Subgroups — C₂×C₁₃×#3268 #15747365

Order 3328.

2966 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3268	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
22	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
23	C₂×C₁₃×#135	—	2	8	no	—
24	C₂×C₁₃×#135	C₂²	1	8	yes	complemented
25	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#550	—	2	4	no	—
37	C₁₃×#550	C₂²	1	8	yes	complemented
38	C₁₃×#546	—	2	4	no	—
39	C₁₃×#546	C₂²	1	8	yes	complemented
40	C₂×C₁₃×#127	—	2	1	no	—
41	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#123	—	2	1	no	—
44	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#121	—	2	1	no	—
46	C₂×C₁₃×#121	—	2	1	no	—
47	C₂×C₁₃×#121	—	2	1	no	—
48	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₁₃×#120	—	2	1	no	—
52	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄×D₄×C₁₃	—	2	1	no	—
54	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
56	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
57	C₁₃×#496	C₂²	1	8	yes	complemented
58	C₁₃×#468	C₂²	1	8	yes	complemented
59	C₁₃×#466	C₂²	1	8	yes	complemented
60	C₁₃×#464	C₂²	1	8	yes	complemented
61	C₁₃×#459	C₂²	1	8	yes	complemented
62	C₁₃×#452	C₂²	1	8	yes	complemented
63	C₁₃×#449	C₂²	1	8	yes	complemented
64	C₁₃×#449	C₂²	1	8	yes	complemented
65	C₁₃×#447	C₂²	1	8	yes	complemented
66	C₁₃×#440	C₂²	1	8	yes	complemented
67	C₁₃×#435	C₂²	1	8	yes	complemented
68	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
73	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
74	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
77	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
79	C₂⁵×C₁₃	—	2	1	no	—
80	C₂×C₁₃×#41	—	2	2	no	—
81	C₂×C₁₃×#41	—	2	2	no	—
82	C₂×C₁₃×#41	—	2	2	no	—
83	C₂×C₁₃×#41	—	2	4	no	—
84	C₂×C₁₃×#41	—	2	4	no	—
85	C₂×C₁₃×#41	—	2	4	no	—
86	C₂×C₁₃×#41	—	4	2	no	—
87	C₂×C₁₃×#41	—	4	2	no	—
88	C₂×C₁₃×#41	—	4	2	no	—
89	C₂×C₁₃×#41	C₂³	1	4	yes	—
90	C₂×C₁₃×#41	C₂³	1	4	yes	—
91	C₂×C₁₃×#41	C₂³	1	4	yes	complemented
92	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₃	—	2	4	no	—
95	C₂²×D₄×C₁₃	—	2	1	no	—
96	C₂²×D₄×C₁₃	—	2	1	no	—
97	C₂²×D₄×C₁₃	—	2	1	no	—
98	C₂²×D₄×C₁₃	—	2	1	no	—
99	C₂²×D₄×C₁₃	—	2	1	no	—
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	—	2	1	no	—
102	C₂²×D₄×C₁₃	—	2	1	no	—
103	C₂²×D₄×C₁₃	—	2	2	no	—
104	C₂²×D₄×C₁₃	—	2	1	no	—
105	C₂²×D₄×C₁₃	—	4	2	no	—
106	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
107	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
111	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃	—	2	1	no	—
113	C₂³×C₄×C₁₃	—	2	1	no	—
114	C₂³×C₄×C₁₃	—	2	1	no	—
115	C₂³×C₄×C₁₃	—	2	1	no	—
116	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₁₃×AGL(1,ℤ/8)	—	2	32	no	—
119	C₁₃×#135	—	2	32	no	—
120	C₂×C₁₃×Q₁₆	—	2	4	no	—
121	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	complemented
122	C₂×C₁₃×SD₁₆	—	2	4	no	—
123	C₂×C₁₃×SD₁₆	—	2	4	no	—
124	C₂×C₁₃×SD₁₆	—	4	2	no	—
125	C₂×C₁₃×SD₁₆	D₄	1	8	yes	complemented
126	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
127	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
128	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
129	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
130	C₂×C₁₃×D₈	—	2	4	no	—
131	C₂×C₁₃×D₈	—	2	4	no	—
132	C₂×C₁₃×D₈	—	2	4	no	—
133	C₂×C₁₃×D₈	—	4	2	no	—
134	C₂×C₁₃×D₈	C₂³	1	4	yes	—
135	C₂×C₁₃×D₈	C₂³	1	4	yes	—
136	C₂×C₁₃×D₈	C₂³	1	4	yes	—
137	C₂×C₁₃×D₈	C₂³	1	4	yes	—
138	C₂×C₁₃×M₁₆	—	2	4	no	—
139	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
140	C₂²×C₈×C₁₃	—	2	4	no	—
141	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
145	C₂²×C₈×C₁₃	C₂³	1	4	yes	complemented
146	C₁₃×#127	—	2	8	no	—
147	C₁₃×#127	—	2	2	no	—
148	C₁₃×#127	C₂³	1	4	yes	complemented
149	C₁₃×#124	—	2	2	no	—
150	C₁₃×#124	C₂³	1	4	yes	—
151	C₁₃×#123	—	2	8	no	—
152	C₁₃×C₂²⋊Q₈	—	2	2	no	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	8	no	—
158	C₁₃×#121	—	2	8	no	—
159	C₁₃×#121	—	2	8	no	—
160	C₁₃×#121	C₂³	1	4	yes	—
161	C₁₃×#121	C₂³	1	4	yes	—
162	C₁₃×#121	C₂³	1	4	yes	complemented
163	C₁₃×#120	—	2	8	no	—
164	C₄×Q₈×C₁₃	—	2	2	no	—
165	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
166	C₄×D₄×C₁₃	—	2	8	no	—
167	C₄×D₄×C₁₃	—	2	2	no	—
168	C₄×D₄×C₁₃	D₄	1	4	yes	—
169	C₄×D₄×C₁₃	C₂³	1	4	yes	—
170	C₄×D₄×C₁₃	C₂³	1	4	yes	—
171	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
177	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
178	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
179	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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	8	no	—
184	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
185	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₁₃	—	2	1	no	—
187	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
188	C₁₃×#107	C₂³	1	4	yes	complemented
189	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
190	C₁₃×#103	C₂³	1	4	yes	complemented
191	C₁₃×#103	C₂³	1	4	yes	complemented
192	C₁₃×#102	C₂³	1	4	yes	—
193	C₁₃×#102	C₂³	1	4	yes	—
194	C₁₃×#102	C₂³	1	4	yes	complemented
195	C₁₃×#102	C₂³	1	4	yes	complemented
196	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
197	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
198	C₁₃×#97	C₂³	1	4	yes	complemented
199	C₂×#3268	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂⁴×C₁₃	—	2	1	no	—
201	C₂⁴×C₁₃	—	2	1	no	—
202	C₂⁴×C₁₃	—	2	1	no	—
203	C₂⁴×C₁₃	—	2	1	no	—
204	C₂⁴×C₁₃	—	2	4	no	—
205	C₂⁴×C₁₃	—	4	4	no	—
206	C₂⁴×C₁₃	—	4	4	no	—
207	C₂⁴×C₁₃	—	8	2	no	—
208	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₁₃×#41	—	2	8	no	—
211	C₁₃×#41	—	2	8	no	—
212	C₁₃×#41	—	2	8	no	—
213	C₁₃×#41	—	4	4	no	—
214	C₁₃×#41	—	4	4	no	—
215	C₁₃×#41	—	4	4	no	—
216	C₁₃×#41	—	4	8	no	—
217	C₁₃×#41	—	4	8	no	—
218	C₁₃×#41	—	4	8	no	—
219	C₂×Q₈×C₁₃	—	2	1	no	—
220	C₂×Q₈×C₁₃	—	2	1	no	—
221	C₂×Q₈×C₁₃	—	2	2	no	—
222	C₂×Q₈×C₁₃	—	2	2	no	—
223	C₂×Q₈×C₁₃	—	2	2	no	—
224	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
225	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
226	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
227	C₂×D₄×C₁₃	—	2	8	no	—
228	C₂×D₄×C₁₃	—	2	4	no	—
229	C₂×D₄×C₁₃	—	2	4	no	—
230	C₂×D₄×C₁₃	—	2	4	no	—
231	C₂×D₄×C₁₃	—	2	4	no	—
232	C₂×D₄×C₁₃	—	2	4	no	—
233	C₂×D₄×C₁₃	—	2	4	no	—
234	C₂×D₄×C₁₃	—	2	1	no	—
235	C₂×D₄×C₁₃	—	2	2	no	—
236	C₂×D₄×C₁₃	—	2	2	no	—
237	C₂×D₄×C₁₃	—	2	2	no	—
238	C₂×D₄×C₁₃	—	2	4	no	—
239	C₂×D₄×C₁₃	—	2	4	no	—
240	C₂×D₄×C₁₃	—	2	1	no	—
241	C₂×D₄×C₁₃	—	2	1	no	—
242	C₂×D₄×C₁₃	—	2	1	no	—
243	C₂×D₄×C₁₃	—	2	4	no	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	4	4	no	—
249	C₂×D₄×C₁₃	—	4	8	no	—
250	C₂×D₄×C₁₃	—	4	2	no	—
251	C₂×D₄×C₁₃	—	4	4	no	—
252	C₂×D₄×C₁₃	—	4	4	no	—
253	C₂×D₄×C₁₃	—	4	4	no	—
254	C₂×D₄×C₁₃	—	4	4	no	—
255	C₂×D₄×C₁₃	—	4	4	no	—
256	C₂×D₄×C₁₃	—	8	2	no	—
257	C₂×D₄×C₁₃	—	8	2	no	—
258	C₂×D₄×C₁₃	—	8	2	no	—
259	C₂×D₄×C₁₃	—	8	2	no	—
260	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
261	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
262	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₃	—	2	1	no	—
267	C₂²×C₄×C₁₃	—	2	2	no	—
268	C₂²×C₄×C₁₃	—	2	2	no	—
269	C₂²×C₄×C₁₃	—	2	2	no	—
270	C₂²×C₄×C₁₃	—	2	2	no	—
271	C₂²×C₄×C₁₃	—	2	1	no	—
272	C₂²×C₄×C₁₃	—	2	1	no	—
273	C₂²×C₄×C₁₃	—	2	1	no	—
274	C₂²×C₄×C₁₃	—	2	4	no	—
275	C₂²×C₄×C₁₃	—	2	4	no	—
276	C₂²×C₄×C₁₃	—	2	4	no	—
277	C₂²×C₄×C₁₃	—	2	4	no	—
278	C₂²×C₄×C₁₃	—	4	4	no	—
279	C₂²×C₄×C₁₃	—	4	4	no	—
280	C₂²×C₄×C₁₃	—	4	4	no	—
281	C₂²×C₄×C₁₃	—	8	2	no	—
282	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
284	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₁₃×Q₁₆	—	2	8	no	—
292	C₁₃×SD₁₆	—	2	8	no	—
293	C₁₃×SD₁₆	—	2	8	no	—
294	C₁₃×SD₁₆	—	4	4	no	—
295	C₁₃×SD₁₆	C₂×D₄	1	16	yes	complemented
296	C₁₃×D₈	—	2	8	no	—
297	C₁₃×D₈	—	2	8	no	—
298	C₁₃×D₈	—	2	8	no	—
299	C₁₃×D₈	—	4	4	no	—
300	C₁₃×M₁₆	—	2	8	no	—
301	C₂×C₈×C₁₃	—	2	2	no	—
302	C₂×C₈×C₁₃	—	2	2	no	—
303	C₂×C₈×C₁₃	—	2	2	no	—
304	C₂×C₈×C₁₃	—	2	8	no	—
305	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
306	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
307	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
308	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
309	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
310	C₁₃×C₄⋊C₄	—	2	4	no	—
311	C₁₃×C₄⋊C₄	—	2	4	no	—
312	C₁₃×C₄⋊C₄	—	2	1	no	—
313	C₁₃×C₄⋊C₄	—	2	1	no	—
314	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
317	C₁₃×C₂²⋊C₄	—	2	4	no	—
318	C₁₃×C₂²⋊C₄	—	2	4	no	—
319	C₁₃×C₂²⋊C₄	—	2	4	no	—
320	C₁₃×C₂²⋊C₄	—	2	4	no	—
321	C₁₃×C₂²⋊C₄	—	2	4	no	—
322	C₁₃×C₂²⋊C₄	—	2	4	no	—
323	C₁₃×C₂²⋊C₄	—	2	4	no	—
324	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
325	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
326	C₄²×C₁₃	—	2	4	no	—
327	C₄²×C₁₃	C₂×D₄	1	2	yes	—
328	C₄²×C₁₃	C₂⁴	1	2	yes	—
329	C₂²×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
330	C₂²×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
331	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
332	C₂×#546	C₂×C₁₃	1	1	yes	characteristic, complemented
333	#3268	C₂×C₁₃	1	16	yes	direct product factor
334	C₂×#496	C₂×C₁₃	1	1	yes	characteristic, complemented
335	C₂×#468	C₂×C₁₃	1	1	yes	characteristic, complemented
336	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
337	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
338	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
339	C₂×#452	C₂×C₁₃	1	1	yes	characteristic, complemented
340	C₂×#449	C₂×C₁₃	1	1	yes	characteristic, complemented
341	C₂×#449	C₂×C₁₃	1	1	yes	characteristic, complemented
342	C₂×#447	C₂×C₁₃	1	1	yes	characteristic, complemented
343	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
344	C₂×#435	C₂×C₁₃	1	1	yes	characteristic, complemented
345	C₂³×C₁₃	—	2	2	no	—
346	C₂³×C₁₃	—	2	2	no	—
347	C₂³×C₁₃	—	2	4	no	—
348	C₂³×C₁₃	—	2	2	no	—
349	C₂³×C₁₃	—	2	2	no	—
350	C₂³×C₁₃	—	2	2	no	—
351	C₂³×C₁₃	—	2	2	no	—
352	C₂³×C₁₃	—	2	2	no	—
353	C₂³×C₁₃	—	2	2	no	—
354	C₂³×C₁₃	—	2	2	no	—
355	C₂³×C₁₃	—	2	2	no	—
356	C₂³×C₁₃	—	4	8	no	—
357	C₂³×C₁₃	—	4	8	no	—
358	C₂³×C₁₃	—	4	2	no	—
359	C₂³×C₁₃	—	4	2	no	—
360	C₂³×C₁₃	—	4	2	no	—
361	C₂³×C₁₃	—	4	2	no	—
362	C₂³×C₁₃	—	4	2	no	—
363	C₂³×C₁₃	—	4	2	no	—
364	C₂³×C₁₃	—	4	2	no	—
365	C₂³×C₁₃	—	4	2	no	—
366	C₂³×C₁₃	—	4	2	no	—
367	C₂³×C₁₃	—	4	2	no	—
368	C₂³×C₁₃	—	4	2	no	—
369	C₂³×C₁₃	—	8	4	no	—
370	C₂³×C₁₃	—	8	16	no	—
371	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
372	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
373	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
374	Q₈×C₁₃	—	2	4	no	—
375	Q₈×C₁₃	—	2	2	no	—
376	Q₈×C₁₃	—	2	2	no	—
377	Q₈×C₁₃	—	2	2	no	—
378	Q₈×C₁₃	—	4	2	no	—
379	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
380	D₄×C₁₃	—	2	4	no	—
381	D₄×C₁₃	—	2	2	no	—
382	D₄×C₁₃	—	2	2	no	—
383	D₄×C₁₃	—	2	2	no	—
384	D₄×C₁₃	—	2	2	no	—
385	D₄×C₁₃	—	2	2	no	—
386	D₄×C₁₃	—	2	2	no	—
387	D₄×C₁₃	—	2	2	no	—
388	D₄×C₁₃	—	4	4	no	—
389	D₄×C₁₃	—	4	8	no	—
390	D₄×C₁₃	—	4	8	no	—
391	D₄×C₁₃	—	4	8	no	—
392	D₄×C₁₃	—	4	8	no	—
393	D₄×C₁₃	—	4	8	no	—
394	D₄×C₁₃	—	4	2	no	—
395	D₄×C₁₃	—	4	2	no	—
396	D₄×C₁₃	—	4	2	no	—
397	D₄×C₁₃	—	8	4	no	—
398	D₄×C₁₃	—	8	4	no	—
399	D₄×C₁₃	—	8	4	no	—
400	D₄×C₁₃	—	8	4	no	—
401	D₄×C₁₃	C₂²×D₄	1	4	yes	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	4	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	4	no	—
409	C₂×C₄×C₁₃	—	2	4	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	4	8	no	—
418	C₂×C₄×C₁₃	—	4	8	no	—
419	C₂×C₄×C₁₃	—	4	8	no	—
420	C₂×C₄×C₁₃	—	4	2	no	—
421	C₂×C₄×C₁₃	—	4	2	no	—
422	C₂×C₄×C₁₃	—	4	2	no	—
423	C₂×C₄×C₁₃	—	8	4	no	—
424	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
425	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
426	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
427	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
428	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
431	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
432	C₈×C₁₃	—	2	2	no	—
433	C₈×C₁₃	—	2	2	no	—
434	C₈×C₁₃	—	2	2	no	—
435	C₈×C₁₃	C₂²×D₄	1	4	yes	—
436	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
437	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
438	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×AGL(1,ℤ/8)	—	2	8	no	—
441	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	8	yes	complemented
442	C₂×#135	—	2	8	no	—
443	C₂×#135	C₂²×C₁₃	1	8	yes	complemented
444	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
445	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
446	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
447	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
448	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
449	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
450	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
451	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
452	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
453	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
454	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
455	#550	—	2	4	no	—
456	#550	C₂²×C₁₃	1	8	yes	complemented
457	#546	—	2	4	no	—
458	#546	C₂²×C₁₃	1	8	yes	complemented
459	C₂×#127	—	2	1	no	—
460	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
461	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
462	C₂×#123	—	2	1	no	—
463	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
464	C₂×#121	—	2	1	no	—
465	C₂×#121	—	2	1	no	—
466	C₂×#121	—	2	1	no	—
467	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
468	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
469	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
470	C₂×#120	—	2	1	no	—
471	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
472	C₂×C₄×D₄	—	2	1	no	—
473	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
474	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
475	C₂²×C₂²⋊C₄	—	2	1	no	—
476	#496	C₂²×C₁₃	1	8	yes	complemented
477	#468	C₂²×C₁₃	1	8	yes	complemented
478	#466	C₂²×C₁₃	1	8	yes	complemented
479	#464	C₂²×C₁₃	1	8	yes	complemented
480	#459	C₂²×C₁₃	1	8	yes	complemented
481	#452	C₂²×C₁₃	1	8	yes	complemented
482	#449	C₂²×C₁₃	1	8	yes	complemented
483	#449	C₂²×C₁₃	1	8	yes	complemented
484	#447	C₂²×C₁₃	1	8	yes	complemented
485	#440	C₂²×C₁₃	1	8	yes	complemented
486	#435	C₂²×C₁₃	1	8	yes	complemented
487	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
488	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
489	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
490	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
491	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
492	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
493	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
494	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
495	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
496	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
497	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
498	C₂²×C₁₃	—	2	2	no	—
499	C₂²×C₁₃	—	2	2	no	—
500	C₂²×C₁₃	—	2	4	no	—
501	C₂²×C₁₃	—	2	2	no	—
502	C₂²×C₁₃	—	2	2	no	—
503	C₂²×C₁₃	—	2	2	no	—
504	C₂²×C₁₃	—	2	2	no	—
505	C₂²×C₁₃	—	4	4	no	—
506	C₂²×C₁₃	—	4	4	no	—
507	C₂²×C₁₃	—	4	8	no	—
508	C₂²×C₁₃	—	4	2	no	—
509	C₂²×C₁₃	—	4	2	no	—
510	C₂²×C₁₃	—	4	2	no	—
511	C₂²×C₁₃	—	4	2	no	—
512	C₂²×C₁₃	—	4	2	no	—
513	C₂²×C₁₃	—	4	2	no	—
514	C₂²×C₁₃	—	4	2	no	—
515	C₂²×C₁₃	—	4	2	no	—
516	C₂²×C₁₃	—	4	2	no	—
517	C₂²×C₁₃	—	4	2	no	—
518	C₂²×C₁₃	—	4	2	no	—
519	C₂²×C₁₃	—	8	16	no	—
520	C₂²×C₁₃	—	8	4	no	—
521	C₂²×C₁₃	—	8	4	no	—
522	C₂²×C₁₃	—	8	4	no	—
523	C₂²×C₁₃	D₄²	1	2	yes	—
524	C₂²×C₁₃	#575	1	2	yes	—
525	C₂²×C₁₃	#576	1	2	yes	—
526	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
527	C₄×C₁₃	—	2	2	no	—
528	C₄×C₁₃	—	2	2	no	—
529	C₄×C₁₃	—	2	4	no	—
530	C₄×C₁₃	—	2	2	no	—
531	C₄×C₁₃	—	2	2	no	—
532	C₄×C₁₃	—	4	2	no	—
533	C₄×C₁₃	—	4	2	no	—
534	C₄×C₁₃	—	4	2	no	—
535	C₄×C₁₃	D₄²	1	2	yes	—
536	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
537	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
538	C₂⁵	—	2	1	no	—
539	C₂×#41	—	2	2	no	—
540	C₂×#41	—	2	2	no	—
541	C₂×#41	—	2	2	no	—
542	C₂×#41	—	2	4	no	—
543	C₂×#41	—	2	4	no	—
544	C₂×#41	—	2	4	no	—
545	C₂×#41	—	4	2	no	—
546	C₂×#41	—	4	2	no	—
547	C₂×#41	—	4	2	no	—
548	C₂×#41	C₂³×C₁₃	1	4	yes	—
549	C₂×#41	C₂³×C₁₃	1	4	yes	—
550	C₂×#41	C₂³×C₁₃	1	4	yes	complemented
551	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
552	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
553	C₂²×D₄	—	2	4	no	—
554	C₂²×D₄	—	2	1	no	—
555	C₂²×D₄	—	2	1	no	—
556	C₂²×D₄	—	2	1	no	—
557	C₂²×D₄	—	2	1	no	—
558	C₂²×D₄	—	2	1	no	—
559	C₂²×D₄	—	2	1	no	—
560	C₂²×D₄	—	2	1	no	—
561	C₂²×D₄	—	2	1	no	—
562	C₂²×D₄	—	2	2	no	—
563	C₂²×D₄	—	2	1	no	—
564	C₂²×D₄	—	4	2	no	—
565	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
567	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
568	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
570	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
571	C₂³×C₄	—	2	1	no	—
572	C₂³×C₄	—	2	1	no	—
573	C₂³×C₄	—	2	1	no	—
574	C₂³×C₄	—	2	1	no	—
575	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
576	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
577	AGL(1,ℤ/8)	—	2	32	no	—
578	#135	—	2	32	no	—
579	C₂×Q₁₆	—	2	4	no	—
580	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	complemented
581	C₂×SD₁₆	—	2	4	no	—
582	C₂×SD₁₆	—	2	4	no	—
583	C₂×SD₁₆	—	4	2	no	—
584	C₂×SD₁₆	D₄×C₁₃	1	8	yes	complemented
585	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
586	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
587	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
588	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
589	C₂×D₈	—	2	4	no	—
590	C₂×D₈	—	2	4	no	—
591	C₂×D₈	—	2	4	no	—
592	C₂×D₈	—	4	2	no	—
593	C₂×D₈	C₂³×C₁₃	1	4	yes	—
594	C₂×D₈	C₂³×C₁₃	1	4	yes	—
595	C₂×D₈	C₂³×C₁₃	1	4	yes	—
596	C₂×D₈	C₂³×C₁₃	1	4	yes	—
597	C₂×M₁₆	—	2	4	no	—
598	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
599	C₂²×C₈	—	2	4	no	—
600	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
601	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
602	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
603	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
604	C₂²×C₈	C₂³×C₁₃	1	4	yes	complemented
605	#127	—	2	8	no	—
606	#127	—	2	2	no	—
607	#127	C₂³×C₁₃	1	4	yes	complemented
608	#124	—	2	2	no	—
609	#124	C₂³×C₁₃	1	4	yes	—
610	#123	—	2	8	no	—
611	C₂²⋊Q₈	—	2	2	no	—
612	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
613	#121	—	2	2	no	—
614	#121	—	2	2	no	—
615	#121	—	2	2	no	—
616	#121	—	2	8	no	—
617	#121	—	2	8	no	—
618	#121	—	2	8	no	—
619	#121	C₂³×C₁₃	1	4	yes	—
620	#121	C₂³×C₁₃	1	4	yes	—
621	#121	C₂³×C₁₃	1	4	yes	complemented
622	#120	—	2	8	no	—
623	C₄×Q₈	—	2	2	no	—
624	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
625	C₄×D₄	—	2	8	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	D₄×C₁₃	1	4	yes	—
628	C₄×D₄	C₂³×C₁₃	1	4	yes	—
629	C₄×D₄	C₂³×C₁₃	1	4	yes	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	—	2	1	no	—
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₂²⋊C₄	—	2	1	no	—
642	C₂×C₂²⋊C₄	—	2	8	no	—
643	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
645	C₂×C₄²	—	2	1	no	—
646	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
647	#107	C₂³×C₁₃	1	4	yes	complemented
648	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
649	#103	C₂³×C₁₃	1	4	yes	complemented
650	#103	C₂³×C₁₃	1	4	yes	complemented
651	#102	C₂³×C₁₃	1	4	yes	—
652	#102	C₂³×C₁₃	1	4	yes	—
653	#102	C₂³×C₁₃	1	4	yes	complemented
654	#102	C₂³×C₁₃	1	4	yes	complemented
655	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
656	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	complemented
657	#97	C₂³×C₁₃	1	4	yes	complemented
658	C₂×C₁₃	—	4	2	no	—
659	C₂×C₁₃	—	4	2	no	—
660	C₂×C₁₃	—	4	4	no	—
661	C₂×C₁₃	—	8	2	no	—
662	C₂×C₁₃	—	8	2	no	—
663	C₂×C₁₃	—	8	2	no	—
664	C₂×C₁₃	#3268	1	4	yes	direct product factor
665	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
666	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
667	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
668	C₂⁴	—	2	1	no	—
669	C₂⁴	—	2	1	no	—
670	C₂⁴	—	2	1	no	—
671	C₂⁴	—	2	1	no	—
672	C₂⁴	—	2	4	no	—
673	C₂⁴	—	4	4	no	—
674	C₂⁴	—	4	4	no	—
675	C₂⁴	—	8	2	no	—
676	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
677	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
678	#41	—	2	8	no	—
679	#41	—	2	8	no	—
680	#41	—	2	8	no	—
681	#41	—	4	4	no	—
682	#41	—	4	4	no	—
683	#41	—	4	4	no	—
684	#41	—	4	8	no	—
685	#41	—	4	8	no	—
686	#41	—	4	8	no	—
687	C₂×Q₈	—	2	1	no	—
688	C₂×Q₈	—	2	1	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	—	2	2	no	—
692	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
693	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
694	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
695	C₂×D₄	—	2	8	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	4	no	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	2	4	no	—
707	C₂×D₄	—	2	4	no	—
708	C₂×D₄	—	2	1	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	1	no	—
711	C₂×D₄	—	2	4	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	4	4	no	—
717	C₂×D₄	—	4	8	no	—
718	C₂×D₄	—	4	2	no	—
719	C₂×D₄	—	4	4	no	—
720	C₂×D₄	—	4	4	no	—
721	C₂×D₄	—	4	4	no	—
722	C₂×D₄	—	4	4	no	—
723	C₂×D₄	—	4	4	no	—
724	C₂×D₄	—	8	2	no	—
725	C₂×D₄	—	8	2	no	—
726	C₂×D₄	—	8	2	no	—
727	C₂×D₄	—	8	2	no	—
728	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
729	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
730	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
731	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
732	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
733	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	2	1	no	—
741	C₂²×C₄	—	2	1	no	—
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	2	4	no	—
744	C₂²×C₄	—	2	4	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	4	4	no	—
747	C₂²×C₄	—	4	4	no	—
748	C₂²×C₄	—	4	4	no	—
749	C₂²×C₄	—	8	2	no	—
750	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
751	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
752	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
753	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
754	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
755	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
759	Q₁₆	—	2	8	no	—
760	SD₁₆	—	2	8	no	—
761	SD₁₆	—	2	8	no	—
762	SD₁₆	—	4	4	no	—
763	SD₁₆	C₂×D₄×C₁₃	1	16	yes	complemented
764	D₈	—	2	8	no	—
765	D₈	—	2	8	no	—
766	D₈	—	2	8	no	—
767	D₈	—	4	4	no	—
768	M₁₆	—	2	8	no	—
769	C₂×C₈	—	2	2	no	—
770	C₂×C₈	—	2	2	no	—
771	C₂×C₈	—	2	2	no	—
772	C₂×C₈	—	2	8	no	—
773	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
774	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
775	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
776	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
777	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	2	1	no	—
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
783	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
784	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
793	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
794	C₄²	—	2	4	no	—
795	C₄²	C₂×D₄×C₁₃	1	2	yes	—
796	C₄²	C₂⁴×C₁₃	1	2	yes	—
797	C₁₃	C₂×#3268	1	1	yes	characteristic, direct product factor, Sylow
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	4	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	4	8	no	—
810	C₂³	—	4	8	no	—
811	C₂³	—	4	2	no	—
812	C₂³	—	4	2	no	—
813	C₂³	—	4	2	no	—
814	C₂³	—	4	2	no	—
815	C₂³	—	4	2	no	—
816	C₂³	—	4	2	no	—
817	C₂³	—	4	2	no	—
818	C₂³	—	4	2	no	—
819	C₂³	—	4	2	no	—
820	C₂³	—	4	2	no	—
821	C₂³	—	4	2	no	—
822	C₂³	—	8	4	no	—
823	C₂³	—	8	16	no	—
824	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
825	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
826	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
827	Q₈	—	2	4	no	—
828	Q₈	—	2	2	no	—
829	Q₈	—	2	2	no	—
830	Q₈	—	2	2	no	—
831	Q₈	—	4	2	no	—
832	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
833	D₄	—	2	4	no	—
834	D₄	—	2	2	no	—
835	D₄	—	2	2	no	—
836	D₄	—	2	2	no	—
837	D₄	—	2	2	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	2	no	—
840	D₄	—	2	2	no	—
841	D₄	—	4	4	no	—
842	D₄	—	4	8	no	—
843	D₄	—	4	8	no	—
844	D₄	—	4	8	no	—
845	D₄	—	4	8	no	—
846	D₄	—	4	8	no	—
847	D₄	—	4	2	no	—
848	D₄	—	4	2	no	—
849	D₄	—	4	2	no	—
850	D₄	—	8	4	no	—
851	D₄	—	8	4	no	—
852	D₄	—	8	4	no	—
853	D₄	—	8	4	no	—
854	D₄	C₂²×D₄×C₁₃	1	4	yes	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	4	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	4	no	—
862	C₂×C₄	—	2	4	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	4	8	no	—
871	C₂×C₄	—	4	8	no	—
872	C₂×C₄	—	4	8	no	—
873	C₂×C₄	—	4	2	no	—
874	C₂×C₄	—	4	2	no	—
875	C₂×C₄	—	4	2	no	—
876	C₂×C₄	—	8	4	no	—
877	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
878	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
879	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
880	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
881	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
882	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
883	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
884	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
885	C₈	—	2	2	no	—
886	C₈	—	2	2	no	—
887	C₈	—	2	2	no	—
888	C₈	C₂²×D₄×C₁₃	1	4	yes	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	4	no	—
896	C₂²	—	4	4	no	—
897	C₂²	—	4	4	no	—
898	C₂²	—	4	8	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	8	16	no	—
911	C₂²	—	8	4	no	—
912	C₂²	—	8	4	no	—
913	C₂²	—	8	4	no	—
914	C₂²	D₄²×C₁₃	1	2	yes	—
915	C₂²	C₁₃×#575	1	2	yes	—
916	C₂²	C₁₃×#576	1	2	yes	—
917	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	2	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	4	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	D₄²×C₁₃	1	2	yes	—
927	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
928	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
929	C₂	—	4	2	no	—
930	C₂	—	4	2	no	—
931	C₂	—	4	4	no	—
932	C₂	—	8	2	no	—
933	C₂	—	8	2	no	—
934	C₂	—	8	2	no	—
935	C₂	C₁₃×#3268	1	4	yes	direct product factor
936	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
937	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
938	C₂	C₂×C₁₃×#576	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. C₂²×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
2. C₂²×C₁₃×#135	C₂	semidirect
3. C₂×C₁₃×#550	C₂	semidirect
4. C₂×C₁₃×#546	C₂	semidirect
5. C₁₃×#3268	C₂	direct (N × H)
6. C₂×C₁₃×#496	C₂	semidirect
7. C₂×C₁₃×#468	C₂	semidirect
8. C₂×C₁₃×#466	C₂	semidirect
9. C₂×C₁₃×#464	C₂	semidirect
10. C₂×C₁₃×#459	C₂	semidirect
11. C₂×C₁₃×#452	C₂	semidirect
12. C₂×C₁₃×#449	C₂	semidirect
13. C₂×C₁₃×#449	C₂	semidirect
14. C₂×C₁₃×#447	C₂	semidirect
15. C₂×C₁₃×#440	C₂	semidirect
16. C₂×C₁₃×#435	C₂	semidirect
19. C₂²×C₁₃×#41	C₂²	semidirect
22. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
24. C₂×C₁₃×#135	C₂²	semidirect
25. C₂²×C₁₃×Q₁₆	C₂²	semidirect
28. C₂²×C₁₃×SD₁₆	C₂²	semidirect
29. C₂²×C₁₃×SD₁₆	C₂²	semidirect
35. C₂³×C₈×C₁₃	C₂²	semidirect
37. C₁₃×#550	C₂²	semidirect
39. C₁₃×#546	C₂²	semidirect
41. C₂×C₁₃×#127	C₂²	semidirect
50. C₂×C₁₃×#121	C₂²	semidirect
52. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
57. C₁₃×#496	C₂²	semidirect
58. C₁₃×#468	C₂²	semidirect
59. C₁₃×#466	C₂²	semidirect
60. C₁₃×#464	C₂²	semidirect
61. C₁₃×#459	C₂²	semidirect
62. C₁₃×#452	C₂²	semidirect
63. C₁₃×#449	C₂²	semidirect
64. C₁₃×#449	C₂²	semidirect
65. C₁₃×#447	C₂²	semidirect
66. C₁₃×#440	C₂²	semidirect
67. C₁₃×#435	C₂²	semidirect
68. C₂×C₁₃×#107	C₂²	semidirect
69. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
70. C₂×C₁₃×#103	C₂²	semidirect
71. C₂×C₁₃×#103	C₂²	semidirect
74. C₂×C₁₃×#102	C₂²	semidirect
75. C₂×C₁₃×#102	C₂²	semidirect
77. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
78. C₂×C₁₃×#97	C₂²	semidirect
91. C₂×C₁₃×#41	C₂³	semidirect
121. C₂×C₁₃×Q₁₆	C₂³	semidirect
125. C₂×C₁₃×SD₁₆	D₄	semidirect
128. C₂×C₁₃×SD₁₆	C₂³	semidirect
129. C₂×C₁₃×SD₁₆	C₂³	semidirect
145. C₂²×C₈×C₁₃	C₂³	semidirect
148. C₁₃×#127	C₂³	semidirect
162. C₁₃×#121	C₂³	semidirect
165. C₄×Q₈×C₁₃	C₂³	semidirect
188. C₁₃×#107	C₂³	semidirect
189. C₁₃×C₄⋊C₈	C₂³	semidirect
190. C₁₃×#103	C₂³	semidirect
191. C₁₃×#103	C₂³	semidirect
194. C₁₃×#102	C₂³	semidirect
195. C₁₃×#102	C₂³	semidirect
197. C₁₃×C₂²⋊C₈	C₂³	semidirect
198. C₁₃×#97	C₂³	semidirect
199. C₂×#3268	C₁₃	direct (N × H)
295. C₁₃×SD₁₆	C₂×D₄	semidirect
329. C₂²×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
330. C₂²×#135	C₂×C₁₃	semidirect
331. C₂×#550	C₂×C₁₃	semidirect
332. C₂×#546	C₂×C₁₃	semidirect
333. #3268	C₂×C₁₃	direct (N × H)
334. C₂×#496	C₂×C₁₃	semidirect
335. C₂×#468	C₂×C₁₃	semidirect
336. C₂×#466	C₂×C₁₃	semidirect
337. C₂×#464	C₂×C₁₃	semidirect
338. C₂×#459	C₂×C₁₃	semidirect
339. C₂×#452	C₂×C₁₃	semidirect
340. C₂×#449	C₂×C₁₃	semidirect
341. C₂×#449	C₂×C₁₃	semidirect
342. C₂×#447	C₂×C₁₃	semidirect
343. C₂×#440	C₂×C₁₃	semidirect
344. C₂×#435	C₂×C₁₃	semidirect
438. C₂²×#41	C₂²×C₁₃	semidirect
441. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
443. C₂×#135	C₂²×C₁₃	semidirect
444. C₂²×Q₁₆	C₂²×C₁₃	semidirect
447. C₂²×SD₁₆	C₂²×C₁₃	semidirect
448. C₂²×SD₁₆	C₂²×C₁₃	semidirect
454. C₂³×C₈	C₂²×C₁₃	semidirect
456. #550	C₂²×C₁₃	semidirect
458. #546	C₂²×C₁₃	semidirect
460. C₂×#127	C₂²×C₁₃	semidirect
469. C₂×#121	C₂²×C₁₃	semidirect
471. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
476. #496	C₂²×C₁₃	semidirect
477. #468	C₂²×C₁₃	semidirect
478. #466	C₂²×C₁₃	semidirect
479. #464	C₂²×C₁₃	semidirect
480. #459	C₂²×C₁₃	semidirect
481. #452	C₂²×C₁₃	semidirect
482. #449	C₂²×C₁₃	semidirect
483. #449	C₂²×C₁₃	semidirect
484. #447	C₂²×C₁₃	semidirect
485. #440	C₂²×C₁₃	semidirect
486. #435	C₂²×C₁₃	semidirect
487. C₂×#107	C₂²×C₁₃	semidirect
488. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
489. C₂×#103	C₂²×C₁₃	semidirect
490. C₂×#103	C₂²×C₁₃	semidirect
493. C₂×#102	C₂²×C₁₃	semidirect
494. C₂×#102	C₂²×C₁₃	semidirect
496. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
497. C₂×#97	C₂²×C₁₃	semidirect
550. C₂×#41	C₂³×C₁₃	semidirect
580. C₂×Q₁₆	C₂³×C₁₃	semidirect
584. C₂×SD₁₆	D₄×C₁₃	semidirect
587. C₂×SD₁₆	C₂³×C₁₃	semidirect
588. C₂×SD₁₆	C₂³×C₁₃	semidirect
604. C₂²×C₈	C₂³×C₁₃	semidirect
607. #127	C₂³×C₁₃	semidirect
621. #121	C₂³×C₁₃	semidirect
624. C₄×Q₈	C₂³×C₁₃	semidirect
647. #107	C₂³×C₁₃	semidirect
648. C₄⋊C₈	C₂³×C₁₃	semidirect
649. #103	C₂³×C₁₃	semidirect
650. #103	C₂³×C₁₃	semidirect
653. #102	C₂³×C₁₃	semidirect
654. #102	C₂³×C₁₃	semidirect
656. C₂²⋊C₈	C₂³×C₁₃	semidirect
657. #97	C₂³×C₁₃	semidirect
664. C₂×C₁₃	#3268	direct (N × H)
763. SD₁₆	C₂×D₄×C₁₃	semidirect
797. C₁₃	C₂×#3268	direct (N × H)
935. C₂	C₁₃×#3268	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×AGL(1,ℤ/8)	2
C₂²×C₁₃×#135	2
C₂×C₁₃×#550	2
C₂×C₁₃×#546	2
C₁₃×#3268	2
C₂×C₁₃×#496	2
C₂×C₁₃×#468	2
C₂×C₁₃×#466	2
C₂×C₁₃×#464	2
C₂×C₁₃×#459	2
C₂×C₁₃×#452	2
C₂×C₁₃×#449	2
C₂×C₁₃×#447	2
C₂×C₁₃×#440	2
C₂×C₁₃×#435	2
C₂×#3268	13

Subgroups — C2×C13×#3268 #15747365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3268 #15747365