Subgroups — C₁₃×#61699 #15748038

Order 3328.

1854 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3339	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3337	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3301	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3297	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3232	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3188	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3187	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3186	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3105	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3091	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#553	—	2	2	no	—
17	C₁₃×#553	—	2	2	no	—
18	C₁₃×#553	—	2	2	no	—
19	C₁₃×#553	C₂²	1	4	yes	—
20	C₁₃×#553	C₂²	1	4	yes	complemented
21	C₁₃×#553	C₂²	1	2	yes	complemented
22	C₁₃×#552	C₂²	1	2	yes	complemented
23	C₁₃×#551	—	2	2	no	—
24	C₁₃×#548	C₂²	1	2	yes	complemented
25	C₁₃×#546	C₂²	1	2	yes	complemented
26	C₁₃×#539	—	2	1	no	—
27	C₁₃×#538	—	2	1	no	—
28	C₁₃×#534	—	2	1	no	—
29	C₁₃×#529	C₂²	1	2	yes	—
30	C₂×C₁₃×#126	—	2	1	no	—
31	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#525	C₂²	1	2	yes	—
33	C₂×C₁₃×#123	—	2	1	no	—
34	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#121	—	2	1	no	—
36	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#518	—	2	1	no	—
40	C₂×C₄×D₄×C₁₃	—	2	1	no	—
41	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₁₃×#499	C₂²	1	4	yes	complemented
46	C₁₃×#488	C₂²	1	4	yes	complemented
47	C₁₃×#485	C₂²	1	4	yes	complemented
48	C₁₃×#484	C₂²	1	4	yes	complemented
49	C₁₃×#484	C₂²	1	2	yes	complemented
50	C₁₃×#484	C₂²	1	2	yes	complemented
51	C₁₃×#483	C₂²	1	2	yes	complemented
52	C₁₃×#482	C₂²	1	4	yes	complemented
53	C₁₃×#482	C₂²	1	4	yes	complemented
54	C₁₃×#481	C₂²	1	2	yes	—
55	C₁₃×#481	C₂²	1	2	yes	—
56	C₁₃×#481	C₂²	1	4	yes	complemented
57	C₁₃×#481	C₂²	1	2	yes	complemented
58	C₁₃×#480	C₂²	1	2	yes	—
59	C₁₃×#480	C₂²	1	2	yes	complemented
60	C₁₃×#479	C₂²	1	4	yes	complemented
61	C₁₃×#478	C₂²	1	4	yes	complemented
62	C₁₃×#478	C₂²	1	4	yes	complemented
63	C₁₃×#466	C₂²	1	4	yes	complemented
64	C₁₃×#466	C₂²	1	4	yes	complemented
65	C₁₃×#465	C₂²	1	4	yes	complemented
66	C₁₃×#465	C₂²	1	4	yes	complemented
67	C₁₃×#463	C₂²	1	4	yes	complemented
68	C₁₃×#450	C₂²	1	2	yes	complemented
69	C₁₃×#449	C₂²	1	4	yes	complemented
70	C₁₃×#448	C₂²	1	2	yes	complemented
71	C₁₃×#447	C₂²	1	2	yes	—
72	C₁₃×#447	C₂²	1	2	yes	complemented
73	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
74	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
75	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
76	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
77	C₁₃×#431	C₂²	1	2	yes	complemented
78	C₁₃×#427	C₂²	1	4	yes	complemented
79	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
80	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
81	C₁₃×#416	C₂²	1	4	yes	complemented
82	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
83	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
84	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
85	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
86	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
87	C₂×C₁₃×#41	C₂³	1	2	yes	—
88	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃	—	2	1	no	—
90	C₂²×D₄×C₁₃	—	2	1	no	—
91	C₂²×D₄×C₁₃	—	2	1	no	—
92	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
93	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	—	2	1	no	—
96	C₂³×C₄×C₁₃	—	2	1	no	—
97	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₁₃×D₈	C₂³	1	4	yes	—
101	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
102	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
103	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
104	C₁₃×#126	—	2	4	no	—
105	C₁₃×#126	—	2	4	no	—
106	C₁₃×#126	—	2	2	no	—
107	C₁₃×#126	—	2	2	no	—
108	C₁₃×#126	—	2	2	no	—
109	C₁₃×#125	—	2	2	no	—
110	C₁₃×#125	—	2	2	no	—
111	C₁₃×#125	C₂³	1	2	yes	—
112	C₁₃×#125	C₂³	1	4	yes	—
113	C₁₃×#124	—	2	2	no	—
114	C₁₃×#124	C₂³	1	2	yes	—
115	C₁₃×#123	—	2	2	no	—
116	C₁₃×#123	—	2	2	no	—
117	C₁₃×#123	—	2	2	no	—
118	C₁₃×#123	—	2	2	no	—
119	C₁₃×#123	—	2	4	no	—
120	C₁₃×#123	—	2	4	no	—
121	C₁₃×#123	—	2	2	no	—
122	C₁₃×C₂²⋊Q₈	—	2	1	no	—
123	C₁₃×C₂²⋊Q₈	—	2	1	no	—
124	C₁₃×C₂²⋊Q₈	—	2	2	no	—
125	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
126	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
127	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
128	C₁₃×#121	—	2	4	no	—
129	C₁₃×#121	—	2	4	no	—
130	C₁₃×#121	—	2	2	no	—
131	C₁₃×#121	—	2	2	no	—
132	C₁₃×#121	—	2	1	no	—
133	C₁₃×#121	—	2	1	no	—
134	C₁₃×#121	—	2	1	no	—
135	C₁₃×#121	—	2	1	no	—
136	C₁₃×#121	—	2	2	no	—
137	C₁₃×#121	—	2	2	no	—
138	C₁₃×#121	C₂³	1	2	yes	—
139	C₁₃×#121	C₂³	1	2	yes	—
140	C₁₃×#121	C₂³	1	2	yes	—
141	C₁₃×#121	C₂³	1	4	yes	—
142	C₁₃×#121	C₂³	1	2	yes	—
143	C₁₃×#121	C₂³	1	2	yes	—
144	C₁₃×#120	—	2	2	no	—
145	C₁₃×#120	—	2	2	no	—
146	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
147	C₄×D₄×C₁₃	—	2	2	no	—
148	C₄×D₄×C₁₃	—	2	2	no	—
149	C₄×D₄×C₁₃	—	2	2	no	—
150	C₄×D₄×C₁₃	—	2	4	no	—
151	C₄×D₄×C₁₃	—	2	4	no	—
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	D₄	1	2	yes	—
156	C₄×D₄×C₁₃	D₄	1	2	yes	—
157	C₄×D₄×C₁₃	C₂³	1	2	yes	—
158	C₄×D₄×C₁₃	C₂³	1	4	yes	—
159	C₄×D₄×C₁₃	C₂³	1	2	yes	—
160	C₄×D₄×C₁₃	C₂³	1	2	yes	—
161	C₁₃×#117	—	2	2	no	—
162	C₁₃×#117	—	2	2	no	—
163	C₁₃×#117	—	2	2	no	—
164	C₁₃×#117	C₂³	1	4	yes	—
165	C₁₃×#117	C₂³	1	2	yes	—
166	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
173	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
181	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
182	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
183	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
184	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
185	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
186	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
187	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
188	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₁₃	—	2	1	no	—
190	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
191	C₁₃×#107	C₂³	1	4	yes	—
192	C₁₃×#107	C₂³	1	4	yes	—
193	C₁₃×#107	C₂³	1	4	yes	—
194	C₁₃×#106	C₂³	1	4	yes	—
195	C₁₃×#106	C₂³	1	4	yes	—
196	C₁₃×#106	C₂³	1	4	yes	—
197	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
198	C₁₃×#103	C₂³	1	4	yes	—
199	C₁₃×#103	C₂³	1	4	yes	—
200	C₁₃×#103	C₂³	1	4	yes	—
201	C₁₃×#102	C₂³	1	4	yes	—
202	C₁₃×#102	C₂³	1	4	yes	—
203	C₁₃×#102	C₂³	1	4	yes	—
204	C₁₃×#102	C₂³	1	4	yes	—
205	C₁₃×#102	C₂³	1	4	yes	—
206	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
207	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
209	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
210	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
211	C₄×C₈×C₁₃	C₂³	1	4	yes	—
212	#61699	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂⁴×C₁₃	—	2	1	no	—
214	C₂⁴×C₁₃	—	2	1	no	—
215	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
216	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₁₃×#41	—	4	4	no	—
218	C₂×Q₈×C₁₃	—	2	1	no	—
219	C₂×Q₈×C₁₃	—	4	2	no	—
220	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
221	C₂×D₄×C₁₃	—	2	4	no	—
222	C₂×D₄×C₁₃	—	2	2	no	—
223	C₂×D₄×C₁₃	—	2	2	no	—
224	C₂×D₄×C₁₃	—	2	2	no	—
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	1	no	—
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	4	2	no	—
232	C₂×D₄×C₁₃	—	4	2	no	—
233	C₂×D₄×C₁₃	—	4	4	no	—
234	C₂×D₄×C₁₃	—	4	4	no	—
235	C₂×D₄×C₁₃	—	8	2	no	—
236	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
237	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃	—	2	1	no	—
241	C₂²×C₄×C₁₃	—	2	1	no	—
242	C₂²×C₄×C₁₃	—	2	1	no	—
243	C₂²×C₄×C₁₃	—	2	1	no	—
244	C₂²×C₄×C₁₃	—	2	1	no	—
245	C₂²×C₄×C₁₃	—	2	1	no	—
246	C₂²×C₄×C₁₃	—	2	2	no	—
247	C₂²×C₄×C₁₃	—	2	2	no	—
248	C₂²×C₄×C₁₃	—	2	2	no	—
249	C₂²×C₄×C₁₃	—	2	2	no	—
250	C₂²×C₄×C₁₃	—	2	4	no	—
251	C₂²×C₄×C₁₃	—	4	2	no	—
252	C₂²×C₄×C₁₃	—	4	2	no	—
253	C₂²×C₄×C₁₃	—	8	2	no	—
254	C₂²×C₄×C₁₃	—	8	2	no	—
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	2	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
266	C₁₃×SD₁₆	—	4	4	no	—
267	C₁₃×D₈	—	4	4	no	—
268	C₂×C₈×C₁₃	—	4	2	no	—
269	C₂×C₈×C₁₃	—	4	4	no	—
270	C₂×C₈×C₁₃	—	4	2	no	—
271	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
272	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	1	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	—	2	4	no	—
279	C₁₃×C₄⋊C₄	—	2	4	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	2	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	C₂×D₄	1	2	yes	—
289	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
290	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
291	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
292	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
293	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
294	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
295	C₁₃×C₂²⋊C₄	—	2	2	no	—
296	C₁₃×C₂²⋊C₄	—	2	4	no	—
297	C₁₃×C₂²⋊C₄	—	2	2	no	—
298	C₁₃×C₂²⋊C₄	—	2	2	no	—
299	C₁₃×C₂²⋊C₄	—	2	2	no	—
300	C₁₃×C₂²⋊C₄	—	2	2	no	—
301	C₁₃×C₂²⋊C₄	—	2	4	no	—
302	C₁₃×C₂²⋊C₄	—	2	2	no	—
303	C₁₃×C₂²⋊C₄	—	2	2	no	—
304	C₁₃×C₂²⋊C₄	—	2	4	no	—
305	C₁₃×C₂²⋊C₄	—	2	2	no	—
306	C₁₃×C₂²⋊C₄	—	2	2	no	—
307	C₁₃×C₂²⋊C₄	—	2	2	no	—
308	C₁₃×C₂²⋊C₄	—	2	2	no	—
309	C₁₃×C₂²⋊C₄	—	2	2	no	—
310	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
311	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
312	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
313	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
314	C₄²×C₁₃	—	2	4	no	—
315	C₄²×C₁₃	—	2	2	no	—
316	C₄²×C₁₃	—	2	2	no	—
317	C₄²×C₁₃	C₂×D₄	1	2	yes	—
318	C₄²×C₁₃	C₂⁴	1	2	yes	—
319	#3505	C₂×C₁₃	1	1	yes	characteristic, complemented
320	C₂×#553	C₂×C₁₃	1	1	yes	characteristic, complemented
321	#3339	C₂×C₁₃	1	4	yes	complemented
322	#3337	C₂×C₁₃	1	4	yes	complemented
323	#3301	C₂×C₁₃	1	4	yes	complemented
324	#3297	C₂×C₁₃	1	4	yes	complemented
325	#3232	C₂×C₁₃	1	2	yes	complemented
326	#3188	C₂×C₁₃	1	2	yes	complemented
327	#3187	C₂×C₁₃	1	1	yes	characteristic, complemented
328	#3186	C₂×C₁₃	1	1	yes	characteristic, complemented
329	#3105	C₂×C₁₃	1	2	yes	complemented
330	#3091	C₂×C₁₃	1	2	yes	complemented
331	C₂×#484	C₂×C₁₃	1	1	yes	characteristic, complemented
332	C₂×#481	C₂×C₁₃	1	1	yes	characteristic, complemented
333	#2972	C₂×C₁₃	1	1	yes	characteristic, complemented
334	C₂³×C₁₃	—	2	2	no	—
335	C₂³×C₁₃	—	2	2	no	—
336	C₂³×C₁₃	—	2	2	no	—
337	C₂³×C₁₃	—	4	1	no	—
338	C₂³×C₁₃	—	4	1	no	—
339	C₂³×C₁₃	—	4	1	no	—
340	C₂³×C₁₃	—	4	1	no	—
341	C₂³×C₁₃	—	4	2	no	—
342	C₂³×C₁₃	—	4	2	no	—
343	C₂³×C₁₃	—	4	2	no	—
344	C₂³×C₁₃	—	4	2	no	—
345	C₂³×C₁₃	—	8	1	no	—
346	C₂³×C₁₃	—	8	1	no	—
347	C₂³×C₁₃	#135	1	4	yes	—
348	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
349	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
350	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
351	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
352	Q₈×C₁₃	—	2	4	no	—
353	Q₈×C₁₃	—	8	1	no	—
354	D₄×C₁₃	—	2	4	no	—
355	D₄×C₁₃	—	2	4	no	—
356	D₄×C₁₃	—	2	4	no	—
357	D₄×C₁₃	—	2	4	no	—
358	D₄×C₁₃	—	4	2	no	—
359	D₄×C₁₃	—	4	4	no	—
360	D₄×C₁₃	—	4	4	no	—
361	D₄×C₁₃	—	4	4	no	—
362	D₄×C₁₃	—	4	4	no	—
363	D₄×C₁₃	—	8	1	no	—
364	D₄×C₁₃	—	8	2	no	—
365	D₄×C₁₃	—	8	4	no	—
366	D₄×C₁₃	—	8	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	2	no	—
370	C₂×C₄×C₁₃	—	2	4	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	—	4	2	no	—
379	C₂×C₄×C₁₃	—	4	1	no	—
380	C₂×C₄×C₁₃	—	4	1	no	—
381	C₂×C₄×C₁₃	—	4	1	no	—
382	C₂×C₄×C₁₃	—	4	1	no	—
383	C₂×C₄×C₁₃	—	4	1	no	—
384	C₂×C₄×C₁₃	—	4	2	no	—
385	C₂×C₄×C₁₃	—	4	2	no	—
386	C₂×C₄×C₁₃	—	4	2	no	—
387	C₂×C₄×C₁₃	—	4	2	no	—
388	C₂×C₄×C₁₃	—	8	2	no	—
389	C₂×C₄×C₁₃	—	8	4	no	—
390	C₂×C₄×C₁₃	—	8	2	no	—
391	C₂×C₄×C₁₃	—	8	1	no	—
392	C₂×C₄×C₁₃	—	8	2	no	—
393	C₂×C₄×C₁₃	—	8	2	no	—
394	C₂×C₄×C₁₃	—	8	1	no	—
395	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
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	2	yes	—
399	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
402	C₈×C₁₃	—	2	4	no	—
403	C₈×C₁₃	—	2	4	no	—
404	#553	—	2	2	no	—
405	#553	—	2	2	no	—
406	#553	—	2	2	no	—
407	#553	C₂²×C₁₃	1	4	yes	—
408	#553	C₂²×C₁₃	1	2	yes	complemented
409	#553	C₂²×C₁₃	1	4	yes	complemented
410	#552	C₂²×C₁₃	1	2	yes	complemented
411	#551	—	2	2	no	—
412	#548	C₂²×C₁₃	1	2	yes	complemented
413	#546	C₂²×C₁₃	1	2	yes	complemented
414	#539	—	2	1	no	—
415	#538	—	2	1	no	—
416	#534	—	2	1	no	—
417	#529	C₂²×C₁₃	1	2	yes	—
418	C₂×#126	—	2	1	no	—
419	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
420	#525	C₂²×C₁₃	1	2	yes	—
421	C₂×#123	—	2	1	no	—
422	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×#121	—	2	1	no	—
424	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
427	#518	—	2	1	no	—
428	C₂×C₄×D₄	—	2	1	no	—
429	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
432	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
433	#499	C₂²×C₁₃	1	4	yes	complemented
434	#488	C₂²×C₁₃	1	4	yes	complemented
435	#485	C₂²×C₁₃	1	4	yes	complemented
436	#484	C₂²×C₁₃	1	4	yes	complemented
437	#484	C₂²×C₁₃	1	2	yes	complemented
438	#484	C₂²×C₁₃	1	2	yes	complemented
439	#483	C₂²×C₁₃	1	2	yes	complemented
440	#482	C₂²×C₁₃	1	4	yes	complemented
441	#482	C₂²×C₁₃	1	4	yes	complemented
442	#481	C₂²×C₁₃	1	2	yes	—
443	#481	C₂²×C₁₃	1	2	yes	—
444	#481	C₂²×C₁₃	1	2	yes	complemented
445	#481	C₂²×C₁₃	1	4	yes	complemented
446	#480	C₂²×C₁₃	1	2	yes	—
447	#480	C₂²×C₁₃	1	2	yes	complemented
448	#479	C₂²×C₁₃	1	4	yes	complemented
449	#478	C₂²×C₁₃	1	4	yes	complemented
450	#478	C₂²×C₁₃	1	4	yes	complemented
451	#466	C₂²×C₁₃	1	4	yes	complemented
452	#466	C₂²×C₁₃	1	4	yes	complemented
453	#465	C₂²×C₁₃	1	4	yes	complemented
454	#465	C₂²×C₁₃	1	4	yes	complemented
455	#463	C₂²×C₁₃	1	4	yes	complemented
456	#450	C₂²×C₁₃	1	2	yes	complemented
457	#449	C₂²×C₁₃	1	4	yes	complemented
458	#448	C₂²×C₁₃	1	2	yes	complemented
459	#447	C₂²×C₁₃	1	2	yes	—
460	#447	C₂²×C₁₃	1	2	yes	complemented
461	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
462	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
463	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
464	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
465	#431	C₂²×C₁₃	1	2	yes	complemented
466	#427	C₂²×C₁₃	1	4	yes	complemented
467	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
468	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
469	#416	C₂²×C₁₃	1	4	yes	complemented
470	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
471	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
472	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
473	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
474	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
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	—	2	2	no	—
482	C₂²×C₁₃	—	2	2	no	—
483	C₂²×C₁₃	—	2	2	no	—
484	C₂²×C₁₃	—	4	4	no	—
485	C₂²×C₁₃	—	4	2	no	—
486	C₂²×C₁₃	—	4	2	no	—
487	C₂²×C₁₃	—	4	2	no	—
488	C₂²×C₁₃	—	4	2	no	—
489	C₂²×C₁₃	—	4	2	no	—
490	C₂²×C₁₃	—	4	2	no	—
491	C₂²×C₁₃	—	8	2	no	—
492	C₂²×C₁₃	—	8	4	no	—
493	C₂²×C₁₃	—	16	2	no	—
494	C₂²×C₁₃	C₂×#135	1	2	yes	—
495	C₂²×C₁₃	C₂×#135	1	2	yes	—
496	C₂²×C₁₃	C₂×#135	1	2	yes	—
497	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
498	C₄×C₁₃	—	2	2	no	—
499	C₄×C₁₃	—	2	1	no	—
500	C₄×C₁₃	—	2	2	no	—
501	C₄×C₁₃	—	2	1	no	—
502	C₄×C₁₃	—	2	1	no	—
503	C₄×C₁₃	—	2	2	no	—
504	C₄×C₁₃	—	4	2	no	—
505	C₄×C₁₃	—	4	2	no	—
506	C₄×C₁₃	—	4	2	no	—
507	C₄×C₁₃	—	4	2	no	—
508	C₄×C₁₃	—	4	2	no	—
509	C₄×C₁₃	—	4	2	no	—
510	C₄×C₁₃	#585	1	2	yes	—
511	C₂×#41	C₂³×C₁₃	1	2	yes	—
512	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
513	C₂²×D₄	—	2	1	no	—
514	C₂²×D₄	—	2	1	no	—
515	C₂²×D₄	—	2	1	no	—
516	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
517	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
518	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
519	C₂³×C₄	—	2	1	no	—
520	C₂³×C₄	—	2	1	no	—
521	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
523	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
524	C₂×D₈	C₂³×C₁₃	1	4	yes	—
525	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
526	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
527	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
528	#126	—	2	4	no	—
529	#126	—	2	4	no	—
530	#126	—	2	2	no	—
531	#126	—	2	2	no	—
532	#126	—	2	2	no	—
533	#125	—	2	2	no	—
534	#125	—	2	2	no	—
535	#125	C₂³×C₁₃	1	4	yes	—
536	#125	C₂³×C₁₃	1	2	yes	—
537	#124	—	2	2	no	—
538	#124	C₂³×C₁₃	1	2	yes	—
539	#123	—	2	2	no	—
540	#123	—	2	2	no	—
541	#123	—	2	2	no	—
542	#123	—	2	2	no	—
543	#123	—	2	4	no	—
544	#123	—	2	4	no	—
545	#123	—	2	2	no	—
546	C₂²⋊Q₈	—	2	1	no	—
547	C₂²⋊Q₈	—	2	1	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
550	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
551	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
552	#121	—	2	4	no	—
553	#121	—	2	4	no	—
554	#121	—	2	2	no	—
555	#121	—	2	2	no	—
556	#121	—	2	1	no	—
557	#121	—	2	1	no	—
558	#121	—	2	1	no	—
559	#121	—	2	1	no	—
560	#121	—	2	2	no	—
561	#121	—	2	2	no	—
562	#121	C₂³×C₁₃	1	2	yes	—
563	#121	C₂³×C₁₃	1	2	yes	—
564	#121	C₂³×C₁₃	1	2	yes	—
565	#121	C₂³×C₁₃	1	2	yes	—
566	#121	C₂³×C₁₃	1	4	yes	—
567	#121	C₂³×C₁₃	1	2	yes	—
568	#120	—	2	2	no	—
569	#120	—	2	2	no	—
570	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	—	2	2	no	—
574	C₄×D₄	—	2	4	no	—
575	C₄×D₄	—	2	4	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	D₄×C₁₃	1	2	yes	—
580	C₄×D₄	D₄×C₁₃	1	2	yes	—
581	C₄×D₄	C₂³×C₁₃	1	4	yes	—
582	C₄×D₄	C₂³×C₁₃	1	2	yes	—
583	C₄×D₄	C₂³×C₁₃	1	2	yes	—
584	C₄×D₄	C₂³×C₁₃	1	2	yes	—
585	#117	—	2	2	no	—
586	#117	—	2	2	no	—
587	#117	—	2	2	no	—
588	#117	C₂³×C₁₃	1	4	yes	—
589	#117	C₂³×C₁₃	1	2	yes	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	—	2	1	no	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
604	C₂×C₂²⋊C₄	—	2	1	no	—
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	—	2	2	no	—
611	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
613	C₂×C₄²	—	2	1	no	—
614	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
615	#107	C₂³×C₁₃	1	4	yes	—
616	#107	C₂³×C₁₃	1	4	yes	—
617	#107	C₂³×C₁₃	1	4	yes	—
618	#106	C₂³×C₁₃	1	4	yes	—
619	#106	C₂³×C₁₃	1	4	yes	—
620	#106	C₂³×C₁₃	1	4	yes	—
621	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
622	#103	C₂³×C₁₃	1	4	yes	—
623	#103	C₂³×C₁₃	1	4	yes	—
624	#103	C₂³×C₁₃	1	4	yes	—
625	#102	C₂³×C₁₃	1	4	yes	—
626	#102	C₂³×C₁₃	1	4	yes	—
627	#102	C₂³×C₁₃	1	4	yes	—
628	#102	C₂³×C₁₃	1	4	yes	—
629	#102	C₂³×C₁₃	1	4	yes	—
630	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
631	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
632	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
633	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
634	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
635	C₄×C₈	C₂³×C₁₃	1	4	yes	—
636	C₂×C₁₃	—	2	2	no	—
637	C₂×C₁₃	—	2	2	no	—
638	C₂×C₁₃	—	2	2	no	—
639	C₂×C₁₃	—	4	2	no	—
640	C₂×C₁₃	—	8	2	no	—
641	C₂×C₁₃	—	8	2	no	—
642	C₂×C₁₃	#3485	1	1	yes	characteristic
643	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
644	C₂×C₁₃	#3585	1	1	yes	characteristic
645	C₂⁴	—	2	1	no	—
646	C₂⁴	—	2	1	no	—
647	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
648	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
649	#41	—	4	4	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	4	2	no	—
652	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	4	2	no	—
664	C₂×D₄	—	4	2	no	—
665	C₂×D₄	—	4	4	no	—
666	C₂×D₄	—	4	4	no	—
667	C₂×D₄	—	8	2	no	—
668	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
669	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
670	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
671	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	8	2	no	—
686	C₂²×C₄	—	8	2	no	—
687	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
688	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	2	yes	—
694	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
698	SD₁₆	—	4	4	no	—
699	D₈	—	4	4	no	—
700	C₂×C₈	—	4	2	no	—
701	C₂×C₈	—	4	4	no	—
702	C₂×C₈	—	4	2	no	—
703	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
704	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
721	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
722	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
723	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
724	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
725	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
726	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	4	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	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
743	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
744	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
745	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
746	C₄²	—	2	4	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	2	2	no	—
749	C₄²	C₂×D₄×C₁₃	1	2	yes	—
750	C₄²	C₂⁴×C₁₃	1	2	yes	—
751	C₁₃	#61699	1	1	yes	characteristic, direct product factor, Sylow
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	4	1	no	—
756	C₂³	—	4	1	no	—
757	C₂³	—	4	1	no	—
758	C₂³	—	4	1	no	—
759	C₂³	—	4	2	no	—
760	C₂³	—	4	2	no	—
761	C₂³	—	4	2	no	—
762	C₂³	—	4	2	no	—
763	C₂³	—	8	1	no	—
764	C₂³	—	8	1	no	—
765	C₂³	C₁₃×#135	1	4	yes	—
766	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
767	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
768	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
769	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
770	Q₈	—	2	4	no	—
771	Q₈	—	8	1	no	—
772	D₄	—	2	4	no	—
773	D₄	—	2	4	no	—
774	D₄	—	2	4	no	—
775	D₄	—	2	4	no	—
776	D₄	—	4	2	no	—
777	D₄	—	4	4	no	—
778	D₄	—	4	4	no	—
779	D₄	—	4	4	no	—
780	D₄	—	4	4	no	—
781	D₄	—	8	1	no	—
782	D₄	—	8	4	no	—
783	D₄	—	8	2	no	—
784	D₄	—	8	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	4	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	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	—	4	2	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	1	no	—
801	C₂×C₄	—	4	1	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	2	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	8	4	no	—
807	C₂×C₄	—	8	2	no	—
808	C₂×C₄	—	8	2	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	—	8	2	no	—
811	C₂×C₄	—	8	1	no	—
812	C₂×C₄	—	8	1	no	—
813	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
815	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
819	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
820	C₈	—	2	4	no	—
821	C₈	—	2	4	no	—
822	C₂²	—	2	1	no	—
823	C₂²	—	2	1	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	8	2	no	—
839	C₂²	—	8	4	no	—
840	C₂²	—	16	2	no	—
841	C₂²	C₂×C₁₃×#135	1	2	yes	—
842	C₂²	C₂×C₁₃×#135	1	2	yes	—
843	C₂²	C₂×C₁₃×#135	1	2	yes	—
844	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
845	C₄	—	2	2	no	—
846	C₄	—	2	2	no	—
847	C₄	—	2	1	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	1	no	—
850	C₄	—	2	1	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	C₁₃×#585	1	2	yes	—
858	C₂	—	2	2	no	—
859	C₂	—	2	2	no	—
860	C₂	—	2	2	no	—
861	C₂	—	4	2	no	—
862	C₂	—	8	2	no	—
863	C₂	—	8	2	no	—
864	C₂	C₁₃×#3485	1	1	yes	characteristic
865	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
866	C₂	C₁₃×#3585	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 ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3505	C₂	semidirect
2. C₂×C₁₃×#553	C₂	semidirect
3. C₁₃×#3339	C₂	semidirect
4. C₁₃×#3337	C₂	semidirect
5. C₁₃×#3301	C₂	semidirect
6. C₁₃×#3297	C₂	semidirect
7. C₁₃×#3232	C₂	semidirect
8. C₁₃×#3188	C₂	semidirect
9. C₁₃×#3187	C₂	semidirect
10. C₁₃×#3186	C₂	semidirect
11. C₁₃×#3105	C₂	semidirect
12. C₁₃×#3091	C₂	semidirect
13. C₂×C₁₃×#484	C₂	semidirect
14. C₂×C₁₃×#481	C₂	semidirect
15. C₁₃×#2972	C₂	semidirect
20. C₁₃×#553	C₂²	semidirect
21. C₁₃×#553	C₂²	semidirect
22. C₁₃×#552	C₂²	semidirect
24. C₁₃×#548	C₂²	semidirect
25. C₁₃×#546	C₂²	semidirect
31. C₂×C₁₃×#125	C₂²	semidirect
38. C₂×C₁₃×#121	C₂²	semidirect
42. C₂×C₄×D₄×C₁₃	C₂²	semidirect
43. C₂×C₁₃×#117	C₂²	semidirect
45. C₁₃×#499	C₂²	semidirect
46. C₁₃×#488	C₂²	semidirect
47. C₁₃×#485	C₂²	semidirect
48. C₁₃×#484	C₂²	semidirect
49. C₁₃×#484	C₂²	semidirect
50. C₁₃×#484	C₂²	semidirect
51. C₁₃×#483	C₂²	semidirect
52. C₁₃×#482	C₂²	semidirect
53. C₁₃×#482	C₂²	semidirect
56. C₁₃×#481	C₂²	semidirect
57. C₁₃×#481	C₂²	semidirect
59. C₁₃×#480	C₂²	semidirect
60. C₁₃×#479	C₂²	semidirect
61. C₁₃×#478	C₂²	semidirect
62. C₁₃×#478	C₂²	semidirect
63. C₁₃×#466	C₂²	semidirect
64. C₁₃×#466	C₂²	semidirect
65. C₁₃×#465	C₂²	semidirect
66. C₁₃×#465	C₂²	semidirect
67. C₁₃×#463	C₂²	semidirect
68. C₁₃×#450	C₂²	semidirect
69. C₁₃×#449	C₂²	semidirect
70. C₁₃×#448	C₂²	semidirect
72. C₁₃×#447	C₂²	semidirect
73. C₄×C₁₃×SD₁₆	C₂²	semidirect
74. C₄×C₁₃×D₈	C₂²	semidirect
75. C₈×D₄×C₁₃	C₂²	semidirect
76. C₈×D₄×C₁₃	C₂²	semidirect
77. C₁₃×#431	C₂²	semidirect
78. C₁₃×#427	C₂²	semidirect
79. C₂×C₁₃×#107	C₂²	semidirect
80. C₂×C₁₃×#106	C₂²	semidirect
81. C₁₃×#416	C₂²	semidirect
82. C₂×C₁₃×#103	C₂²	semidirect
83. C₂×C₁₃×#102	C₂²	semidirect
86. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
212. #61699	C₁₃	direct (N × H)
319. #3505	C₂×C₁₃	semidirect
320. C₂×#553	C₂×C₁₃	semidirect
321. #3339	C₂×C₁₃	semidirect
322. #3337	C₂×C₁₃	semidirect
323. #3301	C₂×C₁₃	semidirect
324. #3297	C₂×C₁₃	semidirect
325. #3232	C₂×C₁₃	semidirect
326. #3188	C₂×C₁₃	semidirect
327. #3187	C₂×C₁₃	semidirect
328. #3186	C₂×C₁₃	semidirect
329. #3105	C₂×C₁₃	semidirect
330. #3091	C₂×C₁₃	semidirect
331. C₂×#484	C₂×C₁₃	semidirect
332. C₂×#481	C₂×C₁₃	semidirect
333. #2972	C₂×C₁₃	semidirect
408. #553	C₂²×C₁₃	semidirect
409. #553	C₂²×C₁₃	semidirect
410. #552	C₂²×C₁₃	semidirect
412. #548	C₂²×C₁₃	semidirect
413. #546	C₂²×C₁₃	semidirect
419. C₂×#125	C₂²×C₁₃	semidirect
426. C₂×#121	C₂²×C₁₃	semidirect
430. C₂×C₄×D₄	C₂²×C₁₃	semidirect
431. C₂×#117	C₂²×C₁₃	semidirect
433. #499	C₂²×C₁₃	semidirect
434. #488	C₂²×C₁₃	semidirect
435. #485	C₂²×C₁₃	semidirect
436. #484	C₂²×C₁₃	semidirect
437. #484	C₂²×C₁₃	semidirect
438. #484	C₂²×C₁₃	semidirect
439. #483	C₂²×C₁₃	semidirect
440. #482	C₂²×C₁₃	semidirect
441. #482	C₂²×C₁₃	semidirect
444. #481	C₂²×C₁₃	semidirect
445. #481	C₂²×C₁₃	semidirect
447. #480	C₂²×C₁₃	semidirect
448. #479	C₂²×C₁₃	semidirect
449. #478	C₂²×C₁₃	semidirect
450. #478	C₂²×C₁₃	semidirect
451. #466	C₂²×C₁₃	semidirect
452. #466	C₂²×C₁₃	semidirect
453. #465	C₂²×C₁₃	semidirect
454. #465	C₂²×C₁₃	semidirect
455. #463	C₂²×C₁₃	semidirect
456. #450	C₂²×C₁₃	semidirect
457. #449	C₂²×C₁₃	semidirect
458. #448	C₂²×C₁₃	semidirect
460. #447	C₂²×C₁₃	semidirect
461. C₄×SD₁₆	C₂²×C₁₃	semidirect
462. C₄×D₈	C₂²×C₁₃	semidirect
463. C₈×D₄	C₂²×C₁₃	semidirect
464. C₈×D₄	C₂²×C₁₃	semidirect
465. #431	C₂²×C₁₃	semidirect
466. #427	C₂²×C₁₃	semidirect
467. C₂×#107	C₂²×C₁₃	semidirect
468. C₂×#106	C₂²×C₁₃	semidirect
469. #416	C₂²×C₁₃	semidirect
470. C₂×#103	C₂²×C₁₃	semidirect
471. C₂×#102	C₂²×C₁₃	semidirect
474. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
751. C₁₃	#61699	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×#3505	2
C₂×C₁₃×#553	2
C₁₃×#3339	2
C₁₃×#3337	2
C₁₃×#3301	2
C₁₃×#3297	2
C₁₃×#3232	2
C₁₃×#3188	2
C₁₃×#3187	2
C₁₃×#3186	2
C₁₃×#3105	2
C₁₃×#3091	2
C₂×C₁₃×#484	2
C₂×C₁₃×#481	2
C₁₃×#2972	2
#61699	13

Subgroups — C13×#61699 #15748038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61699 #15748038