Subgroups — C₁₃×#61038 #15747377

Order 3328.

2790 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#575	C₂	1	2	yes	maximal, complemented
2	D₄×C₁₃×#41	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3278	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3277	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3276	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3275	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3274	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3273	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3272	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3054	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3035	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3002	C₂	1	4	yes	maximal, complemented
14	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	4	yes	complemented
17	C₁₃×#575	—	2	16	no	—
18	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
19	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
21	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
22	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
24	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
25	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
26	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	complemented
27	C₁₃×#550	C₂²	1	2	yes	—
28	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
29	C₁₃×#548	C₂²	1	4	yes	complemented
30	C₁₃×#547	—	2	2	no	—
31	C₁₃×#547	C₂²	1	2	yes	—
32	C₁₃×#546	—	2	4	no	—
33	C₁₃×#546	C₂²	1	4	yes	complemented
34	D₄²×C₁₃	—	2	2	no	—
35	D₄²×C₁₃	C₂²	1	2	yes	complemented
36	C₁₃×#532	—	2	2	no	—
37	C₁₃×#532	C₂²	1	2	yes	complemented
38	C₁₃×#525	—	2	4	no	—
39	C₁₃×#525	C₂²	1	4	yes	complemented
40	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
41	C₂×C₄×D₄×C₁₃	—	2	2	no	—
42	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
43	C₁₃×#495	C₂²	1	2	yes	complemented
44	C₁₃×#495	C₂²	1	2	yes	complemented
45	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#492	C₂²	1	2	yes	complemented
48	C₁₃×#470	C₂²	1	4	yes	complemented
49	C₁₃×#469	C₂²	1	4	yes	complemented
50	C₁₃×#468	C₂²	1	4	yes	complemented
51	C₁₃×#468	C₂²	1	4	yes	complemented
52	C₁₃×#464	C₂²	1	4	yes	complemented
53	C₁₃×#463	C₂²	1	4	yes	complemented
54	C₁₃×#462	C₂²	1	2	yes	complemented
55	C₁₃×#461	C₂²	1	2	yes	complemented
56	C₁₃×#460	C₂²	1	2	yes	complemented
57	C₁₃×#459	C₂²	1	2	yes	complemented
58	C₁₃×#452	C₂²	1	4	yes	complemented
59	C₁₃×#452	C₂²	1	4	yes	complemented
60	C₁₃×#451	C₂²	1	4	yes	complemented
61	C₁₃×#450	C₂²	1	4	yes	complemented
62	C₁₃×#449	C₂²	1	4	yes	complemented
63	C₁₃×#449	C₂²	1	4	yes	complemented
64	C₁₃×#448	C₂²	1	4	yes	complemented
65	C₁₃×#447	C₂²	1	4	yes	complemented
66	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
67	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
68	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
69	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
70	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
71	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
72	C₁₃×#436	C₂²	1	2	yes	complemented
73	C₁₃×#436	C₂²	1	2	yes	complemented
74	C₁₃×#436	C₂²	1	2	yes	complemented
75	C₁₃×#436	C₂²	1	2	yes	complemented
76	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
77	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#416	C₂²	1	4	yes	complemented
79	C₁₃×#416	C₂²	1	2	yes	complemented
80	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
81	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₁₃×#41	—	2	4	no	—
83	C₂×C₁₃×#41	—	2	4	no	—
84	C₂×C₁₃×#41	—	2	16	no	—
85	C₂×C₁₃×#41	—	4	8	no	—
86	C₂×C₁₃×#41	C₂³	1	4	yes	—
87	C₂×C₁₃×#41	C₂³	1	4	yes	—
88	C₂×C₁₃×#41	C₂³	1	4	yes	—
89	C₂×C₁₃×#41	C₂³	1	2	yes	—
90	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
91	C₂²×D₄×C₁₃	—	2	4	no	—
92	C₂²×D₄×C₁₃	—	2	2	no	—
93	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
94	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
95	C₂³×C₄×C₁₃	—	2	4	no	—
96	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
97	C₁₃×#137	—	2	16	no	—
98	C₁₃×#137	—	2	16	no	—
99	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
100	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
101	C₁₃×#135	—	2	16	no	—
102	C₁₃×#135	—	2	8	no	—
103	C₁₃×#135	—	4	4	no	—
104	C₁₃×#135	D₄	1	8	yes	complemented
105	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
107	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
108	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
111	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
112	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
113	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
114	C₂×C₁₃×D₈	C₂³	1	4	yes	—
115	C₂×C₁₃×D₈	C₂³	1	2	yes	—
116	C₂×C₁₃×D₈	C₂³	1	2	yes	—
117	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×M₁₆	—	2	8	no	—
119	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
120	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
121	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
123	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₁₃×C₄⋊Q₈	—	2	2	no	—
125	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
126	C₁₃×#127	—	2	2	no	—
127	C₁₃×#127	C₂³	1	2	yes	—
128	C₁₃×#124	—	2	4	no	—
129	C₁₃×#124	C₂³	1	4	yes	—
130	C₁₃×#123	—	2	4	no	—
131	C₁₃×#123	—	2	4	no	—
132	C₁₃×#123	—	2	4	no	—
133	C₁₃×C₂²⋊Q₈	—	2	4	no	—
134	C₁₃×C₂²⋊Q₈	—	2	4	no	—
135	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
137	C₁₃×#121	—	2	4	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	4	no	—
143	C₁₃×#121	—	2	4	no	—
144	C₁₃×#121	C₂³	1	4	yes	—
145	C₁₃×#121	C₂³	1	4	yes	—
146	C₁₃×#120	—	2	4	no	—
147	C₁₃×#120	—	2	4	no	—
148	C₁₃×#120	—	2	4	no	—
149	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
150	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
151	C₄×D₄×C₁₃	—	2	2	no	—
152	C₄×D₄×C₁₃	—	2	4	no	—
153	C₄×D₄×C₁₃	—	2	2	no	—
154	C₄×D₄×C₁₃	—	2	2	no	—
155	C₄×D₄×C₁₃	—	2	4	no	—
156	C₄×D₄×C₁₃	—	2	2	no	—
157	C₄×D₄×C₁₃	—	2	4	no	—
158	C₄×D₄×C₁₃	—	2	2	no	—
159	C₄×D₄×C₁₃	—	2	2	no	—
160	C₄×D₄×C₁₃	D₄	1	2	yes	—
161	C₄×D₄×C₁₃	D₄	1	2	yes	—
162	C₄×D₄×C₁₃	C₂³	1	2	yes	—
163	C₄×D₄×C₁₃	C₂³	1	2	yes	—
164	C₄×D₄×C₁₃	C₂³	1	2	yes	—
165	C₄×D₄×C₁₃	C₂³	1	2	yes	—
166	C₁₃×#117	—	2	2	no	—
167	C₁₃×#117	C₂³	1	2	yes	—
168	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
170	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
171	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
172	C₂×C₄²×C₁₃	—	2	2	no	—
173	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₁₃×#107	C₂³	1	1	yes	characteristic
175	C₁₃×#107	C₂³	1	1	yes	characteristic
176	C₁₃×#106	C₂³	1	2	yes	—
177	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
179	C₁₃×#103	C₂³	1	2	yes	—
180	C₁₃×#103	C₂³	1	2	yes	—
181	C₁₃×#103	C₂³	1	4	yes	—
182	C₁₃×#103	C₂³	1	4	yes	—
183	C₁₃×#102	C₂³	1	2	yes	—
184	C₁₃×#102	C₂³	1	2	yes	—
185	C₁₃×#102	C₂³	1	4	yes	—
186	C₁₃×#102	C₂³	1	4	yes	—
187	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
188	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
189	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
190	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
191	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
192	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
193	#61038	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂⁴×C₁₃	—	2	4	no	—
195	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
196	C₁₃×#41	—	2	4	no	—
197	C₁₃×#41	—	2	8	no	—
198	C₁₃×#41	—	2	8	no	—
199	C₁₃×#41	—	2	8	no	—
200	C₁₃×#41	—	2	8	no	—
201	C₁₃×#41	—	4	16	no	—
202	C₁₃×#41	—	4	4	no	—
203	C₁₃×#41	—	4	4	no	—
204	C₁₃×#41	—	4	16	no	—
205	C₁₃×#41	C₂×D₄	1	8	yes	complemented
206	C₂×Q₈×C₁₃	—	2	4	no	—
207	C₂×Q₈×C₁₃	—	2	8	no	—
208	C₂×Q₈×C₁₃	—	4	4	no	—
209	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
210	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
211	C₂×D₄×C₁₃	—	2	2	no	—
212	C₂×D₄×C₁₃	—	2	8	no	—
213	C₂×D₄×C₁₃	—	2	4	no	—
214	C₂×D₄×C₁₃	—	2	4	no	—
215	C₂×D₄×C₁₃	—	2	4	no	—
216	C₂×D₄×C₁₃	—	2	4	no	—
217	C₂×D₄×C₁₃	—	2	4	no	—
218	C₂×D₄×C₁₃	—	2	2	no	—
219	C₂×D₄×C₁₃	—	2	4	no	—
220	C₂×D₄×C₁₃	—	2	2	no	—
221	C₂×D₄×C₁₃	—	4	2	no	—
222	C₂×D₄×C₁₃	—	4	4	no	—
223	C₂×D₄×C₁₃	—	4	16	no	—
224	C₂×D₄×C₁₃	—	4	8	no	—
225	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
226	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
227	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
228	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃	—	2	4	no	—
230	C₂²×C₄×C₁₃	—	2	2	no	—
231	C₂²×C₄×C₁₃	—	2	4	no	—
232	C₂²×C₄×C₁₃	—	2	4	no	—
233	C₂²×C₄×C₁₃	—	2	2	no	—
234	C₂²×C₄×C₁₃	—	2	4	no	—
235	C₂²×C₄×C₁₃	—	2	4	no	—
236	C₂²×C₄×C₁₃	—	2	4	no	—
237	C₂²×C₄×C₁₃	—	2	2	no	—
238	C₂²×C₄×C₁₃	—	4	16	no	—
239	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
241	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
242	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₁₃×Q₁₆	—	2	8	no	—
246	C₁₃×Q₁₆	—	2	4	no	—
247	C₁₃×Q₁₆	—	4	2	no	—
248	C₁₃×Q₁₆	C₂×D₄	1	4	yes	complemented
249	C₁₃×SD₁₆	—	2	8	no	—
250	C₁₃×SD₁₆	—	2	8	no	—
251	C₁₃×SD₁₆	—	2	8	no	—
252	C₁₃×SD₁₆	—	4	4	no	—
253	C₁₃×SD₁₆	C₂×D₄	1	8	yes	complemented
254	C₁₃×D₈	—	2	8	no	—
255	C₁₃×D₈	—	2	4	no	—
256	C₁₃×D₈	—	4	2	no	—
257	C₁₃×D₈	C₂×D₄	1	4	yes	complemented
258	C₁₃×M₁₆	—	2	8	no	—
259	C₁₃×M₁₆	—	2	8	no	—
260	C₂×C₈×C₁₃	—	2	4	no	—
261	C₂×C₈×C₁₃	—	2	2	no	—
262	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	complemented
263	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
266	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
267	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
268	C₁₃×C₄⋊C₄	—	2	2	no	—
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	2	2	no	—
271	C₁₃×C₄⋊C₄	—	2	2	no	—
272	C₁₃×C₄⋊C₄	—	2	2	no	—
273	C₁₃×C₄⋊C₄	—	2	4	no	—
274	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
275	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
276	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
277	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
278	C₁₃×C₂²⋊C₄	—	2	4	no	—
279	C₁₃×C₂²⋊C₄	—	2	2	no	—
280	C₁₃×C₂²⋊C₄	—	2	4	no	—
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	4	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
288	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
289	C₄²×C₁₃	—	2	2	no	—
290	C₄²×C₁₃	—	2	2	no	—
291	C₄²×C₁₃	—	2	2	no	—
292	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
293	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
294	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
295	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
296	C₂×#575	C₂×C₁₃	1	2	yes	complemented
297	D₄×#41	C₂×C₁₃	1	2	yes	complemented
298	#3278	C₂×C₁₃	1	2	yes	complemented
299	#3277	C₂×C₁₃	1	2	yes	complemented
300	#3276	C₂×C₁₃	1	2	yes	complemented
301	#3275	C₂×C₁₃	1	4	yes	complemented
302	#3274	C₂×C₁₃	1	2	yes	complemented
303	#3273	C₂×C₁₃	1	2	yes	complemented
304	#3272	C₂×C₁₃	1	2	yes	complemented
305	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
306	#3054	C₂×C₁₃	1	2	yes	complemented
307	#3035	C₂×C₁₃	1	2	yes	complemented
308	#3002	C₂×C₁₃	1	4	yes	complemented
309	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
310	C₂×#436	C₂×C₁₃	1	1	yes	characteristic, complemented
311	C₂³×C₁₃	—	2	2	no	—
312	C₂³×C₁₃	—	2	4	no	—
313	C₂³×C₁₃	—	2	4	no	—
314	C₂³×C₁₃	—	4	2	no	—
315	C₂³×C₁₃	—	4	2	no	—
316	C₂³×C₁₃	—	4	8	no	—
317	C₂³×C₁₃	—	4	8	no	—
318	C₂³×C₁₃	—	8	4	no	—
319	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
320	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
321	Q₈×C₁₃	—	2	2	no	—
322	Q₈×C₁₃	—	2	4	no	—
323	Q₈×C₁₃	—	2	4	no	—
324	Q₈×C₁₃	—	4	8	no	—
325	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
326	D₄×C₁₃	—	2	8	no	—
327	D₄×C₁₃	—	2	4	no	—
328	D₄×C₁₃	—	2	4	no	—
329	D₄×C₁₃	—	2	2	no	—
330	D₄×C₁₃	—	2	4	no	—
331	D₄×C₁₃	—	4	2	no	—
332	D₄×C₁₃	—	4	8	no	—
333	D₄×C₁₃	—	4	8	no	—
334	D₄×C₁₃	—	4	8	no	—
335	D₄×C₁₃	—	4	8	no	—
336	D₄×C₁₃	—	4	8	no	—
337	D₄×C₁₃	—	4	4	no	—
338	D₄×C₁₃	—	8	2	no	—
339	D₄×C₁₃	—	8	4	no	—
340	D₄×C₁₃	C₂²×D₄	1	4	yes	—
341	C₂×C₄×C₁₃	—	2	4	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	8	no	—
344	C₂×C₄×C₁₃	—	2	8	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	4	no	—
347	C₂×C₄×C₁₃	—	2	4	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	4	no	—
351	C₂×C₄×C₁₃	—	4	1	no	—
352	C₂×C₄×C₁₃	—	4	8	no	—
353	C₂×C₄×C₁₃	—	4	8	no	—
354	C₂×C₄×C₁₃	—	4	8	no	—
355	C₂×C₄×C₁₃	—	4	8	no	—
356	C₂×C₄×C₁₃	—	4	4	no	—
357	C₂×C₄×C₁₃	—	8	2	no	—
358	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
362	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
363	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
366	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
367	C₈×C₁₃	—	2	4	no	—
368	C₈×C₁₃	—	2	1	no	—
369	C₈×C₁₃	—	2	1	no	—
370	C₈×C₁₃	C₂²×D₄	1	2	yes	—
371	C₈×C₁₃	C₂²×D₄	1	2	yes	—
372	C₂²×#41	C₂²×C₁₃	1	4	yes	complemented
373	#575	—	2	16	no	—
374	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
375	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
376	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
377	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
378	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
380	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
381	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
382	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	complemented
383	#550	C₂²×C₁₃	1	2	yes	—
384	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
385	#548	C₂²×C₁₃	1	4	yes	complemented
386	#547	—	2	2	no	—
387	#547	C₂²×C₁₃	1	2	yes	—
388	#546	—	2	4	no	—
389	#546	C₂²×C₁₃	1	4	yes	complemented
390	D₄²	—	2	2	no	—
391	D₄²	C₂²×C₁₃	1	2	yes	complemented
392	#532	—	2	2	no	—
393	#532	C₂²×C₁₃	1	2	yes	complemented
394	#525	—	2	4	no	—
395	#525	C₂²×C₁₃	1	4	yes	complemented
396	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
397	C₂×C₄×D₄	—	2	2	no	—
398	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
399	#495	C₂²×C₁₃	1	2	yes	complemented
400	#495	C₂²×C₁₃	1	2	yes	complemented
401	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
402	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
403	#492	C₂²×C₁₃	1	2	yes	complemented
404	#470	C₂²×C₁₃	1	4	yes	complemented
405	#469	C₂²×C₁₃	1	4	yes	complemented
406	#468	C₂²×C₁₃	1	4	yes	complemented
407	#468	C₂²×C₁₃	1	4	yes	complemented
408	#464	C₂²×C₁₃	1	4	yes	complemented
409	#463	C₂²×C₁₃	1	4	yes	complemented
410	#462	C₂²×C₁₃	1	2	yes	complemented
411	#461	C₂²×C₁₃	1	2	yes	complemented
412	#460	C₂²×C₁₃	1	2	yes	complemented
413	#459	C₂²×C₁₃	1	2	yes	complemented
414	#452	C₂²×C₁₃	1	4	yes	complemented
415	#452	C₂²×C₁₃	1	4	yes	complemented
416	#451	C₂²×C₁₃	1	4	yes	complemented
417	#450	C₂²×C₁₃	1	4	yes	complemented
418	#449	C₂²×C₁₃	1	4	yes	complemented
419	#449	C₂²×C₁₃	1	4	yes	complemented
420	#448	C₂²×C₁₃	1	4	yes	complemented
421	#447	C₂²×C₁₃	1	4	yes	complemented
422	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
423	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
424	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
425	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
426	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
427	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
428	#436	C₂²×C₁₃	1	2	yes	complemented
429	#436	C₂²×C₁₃	1	2	yes	complemented
430	#436	C₂²×C₁₃	1	2	yes	complemented
431	#436	C₂²×C₁₃	1	2	yes	complemented
432	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
433	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
434	#416	C₂²×C₁₃	1	2	yes	complemented
435	#416	C₂²×C₁₃	1	4	yes	complemented
436	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
437	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
438	C₂²×C₁₃	—	2	1	no	—
439	C₂²×C₁₃	—	2	1	no	—
440	C₂²×C₁₃	—	2	4	no	—
441	C₂²×C₁₃	—	2	4	no	—
442	C₂²×C₁₃	—	2	4	no	—
443	C₂²×C₁₃	—	2	4	no	—
444	C₂²×C₁₃	—	4	2	no	—
445	C₂²×C₁₃	—	4	2	no	—
446	C₂²×C₁₃	—	4	4	no	—
447	C₂²×C₁₃	—	4	4	no	—
448	C₂²×C₁₃	—	4	4	no	—
449	C₂²×C₁₃	—	8	4	no	—
450	C₂²×C₁₃	—	8	16	no	—
451	C₂²×C₁₃	D₄²	1	2	yes	—
452	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
453	C₄×C₁₃	—	2	1	no	—
454	C₄×C₁₃	—	2	1	no	—
455	C₄×C₁₃	—	2	4	no	—
456	C₄×C₁₃	—	2	4	no	—
457	C₄×C₁₃	—	2	1	no	—
458	C₄×C₁₃	—	4	2	no	—
459	C₄×C₁₃	—	4	4	no	—
460	C₄×C₁₃	—	4	2	no	—
461	C₄×C₁₃	D₄²	1	2	yes	—
462	C₄×C₁₃	#575	1	2	yes	complemented
463	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
464	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
465	C₂×#41	—	2	4	no	—
466	C₂×#41	—	2	4	no	—
467	C₂×#41	—	2	16	no	—
468	C₂×#41	—	4	8	no	—
469	C₂×#41	C₂³×C₁₃	1	4	yes	—
470	C₂×#41	C₂³×C₁₃	1	4	yes	—
471	C₂×#41	C₂³×C₁₃	1	4	yes	—
472	C₂×#41	C₂³×C₁₃	1	2	yes	—
473	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
474	C₂²×D₄	—	2	4	no	—
475	C₂²×D₄	—	2	2	no	—
476	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
477	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
478	C₂³×C₄	—	2	4	no	—
479	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
480	#137	—	2	16	no	—
481	#137	—	2	16	no	—
482	AGL(1,ℤ/8)	—	2	16	no	—
483	AGL(1,ℤ/8)	—	2	16	no	—
484	#135	—	2	16	no	—
485	#135	—	2	8	no	—
486	#135	—	4	4	no	—
487	#135	D₄×C₁₃	1	8	yes	complemented
488	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
489	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
490	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
491	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
492	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
493	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
494	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
495	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
496	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
497	C₂×D₈	C₂³×C₁₃	1	4	yes	—
498	C₂×D₈	C₂³×C₁₃	1	2	yes	—
499	C₂×D₈	C₂³×C₁₃	1	2	yes	—
500	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
501	C₂×M₁₆	—	2	8	no	—
502	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
503	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
504	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
505	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
506	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
507	C₄⋊Q₈	—	2	2	no	—
508	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
509	#127	—	2	2	no	—
510	#127	C₂³×C₁₃	1	2	yes	—
511	#124	—	2	4	no	—
512	#124	C₂³×C₁₃	1	4	yes	—
513	#123	—	2	4	no	—
514	#123	—	2	4	no	—
515	#123	—	2	4	no	—
516	C₂²⋊Q₈	—	2	4	no	—
517	C₂²⋊Q₈	—	2	4	no	—
518	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
519	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
520	#121	—	2	4	no	—
521	#121	—	2	2	no	—
522	#121	—	2	2	no	—
523	#121	—	2	2	no	—
524	#121	—	2	2	no	—
525	#121	—	2	4	no	—
526	#121	—	2	4	no	—
527	#121	C₂³×C₁₃	1	4	yes	—
528	#121	C₂³×C₁₃	1	4	yes	—
529	#120	—	2	4	no	—
530	#120	—	2	4	no	—
531	#120	—	2	4	no	—
532	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
533	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
534	C₄×D₄	—	2	2	no	—
535	C₄×D₄	—	2	4	no	—
536	C₄×D₄	—	2	2	no	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	4	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	4	no	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	D₄×C₁₃	1	2	yes	—
544	C₄×D₄	D₄×C₁₃	1	2	yes	—
545	C₄×D₄	C₂³×C₁₃	1	2	yes	—
546	C₄×D₄	C₂³×C₁₃	1	2	yes	—
547	C₄×D₄	C₂³×C₁₃	1	2	yes	—
548	C₄×D₄	C₂³×C₁₃	1	2	yes	—
549	#117	—	2	2	no	—
550	#117	C₂³×C₁₃	1	2	yes	—
551	C₂×C₄⋊C₄	—	2	2	no	—
552	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	—	2	4	no	—
554	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
555	C₂×C₄²	—	2	2	no	—
556	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
557	#107	C₂³×C₁₃	1	1	yes	characteristic
558	#107	C₂³×C₁₃	1	1	yes	characteristic
559	#106	C₂³×C₁₃	1	2	yes	—
560	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
561	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
562	#103	C₂³×C₁₃	1	2	yes	—
563	#103	C₂³×C₁₃	1	2	yes	—
564	#103	C₂³×C₁₃	1	4	yes	—
565	#103	C₂³×C₁₃	1	4	yes	—
566	#102	C₂³×C₁₃	1	2	yes	—
567	#102	C₂³×C₁₃	1	2	yes	—
568	#102	C₂³×C₁₃	1	4	yes	—
569	#102	C₂³×C₁₃	1	4	yes	—
570	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
571	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
572	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
573	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
574	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
575	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
576	C₂×C₁₃	—	2	2	no	—
577	C₂×C₁₃	—	4	4	no	—
578	C₂×C₁₃	—	4	4	no	—
579	C₂×C₁₃	—	8	4	no	—
580	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
581	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
582	C₂×C₁₃	#3584	1	1	yes	characteristic
583	C₂⁴	—	2	4	no	—
584	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
585	#41	—	2	4	no	—
586	#41	—	2	8	no	—
587	#41	—	2	8	no	—
588	#41	—	2	8	no	—
589	#41	—	2	8	no	—
590	#41	—	4	16	no	—
591	#41	—	4	4	no	—
592	#41	—	4	4	no	—
593	#41	—	4	16	no	—
594	#41	C₂×D₄×C₁₃	1	8	yes	complemented
595	C₂×Q₈	—	2	4	no	—
596	C₂×Q₈	—	2	8	no	—
597	C₂×Q₈	—	4	4	no	—
598	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
599	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	8	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	2	no	—
608	C₂×D₄	—	2	4	no	—
609	C₂×D₄	—	2	2	no	—
610	C₂×D₄	—	4	2	no	—
611	C₂×D₄	—	4	4	no	—
612	C₂×D₄	—	4	16	no	—
613	C₂×D₄	—	4	8	no	—
614	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
615	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
616	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
617	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	4	16	no	—
628	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
629	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
630	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
631	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
633	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
634	Q₁₆	—	2	8	no	—
635	Q₁₆	—	2	4	no	—
636	Q₁₆	—	4	2	no	—
637	Q₁₆	C₂×D₄×C₁₃	1	4	yes	complemented
638	SD₁₆	—	2	8	no	—
639	SD₁₆	—	2	8	no	—
640	SD₁₆	—	2	8	no	—
641	SD₁₆	—	4	4	no	—
642	SD₁₆	C₂×D₄×C₁₃	1	8	yes	complemented
643	D₈	—	2	8	no	—
644	D₈	—	2	4	no	—
645	D₈	—	4	2	no	—
646	D₈	C₂×D₄×C₁₃	1	4	yes	complemented
647	M₁₆	—	2	8	no	—
648	M₁₆	—	2	8	no	—
649	C₂×C₈	—	2	4	no	—
650	C₂×C₈	—	2	2	no	—
651	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	complemented
652	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
653	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
654	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
655	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
656	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
664	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
665	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
666	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
677	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
678	C₄²	—	2	2	no	—
679	C₄²	—	2	2	no	—
680	C₄²	—	2	2	no	—
681	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
682	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
683	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
684	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
685	C₁₃	#61038	1	1	yes	characteristic, direct product factor, Sylow
686	C₂³	—	2	2	no	—
687	C₂³	—	2	4	no	—
688	C₂³	—	2	4	no	—
689	C₂³	—	4	2	no	—
690	C₂³	—	4	2	no	—
691	C₂³	—	4	8	no	—
692	C₂³	—	4	8	no	—
693	C₂³	—	8	4	no	—
694	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
695	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
696	Q₈	—	2	2	no	—
697	Q₈	—	2	4	no	—
698	Q₈	—	2	4	no	—
699	Q₈	—	4	8	no	—
700	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
701	D₄	—	2	8	no	—
702	D₄	—	2	4	no	—
703	D₄	—	2	4	no	—
704	D₄	—	2	2	no	—
705	D₄	—	2	4	no	—
706	D₄	—	4	2	no	—
707	D₄	—	4	8	no	—
708	D₄	—	4	8	no	—
709	D₄	—	4	8	no	—
710	D₄	—	4	8	no	—
711	D₄	—	4	8	no	—
712	D₄	—	4	4	no	—
713	D₄	—	8	2	no	—
714	D₄	—	8	4	no	—
715	D₄	C₂²×D₄×C₁₃	1	4	yes	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	8	no	—
719	C₂×C₄	—	2	8	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	8	no	—
728	C₂×C₄	—	4	8	no	—
729	C₂×C₄	—	4	8	no	—
730	C₂×C₄	—	4	8	no	—
731	C₂×C₄	—	4	4	no	—
732	C₂×C₄	—	8	2	no	—
733	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
734	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
735	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
736	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
737	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
738	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
739	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
740	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
741	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
742	C₈	—	2	4	no	—
743	C₈	—	2	1	no	—
744	C₈	—	2	1	no	—
745	C₈	C₂²×D₄×C₁₃	1	2	yes	—
746	C₈	C₂²×D₄×C₁₃	1	2	yes	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	1	no	—
749	C₂²	—	2	4	no	—
750	C₂²	—	2	4	no	—
751	C₂²	—	2	4	no	—
752	C₂²	—	2	4	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	4	no	—
756	C₂²	—	4	4	no	—
757	C₂²	—	4	4	no	—
758	C₂²	—	8	4	no	—
759	C₂²	—	8	16	no	—
760	C₂²	D₄²×C₁₃	1	2	yes	—
761	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
762	C₄	—	2	1	no	—
763	C₄	—	2	1	no	—
764	C₄	—	2	1	no	—
765	C₄	—	2	4	no	—
766	C₄	—	2	4	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	4	no	—
770	C₄	D₄²×C₁₃	1	2	yes	—
771	C₄	C₁₃×#575	1	2	yes	complemented
772	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
773	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
774	C₂	—	2	2	no	—
775	C₂	—	4	4	no	—
776	C₂	—	4	4	no	—
777	C₂	—	8	4	no	—
778	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
779	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
780	C₂	C₁₃×#3584	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 ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#575	C₂	semidirect
2. D₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#3278	C₂	semidirect
4. C₁₃×#3277	C₂	semidirect
5. C₁₃×#3276	C₂	semidirect
6. C₁₃×#3275	C₂	semidirect
7. C₁₃×#3274	C₂	semidirect
8. C₁₃×#3273	C₂	semidirect
9. C₁₃×#3272	C₂	semidirect
10. C₁₃×#3147	C₂	semidirect
11. C₁₃×#3054	C₂	semidirect
12. C₁₃×#3035	C₂	semidirect
13. C₁₃×#3002	C₂	semidirect
14. C₄×C₁₃×#135	C₂	semidirect
15. C₂×C₁₃×#436	C₂	semidirect
16. C₂²×C₁₃×#41	C₂²	semidirect
18. C₂×C₁₃×#137	C₂²	semidirect
19. C₂×C₁₃×#137	C₂²	semidirect
20. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₁₃×#135	C₂²	semidirect
24. C₂×C₁₃×#135	C₂²	semidirect
25. C₂×C₁₃×#135	C₂²	semidirect
26. C₂²×C₁₃×M₁₆	C₂²	semidirect
28. D₄×Q₈×C₁₃	C₂²	semidirect
29. C₁₃×#548	C₂²	semidirect
33. C₁₃×#546	C₂²	semidirect
35. D₄²×C₁₃	C₂²	semidirect
37. C₁₃×#532	C₂²	semidirect
39. C₁₃×#525	C₂²	semidirect
40. C₄×C₁₃×#41	C₂²	semidirect
43. C₁₃×#495	C₂²	semidirect
44. C₁₃×#495	C₂²	semidirect
45. C₁₃×#494	C₂²	semidirect
46. C₁₃×#493	C₂²	semidirect
47. C₁₃×#492	C₂²	semidirect
48. C₁₃×#470	C₂²	semidirect
49. C₁₃×#469	C₂²	semidirect
50. C₁₃×#468	C₂²	semidirect
51. C₁₃×#468	C₂²	semidirect
52. C₁₃×#464	C₂²	semidirect
53. C₁₃×#463	C₂²	semidirect
54. C₁₃×#462	C₂²	semidirect
55. C₁₃×#461	C₂²	semidirect
56. C₁₃×#460	C₂²	semidirect
57. C₁₃×#459	C₂²	semidirect
58. C₁₃×#452	C₂²	semidirect
59. C₁₃×#452	C₂²	semidirect
60. C₁₃×#451	C₂²	semidirect
61. C₁₃×#450	C₂²	semidirect
62. C₁₃×#449	C₂²	semidirect
63. C₁₃×#449	C₂²	semidirect
64. C₁₃×#448	C₂²	semidirect
65. C₁₃×#447	C₂²	semidirect
66. C₄×C₁₃×Q₁₆	C₂²	semidirect
67. C₄×C₁₃×Q₁₆	C₂²	semidirect
68. C₄×C₁₃×SD₁₆	C₂²	semidirect
69. C₄×C₁₃×SD₁₆	C₂²	semidirect
70. C₄×C₁₃×D₈	C₂²	semidirect
71. C₄×C₁₃×D₈	C₂²	semidirect
72. C₁₃×#436	C₂²	semidirect
73. C₁₃×#436	C₂²	semidirect
74. C₁₃×#436	C₂²	semidirect
75. C₁₃×#436	C₂²	semidirect
76. C₁₃×#427	C₂²	semidirect
77. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
78. C₁₃×#416	C₂²	semidirect
79. C₁₃×#416	C₂²	semidirect
80. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
81. C₂×C₄×C₈×C₁₃	C₂²	semidirect
104. C₁₃×#135	D₄	semidirect
193. #61038	C₁₃	direct (N × H)
205. C₁₃×#41	C₂×D₄	semidirect
248. C₁₃×Q₁₆	C₂×D₄	semidirect
253. C₁₃×SD₁₆	C₂×D₄	semidirect
257. C₁₃×D₈	C₂×D₄	semidirect
262. C₂×C₈×C₁₃	C₂×D₄	semidirect
296. C₂×#575	C₂×C₁₃	semidirect
297. D₄×#41	C₂×C₁₃	semidirect
298. #3278	C₂×C₁₃	semidirect
299. #3277	C₂×C₁₃	semidirect
300. #3276	C₂×C₁₃	semidirect
301. #3275	C₂×C₁₃	semidirect
302. #3274	C₂×C₁₃	semidirect
303. #3273	C₂×C₁₃	semidirect
304. #3272	C₂×C₁₃	semidirect
305. #3147	C₂×C₁₃	semidirect
306. #3054	C₂×C₁₃	semidirect
307. #3035	C₂×C₁₃	semidirect
308. #3002	C₂×C₁₃	semidirect
309. C₄×#135	C₂×C₁₃	semidirect
310. C₂×#436	C₂×C₁₃	semidirect
372. C₂²×#41	C₂²×C₁₃	semidirect
374. C₂×#137	C₂²×C₁₃	semidirect
375. C₂×#137	C₂²×C₁₃	semidirect
376. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
377. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
379. C₂×#135	C₂²×C₁₃	semidirect
380. C₂×#135	C₂²×C₁₃	semidirect
381. C₂×#135	C₂²×C₁₃	semidirect
382. C₂²×M₁₆	C₂²×C₁₃	semidirect
384. D₄×Q₈	C₂²×C₁₃	semidirect
385. #548	C₂²×C₁₃	semidirect
389. #546	C₂²×C₁₃	semidirect
391. D₄²	C₂²×C₁₃	semidirect
393. #532	C₂²×C₁₃	semidirect
395. #525	C₂²×C₁₃	semidirect
396. C₄×#41	C₂²×C₁₃	semidirect
399. #495	C₂²×C₁₃	semidirect
400. #495	C₂²×C₁₃	semidirect
401. #494	C₂²×C₁₃	semidirect
402. #493	C₂²×C₁₃	semidirect
403. #492	C₂²×C₁₃	semidirect
404. #470	C₂²×C₁₃	semidirect
405. #469	C₂²×C₁₃	semidirect
406. #468	C₂²×C₁₃	semidirect
407. #468	C₂²×C₁₃	semidirect
408. #464	C₂²×C₁₃	semidirect
409. #463	C₂²×C₁₃	semidirect
410. #462	C₂²×C₁₃	semidirect
411. #461	C₂²×C₁₃	semidirect
412. #460	C₂²×C₁₃	semidirect
413. #459	C₂²×C₁₃	semidirect
414. #452	C₂²×C₁₃	semidirect
415. #452	C₂²×C₁₃	semidirect
416. #451	C₂²×C₁₃	semidirect
417. #450	C₂²×C₁₃	semidirect
418. #449	C₂²×C₁₃	semidirect
419. #449	C₂²×C₁₃	semidirect
420. #448	C₂²×C₁₃	semidirect
421. #447	C₂²×C₁₃	semidirect
422. C₄×Q₁₆	C₂²×C₁₃	semidirect
423. C₄×Q₁₆	C₂²×C₁₃	semidirect
424. C₄×SD₁₆	C₂²×C₁₃	semidirect
425. C₄×SD₁₆	C₂²×C₁₃	semidirect
426. C₄×D₈	C₂²×C₁₃	semidirect
427. C₄×D₈	C₂²×C₁₃	semidirect
428. #436	C₂²×C₁₃	semidirect
429. #436	C₂²×C₁₃	semidirect
430. #436	C₂²×C₁₃	semidirect
431. #436	C₂²×C₁₃	semidirect
432. #427	C₂²×C₁₃	semidirect
433. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
434. #416	C₂²×C₁₃	semidirect
435. #416	C₂²×C₁₃	semidirect
436. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
437. C₂×C₄×C₈	C₂²×C₁₃	semidirect
462. C₄×C₁₃	#575	semidirect
487. #135	D₄×C₁₃	semidirect
594. #41	C₂×D₄×C₁₃	semidirect
637. Q₁₆	C₂×D₄×C₁₃	semidirect
642. SD₁₆	C₂×D₄×C₁₃	semidirect
646. D₈	C₂×D₄×C₁₃	semidirect
651. C₂×C₈	C₂×D₄×C₁₃	semidirect
685. C₁₃	#61038	direct (N × H)
771. C₄	C₁₃×#575	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#575	2
D₄×C₁₃×#41	2
C₁₃×#3278	2
C₁₃×#3277	2
C₁₃×#3276	2
C₁₃×#3275	2
C₁₃×#3274	2
C₁₃×#3273	2
C₁₃×#3272	2
C₁₃×#3147	2
C₁₃×#3054	2
C₁₃×#3035	2
C₁₃×#3002	2
C₄×C₁₃×#135	2
C₂×C₁₃×#436	2
#61038	13

Subgroups — C13×#61038 #15747377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61038 #15747377