Subgroups — C₂×C₁₃×#3233 #15747184

Order 3328.

1810 conjugacy classes of subgroups.

The subgroup lattice has 574 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×#3233	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#499	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#488	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#485	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#482	C₂	1	2	yes	maximal
8	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#533	—	2	4	no	—
14	C₁₃×#533	C₂²	1	8	yes	complemented
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₁₃×#529	—	2	4	no	—
18	C₁₃×#529	C₂²	1	8	yes	—
19	C₂×C₁₃×#126	—	2	1	no	—
20	C₂×C₁₃×#125	C₂²	1	2	yes	—
21	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#123	—	2	1	no	—
24	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
29	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	—	2	1	no	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#117	—	2	1	no	—
34	C₂×C₁₃×#117	C₂²	1	2	yes	—
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#499	C₂²	1	16	yes	complemented
37	C₁₃×#488	C₂²	1	16	yes	complemented
38	C₁₃×#485	C₂²	1	16	yes	complemented
39	C₁₃×#482	C₂²	1	16	yes	—
40	C₁₃×#477	C₂²	1	8	yes	complemented
41	C₁₃×#476	C₂²	1	8	yes	complemented
42	C₁₃×#475	C₂²	1	8	yes	complemented
43	C₁₃×#474	C₂²	1	8	yes	complemented
44	C₁₃×#431	C₂²	1	8	yes	complemented
45	C₂×C₁₃×#107	C₂²	1	2	yes	—
46	C₂×C₁₃×#107	C₂²	1	2	yes	—
47	C₂×C₁₃×#106	C₂²	1	2	yes	—
48	C₂×C₁₃×#106	C₂²	1	2	yes	—
49	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#103	C₂²	1	2	yes	—
52	C₂×C₁₃×#103	C₂²	1	2	yes	—
53	C₂×C₁₃×#102	C₂²	1	2	yes	—
54	C₂×C₁₃×#102	C₂²	1	2	yes	—
55	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
56	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
57	C₂²×Q₈×C₁₃	—	2	1	no	—
58	C₂²×Q₈×C₁₃	—	2	1	no	—
59	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
67	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
68	C₁₃×C₄⋊Q₈	—	2	2	no	—
69	C₁₃×C₄⋊Q₈	—	2	2	no	—
70	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
71	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
72	C₁₃×#126	—	2	8	no	—
73	C₁₃×#125	—	2	2	no	—
74	C₁₃×#125	—	2	4	no	—
75	C₁₃×#125	C₂³	1	8	yes	—
76	C₁₃×#125	C₂³	1	4	yes	—
77	C₁₃×#124	—	2	2	no	—
78	C₁₃×#124	C₂³	1	4	yes	—
79	C₁₃×#123	—	2	8	no	—
80	C₁₃×C₂²⋊Q₈	—	2	8	no	—
81	C₁₃×C₂²⋊Q₈	—	2	8	no	—
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
84	C₁₃×#121	—	2	2	no	—
85	C₁₃×#121	C₂³	1	4	yes	—
86	C₄×Q₈×C₁₃	—	2	8	no	—
87	C₄×Q₈×C₁₃	—	2	8	no	—
88	C₄×Q₈×C₁₃	—	2	2	no	—
89	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
90	C₄×D₄×C₁₃	—	2	8	no	—
91	C₄×D₄×C₁₃	—	2	2	no	—
92	C₄×D₄×C₁₃	C₂³	1	4	yes	—
93	C₁₃×#117	—	2	4	no	—
94	C₁₃×#117	—	2	8	no	—
95	C₁₃×#117	C₂³	1	8	yes	—
96	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₄²×C₁₃	—	2	1	no	—
115	C₂×C₄²×C₁₃	—	2	2	no	—
116	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₁₃	D₄	1	4	yes	—
119	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
122	C₁₃×#107	C₂³	1	8	yes	—
123	C₁₃×#107	C₂³	1	8	yes	—
124	C₁₃×#106	C₂³	1	8	yes	—
125	C₁₃×#106	C₂³	1	8	yes	—
126	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
127	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
128	C₁₃×#103	C₂³	1	8	yes	—
129	C₁₃×#103	C₂³	1	8	yes	—
130	C₁₃×#102	C₂³	1	8	yes	—
131	C₁₃×#102	C₂³	1	8	yes	—
132	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
133	C₄×C₈×C₁₃	C₂³	1	8	yes	—
134	C₂×#3233	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂⁴×C₁₃	—	2	1	no	—
136	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	2	4	no	—
139	C₂×Q₈×C₁₃	—	2	4	no	—
140	C₂×Q₈×C₁₃	—	2	2	no	—
141	C₂×Q₈×C₁₃	—	2	2	no	—
142	C₂×Q₈×C₁₃	—	4	4	no	—
143	C₂×Q₈×C₁₃	—	4	4	no	—
144	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
145	C₂×D₄×C₁₃	—	2	4	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	2	no	—
148	C₂×D₄×C₁₃	—	2	2	no	—
149	C₂×D₄×C₁₃	—	4	4	no	—
150	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	4	no	—
160	C₂²×C₄×C₁₃	—	4	2	no	—
161	C₂²×C₄×C₁₃	—	4	4	no	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	4	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₈×C₁₃	—	2	4	no	—
173	C₂×C₈×C₁₃	—	2	4	no	—
174	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
175	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
176	C₁₃×C₄⋊C₄	—	2	4	no	—
177	C₁₃×C₄⋊C₄	—	2	4	no	—
178	C₁₃×C₄⋊C₄	—	2	4	no	—
179	C₁₃×C₄⋊C₄	—	2	8	no	—
180	C₁₃×C₄⋊C₄	—	2	8	no	—
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	2	no	—
185	C₁₃×C₄⋊C₄	—	2	2	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
189	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
190	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
191	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
192	C₁₃×C₂²⋊C₄	—	2	8	no	—
193	C₁₃×C₂²⋊C₄	—	2	4	no	—
194	C₁₃×C₂²⋊C₄	—	2	4	no	—
195	C₁₃×C₂²⋊C₄	—	2	4	no	—
196	C₁₃×C₂²⋊C₄	—	2	4	no	—
197	C₁₃×C₂²⋊C₄	—	2	4	no	—
198	C₄²×C₁₃	—	2	4	no	—
199	C₄²×C₁₃	—	2	8	no	—
200	C₄²×C₁₃	C₂×D₄	1	4	yes	—
201	C₄²×C₁₃	C₂×D₄	1	2	yes	—
202	C₄²×C₁₃	C₂×D₄	1	4	yes	—
203	C₄²×C₁₃	C₂×D₄	1	2	yes	—
204	C₄²×C₁₃	C₂⁴	1	2	yes	—
205	C₄²×C₁₃	C₂⁴	1	2	yes	—
206	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
207	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
208	#3233	C₂×C₁₃	1	16	yes	direct product factor
209	C₂×#499	C₂×C₁₃	1	2	yes	complemented
210	C₂×#488	C₂×C₁₃	1	2	yes	complemented
211	C₂×#485	C₂×C₁₃	1	2	yes	complemented
212	C₂×#482	C₂×C₁₃	1	2	yes	—
213	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
217	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
218	C₂³×C₁₃	—	2	2	no	—
219	C₂³×C₁₃	—	2	2	no	—
220	C₂³×C₁₃	—	2	2	no	—
221	C₂³×C₁₃	—	2	2	no	—
222	C₂³×C₁₃	—	4	2	no	—
223	C₂³×C₁₃	—	4	2	no	—
224	C₂³×C₁₃	—	4	2	no	—
225	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
226	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	Q₈×C₁₃	—	2	2	no	—
228	Q₈×C₁₃	—	2	2	no	—
229	Q₈×C₁₃	—	4	8	no	—
230	Q₈×C₁₃	—	4	2	no	—
231	Q₈×C₁₃	—	4	8	no	—
232	D₄×C₁₃	—	2	2	no	—
233	D₄×C₁₃	—	2	2	no	—
234	D₄×C₁₃	—	4	8	no	—
235	D₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	8	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	4	no	—
247	C₂×C₄×C₁₃	—	2	4	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	4	4	no	—
250	C₂×C₄×C₁₃	—	4	2	no	—
251	C₂×C₄×C₁₃	—	4	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	8	no	—
256	C₂×C₄×C₁₃	#135	1	4	yes	—
257	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
260	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
264	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
265	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
266	C₈×C₁₃	—	2	4	no	—
267	C₈×C₁₃	—	2	4	no	—
268	#533	—	2	4	no	—
269	#533	C₂²×C₁₃	1	8	yes	complemented
270	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
272	#529	—	2	4	no	—
273	#529	C₂²×C₁₃	1	8	yes	—
274	C₂×#126	—	2	1	no	—
275	C₂×#125	C₂²×C₁₃	1	2	yes	—
276	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×#123	—	2	1	no	—
279	C₂×C₂²⋊Q₈	—	2	1	no	—
280	C₂×C₂²⋊Q₈	—	2	1	no	—
281	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×C₄×Q₈	—	2	1	no	—
284	C₂×C₄×Q₈	—	2	1	no	—
285	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×C₄×D₄	—	2	1	no	—
287	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×#117	—	2	1	no	—
289	C₂×#117	C₂²×C₁₃	1	2	yes	—
290	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
291	#499	C₂²×C₁₃	1	16	yes	complemented
292	#488	C₂²×C₁₃	1	16	yes	complemented
293	#485	C₂²×C₁₃	1	16	yes	complemented
294	#482	C₂²×C₁₃	1	16	yes	—
295	#477	C₂²×C₁₃	1	8	yes	complemented
296	#476	C₂²×C₁₃	1	8	yes	complemented
297	#475	C₂²×C₁₃	1	8	yes	complemented
298	#474	C₂²×C₁₃	1	8	yes	complemented
299	#431	C₂²×C₁₃	1	8	yes	complemented
300	C₂×#107	C₂²×C₁₃	1	2	yes	—
301	C₂×#107	C₂²×C₁₃	1	2	yes	—
302	C₂×#106	C₂²×C₁₃	1	2	yes	—
303	C₂×#106	C₂²×C₁₃	1	2	yes	—
304	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×#103	C₂²×C₁₃	1	2	yes	—
307	C₂×#103	C₂²×C₁₃	1	2	yes	—
308	C₂×#102	C₂²×C₁₃	1	2	yes	—
309	C₂×#102	C₂²×C₁₃	1	2	yes	—
310	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
311	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
312	C₂²×C₁₃	—	2	2	no	—
313	C₂²×C₁₃	—	2	2	no	—
314	C₂²×C₁₃	—	2	2	no	—
315	C₂²×C₁₃	—	4	4	no	—
316	C₂²×C₁₃	—	4	2	no	—
317	C₂²×C₁₃	—	4	2	no	—
318	C₂²×C₁₃	—	4	2	no	—
319	C₂²×C₁₃	—	8	4	no	—
320	C₂²×C₁₃	#536	1	2	yes	—
321	C₂²×C₁₃	C₂×#135	1	2	yes	—
322	C₂²×C₁₃	#575	1	2	yes	—
323	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
324	C₄×C₁₃	—	2	2	no	—
325	C₄×C₁₃	—	2	2	no	—
326	C₄×C₁₃	—	2	2	no	—
327	C₄×C₁₃	—	2	2	no	—
328	C₄×C₁₃	—	4	2	no	—
329	C₄×C₁₃	—	4	2	no	—
330	C₄×C₁₃	—	4	4	no	—
331	C₄×C₁₃	—	4	2	no	—
332	C₄×C₁₃	—	4	4	no	—
333	C₄×C₁₃	#536	1	2	yes	—
334	C₄×C₁₃	C₂×#135	1	4	yes	—
335	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
336	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
337	C₂²×Q₈	—	2	1	no	—
338	C₂²×Q₈	—	2	1	no	—
339	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
342	C₂³×C₄	—	2	1	no	—
343	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
344	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
345	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
347	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
348	C₄⋊Q₈	—	2	2	no	—
349	C₄⋊Q₈	—	2	2	no	—
350	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
351	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
352	#126	—	2	8	no	—
353	#125	—	2	2	no	—
354	#125	—	2	4	no	—
355	#125	C₂³×C₁₃	1	4	yes	—
356	#125	C₂³×C₁₃	1	8	yes	—
357	#124	—	2	2	no	—
358	#124	C₂³×C₁₃	1	4	yes	—
359	#123	—	2	8	no	—
360	C₂²⋊Q₈	—	2	8	no	—
361	C₂²⋊Q₈	—	2	8	no	—
362	C₂²⋊Q₈	—	2	2	no	—
363	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
364	#121	—	2	2	no	—
365	#121	C₂³×C₁₃	1	4	yes	—
366	C₄×Q₈	—	2	8	no	—
367	C₄×Q₈	—	2	8	no	—
368	C₄×Q₈	—	2	2	no	—
369	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
370	C₄×D₄	—	2	8	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	C₂³×C₁₃	1	4	yes	—
373	#117	—	2	4	no	—
374	#117	—	2	8	no	—
375	#117	C₂³×C₁₃	1	8	yes	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	2	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	—	2	2	no	—
396	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
397	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
398	C₂×C₄²	D₄×C₁₃	1	4	yes	—
399	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
402	#107	C₂³×C₁₃	1	8	yes	—
403	#107	C₂³×C₁₃	1	8	yes	—
404	#106	C₂³×C₁₃	1	8	yes	—
405	#106	C₂³×C₁₃	1	8	yes	—
406	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
407	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
408	#103	C₂³×C₁₃	1	8	yes	—
409	#103	C₂³×C₁₃	1	8	yes	—
410	#102	C₂³×C₁₃	1	8	yes	—
411	#102	C₂³×C₁₃	1	8	yes	—
412	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
413	C₄×C₈	C₂³×C₁₃	1	8	yes	—
414	C₂×C₁₃	—	4	2	no	—
415	C₂×C₁₃	—	8	2	no	—
416	C₂×C₁₃	#3233	1	4	yes	direct product factor
417	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
418	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
419	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
420	C₂⁴	—	2	1	no	—
421	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	4	no	—
424	C₂×Q₈	—	2	4	no	—
425	C₂×Q₈	—	2	2	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	4	4	no	—
428	C₂×Q₈	—	4	4	no	—
429	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	4	4	no	—
435	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	—	4	4	no	—
447	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
449	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
453	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
454	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
456	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
457	C₂×C₈	—	2	4	no	—
458	C₂×C₈	—	2	4	no	—
459	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
460	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
461	C₄⋊C₄	—	2	4	no	—
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	8	no	—
465	C₄⋊C₄	—	2	8	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
474	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
475	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
476	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
477	C₂²⋊C₄	—	2	8	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₄²	—	2	4	no	—
484	C₄²	—	2	8	no	—
485	C₄²	C₂×D₄×C₁₃	1	4	yes	—
486	C₄²	C₂×D₄×C₁₃	1	2	yes	—
487	C₄²	C₂×D₄×C₁₃	1	4	yes	—
488	C₄²	C₂×D₄×C₁₃	1	2	yes	—
489	C₄²	C₂⁴×C₁₃	1	2	yes	—
490	C₄²	C₂⁴×C₁₃	1	2	yes	—
491	C₁₃	C₂×#3233	1	1	yes	characteristic, direct product factor, Sylow
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	2	no	—
499	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
500	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
501	Q₈	—	2	2	no	—
502	Q₈	—	2	2	no	—
503	Q₈	—	4	8	no	—
504	Q₈	—	4	2	no	—
505	Q₈	—	4	8	no	—
506	D₄	—	2	2	no	—
507	D₄	—	2	2	no	—
508	D₄	—	4	8	no	—
509	D₄	—	4	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	8	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	4	4	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	4	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	4	no	—
529	C₂×C₄	—	4	8	no	—
530	C₂×C₄	C₁₃×#135	1	4	yes	—
531	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
532	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
533	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
534	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
535	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
536	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
537	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
538	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
539	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
540	C₈	—	2	4	no	—
541	C₈	—	2	4	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	8	4	no	—
550	C₂²	C₁₃×#536	1	2	yes	—
551	C₂²	C₂×C₁₃×#135	1	2	yes	—
552	C₂²	C₁₃×#575	1	2	yes	—
553	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
554	C₄	—	2	2	no	—
555	C₄	—	2	2	no	—
556	C₄	—	2	2	no	—
557	C₄	—	2	2	no	—
558	C₄	—	4	2	no	—
559	C₄	—	4	4	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	4	no	—
562	C₄	—	4	2	no	—
563	C₄	C₁₃×#536	1	2	yes	—
564	C₄	C₂×C₁₃×#135	1	4	yes	—
565	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
566	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
567	C₂	—	4	2	no	—
568	C₂	—	8	2	no	—
569	C₂	C₁₃×#3233	1	4	yes	direct product factor
570	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
571	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
572	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
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×#533	C₂	semidirect
3. C₁₃×#3233	C₂	direct (N × H)
4. C₂×C₁₃×#499	C₂	semidirect
5. C₂×C₁₃×#488	C₂	semidirect
6. C₂×C₁₃×#485	C₂	semidirect
8. C₂×C₁₃×#477	C₂	semidirect
9. C₂×C₁₃×#475	C₂	semidirect
10. C₂×C₁₃×#476	C₂	semidirect
11. C₂×C₁₃×#474	C₂	semidirect
12. C₂×C₁₃×#431	C₂	semidirect
14. C₁₃×#533	C₂²	semidirect
36. C₁₃×#499	C₂²	semidirect
37. C₁₃×#488	C₂²	semidirect
38. C₁₃×#485	C₂²	semidirect
40. C₁₃×#477	C₂²	semidirect
41. C₁₃×#476	C₂²	semidirect
42. C₁₃×#475	C₂²	semidirect
43. C₁₃×#474	C₂²	semidirect
44. C₁₃×#431	C₂²	semidirect
134. C₂×#3233	C₁₃	direct (N × H)
206. C₂×#533	C₂×C₁₃	semidirect
208. #3233	C₂×C₁₃	direct (N × H)
209. C₂×#499	C₂×C₁₃	semidirect
210. C₂×#488	C₂×C₁₃	semidirect
211. C₂×#485	C₂×C₁₃	semidirect
213. C₂×#477	C₂×C₁₃	semidirect
214. C₂×#475	C₂×C₁₃	semidirect
215. C₂×#476	C₂×C₁₃	semidirect
216. C₂×#474	C₂×C₁₃	semidirect
217. C₂×#431	C₂×C₁₃	semidirect
269. #533	C₂²×C₁₃	semidirect
291. #499	C₂²×C₁₃	semidirect
292. #488	C₂²×C₁₃	semidirect
293. #485	C₂²×C₁₃	semidirect
295. #477	C₂²×C₁₃	semidirect
296. #476	C₂²×C₁₃	semidirect
297. #475	C₂²×C₁₃	semidirect
298. #474	C₂²×C₁₃	semidirect
299. #431	C₂²×C₁₃	semidirect
416. C₂×C₁₃	#3233	direct (N × H)
491. C₁₃	C₂×#3233	direct (N × H)
569. C₂	C₁₃×#3233	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×#3233	2
C₂×C₁₃×#499	2
C₂×C₁₃×#488	2
C₂×C₁₃×#485	2
C₂×C₁₃×#482	2
C₂×C₁₃×#477	2
C₂×C₁₃×#475	2
C₂×C₁₃×#476	2
C₂×C₁₃×#474	2
C₂×C₁₃×#431	2
C₂×#3233	13

Subgroups — C2×C13×#3233 #15747184

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3233 #15747184