Subgroups — C₂×C₁₃×#3306 #15747464

Order 3328.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3306	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#465	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×#447	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#442	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×#102	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×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#547	—	2	4	no	—
26	C₁₃×#547	C₂²	1	8	yes	complemented
27	C₁₃×#546	—	2	4	no	—
28	C₁₃×#546	C₂²	1	8	yes	complemented
29	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#123	—	2	1	no	—
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	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#121	—	2	1	no	—
37	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₃×#120	—	2	1	no	—
41	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
47	C₁₃×#489	C₂²	1	8	yes	complemented
48	C₁₃×#483	C₂²	1	8	yes	complemented
49	C₁₃×#481	C₂²	1	8	yes	complemented
50	C₁₃×#476	C₂²	1	8	yes	complemented
51	C₁₃×#469	C₂²	1	8	yes	complemented
52	C₁₃×#465	C₂²	1	8	yes	complemented
53	C₁₃×#463	C₂²	1	8	yes	complemented
54	C₁₃×#449	C₂²	1	8	yes	complemented
55	C₁₃×#447	C₂²	1	8	yes	complemented
56	C₁₃×#442	C₂²	1	8	yes	complemented
57	C₁₃×#435	C₂²	1	8	yes	complemented
58	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#417	C₂²	1	8	yes	complemented
63	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
72	C₂×C₁₃×#102	C₂²	1	8	yes	complemented
73	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₁₃	—	2	1	no	—
78	C₂×C₁₃×#41	—	2	8	no	—
79	C₂×C₁₃×#41	—	2	2	no	—
80	C₂×C₁₃×#41	—	2	4	no	—
81	C₂×C₁₃×#41	—	4	2	no	—
82	C₂×C₁₃×#41	—	4	8	no	—
83	C₂×C₁₃×#41	C₂³	1	4	yes	—
84	C₂²×Q₈×C₁₃	—	2	1	no	—
85	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₃	—	2	4	no	—
87	C₂²×D₄×C₁₃	—	2	1	no	—
88	C₂²×D₄×C₁₃	—	2	1	no	—
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	—	2	2	no	—
93	C₂²×D₄×C₁₃	—	4	2	no	—
94	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
95	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
98	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
104	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×SD₁₆	—	4	2	no	—
107	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
108	C₂×C₁₃×D₈	—	2	4	no	—
109	C₂×C₁₃×D₈	—	4	2	no	—
110	C₂×C₁₃×D₈	C₂³	1	4	yes	—
111	C₂×C₁₃×D₈	C₂³	1	4	yes	—
112	C₂×C₁₃×M₁₆	—	4	2	no	—
113	C₂×C₁₃×M₁₆	C₂³	1	4	yes	complemented
114	C₂²×C₈×C₁₃	—	4	2	no	—
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	1	yes	characteristic
119	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
120	C₁₃×C₄⋊Q₈	—	2	2	no	—
121	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
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×#123	—	2	8	no	—
127	C₁₃×C₂²⋊Q₈	—	2	2	no	—
128	C₁₃×C₂²⋊Q₈	—	2	8	no	—
129	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
130	C₁₃×#121	—	2	2	no	—
131	C₁₃×#121	—	2	2	no	—
132	C₁₃×#121	—	2	2	no	—
133	C₁₃×#121	—	2	8	no	—
134	C₁₃×#121	C₂³	1	4	yes	—
135	C₁₃×#121	C₂³	1	4	yes	—
136	C₁₃×#121	C₂³	1	4	yes	complemented
137	C₁₃×#120	—	2	8	no	—
138	C₄×D₄×C₁₃	—	2	2	no	—
139	C₄×D₄×C₁₃	—	2	2	no	—
140	C₄×D₄×C₁₃	D₄	1	4	yes	—
141	C₄×D₄×C₁₃	C₂³	1	4	yes	—
142	C₄×D₄×C₁₃	C₂³	1	4	yes	—
143	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
144	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₂×C₁₃×C₄⋊C₄	—	2	1	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	D₄	1	1	yes	characteristic
151	C₂×C₁₃×C₄⋊C₄	C₂³	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	4	yes	—
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
157	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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	—	2	8	no	—
166	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
167	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
168	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₁₃×#106	C₂³	1	4	yes	complemented
170	C₁₃×#106	C₂³	1	4	yes	complemented
171	C₁₃×#106	C₂³	1	4	yes	complemented
172	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
173	C₁₃×#103	C₂³	1	4	yes	complemented
174	C₁₃×#103	C₂³	1	4	yes	complemented
175	C₁₃×#103	C₂³	1	4	yes	complemented
176	C₁₃×#102	C₂³	1	4	yes	—
177	C₁₃×#102	C₂³	1	4	yes	—
178	C₁₃×#102	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	complemented
183	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
184	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
185	C₁₃×#97	C₂³	1	4	yes	complemented
186	C₂×#3306	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	—	2	1	no	—
190	C₂⁴×C₁₃	—	2	4	no	—
191	C₂⁴×C₁₃	—	4	4	no	—
192	C₂⁴×C₁₃	—	4	4	no	—
193	C₂⁴×C₁₃	—	8	2	no	—
194	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₁₃×#41	—	2	8	no	—
197	C₁₃×#41	—	4	4	no	—
198	C₁₃×#41	—	4	8	no	—
199	C₁₃×#41	—	4	32	no	—
200	C₂×Q₈×C₁₃	—	2	1	no	—
201	C₂×Q₈×C₁₃	—	2	4	no	—
202	C₂×Q₈×C₁₃	—	2	2	no	—
203	C₂×Q₈×C₁₃	—	2	2	no	—
204	C₂×Q₈×C₁₃	—	4	4	no	—
205	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
206	C₂×D₄×C₁₃	—	2	4	no	—
207	C₂×D₄×C₁₃	—	2	8	no	—
208	C₂×D₄×C₁₃	—	2	4	no	—
209	C₂×D₄×C₁₃	—	2	4	no	—
210	C₂×D₄×C₁₃	—	2	4	no	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	—	2	1	no	—
213	C₂×D₄×C₁₃	—	2	1	no	—
214	C₂×D₄×C₁₃	—	2	4	no	—
215	C₂×D₄×C₁₃	—	2	1	no	—
216	C₂×D₄×C₁₃	—	2	2	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	8	no	—
223	C₂×D₄×C₁₃	—	4	4	no	—
224	C₂×D₄×C₁₃	—	4	4	no	—
225	C₂×D₄×C₁₃	—	4	4	no	—
226	C₂×D₄×C₁₃	—	4	4	no	—
227	C₂×D₄×C₁₃	—	8	2	no	—
228	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
229	C₂×D₄×C₁₃	#41	1	4	yes	complemented
230	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
231	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
232	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃	—	2	2	no	—
234	C₂²×C₄×C₁₃	—	2	2	no	—
235	C₂²×C₄×C₁₃	—	2	2	no	—
236	C₂²×C₄×C₁₃	—	2	2	no	—
237	C₂²×C₄×C₁₃	—	2	4	no	—
238	C₂²×C₄×C₁₃	—	2	4	no	—
239	C₂²×C₄×C₁₃	—	2	1	no	—
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	4	no	—
245	C₂²×C₄×C₁₃	—	2	4	no	—
246	C₂²×C₄×C₁₃	—	2	4	no	—
247	C₂²×C₄×C₁₃	—	4	4	no	—
248	C₂²×C₄×C₁₃	—	4	4	no	—
249	C₂²×C₄×C₁₃	—	4	4	no	—
250	C₂²×C₄×C₁₃	—	4	4	no	—
251	C₂²×C₄×C₁₃	—	8	2	no	—
252	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₁₃×SD₁₆	—	4	4	no	—
262	C₁₃×D₈	—	2	8	no	—
263	C₁₃×D₈	—	4	4	no	—
264	C₁₃×M₁₆	—	4	4	no	—
265	C₂×C₈×C₁₃	—	2	2	no	—
266	C₂×C₈×C₁₃	—	2	2	no	—
267	C₂×C₈×C₁₃	—	2	2	no	—
268	C₂×C₈×C₁₃	—	2	2	no	—
269	C₂×C₈×C₁₃	—	4	4	no	—
270	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
271	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
272	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
273	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
274	C₁₃×C₄⋊C₄	—	2	1	no	—
275	C₁₃×C₄⋊C₄	—	2	1	no	—
276	C₁₃×C₄⋊C₄	—	2	1	no	—
277	C₁₃×C₄⋊C₄	—	2	4	no	—
278	C₁₃×C₄⋊C₄	—	2	4	no	—
279	C₁₃×C₄⋊C₄	—	2	4	no	—
280	C₁₃×C₄⋊C₄	—	2	4	no	—
281	C₁₃×C₄⋊C₄	—	2	1	no	—
282	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
283	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
284	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
285	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
286	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
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	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	4	no	—
293	C₁₃×C₂²⋊C₄	—	2	4	no	—
294	C₁₃×C₂²⋊C₄	—	2	4	no	—
295	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
296	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
297	C₄²×C₁₃	C₂×D₄	1	2	yes	—
298	C₄²×C₁₃	C₂⁴	1	2	yes	—
299	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
300	C₂×#546	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#3306	C₂×C₁₃	1	16	yes	direct product factor
302	C₂×#489	C₂×C₁₃	1	1	yes	characteristic, complemented
303	C₂×#481	C₂×C₁₃	1	1	yes	characteristic, complemented
304	C₂×#483	C₂×C₁₃	1	1	yes	characteristic, complemented
305	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
306	C₂×#469	C₂×C₁₃	1	1	yes	characteristic, complemented
307	C₂×#465	C₂×C₁₃	1	1	yes	characteristic, complemented
308	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
309	C₂×#449	C₂×C₁₃	1	1	yes	characteristic, complemented
310	C₂×#447	C₂×C₁₃	1	1	yes	characteristic, complemented
311	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
312	C₂×#435	C₂×C₁₃	1	1	yes	characteristic, complemented
313	C₂×#417	C₂×C₁₃	1	1	yes	characteristic, complemented
314	C₂²×#102	C₂×C₁₃	1	1	yes	characteristic, complemented
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	2	4	no	—
319	C₂³×C₁₃	—	2	2	no	—
320	C₂³×C₁₃	—	2	2	no	—
321	C₂³×C₁₃	—	2	2	no	—
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	—	2	2	no	—
324	C₂³×C₁₃	—	4	8	no	—
325	C₂³×C₁₃	—	4	2	no	—
326	C₂³×C₁₃	—	4	2	no	—
327	C₂³×C₁₃	—	4	2	no	—
328	C₂³×C₁₃	—	4	2	no	—
329	C₂³×C₁₃	—	4	2	no	—
330	C₂³×C₁₃	—	4	8	no	—
331	C₂³×C₁₃	—	4	2	no	—
332	C₂³×C₁₃	—	4	2	no	—
333	C₂³×C₁₃	—	4	2	no	—
334	C₂³×C₁₃	—	8	4	no	—
335	C₂³×C₁₃	—	8	16	no	—
336	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
337	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
338	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
339	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
340	Q₈×C₁₃	—	2	2	no	—
341	Q₈×C₁₃	—	2	2	no	—
342	Q₈×C₁₃	—	4	8	no	—
343	Q₈×C₁₃	—	4	2	no	—
344	D₄×C₁₃	—	2	8	no	—
345	D₄×C₁₃	—	2	4	no	—
346	D₄×C₁₃	—	2	2	no	—
347	D₄×C₁₃	—	2	2	no	—
348	D₄×C₁₃	—	2	2	no	—
349	D₄×C₁₃	—	2	2	no	—
350	D₄×C₁₃	—	2	2	no	—
351	D₄×C₁₃	—	4	8	no	—
352	D₄×C₁₃	—	4	8	no	—
353	D₄×C₁₃	—	4	8	no	—
354	D₄×C₁₃	—	4	8	no	—
355	D₄×C₁₃	—	4	2	no	—
356	D₄×C₁₃	—	4	2	no	—
357	D₄×C₁₃	—	8	4	no	—
358	D₄×C₁₃	C₂×#41	1	4	yes	complemented
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	4	no	—
364	C₂×C₄×C₁₃	—	2	4	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	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	2	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	—	4	8	no	—
375	C₂×C₄×C₁₃	—	4	8	no	—
376	C₂×C₄×C₁₃	—	4	8	no	—
377	C₂×C₄×C₁₃	—	4	2	no	—
378	C₂×C₄×C₁₃	—	4	2	no	—
379	C₂×C₄×C₁₃	—	4	2	no	—
380	C₂×C₄×C₁₃	—	4	2	no	—
381	C₂×C₄×C₁₃	—	4	8	no	—
382	C₂×C₄×C₁₃	—	4	2	no	—
383	C₂×C₄×C₁₃	—	8	4	no	—
384	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
390	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
391	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
392	C₈×C₁₃	—	2	2	no	—
393	C₈×C₁₃	—	2	2	no	—
394	C₈×C₁₃	—	2	2	no	—
395	C₈×C₁₃	—	2	2	no	—
396	C₂²×#41	—	2	1	no	—
397	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
398	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
399	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
400	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
401	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
402	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
403	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
404	#547	—	2	4	no	—
405	#547	C₂²×C₁₃	1	8	yes	complemented
406	#546	—	2	4	no	—
407	#546	C₂²×C₁₃	1	8	yes	complemented
408	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
409	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
410	C₂×#123	—	2	1	no	—
411	C₂×#123	—	2	1	no	—
412	C₂×#123	—	2	1	no	—
413	C₂×C₂²⋊Q₈	—	2	1	no	—
414	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×#121	—	2	1	no	—
416	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
419	C₂×#120	—	2	1	no	—
420	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
423	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
424	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
425	C₂²×C₂²⋊C₄	—	2	1	no	—
426	#489	C₂²×C₁₃	1	8	yes	complemented
427	#483	C₂²×C₁₃	1	8	yes	complemented
428	#481	C₂²×C₁₃	1	8	yes	complemented
429	#476	C₂²×C₁₃	1	8	yes	complemented
430	#469	C₂²×C₁₃	1	8	yes	complemented
431	#465	C₂²×C₁₃	1	8	yes	complemented
432	#463	C₂²×C₁₃	1	8	yes	complemented
433	#449	C₂²×C₁₃	1	8	yes	complemented
434	#447	C₂²×C₁₃	1	8	yes	complemented
435	#442	C₂²×C₁₃	1	8	yes	complemented
436	#435	C₂²×C₁₃	1	8	yes	complemented
437	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
438	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
440	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
441	#417	C₂²×C₁₃	1	8	yes	complemented
442	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
443	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
444	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
445	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
447	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
448	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
449	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
450	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
451	C₂×#102	C₂²×C₁₃	1	8	yes	complemented
452	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
453	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
455	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
456	C₂²×C₁₃	—	2	2	no	—
457	C₂²×C₁₃	—	2	8	no	—
458	C₂²×C₁₃	—	2	2	no	—
459	C₂²×C₁₃	—	2	2	no	—
460	C₂²×C₁₃	—	2	4	no	—
461	C₂²×C₁₃	—	2	2	no	—
462	C₂²×C₁₃	—	2	2	no	—
463	C₂²×C₁₃	—	4	4	no	—
464	C₂²×C₁₃	—	4	8	no	—
465	C₂²×C₁₃	—	4	2	no	—
466	C₂²×C₁₃	—	4	2	no	—
467	C₂²×C₁₃	—	4	2	no	—
468	C₂²×C₁₃	—	4	2	no	—
469	C₂²×C₁₃	—	4	2	no	—
470	C₂²×C₁₃	—	4	2	no	—
471	C₂²×C₁₃	—	4	2	no	—
472	C₂²×C₁₃	—	4	2	no	—
473	C₂²×C₁₃	—	8	16	no	—
474	C₂²×C₁₃	—	8	4	no	—
475	C₂²×C₁₃	—	8	4	no	—
476	C₂²×C₁₃	#546	1	2	yes	—
477	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
478	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
479	C₂²×C₁₃	#577	1	2	yes	—
480	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
481	C₄×C₁₃	—	2	2	no	—
482	C₄×C₁₃	—	2	2	no	—
483	C₄×C₁₃	—	2	2	no	—
484	C₄×C₁₃	—	2	2	no	—
485	C₄×C₁₃	—	4	2	no	—
486	C₄×C₁₃	—	4	2	no	—
487	C₄×C₁₃	—	4	2	no	—
488	C₄×C₁₃	—	4	2	no	—
489	C₄×C₁₃	—	4	2	no	—
490	C₄×C₁₃	#546	1	2	yes	—
491	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
492	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
493	C₂⁵	—	2	1	no	—
494	C₂×#41	—	2	8	no	—
495	C₂×#41	—	2	2	no	—
496	C₂×#41	—	2	4	no	—
497	C₂×#41	—	4	2	no	—
498	C₂×#41	—	4	8	no	—
499	C₂×#41	C₂³×C₁₃	1	4	yes	—
500	C₂²×Q₈	—	2	1	no	—
501	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
502	C₂²×D₄	—	2	4	no	—
503	C₂²×D₄	—	2	1	no	—
504	C₂²×D₄	—	2	1	no	—
505	C₂²×D₄	—	2	1	no	—
506	C₂²×D₄	—	2	1	no	—
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	—	2	2	no	—
509	C₂²×D₄	—	4	2	no	—
510	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
511	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
512	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
513	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
514	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
515	C₂³×C₄	—	2	1	no	—
516	C₂³×C₄	—	2	1	no	—
517	C₂³×C₄	—	2	1	no	—
518	C₂³×C₄	—	2	1	no	—
519	C₂³×C₄	—	2	1	no	—
520	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
522	C₂×SD₁₆	—	4	2	no	—
523	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
524	C₂×D₈	—	2	4	no	—
525	C₂×D₈	—	4	2	no	—
526	C₂×D₈	C₂³×C₁₃	1	4	yes	—
527	C₂×D₈	C₂³×C₁₃	1	4	yes	—
528	C₂×M₁₆	—	4	2	no	—
529	C₂×M₁₆	C₂³×C₁₃	1	4	yes	complemented
530	C₂²×C₈	—	4	2	no	—
531	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
532	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
533	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
534	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
535	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
536	C₄⋊Q₈	—	2	2	no	—
537	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
538	#124	—	2	2	no	—
539	#124	C₂³×C₁₃	1	4	yes	—
540	#123	—	2	8	no	—
541	#123	—	2	8	no	—
542	#123	—	2	8	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	2	8	no	—
545	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
546	#121	—	2	2	no	—
547	#121	—	2	2	no	—
548	#121	—	2	2	no	—
549	#121	—	2	8	no	—
550	#121	C₂³×C₁₃	1	4	yes	—
551	#121	C₂³×C₁₃	1	4	yes	—
552	#121	C₂³×C₁₃	1	4	yes	complemented
553	#120	—	2	8	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	D₄×C₁₃	1	4	yes	—
557	C₄×D₄	C₂³×C₁₃	1	4	yes	—
558	C₄×D₄	C₂³×C₁₃	1	4	yes	—
559	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	2	2	no	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	—	2	2	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
573	C₂×C₂²⋊C₄	—	2	1	no	—
574	C₂×C₂²⋊C₄	—	2	1	no	—
575	C₂×C₂²⋊C₄	—	2	1	no	—
576	C₂×C₂²⋊C₄	—	2	1	no	—
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	C₂×C₂²⋊C₄	—	2	1	no	—
579	C₂×C₂²⋊C₄	—	2	1	no	—
580	C₂×C₂²⋊C₄	—	2	1	no	—
581	C₂×C₂²⋊C₄	—	2	8	no	—
582	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
585	#106	C₂³×C₁₃	1	4	yes	complemented
586	#106	C₂³×C₁₃	1	4	yes	complemented
587	#106	C₂³×C₁₃	1	4	yes	complemented
588	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
589	#103	C₂³×C₁₃	1	4	yes	complemented
590	#103	C₂³×C₁₃	1	4	yes	complemented
591	#103	C₂³×C₁₃	1	4	yes	complemented
592	#102	C₂³×C₁₃	1	4	yes	—
593	#102	C₂³×C₁₃	1	4	yes	—
594	#102	C₂³×C₁₃	1	4	yes	—
595	#102	C₂³×C₁₃	1	4	yes	—
596	#102	C₂³×C₁₃	1	4	yes	—
597	#102	C₂³×C₁₃	1	4	yes	—
598	#102	C₂³×C₁₃	1	4	yes	complemented
599	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
600	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	complemented
601	#97	C₂³×C₁₃	1	4	yes	complemented
602	C₂×C₁₃	—	2	4	no	—
603	C₂×C₁₃	—	4	2	no	—
604	C₂×C₁₃	—	4	4	no	—
605	C₂×C₁₃	—	8	2	no	—
606	C₂×C₁₃	—	8	2	no	—
607	C₂×C₁₃	#3306	1	4	yes	direct product factor
608	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
609	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
610	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
611	C₂⁴	—	2	1	no	—
612	C₂⁴	—	2	1	no	—
613	C₂⁴	—	2	1	no	—
614	C₂⁴	—	2	4	no	—
615	C₂⁴	—	4	4	no	—
616	C₂⁴	—	4	4	no	—
617	C₂⁴	—	8	2	no	—
618	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
619	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
620	#41	—	2	8	no	—
621	#41	—	4	4	no	—
622	#41	—	4	8	no	—
623	#41	—	4	32	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	4	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	2	2	no	—
628	C₂×Q₈	—	4	4	no	—
629	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	8	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	2	no	—
641	C₂×D₄	—	2	2	no	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	4	4	no	—
646	C₂×D₄	—	4	8	no	—
647	C₂×D₄	—	4	4	no	—
648	C₂×D₄	—	4	4	no	—
649	C₂×D₄	—	4	4	no	—
650	C₂×D₄	—	4	4	no	—
651	C₂×D₄	—	8	2	no	—
652	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
653	C₂×D₄	C₁₃×#41	1	4	yes	complemented
654	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
655	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
656	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	4	4	no	—
672	C₂²×C₄	—	4	4	no	—
673	C₂²×C₄	—	4	4	no	—
674	C₂²×C₄	—	4	4	no	—
675	C₂²×C₄	—	8	2	no	—
676	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
677	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
681	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
685	SD₁₆	—	4	4	no	—
686	D₈	—	2	8	no	—
687	D₈	—	4	4	no	—
688	M₁₆	—	4	4	no	—
689	C₂×C₈	—	2	2	no	—
690	C₂×C₈	—	2	2	no	—
691	C₂×C₈	—	2	2	no	—
692	C₂×C₈	—	2	2	no	—
693	C₂×C₈	—	4	4	no	—
694	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
695	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
696	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
697	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
707	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
708	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
709	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
710	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
720	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
721	C₄²	C₂×D₄×C₁₃	1	2	yes	—
722	C₄²	C₂⁴×C₁₃	1	2	yes	—
723	C₁₃	C₂×#3306	1	1	yes	characteristic, direct product factor, Sylow
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	4	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	4	8	no	—
734	C₂³	—	4	2	no	—
735	C₂³	—	4	2	no	—
736	C₂³	—	4	2	no	—
737	C₂³	—	4	2	no	—
738	C₂³	—	4	2	no	—
739	C₂³	—	4	8	no	—
740	C₂³	—	4	2	no	—
741	C₂³	—	4	2	no	—
742	C₂³	—	4	2	no	—
743	C₂³	—	8	4	no	—
744	C₂³	—	8	16	no	—
745	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
746	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
747	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
748	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
749	Q₈	—	2	2	no	—
750	Q₈	—	2	2	no	—
751	Q₈	—	4	8	no	—
752	Q₈	—	4	2	no	—
753	D₄	—	2	8	no	—
754	D₄	—	2	4	no	—
755	D₄	—	2	2	no	—
756	D₄	—	2	2	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	2	no	—
759	D₄	—	2	2	no	—
760	D₄	—	4	8	no	—
761	D₄	—	4	8	no	—
762	D₄	—	4	8	no	—
763	D₄	—	4	8	no	—
764	D₄	—	4	2	no	—
765	D₄	—	4	2	no	—
766	D₄	—	8	4	no	—
767	D₄	C₂×C₁₃×#41	1	4	yes	complemented
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	4	8	no	—
784	C₂×C₄	—	4	8	no	—
785	C₂×C₄	—	4	8	no	—
786	C₂×C₄	—	4	2	no	—
787	C₂×C₄	—	4	2	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	2	no	—
790	C₂×C₄	—	4	8	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	—	8	4	no	—
793	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
795	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
796	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
797	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
798	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
799	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
800	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
801	C₈	—	2	2	no	—
802	C₈	—	2	2	no	—
803	C₈	—	2	2	no	—
804	C₈	—	2	2	no	—
805	C₂²	—	2	8	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	2	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	4	no	—
812	C₂²	—	4	4	no	—
813	C₂²	—	4	8	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	8	16	no	—
823	C₂²	—	8	4	no	—
824	C₂²	—	8	4	no	—
825	C₂²	C₁₃×#546	1	2	yes	—
826	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
827	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
828	C₂²	C₁₃×#577	1	2	yes	—
829	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
830	C₄	—	2	2	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	2	no	—
833	C₄	—	2	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	C₁₃×#546	1	2	yes	—
840	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
841	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
842	C₂	—	2	4	no	—
843	C₂	—	4	2	no	—
844	C₂	—	4	4	no	—
845	C₂	—	8	2	no	—
846	C₂	—	8	2	no	—
847	C₂	C₁₃×#3306	1	4	yes	direct product factor
848	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
849	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
850	C₂	C₂×C₁₃×#577	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×#547	C₂	semidirect
2. C₂×C₁₃×#546	C₂	semidirect
3. C₁₃×#3306	C₂	direct (N × H)
4. C₂×C₁₃×#489	C₂	semidirect
5. C₂×C₁₃×#481	C₂	semidirect
6. C₂×C₁₃×#483	C₂	semidirect
7. C₂×C₁₃×#476	C₂	semidirect
8. C₂×C₁₃×#469	C₂	semidirect
9. C₂×C₁₃×#465	C₂	semidirect
10. C₂×C₁₃×#463	C₂	semidirect
11. C₂×C₁₃×#449	C₂	semidirect
12. C₂×C₁₃×#447	C₂	semidirect
13. C₂×C₁₃×#442	C₂	semidirect
14. C₂×C₁₃×#435	C₂	semidirect
15. C₂×C₁₃×#417	C₂	semidirect
16. C₂²×C₁₃×#102	C₂	semidirect
20. C₂²×C₁₃×SD₁₆	C₂²	semidirect
23. C₂²×C₁₃×M₁₆	C₂²	semidirect
26. C₁₃×#547	C₂²	semidirect
28. C₁₃×#546	C₂²	semidirect
29. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₁₃×#121	C₂²	semidirect
43. C₂×C₄×D₄×C₁₃	C₂²	semidirect
45. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
47. C₁₃×#489	C₂²	semidirect
48. C₁₃×#483	C₂²	semidirect
49. C₁₃×#481	C₂²	semidirect
50. C₁₃×#476	C₂²	semidirect
51. C₁₃×#469	C₂²	semidirect
52. C₁₃×#465	C₂²	semidirect
53. C₁₃×#463	C₂²	semidirect
54. C₁₃×#449	C₂²	semidirect
55. C₁₃×#447	C₂²	semidirect
56. C₁₃×#442	C₂²	semidirect
57. C₁₃×#435	C₂²	semidirect
58. C₂×C₁₃×#106	C₂²	semidirect
59. C₂×C₁₃×#106	C₂²	semidirect
60. C₂×C₁₃×#106	C₂²	semidirect
61. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
62. C₁₃×#417	C₂²	semidirect
63. C₂×C₁₃×#103	C₂²	semidirect
64. C₂×C₁₃×#103	C₂²	semidirect
65. C₂×C₁₃×#103	C₂²	semidirect
72. C₂×C₁₃×#102	C₂²	semidirect
73. C₂×C₁₃×#102	C₂²	semidirect
75. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
76. C₂×C₁₃×#97	C₂²	semidirect
107. C₂×C₁₃×SD₁₆	C₂³	semidirect
113. C₂×C₁₃×M₁₆	C₂³	semidirect
121. C₁₃×C₄⋊Q₈	C₂³	semidirect
136. C₁₃×#121	C₂³	semidirect
143. C₄×D₄×C₁₃	C₂³	semidirect
156. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
169. C₁₃×#106	C₂³	semidirect
170. C₁₃×#106	C₂³	semidirect
171. C₁₃×#106	C₂³	semidirect
172. C₁₃×C₄⋊C₈	C₂³	semidirect
173. C₁₃×#103	C₂³	semidirect
174. C₁₃×#103	C₂³	semidirect
175. C₁₃×#103	C₂³	semidirect
182. C₁₃×#102	C₂³	semidirect
184. C₁₃×C₂²⋊C₈	C₂³	semidirect
185. C₁₃×#97	C₂³	semidirect
186. C₂×#3306	C₁₃	direct (N × H)
229. C₂×D₄×C₁₃	#41	semidirect
299. C₂×#547	C₂×C₁₃	semidirect
300. C₂×#546	C₂×C₁₃	semidirect
301. #3306	C₂×C₁₃	direct (N × H)
302. C₂×#489	C₂×C₁₃	semidirect
303. C₂×#481	C₂×C₁₃	semidirect
304. C₂×#483	C₂×C₁₃	semidirect
305. C₂×#476	C₂×C₁₃	semidirect
306. C₂×#469	C₂×C₁₃	semidirect
307. C₂×#465	C₂×C₁₃	semidirect
308. C₂×#463	C₂×C₁₃	semidirect
309. C₂×#449	C₂×C₁₃	semidirect
310. C₂×#447	C₂×C₁₃	semidirect
311. C₂×#442	C₂×C₁₃	semidirect
312. C₂×#435	C₂×C₁₃	semidirect
313. C₂×#417	C₂×C₁₃	semidirect
314. C₂²×#102	C₂×C₁₃	semidirect
358. D₄×C₁₃	C₂×#41	semidirect
399. C₂²×SD₁₆	C₂²×C₁₃	semidirect
402. C₂²×M₁₆	C₂²×C₁₃	semidirect
405. #547	C₂²×C₁₃	semidirect
407. #546	C₂²×C₁₃	semidirect
408. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
418. C₂×#121	C₂²×C₁₃	semidirect
422. C₂×C₄×D₄	C₂²×C₁₃	semidirect
424. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
426. #489	C₂²×C₁₃	semidirect
427. #483	C₂²×C₁₃	semidirect
428. #481	C₂²×C₁₃	semidirect
429. #476	C₂²×C₁₃	semidirect
430. #469	C₂²×C₁₃	semidirect
431. #465	C₂²×C₁₃	semidirect
432. #463	C₂²×C₁₃	semidirect
433. #449	C₂²×C₁₃	semidirect
434. #447	C₂²×C₁₃	semidirect
435. #442	C₂²×C₁₃	semidirect
436. #435	C₂²×C₁₃	semidirect
437. C₂×#106	C₂²×C₁₃	semidirect
438. C₂×#106	C₂²×C₁₃	semidirect
439. C₂×#106	C₂²×C₁₃	semidirect
440. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
441. #417	C₂²×C₁₃	semidirect
442. C₂×#103	C₂²×C₁₃	semidirect
443. C₂×#103	C₂²×C₁₃	semidirect
444. C₂×#103	C₂²×C₁₃	semidirect
451. C₂×#102	C₂²×C₁₃	semidirect
452. C₂×#102	C₂²×C₁₃	semidirect
454. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
455. C₂×#97	C₂²×C₁₃	semidirect
523. C₂×SD₁₆	C₂³×C₁₃	semidirect
529. C₂×M₁₆	C₂³×C₁₃	semidirect
537. C₄⋊Q₈	C₂³×C₁₃	semidirect
552. #121	C₂³×C₁₃	semidirect
559. C₄×D₄	C₂³×C₁₃	semidirect
572. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
585. #106	C₂³×C₁₃	semidirect
586. #106	C₂³×C₁₃	semidirect
587. #106	C₂³×C₁₃	semidirect
588. C₄⋊C₈	C₂³×C₁₃	semidirect
589. #103	C₂³×C₁₃	semidirect
590. #103	C₂³×C₁₃	semidirect
591. #103	C₂³×C₁₃	semidirect
598. #102	C₂³×C₁₃	semidirect
600. C₂²⋊C₈	C₂³×C₁₃	semidirect
601. #97	C₂³×C₁₃	semidirect
607. C₂×C₁₃	#3306	direct (N × H)
653. C₂×D₄	C₁₃×#41	semidirect
723. C₁₃	C₂×#3306	direct (N × H)
767. D₄	C₂×C₁₃×#41	semidirect
847. C₂	C₁₃×#3306	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×#547	2
C₂×C₁₃×#546	2
C₁₃×#3306	2
C₂×C₁₃×#489	2
C₂×C₁₃×#481	2
C₂×C₁₃×#483	2
C₂×C₁₃×#476	2
C₂×C₁₃×#469	2
C₂×C₁₃×#465	2
C₂×C₁₃×#463	2
C₂×C₁₃×#449	2
C₂×C₁₃×#447	2
C₂×C₁₃×#442	2
C₂×C₁₃×#435	2
C₂×C₁₃×#417	2
C₂²×C₁₃×#102	2
C₂×#3306	13

Subgroups — C2×C13×#3306 #15747464

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3306 #15747464