Subgroups — C₂×C₁₃×#3171 #15747013

Order 3328.

2266 conjugacy classes of subgroups.

The subgroup lattice has 608 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×#3171	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#469	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#468	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₁₃×M₁₆	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×#501	C₂²	1	8	yes	complemented
40	C₁₃×#496	C₂²	1	8	yes	complemented
41	C₁₃×#490	C₂²	1	8	yes	complemented
42	C₁₃×#489	C₂²	1	8	yes	complemented
43	C₁₃×#469	C₂²	1	16	yes	complemented
44	C₁₃×#468	C₂²	1	16	yes	complemented
45	C₄×C₁₃×SD₁₆	C₂²	1	16	yes	complemented
46	C₄×C₁₃×D₈	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×#102	C₂²	1	2	yes	—
51	C₂×C₁₃×#102	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	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	—	2	8	no	—
73	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
74	C₂×C₁₃×D₈	—	2	8	no	—
75	C₂×C₁₃×D₈	C₂³	1	8	yes	—
76	C₂×C₁₃×M₁₆	—	2	8	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	4	yes	—
125	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
128	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
129	C₁₃×#107	C₂³	1	8	yes	—
130	C₁₃×#106	C₂³	1	8	yes	—
131	C₁₃×#103	C₂³	1	8	yes	—
132	C₁₃×#102	C₂³	1	8	yes	—
133	C₁₃×#102	C₂³	1	8	yes	—
134	C₁₃×#102	C₂³	1	8	yes	—
135	C₁₃×#97	C₂³	1	4	yes	—
136	C₁₃×#97	C₂³	1	4	yes	—
137	C₄×C₈×C₁₃	C₂³	1	8	yes	—
138	C₂×#3171	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	4	no	—
146	C₂×Q₈×C₁₃	—	4	4	no	—
147	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
148	C₂×D₄×C₁₃	—	2	4	no	—
149	C₂×D₄×C₁₃	—	2	8	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	2	no	—
152	C₂×D₄×C₁₃	—	2	4	no	—
153	C₂×D₄×C₁₃	—	2	4	no	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	2	4	no	—
156	C₂×D₄×C₁₃	—	2	4	no	—
157	C₂×D₄×C₁₃	—	4	4	no	—
158	C₂×D₄×C₁₃	—	4	4	no	—
159	C₂×D₄×C₁₃	—	4	4	no	—
160	C₂×D₄×C₁₃	—	4	8	no	—
161	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
162	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	2	no	—
169	C₂²×C₄×C₁₃	—	2	4	no	—
170	C₂²×C₄×C₁₃	—	2	8	no	—
171	C₂²×C₄×C₁₃	—	4	2	no	—
172	C₂²×C₄×C₁₃	—	4	4	no	—
173	C₂²×C₄×C₁₃	—	4	8	no	—
174	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₁₃×SD₁₆	—	2	16	no	—
185	C₁₃×D₈	—	2	16	no	—
186	C₁₃×M₁₆	—	2	16	no	—
187	C₂×C₈×C₁₃	—	2	4	no	—
188	C₂×C₈×C₁₃	#41	1	8	yes	complemented
189	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
190	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
191	C₁₃×C₄⋊C₄	—	2	4	no	—
192	C₁₃×C₄⋊C₄	—	2	4	no	—
193	C₁₃×C₄⋊C₄	—	2	4	no	—
194	C₁₃×C₄⋊C₄	—	2	4	no	—
195	C₁₃×C₄⋊C₄	—	2	4	no	—
196	C₁₃×C₄⋊C₄	—	2	2	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
200	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
201	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
202	C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₁₃×C₂²⋊C₄	—	2	4	no	—
205	C₁₃×C₂²⋊C₄	—	2	8	no	—
206	C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₁₃×C₂²⋊C₄	—	2	8	no	—
208	C₁₃×C₂²⋊C₄	—	2	4	no	—
209	C₄²×C₁₃	—	2	4	no	—
210	C₄²×C₁₃	C₂×D₄	1	4	yes	—
211	C₄²×C₁₃	C₂×D₄	1	2	yes	—
212	C₄²×C₁₃	C₂×D₄	1	4	yes	—
213	C₄²×C₁₃	C₂×D₄	1	2	yes	—
214	C₄²×C₁₃	C₂⁴	1	2	yes	—
215	C₄²×C₁₃	C₂⁴	1	2	yes	—
216	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
217	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#3171	C₂×C₁₃	1	16	yes	direct product factor
219	C₂×#501	C₂×C₁₃	1	1	yes	characteristic, complemented
220	C₂×#496	C₂×C₁₃	1	1	yes	characteristic, complemented
221	C₂×#490	C₂×C₁₃	1	1	yes	characteristic, complemented
222	C₂×#489	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂×#469	C₂×C₁₃	1	2	yes	complemented
224	C₂×#468	C₂×C₁₃	1	2	yes	complemented
225	C₂×C₄×SD₁₆	C₂×C₁₃	1	2	yes	complemented
226	C₂×C₄×D₈	C₂×C₁₃	1	2	yes	complemented
227	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
228	C₂³×C₁₃	—	2	2	no	—
229	C₂³×C₁₃	—	2	2	no	—
230	C₂³×C₁₃	—	2	2	no	—
231	C₂³×C₁₃	—	2	2	no	—
232	C₂³×C₁₃	—	2	4	no	—
233	C₂³×C₁₃	—	4	2	no	—
234	C₂³×C₁₃	—	4	4	no	—
235	C₂³×C₁₃	—	4	4	no	—
236	C₂³×C₁₃	—	4	2	no	—
237	C₂³×C₁₃	—	4	4	no	—
238	C₂³×C₁₃	—	4	2	no	—
239	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
240	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
241	Q₈×C₁₃	—	2	4	no	—
242	Q₈×C₁₃	—	4	8	no	—
243	Q₈×C₁₃	—	4	2	no	—
244	D₄×C₁₃	—	2	4	no	—
245	D₄×C₁₃	—	2	4	no	—
246	D₄×C₁₃	—	2	4	no	—
247	D₄×C₁₃	—	4	8	no	—
248	D₄×C₁₃	—	4	8	no	—
249	D₄×C₁₃	—	4	8	no	—
250	D₄×C₁₃	—	4	16	no	—
251	D₄×C₁₃	—	4	2	no	—
252	D₄×C₁₃	—	4	4	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	8	no	—
259	C₂×C₄×C₁₃	—	2	4	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	4	4	no	—
265	C₂×C₄×C₁₃	—	4	2	no	—
266	C₂×C₄×C₁₃	—	4	2	no	—
267	C₂×C₄×C₁₃	—	4	4	no	—
268	C₂×C₄×C₁₃	—	4	2	no	—
269	C₂×C₄×C₁₃	—	4	8	no	—
270	C₂×C₄×C₁₃	—	4	16	no	—
271	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
272	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
273	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
274	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
278	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
279	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
280	C₈×C₁₃	—	2	4	no	—
281	C₈×C₁₃	C₂×#41	1	8	yes	complemented
282	C₂²×#41	—	2	1	no	—
283	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
284	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
285	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
286	#532	—	2	4	no	—
287	#532	C₂²×C₁₃	1	8	yes	complemented
288	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
290	#529	—	2	4	no	—
291	#529	C₂²×C₁₃	1	8	yes	complemented
292	C₂×#126	—	2	1	no	—
293	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×#124	—	2	1	no	—
295	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#123	—	2	1	no	—
297	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×#121	—	2	1	no	—
299	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×#121	C₂²×C₁₃	1	2	yes	—
301	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×C₄×D₄	—	2	1	no	—
303	C₂×C₄×D₄	—	2	1	no	—
304	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
306	C₂×#117	—	2	1	no	—
307	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
308	#501	C₂²×C₁₃	1	8	yes	complemented
309	#496	C₂²×C₁₃	1	8	yes	complemented
310	#490	C₂²×C₁₃	1	8	yes	complemented
311	#489	C₂²×C₁₃	1	8	yes	complemented
312	#469	C₂²×C₁₃	1	16	yes	complemented
313	#468	C₂²×C₁₃	1	16	yes	complemented
314	C₄×SD₁₆	C₂²×C₁₃	1	16	yes	complemented
315	C₄×D₈	C₂²×C₁₃	1	16	yes	complemented
316	C₂×#107	C₂²×C₁₃	1	2	yes	—
317	C₂×#106	C₂²×C₁₃	1	2	yes	—
318	C₂×#103	C₂²×C₁₃	1	2	yes	—
319	C₂×#102	C₂²×C₁₃	1	2	yes	—
320	C₂×#102	C₂²×C₁₃	1	2	yes	—
321	C₂×#102	C₂²×C₁₃	1	2	yes	—
322	C₄×M₁₆	C₂²×C₁₃	1	8	yes	complemented
323	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	2	no	—
329	C₂²×C₁₃	—	4	4	no	—
330	C₂²×C₁₃	—	4	2	no	—
331	C₂²×C₁₃	—	4	4	no	—
332	C₂²×C₁₃	—	4	4	no	—
333	C₂²×C₁₃	—	4	2	no	—
334	C₂²×C₁₃	—	4	4	no	—
335	C₂²×C₁₃	—	4	2	no	—
336	C₂²×C₁₃	—	8	8	no	—
337	C₂²×C₁₃	—	8	4	no	—
338	C₂²×C₁₃	#532	1	2	yes	—
339	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
340	C₂²×C₁₃	#575	1	2	yes	—
341	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
342	C₄×C₁₃	—	2	2	no	—
343	C₄×C₁₃	—	2	2	no	—
344	C₄×C₁₃	—	2	2	no	—
345	C₄×C₁₃	—	2	2	no	—
346	C₄×C₁₃	—	4	2	no	—
347	C₄×C₁₃	—	4	2	no	—
348	C₄×C₁₃	—	4	4	no	—
349	C₄×C₁₃	—	4	2	no	—
350	C₄×C₁₃	#532	1	2	yes	—
351	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
352	C₄×C₁₃	C₂²×#41	1	2	yes	—
353	C₂×#41	—	2	8	no	—
354	C₂×#41	—	4	8	no	—
355	C₂²×Q₈	—	2	1	no	—
356	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
357	C₂²×D₄	—	2	1	no	—
358	C₂²×D₄	—	2	2	no	—
359	C₂²×D₄	—	2	1	no	—
360	C₂²×D₄	—	2	1	no	—
361	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
362	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
363	C₂³×C₄	—	2	1	no	—
364	C₂³×C₄	—	2	2	no	—
365	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
366	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
367	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
368	C₂×SD₁₆	—	2	8	no	—
369	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
370	C₂×D₈	—	2	8	no	—
371	C₂×D₈	C₂³×C₁₃	1	8	yes	—
372	C₂×M₁₆	—	2	8	no	—
373	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
374	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
375	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
376	C₄⋊Q₈	—	2	2	no	—
377	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
378	#127	—	2	2	no	—
379	#127	C₂³×C₁₃	1	4	yes	—
380	#126	—	2	8	no	—
381	#125	—	2	2	no	—
382	#125	C₂³×C₁₃	1	4	yes	—
383	#124	—	2	8	no	—
384	#124	—	2	2	no	—
385	#124	C₂³×C₁₃	1	4	yes	—
386	#123	—	2	8	no	—
387	C₂²⋊Q₈	—	2	2	no	—
388	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
389	#121	—	2	8	no	—
390	#121	—	2	2	no	—
391	#121	—	2	4	no	—
392	#121	C₂³×C₁₃	1	4	yes	—
393	#121	C₂³×C₁₃	1	8	yes	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
396	C₄×D₄	—	2	8	no	—
397	C₄×D₄	—	2	8	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	4	no	—
400	C₄×D₄	C₂³×C₁₃	1	4	yes	—
401	C₄×D₄	C₂³×C₁₃	1	8	yes	—
402	#117	—	2	8	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
409	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	2	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	2	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
420	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
421	C₂×C₄²	D₄×C₁₃	1	4	yes	—
422	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
425	#107	C₂³×C₁₃	1	8	yes	—
426	#106	C₂³×C₁₃	1	8	yes	—
427	#103	C₂³×C₁₃	1	8	yes	—
428	#102	C₂³×C₁₃	1	8	yes	—
429	#102	C₂³×C₁₃	1	8	yes	—
430	#102	C₂³×C₁₃	1	8	yes	—
431	#97	C₂³×C₁₃	1	4	yes	—
432	#97	C₂³×C₁₃	1	4	yes	—
433	C₄×C₈	C₂³×C₁₃	1	8	yes	—
434	C₂×C₁₃	—	4	2	no	—
435	C₂×C₁₃	—	8	4	no	—
436	C₂×C₁₃	—	8	2	no	—
437	C₂×C₁₃	#3171	1	4	yes	direct product factor
438	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
439	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
440	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
441	C₂⁴	—	2	1	no	—
442	C₂⁴	—	2	2	no	—
443	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
444	#41	—	4	32	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	4	no	—
447	C₂×Q₈	—	2	4	no	—
448	C₂×Q₈	—	4	4	no	—
449	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	2	8	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	4	4	no	—
460	C₂×D₄	—	4	4	no	—
461	C₂×D₄	—	4	8	no	—
462	C₂×D₄	—	4	4	no	—
463	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
464	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	8	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	—	4	8	no	—
475	C₂²×C₄	—	4	4	no	—
476	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
478	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
482	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
483	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
486	SD₁₆	—	2	16	no	—
487	D₈	—	2	16	no	—
488	M₁₆	—	2	16	no	—
489	C₂×C₈	—	2	4	no	—
490	C₂×C₈	C₁₃×#41	1	8	yes	complemented
491	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
492	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
502	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
503	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
504	C₂²⋊C₄	—	2	4	no	—
505	C₂²⋊C₄	—	2	4	no	—
506	C₂²⋊C₄	—	2	4	no	—
507	C₂²⋊C₄	—	2	8	no	—
508	C₂²⋊C₄	—	2	4	no	—
509	C₂²⋊C₄	—	2	8	no	—
510	C₂²⋊C₄	—	2	4	no	—
511	C₄²	—	2	4	no	—
512	C₄²	C₂×D₄×C₁₃	1	4	yes	—
513	C₄²	C₂×D₄×C₁₃	1	2	yes	—
514	C₄²	C₂×D₄×C₁₃	1	4	yes	—
515	C₄²	C₂×D₄×C₁₃	1	2	yes	—
516	C₄²	C₂⁴×C₁₃	1	2	yes	—
517	C₄²	C₂⁴×C₁₃	1	2	yes	—
518	C₁₃	C₂×#3171	1	1	yes	characteristic, direct product factor, Sylow
519	C₂³	—	2	2	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	4	no	—
524	C₂³	—	4	2	no	—
525	C₂³	—	4	4	no	—
526	C₂³	—	4	4	no	—
527	C₂³	—	4	2	no	—
528	C₂³	—	4	4	no	—
529	C₂³	—	4	2	no	—
530	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
531	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
532	Q₈	—	2	4	no	—
533	Q₈	—	4	8	no	—
534	Q₈	—	4	2	no	—
535	D₄	—	2	4	no	—
536	D₄	—	2	4	no	—
537	D₄	—	2	4	no	—
538	D₄	—	4	8	no	—
539	D₄	—	4	8	no	—
540	D₄	—	4	8	no	—
541	D₄	—	4	16	no	—
542	D₄	—	4	2	no	—
543	D₄	—	4	4	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	8	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	4	4	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	8	no	—
561	C₂×C₄	—	4	16	no	—
562	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
563	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
564	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
565	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
566	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
567	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
569	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
570	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
571	C₈	—	2	4	no	—
572	C₈	C₂×C₁₃×#41	1	8	yes	complemented
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	4	4	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	4	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	8	8	no	—
584	C₂²	—	8	4	no	—
585	C₂²	C₁₃×#532	1	2	yes	—
586	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
587	C₂²	C₁₃×#575	1	2	yes	—
588	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
589	C₄	—	2	2	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	2	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	4	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	2	no	—
597	C₄	C₁₃×#532	1	2	yes	—
598	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
599	C₄	C₂²×C₁₃×#41	1	2	yes	—
600	C₂	—	4	2	no	—
601	C₂	—	8	4	no	—
602	C₂	—	8	2	no	—
603	C₂	C₁₃×#3171	1	4	yes	direct product factor
604	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
605	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
606	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
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×#532	C₂	semidirect
2. C₂×C₁₃×#529	C₂	semidirect
3. C₁₃×#3171	C₂	direct (N × H)
4. C₂×C₁₃×#501	C₂	semidirect
5. C₂×C₁₃×#496	C₂	semidirect
6. C₂×C₁₃×#490	C₂	semidirect
7. C₂×C₁₃×#489	C₂	semidirect
8. C₂×C₁₃×#469	C₂	semidirect
9. C₂×C₁₃×#468	C₂	semidirect
10. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
11. C₂×C₄×C₁₃×D₈	C₂	semidirect
12. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
18. C₁₃×#532	C₂²	semidirect
22. C₁₃×#529	C₂²	semidirect
39. C₁₃×#501	C₂²	semidirect
40. C₁₃×#496	C₂²	semidirect
41. C₁₃×#490	C₂²	semidirect
42. C₁₃×#489	C₂²	semidirect
43. C₁₃×#469	C₂²	semidirect
44. C₁₃×#468	C₂²	semidirect
45. C₄×C₁₃×SD₁₆	C₂²	semidirect
46. C₄×C₁₃×D₈	C₂²	semidirect
53. C₄×C₁₃×M₁₆	C₂²	semidirect
138. C₂×#3171	C₁₃	direct (N × H)
188. C₂×C₈×C₁₃	#41	semidirect
216. C₂×#532	C₂×C₁₃	semidirect
217. C₂×#529	C₂×C₁₃	semidirect
218. #3171	C₂×C₁₃	direct (N × H)
219. C₂×#501	C₂×C₁₃	semidirect
220. C₂×#496	C₂×C₁₃	semidirect
221. C₂×#490	C₂×C₁₃	semidirect
222. C₂×#489	C₂×C₁₃	semidirect
223. C₂×#469	C₂×C₁₃	semidirect
224. C₂×#468	C₂×C₁₃	semidirect
225. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
226. C₂×C₄×D₈	C₂×C₁₃	semidirect
227. C₂×C₄×M₁₆	C₂×C₁₃	semidirect
281. C₈×C₁₃	C₂×#41	semidirect
287. #532	C₂²×C₁₃	semidirect
291. #529	C₂²×C₁₃	semidirect
308. #501	C₂²×C₁₃	semidirect
309. #496	C₂²×C₁₃	semidirect
310. #490	C₂²×C₁₃	semidirect
311. #489	C₂²×C₁₃	semidirect
312. #469	C₂²×C₁₃	semidirect
313. #468	C₂²×C₁₃	semidirect
314. C₄×SD₁₆	C₂²×C₁₃	semidirect
315. C₄×D₈	C₂²×C₁₃	semidirect
322. C₄×M₁₆	C₂²×C₁₃	semidirect
437. C₂×C₁₃	#3171	direct (N × H)
490. C₂×C₈	C₁₃×#41	semidirect
518. C₁₃	C₂×#3171	direct (N × H)
572. C₈	C₂×C₁₃×#41	semidirect
603. C₂	C₁₃×#3171	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×#3171	2
C₂×C₁₃×#501	2
C₂×C₁₃×#496	2
C₂×C₁₃×#490	2
C₂×C₁₃×#489	2
C₂×C₁₃×#469	2
C₂×C₁₃×#468	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×C₄×C₁₃×D₈	2
C₂×C₄×C₁₃×M₁₆	2
C₂×#3171	13

Subgroups — C2×C13×#3171 #15747013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3171 #15747013