Subgroups — C₈×#88139 #15870780

Order 3328.

974 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₄×#88139	C₂	1	1	yes	maximal, characteristic
4	#13115770	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115628	C₂	1	1	yes	maximal, characteristic
6	#13115444	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115443	C₂	1	1	yes	maximal, characteristic, complemented
8	#13115440	C₂	1	1	yes	maximal, characteristic, complemented
9	#13115439	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114951	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#6103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×#6103	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×C₂²⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
19	C₂×#88139	C₄	1	1	yes	characteristic
20	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₄×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
28	C₈×C₂²⋊D₁₃	—	2	4	no	—
29	C₂×#88060	C₂²	1	1	yes	characteristic
30	C₂×#88060	C₂²	1	1	yes	characteristic
31	C₂×#88060	C₂²	1	1	yes	characteristic
32	C₂×#88054	C₂²	1	1	yes	characteristic
33	C₂×#88054	C₂²	1	1	yes	characteristic
34	C₂×#88054	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
40	#11718618	C₄	1	1	yes	characteristic
41	#11718612	C₄	1	1	yes	characteristic
42	#11718605	C₄	1	1	yes	characteristic
43	C₄×#6103	C₂²	1	1	yes	characteristic
44	C₄×#6103	C₂²	1	1	yes	characteristic
45	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
47	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
48	C₈×Dic₂₆	—	2	4	no	—
49	#11718331	C₄	1	1	yes	characteristic
50	#11718330	C₄	1	1	yes	characteristic
51	#11718311	C₄	1	1	yes	characteristic
52	#11718307	C₄	1	1	yes	characteristic
53	C₁₃×#336	C₂²	1	1	yes	characteristic
54	C₁₃×#336	C₂²	1	1	yes	characteristic
55	#11718142	C₂²	1	1	yes	characteristic
56	#11718142	C₂²	1	1	yes	characteristic
57	#11718142	C₂²	1	1	yes	characteristic
58	#11718142	C₂²	1	1	yes	characteristic
59	#11718116	C₂²	1	1	yes	characteristic
60	#11718116	C₂²	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
64	C₂²×Dic₂₆	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	—	2	2	no	—
66	C₂²×C₈×C₁₃	—	2	2	no	—
67	C₂²×C₈×C₁₃	—	2	2	no	—
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₂²⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
79	C₄×C₂²⋊D₁₃	—	2	2	no	—
80	C₄×C₂²⋊D₁₃	—	2	2	no	—
81	C₂×#6103	C₂×C₄	1	1	yes	characteristic
82	C₂×#6103	C₂×C₄	1	1	yes	characteristic
83	C₂×#6103	C₂×C₄	1	1	yes	characteristic
84	C₂×#6103	C₂×C₄	1	1	yes	characteristic
85	C₂×#6103	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
87	C₂×#6101	C₂×C₄	1	1	yes	characteristic
88	C₂×#6101	C₂×C₄	1	1	yes	characteristic
89	C₂×#6101	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
95	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
96	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
97	C₂²×#1055	C₂³	1	1	yes	characteristic
98	C₂²×#1055	C₂³	1	1	yes	characteristic
99	C₂²×#1055	C₂³	1	1	yes	characteristic
100	C₂²×#1055	C₂³	1	1	yes	characteristic
101	C₂×C₈×D₁₃	—	2	2	no	—
102	C₂×C₈×D₁₃	—	2	2	no	—
103	C₂×C₈×D₁₃	—	2	2	no	—
104	#88139	C₈	1	8	yes	direct product factor
105	C₄×Dic₂₆	—	2	2	no	—
106	C₄×Dic₂₆	—	2	2	no	—
107	C₁₃×C₂²⋊C₈	—	2	2	no	—
108	C₄×C₈×C₁₃	—	2	2	no	—
109	C₄×C₈×C₁₃	—	2	2	no	—
110	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
111	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
112	#88071	C₂×C₄	1	1	yes	characteristic
113	#88071	C₂×C₄	1	1	yes	characteristic
114	#88071	C₂×C₄	1	1	yes	characteristic
115	#88071	C₂×C₄	1	1	yes	characteristic
116	#88071	C₂×C₄	1	1	yes	characteristic
117	#88071	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊#1055	—	2	2	no	—
119	C₂²⋊#1055	—	2	2	no	—
120	#88060	—	2	2	no	—
121	#88060	—	2	2	no	—
122	#88060	—	2	2	no	—
123	#88054	—	2	2	no	—
124	#88054	—	2	2	no	—
125	#88054	—	2	2	no	—
126	C₈×Dic₁₃	—	2	2	no	—
127	C₈×Dic₁₃	—	2	2	no	—
128	C₈×Dic₁₃	—	2	2	no	—
129	C₈×Dic₁₃	—	2	2	no	—
130	C₈×Dic₁₃	D₄	1	4	yes	—
131	C₄⋊#1055	—	2	2	no	—
132	C₄×#1055	—	2	2	no	—
133	C₈×#124	—	13	1	no	maximal, Sylow
134	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₂×C₂²⋊D₁₃	—	2	2	no	—
149	C₂×C₂²⋊D₁₃	—	2	2	no	—
150	C₂×C₂²⋊D₁₃	C₂×C₈	1	4	yes	—
151	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×D₁₃	—	2	1	no	—
159	C₂×C₄×D₁₃	—	2	1	no	—
160	C₂×C₄×D₁₃	—	2	1	no	—
161	C₂×C₄×D₁₃	—	2	1	no	—
162	C₂×C₄×D₁₃	—	2	1	no	—
163	C₂×C₄×D₁₃	—	2	1	no	—
164	C₂×Dic₂₆	—	2	2	no	—
165	C₂×Dic₂₆	—	2	2	no	—
166	C₂×Dic₂₆	C₂×C₈	1	4	yes	complemented
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	4	4	no	—
176	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
177	C₂×C₈×C₁₃	#41	1	2	yes	—
178	C₂×C₈×C₁₃	#41	1	2	yes	—
179	C₂×C₈×C₁₃	#41	1	2	yes	—
180	C₁₃×C₂²⋊C₄	—	2	2	no	—
181	C₁₃×C₂²⋊C₄	C₂×C₈	1	4	yes	complemented
182	C₄²×C₁₃	—	2	1	no	—
183	C₄²×C₁₃	—	2	1	no	—
184	C₄²×C₁₃	—	2	1	no	—
185	C₄²×C₁₃	—	2	1	no	—
186	C₂²⋊Dic₁₃	—	2	2	no	—
187	C₂²⋊Dic₁₃	—	2	2	no	—
188	C₂²⋊Dic₁₃	C₂×C₈	1	4	yes	complemented
189	#6103	—	2	2	no	—
190	#6103	—	2	2	no	—
191	#6103	—	2	2	no	—
192	#6103	C₂×C₈	1	4	yes	complemented
193	#6103	C₂×C₈	1	4	yes	complemented
194	C₄⋊Dic₁₃	—	2	2	no	—
195	#6101	—	2	2	no	—
196	#6101	—	2	2	no	—
197	#6101	—	2	2	no	—
198	C₄×Dic₁₃	—	2	2	no	—
199	C₄×Dic₁₃	—	2	1	no	—
200	C₄×Dic₁₃	—	2	1	no	—
201	C₄×Dic₁₃	—	2	1	no	—
202	C₄×Dic₁₃	—	2	1	no	—
203	C₄×Dic₁₃	—	2	2	no	—
204	C₄×Dic₁₃	—	2	2	no	—
205	C₄×Dic₁₃	C₂×C₈	1	4	yes	complemented
206	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
207	C₄×Dic₁₃	#41	1	2	yes	—
208	C₂×#1055	—	2	1	no	—
209	C₂×#1055	—	2	1	no	—
210	C₂×#1055	—	2	1	no	—
211	C₂×#1055	—	2	1	no	—
212	C₂×#1055	—	2	1	no	—
213	C₂×#1055	—	2	1	no	—
214	C₂×#1055	—	2	1	no	—
215	C₂×#1055	—	2	1	no	—
216	C₂×#1055	—	2	1	no	—
217	C₂×#1055	—	2	1	no	—
218	C₂×#1055	C₂×D₄	1	2	yes	—
219	C₂×#1055	#41	1	2	yes	—
220	C₈×D₁₃	—	4	4	no	—
221	C₂×C₈×Q₈	—	13	1	no	—
222	C₂×C₈×D₄	—	13	1	no	—
223	C₄×#124	—	13	1	no	—
224	#1984	—	13	1	no	—
225	#1954	—	13	1	no	—
226	#1923	—	13	1	no	—
227	#1923	—	13	1	no	—
228	#1923	—	13	1	no	—
229	#1923	—	13	1	no	—
230	#1831	—	13	1	no	—
231	C₈×C₂²⋊C₄	—	13	1	no	—
232	C₈×C₂²⋊C₄	—	13	1	no	—
233	C₈×C₂²⋊C₄	—	13	1	no	—
234	C₈×C₂²⋊C₄	D₁₃	1	1	yes	characteristic, complemented
235	C₄²×C₈	—	13	1	no	—
236	C₂³×C₁₃	—	2	1	no	—
237	C₂³×C₁₃	—	2	1	no	—
238	C₂³×C₁₃	—	2	1	no	—
239	C₂³×C₁₃	—	2	1	no	—
240	C₂³×C₁₃	—	2	1	no	—
241	C₂³×C₁₃	—	2	1	no	—
242	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
243	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
244	C₂²×D₁₃	—	2	1	no	—
245	C₂²×D₁₃	—	2	1	no	—
246	C₂²×D₁₃	—	2	1	no	—
247	C₂²×D₁₃	—	2	1	no	—
248	C₂²×D₁₃	—	2	1	no	—
249	C₂²×D₁₃	—	2	1	no	—
250	C₂²×D₁₃	C₂²×C₈	1	2	yes	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
268	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
269	C₂×C₄×C₁₃	#131	1	2	yes	—
270	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
276	C₂²⋊D₁₃	—	2	8	no	—
277	C₂×Dic₁₃	—	2	1	no	—
278	C₂×Dic₁₃	—	2	1	no	—
279	C₂×Dic₁₃	—	2	1	no	—
280	C₂×Dic₁₃	—	2	1	no	—
281	C₂×Dic₁₃	—	2	1	no	—
282	C₂×Dic₁₃	—	2	1	no	—
283	C₂×Dic₁₃	—	2	1	no	—
284	C₂×Dic₁₃	—	2	1	no	—
285	C₂×Dic₁₃	—	2	1	no	—
286	C₂×Dic₁₃	—	2	1	no	—
287	C₂×Dic₁₃	—	2	1	no	—
288	C₂×Dic₁₃	—	2	1	no	—
289	C₂×Dic₁₃	—	2	1	no	—
290	C₂×Dic₁₃	—	2	1	no	—
291	C₂×Dic₁₃	C₄×D₄	1	2	yes	—
292	C₂×Dic₁₃	C₄×D₄	1	2	yes	—
293	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
294	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
295	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
296	C₂×Dic₁₃	#131	1	2	yes	—
297	C₂×Dic₁₃	#131	1	2	yes	—
298	C₄×D₁₃	—	4	1	no	—
299	C₄×D₁₃	—	4	1	no	—
300	C₄×D₁₃	—	4	1	no	—
301	C₄×D₁₃	—	4	1	no	—
302	Dic₂₆	—	2	8	no	—
303	C₈×C₁₃	—	2	2	no	—
304	C₈×C₁₃	—	4	1	no	—
305	C₈×C₁₃	—	4	1	no	—
306	C₈×C₁₃	#124	1	4	yes	complemented
307	#1055	—	2	2	no	—
308	#1055	—	2	2	no	—
309	#1055	—	4	1	no	—
310	#1055	—	4	1	no	—
311	C₂³×C₈	—	13	1	no	—
312	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
313	C₂×#124	—	13	1	no	—
314	C₂×C₄×Q₈	—	13	1	no	—
315	C₂×C₄×D₄	—	13	1	no	—
316	C₈×Q₈	—	26	4	no	—
317	C₈×D₄	—	26	4	no	—
318	C₂×C₄⋊C₈	—	13	1	no	—
319	C₂×C₄⋊C₈	—	13	1	no	—
320	C₂×C₄⋊C₈	—	13	1	no	—
321	C₂×C₄⋊C₈	—	13	1	no	—
322	C₂×C₂²⋊C₈	—	13	1	no	—
323	C₂×C₂²⋊C₈	—	13	1	no	—
324	C₂×C₂²⋊C₈	—	13	1	no	—
325	C₂×C₂²⋊C₈	—	13	1	no	—
326	C₂×C₂²⋊C₈	—	13	1	no	—
327	C₂×C₂²⋊C₈	C₂×D₁₃	1	1	yes	characteristic
328	C₂×C₄×C₈	—	13	1	no	—
329	C₂×C₄×C₈	—	13	1	no	—
330	C₂×C₄×C₈	—	13	1	no	—
331	C₂×C₄×C₈	—	13	1	no	—
332	C₂×C₄×C₈	—	13	1	no	—
333	C₂×C₄×C₈	—	13	1	no	—
334	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
335	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
336	#391	—	13	1	no	—
337	#390	—	13	1	no	—
338	#388	—	13	1	no	—
339	#388	—	13	1	no	—
340	#388	—	13	1	no	—
341	#388	—	13	1	no	—
342	#382	—	13	1	no	—
343	C₄×C₂²⋊C₄	—	13	1	no	—
344	C₄×C₂²⋊C₄	—	13	1	no	—
345	C₄×C₂²⋊C₄	—	13	1	no	—
346	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
347	C₄³	—	13	1	no	—
348	#336	—	13	1	no	—
349	#336	—	13	1	no	—
350	#336	—	13	1	no	—
351	#336	—	13	1	no	—
352	#336	—	13	1	no	—
353	#336	—	13	1	no	—
354	#336	C₂×D₁₃	1	1	yes	characteristic
355	#336	C₂×D₁₃	1	1	yes	characteristic
356	C₂²×C₁₃	—	2	2	no	—
357	C₂²×C₁₃	—	2	2	no	—
358	C₂²×C₁₃	—	2	2	no	—
359	C₂²×C₁₃	—	4	1	no	—
360	C₂²×C₁₃	—	4	1	no	—
361	C₂²×C₁₃	—	4	1	no	—
362	C₂²×C₁₃	—	4	1	no	—
363	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
364	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
365	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
366	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
367	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
368	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
369	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
370	C₂×D₁₃	—	2	2	no	—
371	C₂×D₁₃	—	2	2	no	—
372	C₂×D₁₃	—	2	2	no	—
373	C₂×D₁₃	—	4	1	no	—
374	C₂×D₁₃	—	4	1	no	—
375	C₂×D₁₃	—	4	1	no	—
376	C₂×D₁₃	—	4	1	no	—
377	C₄×C₁₃	—	2	2	no	—
378	C₄×C₁₃	—	2	2	no	—
379	C₄×C₁₃	—	2	2	no	—
380	C₄×C₁₃	—	4	1	no	—
381	C₄×C₁₃	—	4	1	no	—
382	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
383	C₄×C₁₃	#529	1	1	yes	characteristic
384	C₄×C₁₃	#529	1	1	yes	characteristic
385	C₄×C₁₃	#532	1	1	yes	characteristic
386	Dic₁₃	—	2	2	no	—
387	Dic₁₃	—	2	2	no	—
388	Dic₁₃	—	2	2	no	—
389	Dic₁₃	—	2	2	no	—
390	Dic₁₃	—	4	1	no	—
391	Dic₁₃	—	4	1	no	—
392	Dic₁₃	C₈×D₄	1	4	yes	—
393	C₂²×Q₈	—	13	1	no	—
394	C₂²×D₄	—	13	1	no	—
395	C₂³×C₄	—	13	1	no	—
396	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
397	C₂²×C₈	—	2	2	no	—
398	C₂²×C₈	—	2	2	no	—
399	C₂²×C₈	—	2	2	no	—
400	C₂²×C₈	—	13	1	no	—
401	C₂²×C₈	—	13	1	no	—
402	C₂²×C₈	—	13	1	no	—
403	C₂²×C₈	—	13	1	no	—
404	C₂²×C₈	—	26	2	no	—
405	C₂²×C₈	—	26	2	no	—
406	C₂²×C₈	—	26	2	no	—
407	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
408	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
409	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
410	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
411	#124	—	13	8	no	—
412	C₄×Q₈	—	26	2	no	—
413	C₄×Q₈	—	26	2	no	—
414	C₄×D₄	—	26	2	no	—
415	C₄×D₄	—	26	2	no	—
416	C₂×C₄⋊C₄	—	13	1	no	—
417	C₂×C₄⋊C₄	—	13	1	no	—
418	C₂×C₄⋊C₄	—	13	1	no	—
419	C₂×C₄⋊C₄	—	13	1	no	—
420	C₂×C₂²⋊C₄	—	13	1	no	—
421	C₂×C₂²⋊C₄	—	13	1	no	—
422	C₂×C₂²⋊C₄	—	13	1	no	—
423	C₂×C₂²⋊C₄	—	13	1	no	—
424	C₂×C₂²⋊C₄	—	13	1	no	—
425	C₂×C₂²⋊C₄	—	13	1	no	—
426	C₂×C₂²⋊C₄	—	13	1	no	—
427	C₂×C₂²⋊C₄	—	13	1	no	—
428	C₂×C₂²⋊C₄	C₄×D₁₃	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	C₄×D₁₃	1	1	yes	characteristic
430	C₂×C₄²	—	13	1	no	—
431	C₂×C₄²	—	13	1	no	—
432	C₂×C₄²	—	13	1	no	—
433	C₂×C₄²	—	13	1	no	—
434	C₂×C₄²	—	13	1	no	—
435	C₂×C₄²	—	13	1	no	—
436	C₂×C₄²	—	13	1	no	—
437	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
438	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
439	C₄⋊C₈	—	26	2	no	—
440	C₄⋊C₈	—	26	2	no	—
441	C₄⋊C₈	—	26	2	no	—
442	C₄⋊C₈	—	26	2	no	—
443	C₂²⋊C₈	—	2	2	no	—
444	C₂²⋊C₈	—	26	2	no	—
445	C₂²⋊C₈	—	26	2	no	—
446	C₂²⋊C₈	—	26	2	no	—
447	C₂²⋊C₈	—	26	2	no	—
448	C₂²⋊C₈	—	26	2	no	—
449	C₄×C₈	—	2	2	no	—
450	C₄×C₈	—	2	2	no	—
451	C₄×C₈	—	13	4	no	—
452	C₄×C₈	—	26	2	no	—
453	C₄×C₈	—	26	2	no	—
454	C₄×C₈	—	26	2	no	—
455	C₄×C₈	—	26	2	no	—
456	C₄×C₈	—	26	2	no	—
457	#95	—	13	1	no	—
458	#95	—	13	1	no	—
459	#95	—	13	1	no	—
460	#95	—	13	1	no	—
461	#95	—	13	1	no	—
462	#95	—	13	1	no	—
463	#95	C₄×D₁₃	1	1	yes	characteristic
464	#95	C₄×D₁₃	1	1	yes	characteristic
465	C₂×C₁₃	—	4	2	no	—
466	C₂×C₁₃	C₄×#124	1	1	yes	characteristic
467	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
468	C₂×C₁₃	#2931	1	1	yes	characteristic
469	C₂×C₁₃	C₈×#41	1	1	yes	characteristic
470	C₂×C₁₃	C₈×#41	1	1	yes	characteristic
471	C₂×C₁₃	#2966	1	1	yes	characteristic
472	C₂×C₁₃	#2966	1	1	yes	characteristic
473	D₁₃	—	4	2	no	—
474	C₂⁴	—	13	1	no	—
475	C₂⁴	C₂×C₄×D₁₃	1	1	yes	characteristic
476	C₂×Q₈	—	13	4	no	—
477	C₂×Q₈	—	26	2	no	—
478	C₂×Q₈	—	26	2	no	—
479	C₂×D₄	—	13	4	no	—
480	C₂×D₄	—	26	2	no	—
481	C₂×D₄	—	26	2	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	13	1	no	—
489	C₂²×C₄	—	13	1	no	—
490	C₂²×C₄	—	13	1	no	—
491	C₂²×C₄	—	13	1	no	—
492	C₂²×C₄	—	13	1	no	—
493	C₂²×C₄	—	13	1	no	—
494	C₂²×C₄	—	13	1	no	—
495	C₂²×C₄	—	26	1	no	—
496	C₂²×C₄	—	26	1	no	—
497	C₂²×C₄	—	26	1	no	—
498	C₂²×C₄	—	26	1	no	—
499	C₂²×C₄	—	26	1	no	—
500	C₂²×C₄	—	26	1	no	—
501	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
502	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
503	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
504	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
505	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
506	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	4	4	no	—
516	C₂×C₈	—	13	2	no	—
517	C₂×C₈	—	13	2	no	—
518	C₂×C₈	—	26	1	no	—
519	C₂×C₈	—	26	1	no	—
520	C₂×C₈	—	26	1	no	—
521	C₂×C₈	—	26	1	no	—
522	C₂×C₈	—	26	1	no	—
523	C₂×C₈	—	26	1	no	—
524	C₂×C₈	—	26	1	no	—
525	C₂×C₈	—	26	1	no	—
526	C₂×C₈	—	26	1	no	—
527	C₂×C₈	—	26	1	no	—
528	C₂×C₈	—	52	4	no	—
529	C₂×C₈	#6127	1	2	yes	—
530	C₂×C₈	#6127	1	2	yes	—
531	C₂×C₈	D₄×D₁₃	1	2	yes	—
532	C₂×C₈	#6129	1	2	yes	—
533	C₄⋊C₄	—	26	2	no	—
534	C₄⋊C₄	—	26	2	no	—
535	C₄⋊C₄	—	26	2	no	—
536	C₄⋊C₄	—	26	2	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	13	4	no	—
539	C₂²⋊C₄	—	13	4	no	—
540	C₂²⋊C₄	—	13	4	no	—
541	C₂²⋊C₄	—	26	2	no	—
542	C₂²⋊C₄	—	26	2	no	—
543	C₂²⋊C₄	—	26	2	no	—
544	C₂²⋊C₄	—	26	2	no	—
545	C₂²⋊C₄	—	26	2	no	—
546	C₂²⋊C₄	C₈×D₁₃	1	4	yes	complemented
547	C₄²	—	2	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	13	4	no	—
552	C₄²	—	13	2	no	—
553	C₄²	—	13	2	no	—
554	C₄²	—	26	2	no	—
555	C₄²	—	26	2	no	—
556	C₄²	—	26	2	no	—
557	C₄²	—	26	1	no	—
558	C₄²	—	26	1	no	—
559	C₄²	—	26	1	no	—
560	C₄²	—	26	1	no	—
561	C₁₃	C₈×#124	1	1	yes	characteristic, complemented, Sylow
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	13	2	no	—
569	C₂³	—	26	1	no	—
570	C₂³	—	26	1	no	—
571	C₂³	—	26	1	no	—
572	C₂³	—	26	1	no	—
573	C₂³	—	26	1	no	—
574	C₂³	—	26	1	no	—
575	C₂³	C₂×C₈×D₁₃	1	2	yes	—
576	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
577	Q₈	—	26	8	no	—
578	D₄	—	26	8	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	13	2	no	—
596	C₂×C₄	—	13	2	no	—
597	C₂×C₄	—	13	2	no	—
598	C₂×C₄	—	13	2	no	—
599	C₂×C₄	—	13	2	no	—
600	C₂×C₄	—	13	2	no	—
601	C₂×C₄	—	13	2	no	—
602	C₂×C₄	—	26	1	no	—
603	C₂×C₄	—	26	1	no	—
604	C₂×C₄	—	26	1	no	—
605	C₂×C₄	—	26	1	no	—
606	C₂×C₄	—	26	1	no	—
607	C₂×C₄	—	26	1	no	—
608	C₂×C₄	—	26	1	no	—
609	C₂×C₄	—	26	1	no	—
610	C₂×C₄	—	26	1	no	—
611	C₂×C₄	—	26	1	no	—
612	C₂×C₄	—	26	1	no	—
613	C₂×C₄	—	26	1	no	—
614	C₂×C₄	—	26	1	no	—
615	C₂×C₄	—	26	1	no	—
616	C₂×C₄	—	52	1	no	—
617	C₂×C₄	—	52	1	no	—
618	C₂×C₄	—	52	1	no	—
619	C₂×C₄	—	52	1	no	—
620	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
621	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
622	C₂×C₄	#88155	1	2	yes	—
623	C₂×C₄	C₂×#6127	1	1	yes	characteristic
624	C₂×C₄	C₂×#6127	1	1	yes	characteristic
625	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
626	C₂×C₄	C₂×#6129	1	1	yes	characteristic
627	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
628	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
629	C₈	—	2	2	no	—
630	C₈	—	4	1	no	—
631	C₈	—	4	1	no	—
632	C₈	—	26	2	no	—
633	C₈	—	26	2	no	—
634	C₈	—	52	1	no	—
635	C₈	—	52	1	no	—
636	C₈	#88139	1	4	yes	direct product factor
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	1	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	26	2	no	—
645	C₂²	—	26	2	no	—
646	C₂²	—	26	2	no	—
647	C₂²	—	52	1	no	—
648	C₂²	—	52	1	no	—
649	C₂²	—	52	1	no	—
650	C₂²	—	52	1	no	—
651	C₂²	C₄×#6127	1	1	yes	characteristic
652	C₂²	C₄×#6129	1	1	yes	characteristic
653	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
654	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
655	C₂²	C₂×#88155	1	1	yes	characteristic
656	C₂²	D₁₃×#131	1	1	yes	characteristic
657	C₂²	D₁₃×#131	1	1	yes	characteristic
658	C₄	—	2	2	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	2	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	1	no	—
663	C₄	—	13	4	no	—
664	C₄	—	26	2	no	—
665	C₄	—	26	2	no	—
666	C₄	—	26	2	no	—
667	C₄	—	26	2	no	—
668	C₄	—	52	1	no	—
669	C₄	—	52	1	no	—
670	C₄	C₂×#88139	1	1	yes	characteristic
671	C₄	#11719233	1	1	yes	characteristic
672	C₄	#11719243	1	1	yes	characteristic
673	C₄	#11719253	1	1	yes	characteristic
674	C₂	—	4	2	no	—
675	C₂	—	52	2	no	—
676	C₂	C₄×#88139	1	1	yes	characteristic
677	C₂	C₈×D₄×D₁₃	1	1	yes	characteristic
678	C₂	#13123543	1	1	yes	characteristic
679	C₂	C₈×#6129	1	1	yes	characteristic
680	C₂	C₈×#6127	1	1	yes	characteristic
681	C₂	#13123804	1	1	yes	characteristic
682	C₂	#13123807	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₈×C₁₃×C₂²⋊C₄	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂²×C₂²⋊D₁₃	C₂×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₈×C₂²⋊C₄	D₁₃
hypocenter	C₁₃	C₈×#124
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₈×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×Dic₂₆	C₂	semidirect
4. #13115770	C₂	semidirect
6. #13115444	C₂	semidirect
7. #13115443	C₂	semidirect
8. #13115440	C₂	semidirect
9. #13115439	C₂	semidirect
10. #13114951	C₂	semidirect
11. C₈×#6103	C₂	semidirect
12. C₈×#6103	C₂	semidirect
13. C₈×C₂²⋊Dic₁₃	C₂	semidirect
14. C₄×C₈×Dic₁₃	C₂	semidirect
15. C₈×C₁₃×C₂²⋊C₄	C₂	semidirect
104. #88139	C₈	direct (N × H)
166. C₂×Dic₂₆	C₂×C₈	semidirect
181. C₁₃×C₂²⋊C₄	C₂×C₈	semidirect
188. C₂²⋊Dic₁₃	C₂×C₈	semidirect
192. #6103	C₂×C₈	semidirect
193. #6103	C₂×C₈	semidirect
205. C₄×Dic₁₃	C₂×C₈	semidirect
234. C₈×C₂²⋊C₄	D₁₃	semidirect
306. C₈×C₁₃	#124	semidirect
546. C₂²⋊C₄	C₈×D₁₃	semidirect
561. C₁₃	C₈×#124	semidirect
636. C₈	#88139	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×C₈×Dic₂₆	2
C₂×C₈×C₂²⋊D₁₃	2
C₄×#88139	2
#13115770	2
#13115628	2
#13115444	2
#13115443	2
#13115440	2
#13115439	2
#13114951	2
C₈×#6103	2
C₈×C₂²⋊Dic₁₃	2
C₄×C₈×Dic₁₃	2
C₈×C₁₃×C₂²⋊C₄	2
C₈×#124	13

Subgroups — C8×#88139 #15870780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#88139 #15870780