Subgroups — C₂×C₁₃×#3251 #15747240

Order 3328.

2178 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3251	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#478	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#469	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#468	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#463	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	—	2	1	no	—
14	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
16	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
17	C₁₃×#532	—	2	4	no	—
18	C₁₃×#532	C₂²	1	8	yes	complemented
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
21	C₁₃×#529	—	2	4	no	—
22	C₁₃×#529	C₂²	1	8	yes	complemented
23	C₂×C₁₃×#126	—	2	1	no	—
24	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#124	—	2	1	no	—
26	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#123	—	2	1	no	—
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#121	—	2	1	no	—
30	C₂×C₁₃×#121	C₂²	1	2	yes	—
31	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	—	2	1	no	—
34	C₂×C₄×D₄×C₁₃	—	2	1	no	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
37	C₂×C₁₃×#117	—	2	1	no	—
38	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#478	C₂²	1	16	yes	complemented
40	C₁₃×#475	C₂²	1	8	yes	complemented
41	C₁₃×#474	C₂²	1	8	yes	complemented
42	C₁₃×#469	C₂²	1	16	yes	complemented
43	C₁₃×#468	C₂²	1	16	yes	complemented
44	C₁₃×#463	C₂²	1	16	yes	complemented
45	C₁₃×#460	C₂²	1	8	yes	complemented
46	C₁₃×#459	C₂²	1	8	yes	complemented
47	C₂×C₁₃×#107	C₂²	1	2	yes	—
48	C₂×C₁₃×#106	C₂²	1	2	yes	—
49	C₁₃×#423	C₂²	1	8	yes	complemented
50	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
52	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#103	C₂²	1	2	yes	—
54	C₂×C₁₃×#102	C₂²	1	2	yes	—
55	C₂×C₁₃×#102	C₂²	1	2	yes	—
56	C₂×C₁₃×#102	C₂²	1	2	yes	—
57	C₂×C₁₃×#41	—	2	8	no	—
58	C₂×C₁₃×#41	—	4	8	no	—
59	C₂²×Q₈×C₁₃	—	2	1	no	—
60	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₁₃	—	2	1	no	—
62	C₂²×D₄×C₁₃	—	2	2	no	—
63	C₂²×D₄×C₁₃	—	2	1	no	—
64	C₂²×D₄×C₁₃	—	2	1	no	—
65	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃	—	2	1	no	—
68	C₂³×C₄×C₁₃	—	2	2	no	—
69	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×SD₁₆	—	4	4	no	—
73	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
74	C₂×C₁₃×D₈	—	4	4	no	—
75	C₂×C₁₃×D₈	C₂³	1	8	yes	—
76	C₂×C₁₃×M₁₆	—	4	4	no	—
77	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
78	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
79	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
80	C₁₃×C₄⋊Q₈	—	2	2	no	—
81	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
82	C₁₃×#127	—	2	2	no	—
83	C₁₃×#127	C₂³	1	4	yes	—
84	C₁₃×#126	—	2	8	no	—
85	C₁₃×#125	—	2	2	no	—
86	C₁₃×#125	C₂³	1	4	yes	—
87	C₁₃×#124	—	2	8	no	—
88	C₁₃×#124	—	2	2	no	—
89	C₁₃×#124	C₂³	1	4	yes	—
90	C₁₃×#123	—	2	8	no	—
91	C₁₃×C₂²⋊Q₈	—	2	2	no	—
92	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
93	C₁₃×#121	—	2	8	no	—
94	C₁₃×#121	—	2	2	no	—
95	C₁₃×#121	—	2	4	no	—
96	C₁₃×#121	C₂³	1	8	yes	—
97	C₁₃×#121	C₂³	1	4	yes	—
98	C₄×Q₈×C₁₃	—	2	2	no	—
99	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
100	C₄×D₄×C₁₃	—	2	8	no	—
101	C₄×D₄×C₁₃	—	2	8	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	—	2	4	no	—
104	C₄×D₄×C₁₃	C₂³	1	4	yes	—
105	C₄×D₄×C₁₃	C₂³	1	8	yes	—
106	C₁₃×#117	—	2	8	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₄²×C₁₃	—	2	1	no	—
123	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
124	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₁₃	D₄	1	4	yes	—
126	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
129	C₁₃×#107	C₂³	1	8	yes	—
130	C₁₃×#106	C₂³	1	8	yes	—
131	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
132	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
133	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
134	C₁₃×#103	C₂³	1	8	yes	—
135	C₁₃×#102	C₂³	1	8	yes	—
136	C₁₃×#102	C₂³	1	8	yes	—
137	C₁₃×#102	C₂³	1	8	yes	—
138	C₂×#3251	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂⁴×C₁₃	—	2	1	no	—
140	C₂⁴×C₁₃	—	2	2	no	—
141	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₁₃×#41	—	4	32	no	—
143	C₂×Q₈×C₁₃	—	2	1	no	—
144	C₂×Q₈×C₁₃	—	2	4	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	2	2	no	—
147	C₂×Q₈×C₁₃	—	4	4	no	—
148	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	8	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	2	4	no	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	2	2	no	—
156	C₂×D₄×C₁₃	—	2	4	no	—
157	C₂×D₄×C₁₃	—	2	2	no	—
158	C₂×D₄×C₁₃	—	2	4	no	—
159	C₂×D₄×C₁₃	—	4	4	no	—
160	C₂×D₄×C₁₃	—	4	4	no	—
161	C₂×D₄×C₁₃	—	4	8	no	—
162	C₂×D₄×C₁₃	—	4	4	no	—
163	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
164	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	2	no	—
167	C₂²×C₄×C₁₃	—	2	2	no	—
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	2	no	—
172	C₂²×C₄×C₁₃	—	2	4	no	—
173	C₂²×C₄×C₁₃	—	2	8	no	—
174	C₂²×C₄×C₁₃	—	4	2	no	—
175	C₂²×C₄×C₁₃	—	4	8	no	—
176	C₂²×C₄×C₁₃	—	4	4	no	—
177	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
179	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
184	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₁₃×SD₁₆	—	4	8	no	—
188	C₁₃×D₈	—	4	8	no	—
189	C₁₃×M₁₆	—	4	8	no	—
190	C₂×C₈×C₁₃	—	2	4	no	—
191	C₂×C₈×C₁₃	—	2	4	no	—
192	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
193	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
194	C₁₃×C₄⋊C₄	—	2	4	no	—
195	C₁₃×C₄⋊C₄	—	2	4	no	—
196	C₁₃×C₄⋊C₄	—	2	4	no	—
197	C₁₃×C₄⋊C₄	—	2	4	no	—
198	C₁₃×C₄⋊C₄	—	2	4	no	—
199	C₁₃×C₄⋊C₄	—	2	2	no	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
203	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
204	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
205	C₁₃×C₂²⋊C₄	—	2	4	no	—
206	C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₁₃×C₂²⋊C₄	—	2	4	no	—
208	C₁₃×C₂²⋊C₄	—	2	8	no	—
209	C₁₃×C₂²⋊C₄	—	2	4	no	—
210	C₁₃×C₂²⋊C₄	—	2	8	no	—
211	C₁₃×C₂²⋊C₄	—	2	4	no	—
212	C₄²×C₁₃	—	2	4	no	—
213	C₄²×C₁₃	C₂×D₄	1	4	yes	—
214	C₄²×C₁₃	C₂×D₄	1	2	yes	—
215	C₄²×C₁₃	C₂×D₄	1	4	yes	—
216	C₄²×C₁₃	C₂×D₄	1	2	yes	—
217	C₄²×C₁₃	C₂⁴	1	2	yes	—
218	C₄²×C₁₃	C₂⁴	1	2	yes	—
219	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
220	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#3251	C₂×C₁₃	1	16	yes	direct product factor
222	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂×#478	C₂×C₁₃	1	2	yes	complemented
224	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
225	C₂×#469	C₂×C₁₃	1	2	yes	complemented
226	C₂×#468	C₂×C₁₃	1	2	yes	complemented
227	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
228	C₂×#463	C₂×C₁₃	1	2	yes	complemented
229	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
230	C₂×#423	C₂×C₁₃	1	1	yes	characteristic, complemented
231	C₂³×C₁₃	—	2	2	no	—
232	C₂³×C₁₃	—	2	2	no	—
233	C₂³×C₁₃	—	2	2	no	—
234	C₂³×C₁₃	—	2	2	no	—
235	C₂³×C₁₃	—	2	4	no	—
236	C₂³×C₁₃	—	4	2	no	—
237	C₂³×C₁₃	—	4	4	no	—
238	C₂³×C₁₃	—	4	4	no	—
239	C₂³×C₁₃	—	4	2	no	—
240	C₂³×C₁₃	—	4	4	no	—
241	C₂³×C₁₃	—	4	2	no	—
242	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
243	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
244	Q₈×C₁₃	—	2	2	no	—
245	Q₈×C₁₃	—	2	2	no	—
246	Q₈×C₁₃	—	4	2	no	—
247	Q₈×C₁₃	—	4	8	no	—
248	D₄×C₁₃	—	2	2	no	—
249	D₄×C₁₃	—	2	4	no	—
250	D₄×C₁₃	—	2	2	no	—
251	D₄×C₁₃	—	2	4	no	—
252	D₄×C₁₃	—	4	8	no	—
253	D₄×C₁₃	—	4	8	no	—
254	D₄×C₁₃	—	4	16	no	—
255	D₄×C₁₃	—	4	2	no	—
256	D₄×C₁₃	—	4	4	no	—
257	D₄×C₁₃	—	4	8	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	2	4	no	—
263	C₂×C₄×C₁₃	—	2	8	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	2	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	4	no	—
270	C₂×C₄×C₁₃	—	4	4	no	—
271	C₂×C₄×C₁₃	—	4	16	no	—
272	C₂×C₄×C₁₃	—	4	2	no	—
273	C₂×C₄×C₁₃	—	4	2	no	—
274	C₂×C₄×C₁₃	—	4	4	no	—
275	C₂×C₄×C₁₃	—	4	2	no	—
276	C₂×C₄×C₁₃	—	4	8	no	—
277	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
278	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
279	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
281	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
282	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
284	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
285	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
286	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
287	C₈×C₁₃	—	2	4	no	—
288	C₈×C₁₃	—	2	4	no	—
289	C₂²×#41	—	2	1	no	—
290	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
291	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
292	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
293	#532	—	2	4	no	—
294	#532	C₂²×C₁₃	1	8	yes	complemented
295	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
297	#529	—	2	4	no	—
298	#529	C₂²×C₁₃	1	8	yes	complemented
299	C₂×#126	—	2	1	no	—
300	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#124	—	2	1	no	—
302	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×#123	—	2	1	no	—
304	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#121	—	2	1	no	—
306	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×#121	C₂²×C₁₃	1	2	yes	—
308	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×C₄×D₄	—	2	1	no	—
310	C₂×C₄×D₄	—	2	1	no	—
311	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
312	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×#117	—	2	1	no	—
314	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
315	#478	C₂²×C₁₃	1	16	yes	complemented
316	#475	C₂²×C₁₃	1	8	yes	complemented
317	#474	C₂²×C₁₃	1	8	yes	complemented
318	#469	C₂²×C₁₃	1	16	yes	complemented
319	#468	C₂²×C₁₃	1	16	yes	complemented
320	#463	C₂²×C₁₃	1	16	yes	complemented
321	#460	C₂²×C₁₃	1	8	yes	complemented
322	#459	C₂²×C₁₃	1	8	yes	complemented
323	C₂×#107	C₂²×C₁₃	1	2	yes	—
324	C₂×#106	C₂²×C₁₃	1	2	yes	—
325	#423	C₂²×C₁₃	1	8	yes	complemented
326	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
327	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×#103	C₂²×C₁₃	1	2	yes	—
330	C₂×#102	C₂²×C₁₃	1	2	yes	—
331	C₂×#102	C₂²×C₁₃	1	2	yes	—
332	C₂×#102	C₂²×C₁₃	1	2	yes	—
333	C₂²×C₁₃	—	2	2	no	—
334	C₂²×C₁₃	—	2	2	no	—
335	C₂²×C₁₃	—	2	2	no	—
336	C₂²×C₁₃	—	4	4	no	—
337	C₂²×C₁₃	—	4	2	no	—
338	C₂²×C₁₃	—	4	4	no	—
339	C₂²×C₁₃	—	4	4	no	—
340	C₂²×C₁₃	—	4	2	no	—
341	C₂²×C₁₃	—	4	4	no	—
342	C₂²×C₁₃	—	4	2	no	—
343	C₂²×C₁₃	—	8	8	no	—
344	C₂²×C₁₃	—	8	4	no	—
345	C₂²×C₁₃	#537	1	2	yes	—
346	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
347	C₂²×C₁₃	#575	1	2	yes	—
348	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
349	C₄×C₁₃	—	2	2	no	—
350	C₄×C₁₃	—	2	2	no	—
351	C₄×C₁₃	—	2	2	no	—
352	C₄×C₁₃	—	2	2	no	—
353	C₄×C₁₃	—	4	2	no	—
354	C₄×C₁₃	—	4	2	no	—
355	C₄×C₁₃	—	4	4	no	—
356	C₄×C₁₃	—	4	2	no	—
357	C₄×C₁₃	#537	1	2	yes	—
358	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
359	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
360	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
361	C₂×#41	—	2	8	no	—
362	C₂×#41	—	4	8	no	—
363	C₂²×Q₈	—	2	1	no	—
364	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
365	C₂²×D₄	—	2	1	no	—
366	C₂²×D₄	—	2	2	no	—
367	C₂²×D₄	—	2	1	no	—
368	C₂²×D₄	—	2	1	no	—
369	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
370	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	—	2	2	no	—
373	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
374	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
375	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
376	C₂×SD₁₆	—	4	4	no	—
377	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
378	C₂×D₈	—	4	4	no	—
379	C₂×D₈	C₂³×C₁₃	1	8	yes	—
380	C₂×M₁₆	—	4	4	no	—
381	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
382	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
383	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
384	C₄⋊Q₈	—	2	2	no	—
385	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
386	#127	—	2	2	no	—
387	#127	C₂³×C₁₃	1	4	yes	—
388	#126	—	2	8	no	—
389	#125	—	2	2	no	—
390	#125	C₂³×C₁₃	1	4	yes	—
391	#124	—	2	8	no	—
392	#124	—	2	2	no	—
393	#124	C₂³×C₁₃	1	4	yes	—
394	#123	—	2	8	no	—
395	C₂²⋊Q₈	—	2	2	no	—
396	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
397	#121	—	2	8	no	—
398	#121	—	2	2	no	—
399	#121	—	2	4	no	—
400	#121	C₂³×C₁₃	1	4	yes	—
401	#121	C₂³×C₁₃	1	8	yes	—
402	C₄×Q₈	—	2	2	no	—
403	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
404	C₄×D₄	—	2	8	no	—
405	C₄×D₄	—	2	8	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	4	no	—
408	C₄×D₄	C₂³×C₁₃	1	4	yes	—
409	C₄×D₄	C₂³×C₁₃	1	8	yes	—
410	#117	—	2	8	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	2	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	2	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
428	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
429	C₂×C₄²	D₄×C₁₃	1	4	yes	—
430	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
433	#107	C₂³×C₁₃	1	8	yes	—
434	#106	C₂³×C₁₃	1	8	yes	—
435	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
436	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
437	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
438	#103	C₂³×C₁₃	1	8	yes	—
439	#102	C₂³×C₁₃	1	8	yes	—
440	#102	C₂³×C₁₃	1	8	yes	—
441	#102	C₂³×C₁₃	1	8	yes	—
442	C₂×C₁₃	—	4	2	no	—
443	C₂×C₁₃	—	8	4	no	—
444	C₂×C₁₃	—	8	2	no	—
445	C₂×C₁₃	#3251	1	4	yes	direct product factor
446	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
447	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
448	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
449	C₂⁴	—	2	1	no	—
450	C₂⁴	—	2	2	no	—
451	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
452	#41	—	4	32	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	4	no	—
455	C₂×Q₈	—	2	2	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	—	4	4	no	—
458	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
459	C₂×D₄	—	2	4	no	—
460	C₂×D₄	—	2	8	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	4	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	4	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	—	4	4	no	—
470	C₂×D₄	—	4	8	no	—
471	C₂×D₄	—	4	4	no	—
472	C₂×D₄	—	4	4	no	—
473	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
474	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	8	no	—
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	—	4	8	no	—
486	C₂²×C₄	—	4	4	no	—
487	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
489	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
491	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
493	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
494	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
495	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
497	SD₁₆	—	4	8	no	—
498	D₈	—	4	8	no	—
499	M₁₆	—	4	8	no	—
500	C₂×C₈	—	2	4	no	—
501	C₂×C₈	—	2	4	no	—
502	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
503	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	4	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	4	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
513	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
514	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
515	C₂²⋊C₄	—	2	4	no	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	2	4	no	—
518	C₂²⋊C₄	—	2	8	no	—
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	—	2	8	no	—
521	C₂²⋊C₄	—	2	4	no	—
522	C₄²	—	2	4	no	—
523	C₄²	C₂×D₄×C₁₃	1	4	yes	—
524	C₄²	C₂×D₄×C₁₃	1	2	yes	—
525	C₄²	C₂×D₄×C₁₃	1	4	yes	—
526	C₄²	C₂×D₄×C₁₃	1	2	yes	—
527	C₄²	C₂⁴×C₁₃	1	2	yes	—
528	C₄²	C₂⁴×C₁₃	1	2	yes	—
529	C₁₃	C₂×#3251	1	1	yes	characteristic, direct product factor, Sylow
530	C₂³	—	2	2	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	4	no	—
535	C₂³	—	4	2	no	—
536	C₂³	—	4	4	no	—
537	C₂³	—	4	4	no	—
538	C₂³	—	4	2	no	—
539	C₂³	—	4	4	no	—
540	C₂³	—	4	2	no	—
541	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
542	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
543	Q₈	—	2	2	no	—
544	Q₈	—	2	2	no	—
545	Q₈	—	4	2	no	—
546	Q₈	—	4	8	no	—
547	D₄	—	2	2	no	—
548	D₄	—	2	4	no	—
549	D₄	—	2	2	no	—
550	D₄	—	2	4	no	—
551	D₄	—	4	8	no	—
552	D₄	—	4	8	no	—
553	D₄	—	4	16	no	—
554	D₄	—	4	2	no	—
555	D₄	—	4	4	no	—
556	D₄	—	4	8	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	8	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	4	4	no	—
570	C₂×C₄	—	4	16	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	4	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	8	no	—
576	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
577	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
578	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
579	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
580	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
581	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
582	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
583	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
584	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
585	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
586	C₈	—	2	4	no	—
587	C₈	—	2	4	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	4	4	no	—
592	C₂²	—	4	4	no	—
593	C₂²	—	4	2	no	—
594	C₂²	—	4	4	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	4	no	—
598	C₂²	—	8	8	no	—
599	C₂²	—	8	4	no	—
600	C₂²	C₁₃×#537	1	2	yes	—
601	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
602	C₂²	C₁₃×#575	1	2	yes	—
603	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	4	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	2	no	—
612	C₄	C₁₃×#537	1	2	yes	—
613	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
614	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
615	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
616	C₂	—	4	2	no	—
617	C₂	—	8	4	no	—
618	C₂	—	8	2	no	—
619	C₂	C₁₃×#3251	1	4	yes	direct product factor
620	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
621	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
622	C₂	C₂×C₁₃×#575	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 ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#532	C₂	semidirect
2. C₂×C₁₃×#529	C₂	semidirect
3. C₁₃×#3251	C₂	direct (N × H)
4. C₂×C₁₃×#475	C₂	semidirect
5. C₂×C₁₃×#478	C₂	semidirect
6. C₂×C₁₃×#474	C₂	semidirect
7. C₂×C₁₃×#469	C₂	semidirect
8. C₂×C₁₃×#468	C₂	semidirect
9. C₂×C₁₃×#460	C₂	semidirect
10. C₂×C₁₃×#463	C₂	semidirect
11. C₂×C₁₃×#459	C₂	semidirect
12. C₂×C₁₃×#423	C₂	semidirect
18. C₁₃×#532	C₂²	semidirect
22. C₁₃×#529	C₂²	semidirect
39. C₁₃×#478	C₂²	semidirect
40. C₁₃×#475	C₂²	semidirect
41. C₁₃×#474	C₂²	semidirect
42. C₁₃×#469	C₂²	semidirect
43. C₁₃×#468	C₂²	semidirect
44. C₁₃×#463	C₂²	semidirect
45. C₁₃×#460	C₂²	semidirect
46. C₁₃×#459	C₂²	semidirect
49. C₁₃×#423	C₂²	semidirect
138. C₂×#3251	C₁₃	direct (N × H)
219. C₂×#532	C₂×C₁₃	semidirect
220. C₂×#529	C₂×C₁₃	semidirect
221. #3251	C₂×C₁₃	direct (N × H)
222. C₂×#475	C₂×C₁₃	semidirect
223. C₂×#478	C₂×C₁₃	semidirect
224. C₂×#474	C₂×C₁₃	semidirect
225. C₂×#469	C₂×C₁₃	semidirect
226. C₂×#468	C₂×C₁₃	semidirect
227. C₂×#460	C₂×C₁₃	semidirect
228. C₂×#463	C₂×C₁₃	semidirect
229. C₂×#459	C₂×C₁₃	semidirect
230. C₂×#423	C₂×C₁₃	semidirect
294. #532	C₂²×C₁₃	semidirect
298. #529	C₂²×C₁₃	semidirect
315. #478	C₂²×C₁₃	semidirect
316. #475	C₂²×C₁₃	semidirect
317. #474	C₂²×C₁₃	semidirect
318. #469	C₂²×C₁₃	semidirect
319. #468	C₂²×C₁₃	semidirect
320. #463	C₂²×C₁₃	semidirect
321. #460	C₂²×C₁₃	semidirect
322. #459	C₂²×C₁₃	semidirect
325. #423	C₂²×C₁₃	semidirect
445. C₂×C₁₃	#3251	direct (N × H)
529. C₁₃	C₂×#3251	direct (N × H)
619. C₂	C₁₃×#3251	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×#532	2
C₂×C₁₃×#529	2
C₁₃×#3251	2
C₂×C₁₃×#475	2
C₂×C₁₃×#478	2
C₂×C₁₃×#474	2
C₂×C₁₃×#469	2
C₂×C₁₃×#468	2
C₂×C₁₃×#460	2
C₂×C₁₃×#463	2
C₂×C₁₃×#459	2
C₂×C₁₃×#423	2
C₂×#3251	13

Subgroups — C2×C13×#3251 #15747240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3251 #15747240