Subgroups — C₂×C₁₃×#3172 #15747014

Order 3328.

1986 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3172	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#491	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#470	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#468	C₂	1	2	yes	maximal
10	C₂×C₄×C₁₃×Q₁₆	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
16	C₁₃×#533	—	2	4	no	—
17	C₁₃×#533	C₂²	1	8	yes	complemented
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₃×#529	—	2	4	no	—
21	C₁₃×#529	C₂²	1	8	yes	—
22	C₂×C₁₃×#126	—	2	1	no	—
23	C₂×C₁₃×#125	—	2	1	no	—
24	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#123	—	2	1	no	—
27	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃	—	2	1	no	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#117	—	2	1	no	—
37	C₂×C₁₃×#117	—	2	1	no	—
38	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#501	C₂²	1	8	yes	complemented
40	C₁₃×#497	C₂²	1	8	yes	complemented
41	C₁₃×#491	C₂²	1	8	yes	complemented
42	C₁₃×#489	C₂²	1	8	yes	complemented
43	C₁₃×#470	C₂²	1	16	yes	complemented
44	C₁₃×#468	C₂²	1	16	yes	—
45	C₄×C₁₃×Q₁₆	C₂²	1	16	yes	complemented
46	C₄×C₁₃×SD₁₆	C₂²	1	16	yes	complemented
47	C₂×C₁₃×#107	C₂²	1	2	yes	—
48	C₂×C₁₃×#106	C₂²	1	2	yes	—
49	C₂×C₁₃×#103	C₂²	1	2	yes	—
50	C₂×C₁₃×#103	C₂²	1	2	yes	—
51	C₂×C₁₃×#103	C₂²	1	2	yes	—
52	C₂×C₁₃×#102	C₂²	1	2	yes	—
53	C₄×C₁₃×M₁₆	C₂²	1	8	yes	complemented
54	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
57	C₂²×Q₈×C₁₃	—	2	1	no	—
58	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₃	—	2	1	no	—
61	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	—	2	1	no	—
63	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×Q₁₆	—	2	8	no	—
67	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
68	C₂×C₁₃×SD₁₆	—	2	8	no	—
69	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
70	C₂×C₁₃×M₁₆	—	2	8	no	—
71	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
72	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
73	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
74	C₁₃×C₄⋊Q₈	—	2	2	no	—
75	C₁₃×C₄⋊Q₈	—	2	2	no	—
76	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
77	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
78	C₁₃×#126	—	2	8	no	—
79	C₁₃×#125	—	2	8	no	—
80	C₁₃×#125	—	2	2	no	—
81	C₁₃×#125	C₂³	1	4	yes	—
82	C₁₃×#124	—	2	2	no	—
83	C₁₃×#124	C₂³	1	4	yes	—
84	C₁₃×#123	—	2	8	no	—
85	C₁₃×C₂²⋊Q₈	—	2	8	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	—	2	4	no	—
88	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
89	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
90	C₁₃×#121	—	2	2	no	—
91	C₁₃×#121	C₂³	1	4	yes	—
92	C₄×Q₈×C₁₃	—	2	8	no	—
93	C₄×Q₈×C₁₃	—	2	2	no	—
94	C₄×Q₈×C₁₃	—	2	4	no	—
95	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
96	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
97	C₄×D₄×C₁₃	—	2	8	no	—
98	C₄×D₄×C₁₃	—	2	2	no	—
99	C₄×D₄×C₁₃	C₂³	1	4	yes	—
100	C₁₃×#117	—	2	8	no	—
101	C₁₃×#117	—	2	8	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
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	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₄²×C₁₃	—	2	1	no	—
121	C₂×C₄²×C₁₃	—	2	2	no	—
122	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₁₃	D₄	1	4	yes	—
124	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₁₃×#107	C₂³	1	8	yes	—
129	C₁₃×#106	C₂³	1	8	yes	—
130	C₁₃×#103	C₂³	1	8	yes	—
131	C₁₃×#103	C₂³	1	8	yes	—
132	C₁₃×#103	C₂³	1	8	yes	—
133	C₁₃×#102	C₂³	1	8	yes	—
134	C₁₃×#97	C₂³	1	4	yes	—
135	C₁₃×#97	C₂³	1	4	yes	—
136	C₄×C₈×C₁₃	C₂³	1	8	yes	—
137	C₂×#3172	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂⁴×C₁₃	—	2	1	no	—
139	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×Q₈×C₁₃	—	2	1	no	—
141	C₂×Q₈×C₁₃	—	2	2	no	—
142	C₂×Q₈×C₁₃	—	2	4	no	—
143	C₂×Q₈×C₁₃	—	2	4	no	—
144	C₂×Q₈×C₁₃	—	2	4	no	—
145	C₂×Q₈×C₁₃	—	2	4	no	—
146	C₂×Q₈×C₁₃	—	4	4	no	—
147	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
148	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	4	no	—
152	C₂×D₄×C₁₃	—	4	4	no	—
153	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	2	4	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	2	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	4	no	—
162	C₂²×C₄×C₁₃	—	4	2	no	—
163	C₂²×C₄×C₁₃	—	4	4	no	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₁₃×Q₁₆	—	2	16	no	—
175	C₁₃×SD₁₆	—	2	16	no	—
176	C₁₃×M₁₆	—	2	16	no	—
177	C₂×C₈×C₁₃	—	2	4	no	—
178	C₂×C₈×C₁₃	#41	1	8	yes	—
179	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
180	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
181	C₁₃×C₄⋊C₄	—	2	4	no	—
182	C₁₃×C₄⋊C₄	—	2	4	no	—
183	C₁₃×C₄⋊C₄	—	2	4	no	—
184	C₁₃×C₄⋊C₄	—	2	4	no	—
185	C₁₃×C₄⋊C₄	—	2	4	no	—
186	C₁₃×C₄⋊C₄	—	2	4	no	—
187	C₁₃×C₄⋊C₄	—	2	8	no	—
188	C₁₃×C₄⋊C₄	—	2	8	no	—
189	C₁₃×C₄⋊C₄	—	2	4	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
194	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
195	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
196	C₁₃×C₂²⋊C₄	—	2	8	no	—
197	C₁₃×C₂²⋊C₄	—	2	4	no	—
198	C₁₃×C₂²⋊C₄	—	2	4	no	—
199	C₁₃×C₂²⋊C₄	—	2	4	no	—
200	C₁₃×C₂²⋊C₄	—	2	4	no	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₄²×C₁₃	—	2	4	no	—
203	C₄²×C₁₃	—	2	8	no	—
204	C₄²×C₁₃	C₂×D₄	1	4	yes	—
205	C₄²×C₁₃	C₂×D₄	1	2	yes	—
206	C₄²×C₁₃	C₂×D₄	1	2	yes	—
207	C₄²×C₁₃	C₂×D₄	1	4	yes	—
208	C₄²×C₁₃	C₂⁴	1	2	yes	—
209	C₄²×C₁₃	C₂⁴	1	2	yes	—
210	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
211	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
212	#3172	C₂×C₁₃	1	16	yes	direct product factor
213	C₂×#501	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂×#497	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₂×#491	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂×#489	C₂×C₁₃	1	1	yes	characteristic, complemented
217	C₂×#470	C₂×C₁₃	1	2	yes	complemented
218	C₂×#468	C₂×C₁₃	1	2	yes	—
219	C₂×C₄×Q₁₆	C₂×C₁₃	1	2	yes	complemented
220	C₂×C₄×SD₁₆	C₂×C₁₃	1	2	yes	complemented
221	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
222	C₂³×C₁₃	—	2	2	no	—
223	C₂³×C₁₃	—	2	2	no	—
224	C₂³×C₁₃	—	2	2	no	—
225	C₂³×C₁₃	—	2	2	no	—
226	C₂³×C₁₃	—	4	2	no	—
227	C₂³×C₁₃	—	4	2	no	—
228	C₂³×C₁₃	—	4	2	no	—
229	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
230	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	Q₈×C₁₃	—	2	4	no	—
232	Q₈×C₁₃	—	2	4	no	—
233	Q₈×C₁₃	—	2	4	no	—
234	Q₈×C₁₃	—	4	8	no	—
235	Q₈×C₁₃	—	4	2	no	—
236	Q₈×C₁₃	—	4	4	no	—
237	D₄×C₁₃	—	2	4	no	—
238	D₄×C₁₃	—	4	8	no	—
239	D₄×C₁₃	—	4	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	4	no	—
245	C₂×C₄×C₁₃	—	2	8	no	—
246	C₂×C₄×C₁₃	—	2	4	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	4	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	4	4	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
254	C₂×C₄×C₁₃	—	4	4	no	—
255	C₂×C₄×C₁₃	—	4	2	no	—
256	C₂×C₄×C₁₃	—	4	2	no	—
257	C₂×C₄×C₁₃	—	4	4	no	—
258	C₂×C₄×C₁₃	—	4	8	no	—
259	C₂×C₄×C₁₃	#137	1	4	yes	—
260	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
266	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
267	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
268	C₈×C₁₃	—	2	4	no	—
269	C₈×C₁₃	C₂×#41	1	8	yes	—
270	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
271	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
272	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
273	#533	—	2	4	no	—
274	#533	C₂²×C₁₃	1	8	yes	complemented
275	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
277	#529	—	2	4	no	—
278	#529	C₂²×C₁₃	1	8	yes	—
279	C₂×#126	—	2	1	no	—
280	C₂×#125	—	2	1	no	—
281	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×#123	—	2	1	no	—
284	C₂×C₂²⋊Q₈	—	2	1	no	—
285	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
287	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×C₄×Q₈	—	2	1	no	—
289	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
291	C₂×C₄×D₄	—	2	1	no	—
292	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×#117	—	2	1	no	—
294	C₂×#117	—	2	1	no	—
295	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
296	#501	C₂²×C₁₃	1	8	yes	complemented
297	#497	C₂²×C₁₃	1	8	yes	complemented
298	#491	C₂²×C₁₃	1	8	yes	complemented
299	#489	C₂²×C₁₃	1	8	yes	complemented
300	#470	C₂²×C₁₃	1	16	yes	complemented
301	#468	C₂²×C₁₃	1	16	yes	—
302	C₄×Q₁₆	C₂²×C₁₃	1	16	yes	complemented
303	C₄×SD₁₆	C₂²×C₁₃	1	16	yes	complemented
304	C₂×#107	C₂²×C₁₃	1	2	yes	—
305	C₂×#106	C₂²×C₁₃	1	2	yes	—
306	C₂×#103	C₂²×C₁₃	1	2	yes	—
307	C₂×#103	C₂²×C₁₃	1	2	yes	—
308	C₂×#103	C₂²×C₁₃	1	2	yes	—
309	C₂×#102	C₂²×C₁₃	1	2	yes	—
310	C₄×M₁₆	C₂²×C₁₃	1	8	yes	complemented
311	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
314	C₂²×C₁₃	—	2	2	no	—
315	C₂²×C₁₃	—	2	2	no	—
316	C₂²×C₁₃	—	2	2	no	—
317	C₂²×C₁₃	—	4	4	no	—
318	C₂²×C₁₃	—	4	2	no	—
319	C₂²×C₁₃	—	4	2	no	—
320	C₂²×C₁₃	—	4	2	no	—
321	C₂²×C₁₃	—	8	4	no	—
322	C₂²×C₁₃	#532	1	2	yes	—
323	C₂²×C₁₃	C₂×#137	1	2	yes	—
324	C₂²×C₁₃	#575	1	2	yes	—
325	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
326	C₄×C₁₃	—	2	2	no	—
327	C₄×C₁₃	—	2	2	no	—
328	C₄×C₁₃	—	2	2	no	—
329	C₄×C₁₃	—	2	2	no	—
330	C₄×C₁₃	—	4	2	no	—
331	C₄×C₁₃	—	4	4	no	—
332	C₄×C₁₃	—	4	2	no	—
333	C₄×C₁₃	—	4	2	no	—
334	C₄×C₁₃	—	4	4	no	—
335	C₄×C₁₃	#532	1	2	yes	—
336	C₄×C₁₃	C₂×#137	1	4	yes	—
337	C₄×C₁₃	C₂²×#41	1	2	yes	—
338	C₂²×Q₈	—	2	1	no	—
339	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
340	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
343	C₂³×C₄	—	2	1	no	—
344	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
345	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₂×Q₁₆	—	2	8	no	—
348	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
349	C₂×SD₁₆	—	2	8	no	—
350	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
351	C₂×M₁₆	—	2	8	no	—
352	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
353	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
354	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
355	C₄⋊Q₈	—	2	2	no	—
356	C₄⋊Q₈	—	2	2	no	—
357	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
358	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
359	#126	—	2	8	no	—
360	#125	—	2	8	no	—
361	#125	—	2	2	no	—
362	#125	C₂³×C₁₃	1	4	yes	—
363	#124	—	2	2	no	—
364	#124	C₂³×C₁₃	1	4	yes	—
365	#123	—	2	8	no	—
366	C₂²⋊Q₈	—	2	8	no	—
367	C₂²⋊Q₈	—	2	2	no	—
368	C₂²⋊Q₈	—	2	4	no	—
369	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
370	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
371	#121	—	2	2	no	—
372	#121	C₂³×C₁₃	1	4	yes	—
373	C₄×Q₈	—	2	8	no	—
374	C₄×Q₈	—	2	2	no	—
375	C₄×Q₈	—	2	4	no	—
376	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
377	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
378	C₄×D₄	—	2	8	no	—
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	C₂³×C₁₃	1	4	yes	—
381	#117	—	2	8	no	—
382	#117	—	2	8	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	2	no	—
390	C₂×C₄⋊C₄	—	2	2	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
395	C₂×C₂²⋊C₄	—	2	2	no	—
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₄²	—	2	1	no	—
402	C₂×C₄²	—	2	2	no	—
403	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
404	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
405	C₂×C₄²	D₄×C₁₃	1	4	yes	—
406	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
409	#107	C₂³×C₁₃	1	8	yes	—
410	#106	C₂³×C₁₃	1	8	yes	—
411	#103	C₂³×C₁₃	1	8	yes	—
412	#103	C₂³×C₁₃	1	8	yes	—
413	#103	C₂³×C₁₃	1	8	yes	—
414	#102	C₂³×C₁₃	1	8	yes	—
415	#97	C₂³×C₁₃	1	4	yes	—
416	#97	C₂³×C₁₃	1	4	yes	—
417	C₄×C₈	C₂³×C₁₃	1	8	yes	—
418	C₂×C₁₃	—	4	2	no	—
419	C₂×C₁₃	—	8	2	no	—
420	C₂×C₁₃	#3172	1	4	yes	direct product factor
421	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
422	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
423	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
424	C₂⁴	—	2	1	no	—
425	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	—	2	4	no	—
429	C₂×Q₈	—	2	4	no	—
430	C₂×Q₈	—	2	4	no	—
431	C₂×Q₈	—	2	4	no	—
432	C₂×Q₈	—	4	4	no	—
433	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
434	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	4	4	no	—
439	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	4	2	no	—
449	C₂²×C₄	—	4	4	no	—
450	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
452	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
456	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
457	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
458	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
460	Q₁₆	—	2	16	no	—
461	SD₁₆	—	2	16	no	—
462	M₁₆	—	2	16	no	—
463	C₂×C₈	—	2	4	no	—
464	C₂×C₈	C₁₃×#41	1	8	yes	—
465	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
466	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	4	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	8	no	—
474	C₄⋊C₄	—	2	8	no	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
480	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
481	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
482	C₂²⋊C₄	—	2	8	no	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	2	4	no	—
486	C₂²⋊C₄	—	2	4	no	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₄²	—	2	4	no	—
489	C₄²	—	2	8	no	—
490	C₄²	C₂×D₄×C₁₃	1	4	yes	—
491	C₄²	C₂×D₄×C₁₃	1	2	yes	—
492	C₄²	C₂×D₄×C₁₃	1	2	yes	—
493	C₄²	C₂×D₄×C₁₃	1	4	yes	—
494	C₄²	C₂⁴×C₁₃	1	2	yes	—
495	C₄²	C₂⁴×C₁₃	1	2	yes	—
496	C₁₃	C₂×#3172	1	1	yes	characteristic, direct product factor, Sylow
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
505	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
506	Q₈	—	2	4	no	—
507	Q₈	—	2	4	no	—
508	Q₈	—	2	4	no	—
509	Q₈	—	4	8	no	—
510	Q₈	—	4	2	no	—
511	Q₈	—	4	4	no	—
512	D₄	—	2	4	no	—
513	D₄	—	4	8	no	—
514	D₄	—	4	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	8	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	4	4	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	4	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	4	no	—
533	C₂×C₄	—	4	8	no	—
534	C₂×C₄	C₁₃×#137	1	4	yes	—
535	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
536	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
537	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
538	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
539	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
540	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
541	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
542	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
543	C₈	—	2	4	no	—
544	C₈	C₂×C₁₃×#41	1	8	yes	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	4	4	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	8	4	no	—
553	C₂²	C₁₃×#532	1	2	yes	—
554	C₂²	C₂×C₁₃×#137	1	2	yes	—
555	C₂²	C₁₃×#575	1	2	yes	—
556	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
557	C₄	—	2	2	no	—
558	C₄	—	2	2	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	2	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	4	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	4	no	—
566	C₄	C₁₃×#532	1	2	yes	—
567	C₄	C₂×C₁₃×#137	1	4	yes	—
568	C₄	C₂²×C₁₃×#41	1	2	yes	—
569	C₂	—	4	2	no	—
570	C₂	—	8	2	no	—
571	C₂	C₁₃×#3172	1	4	yes	direct product factor
572	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
573	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
574	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#533	C₂	semidirect
3. C₁₃×#3172	C₂	direct (N × H)
4. C₂×C₁₃×#501	C₂	semidirect
5. C₂×C₁₃×#497	C₂	semidirect
6. C₂×C₁₃×#491	C₂	semidirect
7. C₂×C₁₃×#489	C₂	semidirect
8. C₂×C₁₃×#470	C₂	semidirect
10. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
11. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
12. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
17. C₁₃×#533	C₂²	semidirect
39. C₁₃×#501	C₂²	semidirect
40. C₁₃×#497	C₂²	semidirect
41. C₁₃×#491	C₂²	semidirect
42. C₁₃×#489	C₂²	semidirect
43. C₁₃×#470	C₂²	semidirect
45. C₄×C₁₃×Q₁₆	C₂²	semidirect
46. C₄×C₁₃×SD₁₆	C₂²	semidirect
53. C₄×C₁₃×M₁₆	C₂²	semidirect
137. C₂×#3172	C₁₃	direct (N × H)
210. C₂×#533	C₂×C₁₃	semidirect
212. #3172	C₂×C₁₃	direct (N × H)
213. C₂×#501	C₂×C₁₃	semidirect
214. C₂×#497	C₂×C₁₃	semidirect
215. C₂×#491	C₂×C₁₃	semidirect
216. C₂×#489	C₂×C₁₃	semidirect
217. C₂×#470	C₂×C₁₃	semidirect
219. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
220. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
221. C₂×C₄×M₁₆	C₂×C₁₃	semidirect
274. #533	C₂²×C₁₃	semidirect
296. #501	C₂²×C₁₃	semidirect
297. #497	C₂²×C₁₃	semidirect
298. #491	C₂²×C₁₃	semidirect
299. #489	C₂²×C₁₃	semidirect
300. #470	C₂²×C₁₃	semidirect
302. C₄×Q₁₆	C₂²×C₁₃	semidirect
303. C₄×SD₁₆	C₂²×C₁₃	semidirect
310. C₄×M₁₆	C₂²×C₁₃	semidirect
420. C₂×C₁₃	#3172	direct (N × H)
496. C₁₃	C₂×#3172	direct (N × H)
571. C₂	C₁₃×#3172	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×#533	2
C₂×C₁₃×#529	2
C₁₃×#3172	2
C₂×C₁₃×#501	2
C₂×C₁₃×#497	2
C₂×C₁₃×#491	2
C₂×C₁₃×#489	2
C₂×C₁₃×#470	2
C₂×C₁₃×#468	2
C₂×C₄×C₁₃×Q₁₆	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×C₄×C₁₃×M₁₆	2
C₂×#3172	13

Subgroups — C2×C13×#3172 #15747014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3172 #15747014