	—
433	#497	C₂²×C₁₃	1	4	yes	—
434	#497	C₂²×C₁₃	1	2	yes	complemented
435	#495	C₂²×C₁₃	1	4	yes	—
436	#494	C₂²×C₁₃	1	2	yes	complemented
437	#491	C₂²×C₁₃	1	2	yes	complemented
438	#489	C₂²×C₁₃	1	4	yes	—
439	#488	C₂²×C₁₃	1	4	yes	—
440	#487	C₂²×C₁₃	1	2	yes	complemented
441	#484	C₂²×C₁₃	1	1	yes	characteristic
442	#484	C₂²×C₁₃	1	2	yes	—
443	#481	C₂²×C₁₃	1	1	yes	characteristic
444	#479	C₂²×C₁₃	1	4	yes	complemented
445	#478	C₂²×C₁₃	1	2	yes	—
446	#477	C₂²×C₁₃	1	4	yes	complemented
447	#474	C₂²×C₁₃	1	2	yes	—
448	#464	C₂²×C₁₃	1	4	yes	—
449	#464	C₂²×C₁₃	1	4	yes	—
450	#464	C₂²×C₁₃	1	4	yes	—
451	#464	C₂²×C₁₃	1	4	yes	complemented
452	#463	C₂²×C₁₃	1	2	yes	—
453	#463	C₂²×C₁₃	1	4	yes	—
454	#462	C₂²×C₁₃	1	4	yes	complemented
455	#462	C₂²×C₁₃	1	2	yes	complemented
456	#462	C₂²×C₁₃	1	4	yes	complemented
457	#461	C₂²×C₁₃	1	2	yes	—
458	#461	C₂²×C₁₃	1	2	yes	complemented
459	#451	C₂²×C₁₃	1	2	yes	—
460	#451	C₂²×C₁₃	1	2	yes	—
461	#451	C₂²×C₁₃	1	2	yes	—
462	#450	C₂²×C₁₃	1	1	yes	characteristic
463	#450	C₂²×C₁₃	1	2	yes	—
464	#448	C₂²×C₁₃	1	2	yes	—
465	#447	C₂²×C₁₃	1	1	yes	characteristic
466	#446	C₂²×C₁₃	1	2	yes	complemented
467	#446	C₂²×C₁₃	1	4	yes	complemented
468	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
469	#441	C₂²×C₁₃	1	4	yes	complemented
470	#440	C₂²×C₁₃	1	4	yes	—
471	#440	C₂²×C₁₃	1	4	yes	complemented
472	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
473	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
474	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
475	C₄×D₈	C₂²×C₁₃	1	2	yes	—
476	#432	C₂²×C₁₃	1	1	yes	characteristic
477	#432	C₂²×C₁₃	1	2	yes	—
478	#431	C₂²×C₁₃	1	2	yes	—
479	#431	C₂²×C₁₃	1	1	yes	characteristic
480	C₂²×C₁₃	—	2	1	no	—
481	C₂²×C₁₃	—	2	1	no	—
482	C₂²×C₁₃	—	4	2	no	—
483	C₂²×C₁₃	—	4	1	no	—
484	C₂²×C₁₃	—	4	1	no	—
485	C₂²×C₁₃	—	4	2	no	—
486	C₂²×C₁₃	—	4	1	no	—
487	C₂²×C₁₃	—	4	2	no	—
488	C₂²×C₁₃	—	8	4	no	—
489	C₂²×C₁₃	#578	1	2	yes	—
490	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
491	C₄×C₁₃	—	2	1	no	—
492	C₄×C₁₃	—	2	1	no	—
493	C₄×C₁₃	—	2	2	no	—
494	C₄×C₁₃	—	2	2	no	—
495	C₄×C₁₃	—	2	2	no	—
496	C₄×C₁₃	—	2	2	no	—
497	C₄×C₁₃	—	2	1	no	—
498	C₄×C₁₃	—	2	1	no	—
499	C₄×C₁₃	—	4	4	no	—
500	C₄×C₁₃	—	4	1	no	—
501	C₄×C₁₃	—	4	2	no	—
502	C₄×C₁₃	—	4	2	no	—
503	C₄×C₁₃	—	4	2	no	—
504	C₄×C₁₃	—	4	1	no	—
505	C₄×C₁₃	—	4	1	no	—
506	C₄×C₁₃	#575	1	2	yes	—
507	C₄×C₁₃	#585	1	2	yes	—
508	C₂²×Q₈	—	2	1	no	—
509	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
510	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
511	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
512	C₂³×C₄	—	2	1	no	—
513	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
514	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
515	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
516	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
517	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
518	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
519	C₂×D₈	C₂³×C₁₃	1	2	yes	—
520	C₄⋊Q₈	—	2	1	no	—
521	C₄⋊Q₈	—	2	2	no	—
522	C₄⋊Q₈	—	2	1	no	—
523	C₄⋊Q₈	—	2	1	no	—
524	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
525	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
526	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
527	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
528	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
529	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
530	#126	—	2	4	no	—
531	#126	—	2	4	no	—
532	#126	—	2	4	no	—
533	#126	—	2	4	no	—
534	#126	—	2	2	no	—
535	#126	—	2	2	no	—
536	#126	—	2	2	no	—
537	#126	—	2	1	no	—
538	#126	—	2	2	no	—
539	#125	—	2	2	no	—
540	#125	—	2	2	no	—
541	#125	—	2	2	no	—
542	#125	—	2	1	no	—
543	#125	—	2	2	no	—
544	#125	—	2	1	no	—
545	#125	—	2	2	no	—
546	#125	C₂³×C₁₃	1	1	yes	characteristic
547	#125	C₂³×C₁₃	1	2	yes	—
548	#124	—	2	2	no	—
549	#124	—	2	2	no	—
550	#124	C₂³×C₁₃	1	4	yes	—
551	#124	C₂³×C₁₃	1	4	yes	—
552	#124	C₂³×C₁₃	1	1	yes	characteristic
553	#124	C₂³×C₁₃	1	2	yes	—
554	#123	—	2	2	no	—
555	#123	—	2	1	no	—
556	C₂²⋊Q₈	—	2	2	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	4	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	2	1	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	1	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
566	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
567	#121	C₂³×C₁₃	1	1	yes	characteristic
568	C₄×Q₈	—	2	1	no	—
569	C₄×Q₈	—	2	1	no	—
570	C₄×Q₈	—	2	2	no	—
571	C₄×Q₈	—	2	2	no	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	—	2	1	no	—
574	C₄×Q₈	—	2	2	no	—
575	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
576	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
577	C₄×Q₈	D₄×C₁₃	1	2	yes	—
578	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
579	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
580	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
581	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
582	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
583	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
584	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
585	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
586	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
587	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	—	2	2	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	C₂³×C₁₃	1	2	yes	—
593	C₄×D₄	C₂³×C₁₃	1	2	yes	—
594	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
595	C₄×D₄	C₂³×C₁₃	1	2	yes	—
596	#117	—	2	2	no	—
597	#117	—	2	1	no	—
598	#117	—	2	2	no	—
599	#117	—	2	2	no	—
600	#117	—	2	4	no	—
601	#117	—	2	1	no	—
602	#117	—	2	2	no	—
603	#117	—	2	1	no	—
604	#117	—	2	2	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	2	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
609	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	—	2	2	no	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	2	no	—
614	C₂×C₄²	—	2	2	no	—
615	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
617	#107	C₂³×C₁₃	1	2	yes	—
618	#107	C₂³×C₁₃	1	4	yes	—
619	#106	C₂³×C₁₃	1	2	yes	—
620	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
621	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
622	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
623	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
624	#103	C₂³×C₁₃	1	2	yes	—
625	#103	C₂³×C₁₃	1	4	yes	—
626	#103	C₂³×C₁₃	1	4	yes	—
627	#103	C₂³×C₁₃	1	4	yes	—
628	#103	C₂³×C₁₃	1	4	yes	—
629	#103	C₂³×C₁₃	1	4	yes	—
630	#102	C₂³×C₁₃	1	2	yes	—
631	#102	C₂³×C₁₃	1	2	yes	—
632	#102	C₂³×C₁₃	1	2	yes	—
633	#102	C₂³×C₁₃	1	4	yes	—
634	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
635	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
636	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
637	#97	C₂³×C₁₃	1	2	yes	—
638	#97	C₂³×C₁₃	1	4	yes	—
639	C₄×C₈	C₂³×C₁₃	1	2	yes	—
640	C₄×C₈	C₂³×C₁₃	1	4	yes	—
641	C₂×C₁₃	—	2	2	no	—
642	C₂×C₁₃	—	8	1	no	—
643	C₂×C₁₃	—	8	2	no	—
644	C₂×C₁₃	#3487	1	1	yes	characteristic
645	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
646	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
647	C₂⁴	—	2	1	no	—
648	C₂×Q₈	—	2	2	no	—
649	C₂×Q₈	—	2	1	no	—
650	C₂×Q₈	—	2	2	no	—
651	C₂×Q₈	—	4	2	no	—
652	C₂×Q₈	—	4	4	no	—
653	C₂×Q₈	—	4	4	no	—
654	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
655	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
656	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
657	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
658	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
659	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	4	2	no	—
663	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
664	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	4	4	no	—
672	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
673	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
677	Q₁₆	—	4	4	no	—
678	Q₁₆	—	4	4	no	—
679	Q₁₆	—	4	4	no	—
680	SD₁₆	—	4	4	no	—
681	SD₁₆	—	4	4	no	—
682	SD₁₆	—	4	2	no	—
683	D₈	—	4	2	no	—
684	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
685	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
686	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
712	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
713	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
714	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
715	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
716	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
717	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
719	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
720	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
721	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
722	C₂²⋊C₄	—	2	1	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	1	no	—
737	C₄²	—	2	4	no	—
738	C₄²	—	2	4	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	2	no	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	1	no	—
744	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
745	C₄²	C₂×D₄×C₁₃	1	2	yes	—
746	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
747	C₄²	C₂×D₄×C₁₃	1	2	yes	—
748	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
749	C₄²	C₂⁴×C₁₃	1	2	yes	—
750	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
751	C₄²	C₂⁴×C₁₃	1	2	yes	—
752	C₁₃	#61905	1	1	yes	characteristic, direct product factor, Sylow
753	C₂³	—	2	1	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	4	2	no	—
757	C₂³	—	4	2	no	—
758	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
759	Q₈	—	2	2	no	—
760	Q₈	—	2	2	no	—
761	Q₈	—	2	4	no	—
762	Q₈	—	2	2	no	—
763	Q₈	—	2	4	no	—
764	Q₈	—	2	4	no	—
765	Q₈	—	4	2	no	—
766	Q₈	—	4	4	no	—
767	Q₈	—	4	4	no	—
768	Q₈	—	4	2	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	2	no	—
771	D₄	—	2	2	no	—
772	D₄	—	4	2	no	—
773	D₄	—	4	2	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	4	2	no	—
786	C₂×C₄	—	4	4	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
793	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
795	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
796	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
797	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
799	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
800	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
801	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
802	C₈	—	2	2	no	—
803	C₈	—	2	4	no	—
804	C₈	—	2	2	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	8	4	no	—
814	C₂²	C₁₃×#578	1	2	yes	—
815	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
816	C₄	—	2	1	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	1	no	—
822	C₄	—	2	1	no	—
823	C₄	—	2	1	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	4	no	—
829	C₄	—	4	1	no	—
830	C₄	—	4	2	no	—
831	C₄	C₁₃×#575	1	2	yes	—
832	C₄	C₁₃×#585	1	2	yes	—
833	C₂	—	2	2	no	—
834	C₂	—	8	2	no	—
835	C₂	—	8	1	no	—
836	C₂	C₁₃×#3487	1	1	yes	characteristic
837	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
838	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#447	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3523	C₂	semidirect
2. C₂×C₁₃×#556	C₂	semidirect
3. C₁₃×#3402	C₂	semidirect
4. C₁₃×#3398	C₂	semidirect
5. C₁₃×#3393	C₂	semidirect
6. C₁₃×#3377	C₂	semidirect
7. C₁₃×#3367	C₂	semidirect
8. C₁₃×#3364	C₂	semidirect
9. C₁₃×#3218	C₂	semidirect
10. C₁₃×#3215	C₂	semidirect
12. C₁₃×#3209	C₂	semidirect
13. C₁₃×#3117	C₂	semidirect
14. C₁₃×#3110	C₂	semidirect
16. C₁₃×#3104	C₂	semidirect
17. C₁₃×#2984	C₂	semidirect
18. C₁₃×#557	C₂²	semidirect
19. C₁₃×#557	C₂²	semidirect
20. C₁₃×#557	C₂²	semidirect
27. C₁₃×#556	C₂²	semidirect
28. C₁₃×#556	C₂²	semidirect
32. D₄×Q₈×C₁₃	C₂²	semidirect
49. C₁₃×#497	C₂²	semidirect
51. C₁₃×#494	C₂²	semidirect
52. C₁₃×#491	C₂²	semidirect
55. C₁₃×#487	C₂²	semidirect
59. C₁₃×#479	C₂²	semidirect
61. C₁₃×#477	C₂²	semidirect
66. C₁₃×#464	C₂²	semidirect
69. C₁₃×#462	C₂²	semidirect
70. C₁₃×#462	C₂²	semidirect
71. C₁₃×#462	C₂²	semidirect
73. C₁₃×#461	C₂²	semidirect
81. C₁₃×#446	C₂²	semidirect
82. C₁₃×#446	C₂²	semidirect
83. C₈×Q₈×C₁₃	C₂²	semidirect
84. C₁₃×#441	C₂²	semidirect
86. C₁₃×#440	C₂²	semidirect
87. C₄×C₁₃×Q₁₆	C₂²	semidirect
88. C₄×C₁₃×Q₁₆	C₂²	semidirect
228. #61905	C₁₃	direct (N × H)
334. #3523	C₂×C₁₃	semidirect
335. C₂×#556	C₂×C₁₃	semidirect
336. #3402	C₂×C₁₃	semidirect
337. #3398	C₂×C₁₃	semidirect
338. #3393	C₂×C₁₃	semidirect
339. #3377	C₂×C₁₃	semidirect
340. #3367	C₂×C₁₃	semidirect
341. #3364	C₂×C₁₃	semidirect
342. #3218	C₂×C₁₃	semidirect
343. #3215	C₂×C₁₃	semidirect
345. #3209	C₂×C₁₃	semidirect
346. #3117	C₂×C₁₃	semidirect
347. #3110	C₂×C₁₃	semidirect
349. #3104	C₂×C₁₃	semidirect
350. #2984	C₂×C₁₃	semidirect
403. #557	C₂²×C₁₃	semidirect
404. #557	C₂²×C₁₃	semidirect
405. #557	C₂²×C₁₃	semidirect
412. #556	C₂²×C₁₃	semidirect
413. #556	C₂²×C₁₃	semidirect
417. D₄×Q₈	C₂²×C₁₃	semidirect
434. #497	C₂²×C₁₃	semidirect
436. #494	C₂²×C₁₃	semidirect
437. #491	C₂²×C₁₃	semidirect
440. #487	C₂²×C₁₃	semidirect
444. #479	C₂²×C₁₃	semidirect
446. #477	C₂²×C₁₃	semidirect
451. #464	C₂²×C₁₃	semidirect
454. #462	C₂²×C₁₃	semidirect
455. #462	C₂²×C₁₃	semidirect
456. #462	C₂²×C₁₃	semidirect
458. #461	C₂²×C₁₃	semidirect
466. #446	C₂²×C₁₃	semidirect
467. #446	C₂²×C₁₃	semidirect
468. C₈×Q₈	C₂²×C₁₃	semidirect
469. #441	C₂²×C₁₃	semidirect
471. #440	C₂²×C₁₃	semidirect
472. C₄×Q₁₆	C₂²×C₁₃	semidirect
473. C₄×Q₁₆	C₂²×C₁₃	semidirect
752. C₁₃	#61905	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×#3523	2
C₂×C₁₃×#556	2
C₁₃×#3402	2
C₁₃×#3398	2
C₁₃×#3393	2
C₁₃×#3377	2
C₁₃×#3367	2
C₁₃×#3364	2
C₁₃×#3218	2
C₁₃×#3215	2
C₁₃×#3211	2
C₁₃×#3209	2
C₁₃×#3117	2
C₁₃×#3110	2
C₁₃×#3105	2
C₁₃×#3104	2
C₁₃×#2984	2
#61905	13

Subgroups — C13×#61905 #15748244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61905 #15748244