Subgroups — C₂×C₁₃×#3308 #15747468

Order 3328.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3308	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×#41	—	2	1	no	—
18	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
24	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#548	—	2	4	no	—
26	C₁₃×#548	C₂²	1	8	yes	complemented
27	C₁₃×#547	—	2	4	no	—
28	C₁₃×#547	C₂²	1	8	yes	complemented
29	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#124	—	2	1	no	—
31	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#123	—	2	1	no	—
33	C₂×C₁₃×#123	—	2	1	no	—
34	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
35	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#121	—	2	1	no	—
38	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃	—	2	1	no	—
43	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
45	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₁₃×#489	C₂²	1	8	yes	complemented
48	C₁₃×#484	C₂²	1	8	yes	complemented
49	C₁₃×#480	C₂²	1	8	yes	complemented
50	C₁₃×#477	C₂²	1	8	yes	complemented
51	C₁₃×#468	C₂²	1	8	yes	complemented
52	C₁₃×#466	C₂²	1	8	yes	complemented
53	C₁₃×#463	C₂²	1	8	yes	complemented
54	C₁₃×#449	C₂²	1	8	yes	complemented
55	C₁₃×#448	C₂²	1	8	yes	complemented
56	C₁₃×#440	C₂²	1	8	yes	complemented
57	C₁₃×#435	C₂²	1	8	yes	complemented
58	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₁₃×#417	C₂²	1	8	yes	complemented
63	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#103	C₂²	1	8	yes	complemented
70	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
72	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
73	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
74	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
77	C₂×C₁₃×#41	—	2	8	no	—
78	C₂×C₁₃×#41	—	2	2	no	—
79	C₂×C₁₃×#41	—	2	4	no	—
80	C₂×C₁₃×#41	—	4	2	no	—
81	C₂×C₁₃×#41	—	4	8	no	—
82	C₂×C₁₃×#41	C₂³	1	4	yes	—
83	C₂²×Q₈×C₁₃	—	2	1	no	—
84	C₂²×Q₈×C₁₃	—	2	1	no	—
85	C₂²×Q₈×C₁₃	—	2	2	no	—
86	C₂²×Q₈×C₁₃	—	2	4	no	—
87	C₂²×Q₈×C₁₃	—	4	2	no	—
88	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
90	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃	—	2	1	no	—
92	C₂²×D₄×C₁₃	—	2	1	no	—
93	C₂²×D₄×C₁₃	—	2	1	no	—
94	C₂²×D₄×C₁₃	—	2	1	no	—
95	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
96	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃	—	2	1	no	—
99	C₂³×C₄×C₁₃	—	2	1	no	—
100	C₂³×C₄×C₁₃	—	2	1	no	—
101	C₂³×C₄×C₁₃	—	2	1	no	—
102	C₂³×C₄×C₁₃	—	2	1	no	—
103	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×SD₁₆	—	2	4	no	—
106	C₂×C₁₃×SD₁₆	—	4	2	no	—
107	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
108	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
109	C₂×C₁₃×D₈	—	4	2	no	—
110	C₂×C₁₃×D₈	C₂³	1	4	yes	—
111	C₂×C₁₃×M₁₆	—	4	2	no	—
112	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
113	C₂²×C₈×C₁₃	—	4	2	no	—
114	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
119	C₁₃×C₄⋊Q₈	—	2	2	no	—
120	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
121	C₁₃×#124	—	2	8	no	—
122	C₁₃×#124	—	2	2	no	—
123	C₁₃×#124	C₂³	1	4	yes	—
124	C₁₃×#123	—	2	8	no	—
125	C₁₃×#123	—	2	8	no	—
126	C₁₃×C₂²⋊Q₈	—	2	2	no	—
127	C₁₃×C₂²⋊Q₈	—	2	8	no	—
128	C₁₃×C₂²⋊Q₈	—	2	8	no	—
129	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
130	C₁₃×#121	—	2	8	no	—
131	C₁₃×#121	—	2	2	no	—
132	C₁₃×#121	—	2	2	no	—
133	C₁₃×#121	—	2	2	no	—
134	C₁₃×#121	C₂³	1	4	yes	—
135	C₁₃×#121	C₂³	1	4	yes	—
136	C₁₃×#121	C₂³	1	4	yes	—
137	C₄×Q₈×C₁₃	—	2	2	no	—
138	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
139	C₄×D₄×C₁₃	—	2	8	no	—
140	C₄×D₄×C₁₃	—	2	2	no	—
141	C₄×D₄×C₁₃	D₄	1	4	yes	—
142	C₄×D₄×C₁₃	C₂³	1	4	yes	—
143	C₄×D₄×C₁₃	C₂³	1	4	yes	—
144	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
158	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
159	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
160	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
161	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
162	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
163	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
164	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
165	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
166	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
167	C₂×C₄²×C₁₃	—	2	1	no	—
168	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₁₃×#107	C₂³	1	4	yes	—
170	C₁₃×#107	C₂³	1	4	yes	—
171	C₁₃×#107	C₂³	1	4	yes	—
172	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
173	C₁₃×#103	C₂³	1	4	yes	—
174	C₁₃×#103	C₂³	1	4	yes	—
175	C₁₃×#103	C₂³	1	4	yes	—
176	C₁₃×#103	C₂³	1	4	yes	—
177	C₁₃×#103	C₂³	1	4	yes	—
178	C₁₃×#103	C₂³	1	4	yes	—
179	C₁₃×#102	C₂³	1	4	yes	—
180	C₁₃×#102	C₂³	1	4	yes	—
181	C₁₃×#102	C₂³	1	4	yes	—
182	C₁₃×#102	C₂³	1	4	yes	—
183	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
184	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
185	C₁₃×#97	C₂³	1	4	yes	—
186	C₂×#3308	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂⁴×C₁₃	—	2	1	no	—
188	C₂⁴×C₁₃	—	2	1	no	—
189	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₁₃×#41	—	2	8	no	—
192	C₁₃×#41	—	4	4	no	—
193	C₁₃×#41	—	4	8	no	—
194	C₁₃×#41	—	4	32	no	—
195	C₂×Q₈×C₁₃	—	2	1	no	—
196	C₂×Q₈×C₁₃	—	2	4	no	—
197	C₂×Q₈×C₁₃	—	2	1	no	—
198	C₂×Q₈×C₁₃	—	2	4	no	—
199	C₂×Q₈×C₁₃	—	2	2	no	—
200	C₂×Q₈×C₁₃	—	2	8	no	—
201	C₂×Q₈×C₁₃	—	2	2	no	—
202	C₂×Q₈×C₁₃	—	2	2	no	—
203	C₂×Q₈×C₁₃	—	4	4	no	—
204	C₂×Q₈×C₁₃	—	4	4	no	—
205	C₂×Q₈×C₁₃	—	4	8	no	—
206	C₂×Q₈×C₁₃	—	4	4	no	—
207	C₂×Q₈×C₁₃	#41	1	4	yes	complemented
208	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
209	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
210	C₂×D₄×C₁₃	—	2	4	no	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	—	2	4	no	—
213	C₂×D₄×C₁₃	—	2	4	no	—
214	C₂×D₄×C₁₃	—	2	4	no	—
215	C₂×D₄×C₁₃	—	2	1	no	—
216	C₂×D₄×C₁₃	—	2	1	no	—
217	C₂×D₄×C₁₃	—	2	2	no	—
218	C₂×D₄×C₁₃	—	2	2	no	—
219	C₂×D₄×C₁₃	—	2	2	no	—
220	C₂×D₄×C₁₃	—	2	2	no	—
221	C₂×D₄×C₁₃	—	4	4	no	—
222	C₂×D₄×C₁₃	—	4	4	no	—
223	C₂×D₄×C₁₃	—	4	4	no	—
224	C₂×D₄×C₁₃	—	4	4	no	—
225	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
226	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
227	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃	—	2	1	no	—
229	C₂²×C₄×C₁₃	—	2	2	no	—
230	C₂²×C₄×C₁₃	—	2	2	no	—
231	C₂²×C₄×C₁₃	—	2	2	no	—
232	C₂²×C₄×C₁₃	—	2	2	no	—
233	C₂²×C₄×C₁₃	—	2	4	no	—
234	C₂²×C₄×C₁₃	—	2	4	no	—
235	C₂²×C₄×C₁₃	—	2	4	no	—
236	C₂²×C₄×C₁₃	—	2	1	no	—
237	C₂²×C₄×C₁₃	—	2	1	no	—
238	C₂²×C₄×C₁₃	—	2	1	no	—
239	C₂²×C₄×C₁₃	—	2	1	no	—
240	C₂²×C₄×C₁₃	—	2	1	no	—
241	C₂²×C₄×C₁₃	—	2	4	no	—
242	C₂²×C₄×C₁₃	—	2	4	no	—
243	C₂²×C₄×C₁₃	—	4	4	no	—
244	C₂²×C₄×C₁₃	—	4	4	no	—
245	C₂²×C₄×C₁₃	—	4	4	no	—
246	C₂²×C₄×C₁₃	—	4	4	no	—
247	C₂²×C₄×C₁₃	—	4	4	no	—
248	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
249	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
250	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₁₃×SD₁₆	—	2	8	no	—
258	C₁₃×SD₁₆	—	4	4	no	—
259	C₁₃×D₈	—	4	4	no	—
260	C₁₃×M₁₆	—	4	4	no	—
261	C₂×C₈×C₁₃	—	2	2	no	—
262	C₂×C₈×C₁₃	—	2	2	no	—
263	C₂×C₈×C₁₃	—	2	2	no	—
264	C₂×C₈×C₁₃	—	2	2	no	—
265	C₂×C₈×C₁₃	—	4	4	no	—
266	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
267	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
268	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
269	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
270	C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	1	no	—
273	C₁₃×C₄⋊C₄	—	2	4	no	—
274	C₁₃×C₄⋊C₄	—	2	4	no	—
275	C₁₃×C₄⋊C₄	—	2	4	no	—
276	C₁₃×C₄⋊C₄	—	2	4	no	—
277	C₁₃×C₄⋊C₄	—	2	4	no	—
278	C₁₃×C₄⋊C₄	—	2	1	no	—
279	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
282	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
283	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
292	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
293	C₄²×C₁₃	—	2	4	no	—
294	C₄²×C₁₃	C₂×D₄	1	2	yes	—
295	C₄²×C₁₃	C₂⁴	1	2	yes	—
296	C₂×#548	C₂×C₁₃	1	1	yes	characteristic, complemented
297	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#3308	C₂×C₁₃	1	16	yes	direct product factor
299	C₂×#489	C₂×C₁₃	1	1	yes	characteristic, complemented
300	C₂×#484	C₂×C₁₃	1	1	yes	characteristic, complemented
301	C₂×#480	C₂×C₁₃	1	1	yes	characteristic, complemented
302	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
303	C₂×#468	C₂×C₁₃	1	1	yes	characteristic, complemented
304	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
305	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
306	C₂×#449	C₂×C₁₃	1	1	yes	characteristic, complemented
307	C₂×#448	C₂×C₁₃	1	1	yes	characteristic, complemented
308	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
309	C₂×#435	C₂×C₁₃	1	1	yes	characteristic, complemented
310	C₂×#417	C₂×C₁₃	1	1	yes	characteristic, complemented
311	C₂²×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
312	C₂³×C₁₃	—	2	2	no	—
313	C₂³×C₁₃	—	2	2	no	—
314	C₂³×C₁₃	—	2	2	no	—
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	2	2	no	—
319	C₂³×C₁₃	—	4	2	no	—
320	C₂³×C₁₃	—	4	2	no	—
321	C₂³×C₁₃	—	4	2	no	—
322	C₂³×C₁₃	—	4	2	no	—
323	C₂³×C₁₃	—	4	2	no	—
324	C₂³×C₁₃	—	4	2	no	—
325	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
326	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
327	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
328	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
329	Q₈×C₁₃	—	2	4	no	—
330	Q₈×C₁₃	—	2	2	no	—
331	Q₈×C₁₃	—	2	2	no	—
332	Q₈×C₁₃	—	2	2	no	—
333	Q₈×C₁₃	—	4	8	no	—
334	Q₈×C₁₃	—	4	8	no	—
335	Q₈×C₁₃	—	4	2	no	—
336	Q₈×C₁₃	C₂×#41	1	4	yes	complemented
337	D₄×C₁₃	—	2	8	no	—
338	D₄×C₁₃	—	2	2	no	—
339	D₄×C₁₃	—	2	2	no	—
340	D₄×C₁₃	—	2	2	no	—
341	D₄×C₁₃	—	2	2	no	—
342	D₄×C₁₃	—	4	8	no	—
343	D₄×C₁₃	—	4	8	no	—
344	D₄×C₁₃	—	4	8	no	—
345	D₄×C₁₃	—	4	8	no	—
346	D₄×C₁₃	—	4	2	no	—
347	D₄×C₁₃	—	4	2	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	4	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	4	no	—
355	C₂×C₄×C₁₃	—	2	4	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	4	8	no	—
366	C₂×C₄×C₁₃	—	4	8	no	—
367	C₂×C₄×C₁₃	—	4	8	no	—
368	C₂×C₄×C₁₃	—	4	8	no	—
369	C₂×C₄×C₁₃	—	4	2	no	—
370	C₂×C₄×C₁₃	—	4	2	no	—
371	C₂×C₄×C₁₃	—	4	2	no	—
372	C₂×C₄×C₁₃	—	4	2	no	—
373	C₂×C₄×C₁₃	—	4	8	no	—
374	C₂×C₄×C₁₃	—	4	2	no	—
375	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
381	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
382	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
383	C₈×C₁₃	—	2	2	no	—
384	C₈×C₁₃	—	2	2	no	—
385	C₈×C₁₃	—	2	2	no	—
386	C₈×C₁₃	—	2	2	no	—
387	C₂²×#41	—	2	1	no	—
388	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
389	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
390	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
391	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
392	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
393	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
394	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
395	#548	—	2	4	no	—
396	#548	C₂²×C₁₃	1	8	yes	complemented
397	#547	—	2	4	no	—
398	#547	C₂²×C₁₃	1	8	yes	complemented
399	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×#124	—	2	1	no	—
401	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×#123	—	2	1	no	—
403	C₂×#123	—	2	1	no	—
404	C₂×C₂²⋊Q₈	—	2	1	no	—
405	C₂×C₂²⋊Q₈	—	2	1	no	—
406	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×#121	—	2	1	no	—
408	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
409	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
410	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
411	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×C₄×D₄	—	2	1	no	—
413	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
415	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
416	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
417	#489	C₂²×C₁₃	1	8	yes	complemented
418	#484	C₂²×C₁₃	1	8	yes	complemented
419	#480	C₂²×C₁₃	1	8	yes	complemented
420	#477	C₂²×C₁₃	1	8	yes	complemented
421	#468	C₂²×C₁₃	1	8	yes	complemented
422	#466	C₂²×C₁₃	1	8	yes	complemented
423	#463	C₂²×C₁₃	1	8	yes	complemented
424	#449	C₂²×C₁₃	1	8	yes	complemented
425	#448	C₂²×C₁₃	1	8	yes	complemented
426	#440	C₂²×C₁₃	1	8	yes	complemented
427	#435	C₂²×C₁₃	1	8	yes	complemented
428	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
429	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
432	#417	C₂²×C₁₃	1	8	yes	complemented
433	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
434	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
435	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
436	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
439	C₂×#103	C₂²×C₁₃	1	8	yes	complemented
440	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
441	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
442	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
443	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
444	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
445	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
447	C₂²×C₁₃	—	2	2	no	—
448	C₂²×C₁₃	—	2	8	no	—
449	C₂²×C₁₃	—	2	2	no	—
450	C₂²×C₁₃	—	2	2	no	—
451	C₂²×C₁₃	—	2	2	no	—
452	C₂²×C₁₃	—	2	2	no	—
453	C₂²×C₁₃	—	4	4	no	—
454	C₂²×C₁₃	—	4	2	no	—
455	C₂²×C₁₃	—	4	2	no	—
456	C₂²×C₁₃	—	4	2	no	—
457	C₂²×C₁₃	—	4	2	no	—
458	C₂²×C₁₃	—	4	2	no	—
459	C₂²×C₁₃	—	4	2	no	—
460	C₂²×C₁₃	—	8	4	no	—
461	C₂²×C₁₃	—	8	4	no	—
462	C₂²×C₁₃	#546	1	2	yes	—
463	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
464	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
465	C₂²×C₁₃	#578	1	2	yes	—
466	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
467	C₄×C₁₃	—	2	2	no	—
468	C₄×C₁₃	—	2	2	no	—
469	C₄×C₁₃	—	2	4	no	—
470	C₄×C₁₃	—	2	2	no	—
471	C₄×C₁₃	—	2	2	no	—
472	C₄×C₁₃	—	4	2	no	—
473	C₄×C₁₃	—	4	2	no	—
474	C₄×C₁₃	—	4	2	no	—
475	C₄×C₁₃	—	4	2	no	—
476	C₄×C₁₃	—	4	2	no	—
477	C₄×C₁₃	#546	1	2	yes	—
478	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
479	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
480	C₂×#41	—	2	8	no	—
481	C₂×#41	—	2	2	no	—
482	C₂×#41	—	2	4	no	—
483	C₂×#41	—	4	2	no	—
484	C₂×#41	—	4	8	no	—
485	C₂×#41	C₂³×C₁₃	1	4	yes	—
486	C₂²×Q₈	—	2	1	no	—
487	C₂²×Q₈	—	2	1	no	—
488	C₂²×Q₈	—	2	2	no	—
489	C₂²×Q₈	—	2	4	no	—
490	C₂²×Q₈	—	4	2	no	—
491	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
492	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
493	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	—	2	1	no	—
498	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
499	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
500	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
501	C₂³×C₄	—	2	1	no	—
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
508	C₂×SD₁₆	—	2	4	no	—
509	C₂×SD₁₆	—	4	2	no	—
510	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
511	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
512	C₂×D₈	—	4	2	no	—
513	C₂×D₈	C₂³×C₁₃	1	4	yes	—
514	C₂×M₁₆	—	4	2	no	—
515	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
516	C₂²×C₈	—	4	2	no	—
517	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
518	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
519	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
520	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
521	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
522	C₄⋊Q₈	—	2	2	no	—
523	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
524	#124	—	2	8	no	—
525	#124	—	2	2	no	—
526	#124	C₂³×C₁₃	1	4	yes	—
527	#123	—	2	8	no	—
528	#123	—	2	8	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	8	no	—
531	C₂²⋊Q₈	—	2	8	no	—
532	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
533	#121	—	2	8	no	—
534	#121	—	2	2	no	—
535	#121	—	2	2	no	—
536	#121	—	2	2	no	—
537	#121	C₂³×C₁₃	1	4	yes	—
538	#121	C₂³×C₁₃	1	4	yes	—
539	#121	C₂³×C₁₃	1	4	yes	—
540	C₄×Q₈	—	2	2	no	—
541	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
542	C₄×D₄	—	2	8	no	—
543	C₄×D₄	—	2	2	no	—
544	C₄×D₄	D₄×C₁₃	1	4	yes	—
545	C₄×D₄	C₂³×C₁₃	1	4	yes	—
546	C₄×D₄	C₂³×C₁₃	1	4	yes	—
547	C₂×C₄⋊C₄	—	2	1	no	—
548	C₂×C₄⋊C₄	—	2	1	no	—
549	C₂×C₄⋊C₄	—	2	2	no	—
550	C₂×C₄⋊C₄	—	2	2	no	—
551	C₂×C₄⋊C₄	—	2	1	no	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
559	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
560	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
561	C₂×C₂²⋊C₄	—	2	1	no	—
562	C₂×C₂²⋊C₄	—	2	1	no	—
563	C₂×C₂²⋊C₄	—	2	1	no	—
564	C₂×C₂²⋊C₄	—	2	1	no	—
565	C₂×C₂²⋊C₄	—	2	1	no	—
566	C₂×C₂²⋊C₄	—	2	1	no	—
567	C₂×C₂²⋊C₄	—	2	1	no	—
568	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
569	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
570	C₂×C₄²	—	2	1	no	—
571	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
572	#107	C₂³×C₁₃	1	4	yes	—
573	#107	C₂³×C₁₃	1	4	yes	—
574	#107	C₂³×C₁₃	1	4	yes	—
575	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
576	#103	C₂³×C₁₃	1	4	yes	—
577	#103	C₂³×C₁₃	1	4	yes	—
578	#103	C₂³×C₁₃	1	4	yes	—
579	#103	C₂³×C₁₃	1	4	yes	—
580	#103	C₂³×C₁₃	1	4	yes	—
581	#103	C₂³×C₁₃	1	4	yes	—
582	#102	C₂³×C₁₃	1	4	yes	—
583	#102	C₂³×C₁₃	1	4	yes	—
584	#102	C₂³×C₁₃	1	4	yes	—
585	#102	C₂³×C₁₃	1	4	yes	—
586	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
587	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
588	#97	C₂³×C₁₃	1	4	yes	—
589	C₂×C₁₃	—	2	4	no	—
590	C₂×C₁₃	—	4	2	no	—
591	C₂×C₁₃	—	8	2	no	—
592	C₂×C₁₃	—	8	2	no	—
593	C₂×C₁₃	#3308	1	4	yes	direct product factor
594	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
595	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
596	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
597	C₂⁴	—	2	1	no	—
598	C₂⁴	—	2	1	no	—
599	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
600	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
601	#41	—	2	8	no	—
602	#41	—	4	4	no	—
603	#41	—	4	8	no	—
604	#41	—	4	32	no	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	2	4	no	—
607	C₂×Q₈	—	2	1	no	—
608	C₂×Q₈	—	2	4	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	2	8	no	—
611	C₂×Q₈	—	2	2	no	—
612	C₂×Q₈	—	2	2	no	—
613	C₂×Q₈	—	4	4	no	—
614	C₂×Q₈	—	4	4	no	—
615	C₂×Q₈	—	4	8	no	—
616	C₂×Q₈	—	4	4	no	—
617	C₂×Q₈	C₁₃×#41	1	4	yes	complemented
618	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
619	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	2	no	—
629	C₂×D₄	—	2	2	no	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	4	4	no	—
632	C₂×D₄	—	4	4	no	—
633	C₂×D₄	—	4	4	no	—
634	C₂×D₄	—	4	4	no	—
635	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
636	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
637	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	4	4	no	—
654	C₂²×C₄	—	4	4	no	—
655	C₂²×C₄	—	4	4	no	—
656	C₂²×C₄	—	4	4	no	—
657	C₂²×C₄	—	4	4	no	—
658	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
660	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
661	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
662	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
663	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
667	SD₁₆	—	2	8	no	—
668	SD₁₆	—	4	4	no	—
669	D₈	—	4	4	no	—
670	M₁₆	—	4	4	no	—
671	C₂×C₈	—	2	2	no	—
672	C₂×C₈	—	2	2	no	—
673	C₂×C₈	—	2	2	no	—
674	C₂×C₈	—	2	2	no	—
675	C₂×C₈	—	4	4	no	—
676	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
677	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
678	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
679	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
690	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
691	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
692	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
693	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
702	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
703	C₄²	—	2	4	no	—
704	C₄²	C₂×D₄×C₁₃	1	2	yes	—
705	C₄²	C₂⁴×C₁₃	1	2	yes	—
706	C₁₃	C₂×#3308	1	1	yes	characteristic, direct product factor, Sylow
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	4	2	no	—
715	C₂³	—	4	2	no	—
716	C₂³	—	4	2	no	—
717	C₂³	—	4	2	no	—
718	C₂³	—	4	2	no	—
719	C₂³	—	4	2	no	—
720	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
721	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
722	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
723	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
724	Q₈	—	2	4	no	—
725	Q₈	—	2	2	no	—
726	Q₈	—	2	2	no	—
727	Q₈	—	2	2	no	—
728	Q₈	—	4	8	no	—
729	Q₈	—	4	8	no	—
730	Q₈	—	4	2	no	—
731	Q₈	C₂×C₁₃×#41	1	4	yes	complemented
732	D₄	—	2	8	no	—
733	D₄	—	2	2	no	—
734	D₄	—	2	2	no	—
735	D₄	—	2	2	no	—
736	D₄	—	2	2	no	—
737	D₄	—	4	8	no	—
738	D₄	—	4	8	no	—
739	D₄	—	4	8	no	—
740	D₄	—	4	8	no	—
741	D₄	—	4	2	no	—
742	D₄	—	4	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	4	8	no	—
761	C₂×C₄	—	4	8	no	—
762	C₂×C₄	—	4	8	no	—
763	C₂×C₄	—	4	8	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	4	2	no	—
766	C₂×C₄	—	4	2	no	—
767	C₂×C₄	—	4	2	no	—
768	C₂×C₄	—	4	8	no	—
769	C₂×C₄	—	4	2	no	—
770	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
771	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
772	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
773	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
774	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
775	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
776	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
777	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
778	C₈	—	2	2	no	—
779	C₈	—	2	2	no	—
780	C₈	—	2	2	no	—
781	C₈	—	2	2	no	—
782	C₂²	—	2	8	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	2	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	2	no	—
788	C₂²	—	4	4	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	8	4	no	—
796	C₂²	—	8	4	no	—
797	C₂²	C₁₃×#546	1	2	yes	—
798	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
799	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
800	C₂²	C₁₃×#578	1	2	yes	—
801	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
802	C₄	—	2	2	no	—
803	C₄	—	2	2	no	—
804	C₄	—	2	2	no	—
805	C₄	—	2	2	no	—
806	C₄	—	2	4	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	2	no	—
812	C₄	C₁₃×#546	1	2	yes	—
813	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
814	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
815	C₂	—	2	4	no	—
816	C₂	—	4	2	no	—
817	C₂	—	8	2	no	—
818	C₂	—	8	2	no	—
819	C₂	C₁₃×#3308	1	4	yes	direct product factor
820	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
821	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
822	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×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×#548	C₂	semidirect
2. C₂×C₁₃×#547	C₂	semidirect
3. C₁₃×#3308	C₂	direct (N × H)
4. C₂×C₁₃×#489	C₂	semidirect
5. C₂×C₁₃×#484	C₂	semidirect
6. C₂×C₁₃×#480	C₂	semidirect
7. C₂×C₁₃×#477	C₂	semidirect
8. C₂×C₁₃×#468	C₂	semidirect
9. C₂×C₁₃×#466	C₂	semidirect
10. C₂×C₁₃×#463	C₂	semidirect
11. C₂×C₁₃×#449	C₂	semidirect
12. C₂×C₁₃×#448	C₂	semidirect
13. C₂×C₁₃×#440	C₂	semidirect
14. C₂×C₁₃×#435	C₂	semidirect
15. C₂×C₁₃×#417	C₂	semidirect
16. C₂²×C₁₃×#103	C₂	semidirect
26. C₁₃×#548	C₂²	semidirect
28. C₁₃×#547	C₂²	semidirect
47. C₁₃×#489	C₂²	semidirect
48. C₁₃×#484	C₂²	semidirect
49. C₁₃×#480	C₂²	semidirect
50. C₁₃×#477	C₂²	semidirect
51. C₁₃×#468	C₂²	semidirect
52. C₁₃×#466	C₂²	semidirect
53. C₁₃×#463	C₂²	semidirect
54. C₁₃×#449	C₂²	semidirect
55. C₁₃×#448	C₂²	semidirect
56. C₁₃×#440	C₂²	semidirect
57. C₁₃×#435	C₂²	semidirect
62. C₁₃×#417	C₂²	semidirect
69. C₂×C₁₃×#103	C₂²	semidirect
186. C₂×#3308	C₁₃	direct (N × H)
207. C₂×Q₈×C₁₃	#41	semidirect
296. C₂×#548	C₂×C₁₃	semidirect
297. C₂×#547	C₂×C₁₃	semidirect
298. #3308	C₂×C₁₃	direct (N × H)
299. C₂×#489	C₂×C₁₃	semidirect
300. C₂×#484	C₂×C₁₃	semidirect
301. C₂×#480	C₂×C₁₃	semidirect
302. C₂×#477	C₂×C₁₃	semidirect
303. C₂×#468	C₂×C₁₃	semidirect
304. C₂×#466	C₂×C₁₃	semidirect
305. C₂×#463	C₂×C₁₃	semidirect
306. C₂×#449	C₂×C₁₃	semidirect
307. C₂×#448	C₂×C₁₃	semidirect
308. C₂×#440	C₂×C₁₃	semidirect
309. C₂×#435	C₂×C₁₃	semidirect
310. C₂×#417	C₂×C₁₃	semidirect
311. C₂²×#103	C₂×C₁₃	semidirect
336. Q₈×C₁₃	C₂×#41	semidirect
396. #548	C₂²×C₁₃	semidirect
398. #547	C₂²×C₁₃	semidirect
417. #489	C₂²×C₁₃	semidirect
418. #484	C₂²×C₁₃	semidirect
419. #480	C₂²×C₁₃	semidirect
420. #477	C₂²×C₁₃	semidirect
421. #468	C₂²×C₁₃	semidirect
422. #466	C₂²×C₁₃	semidirect
423. #463	C₂²×C₁₃	semidirect
424. #449	C₂²×C₁₃	semidirect
425. #448	C₂²×C₁₃	semidirect
426. #440	C₂²×C₁₃	semidirect
427. #435	C₂²×C₁₃	semidirect
432. #417	C₂²×C₁₃	semidirect
439. C₂×#103	C₂²×C₁₃	semidirect
593. C₂×C₁₃	#3308	direct (N × H)
617. C₂×Q₈	C₁₃×#41	semidirect
706. C₁₃	C₂×#3308	direct (N × H)
731. Q₈	C₂×C₁₃×#41	semidirect
819. C₂	C₁₃×#3308	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#548	2
C₂×C₁₃×#547	2
C₁₃×#3308	2
C₂×C₁₃×#489	2
C₂×C₁₃×#484	2
C₂×C₁₃×#480	2
C₂×C₁₃×#477	2
C₂×C₁₃×#468	2
C₂×C₁₃×#466	2
C₂×C₁₃×#463	2
C₂×C₁₃×#449	2
C₂×C₁₃×#448	2
C₂×C₁₃×#440	2
C₂×C₁₃×#435	2
C₂×C₁₃×#417	2
C₂²×C₁₃×#103	2
C₂×#3308	13

Subgroups — C2×C13×#3308 #15747468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3308 #15747468