Subgroups — C₈×D₄×#261 #16797335

Order 3328.

1422 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×#261	C₂	1	2	yes	maximal, complemented
3	C₄×D₄×#261	C₂	1	1	yes	maximal, characteristic
4	#13130629	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×C₄⋊#261	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄⋊C₈×#261	C₂	1	1	yes	maximal, characteristic, complemented
7	#13130571	C₂	1	2	yes	maximal, complemented
8	C₈×C₂²⋊#261	C₂	1	2	yes	maximal, complemented
9	C₂²⋊C₈×#261	C₂	1	2	yes	maximal, complemented
10	C₄×C₈×#261	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic
12	C₂×D₄×#261	C₄	1	2	yes	—
13	C₂²×C₄×#261	C₂²	1	2	yes	—
14	C₂²×D₁₃⋊C₈	C₂²	1	2	yes	—
15	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
16	C₄×D₄×D₁₃	C₂²	1	1	yes	characteristic
17	D₄×#1057	C₄	1	2	yes	complemented
18	C₄×C₂²⋊#261	C₂²	1	2	yes	—
19	D₁₃⋊(C₂²⋊C₈)	C₂²	1	2	yes	—
20	C₂×C₈×#261	—	2	8	no	—
21	C₂×C₈×#261	C₂²	1	1	yes	characteristic
22	C₂×C₈×#261	C₂²	1	2	yes	—
23	C₂×C₈×#261	C₂²	1	1	yes	characteristic
24	C₂×C₈×#261	C₂²	1	2	yes	—
25	C₂×C₈×#261	C₂²	1	1	yes	characteristic
26	C₂×C₈×#261	C₂²	1	2	yes	—
27	C₂×C₈×#261	C₂²	1	1	yes	characteristic
28	C₄⋊C₄×#261	C₄	1	2	yes	—
29	#11719073	C₄	1	2	yes	complemented
30	C₂²⋊C₄×#261	C₄	1	4	yes	—
31	#11719063	C₄	1	4	yes	complemented
32	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
33	C₄²×#261	C₂²	1	1	yes	characteristic
34	D₁₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
35	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
36	C₈×D₄×C₁₃	C₄	1	1	yes	characteristic, complemented
37	C₈×C₂²⋊D₁₃	C₄	1	2	yes	complemented
38	D₄×#1055	C₄	1	1	yes	characteristic, complemented
39	#11718495	C₄	1	1	yes	characteristic, complemented
40	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	#11718386	C₄	1	2	yes	complemented
42	D₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
43	C₈×D₅₂	C₄	1	1	yes	characteristic, complemented
44	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
45	(C₂×#261)⋊C₈	C₂²	1	2	yes	—
46	(C₂×#261)⋊C₈	C₂²	1	2	yes	—
47	(C₂×#261)⋊C₈	C₂²	1	2	yes	—
48	C₂³×#261	C₂×C₄	1	4	yes	—
49	C₂×D₄×D₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
51	C₂×C₂²⋊#261	C₂×C₄	1	4	yes	—
52	C₂²×#1057	C₂×C₄	1	4	yes	complemented
53	D₄×#261	C₈	1	16	yes	direct product factor
54	C₂×C₄⋊#261	C₂×C₄	1	2	yes	—
55	C₂×C₄×#261	—	2	4	no	—
56	C₂×C₄×#261	—	2	4	no	—
57	C₂×C₄×#261	C₂×C₄	1	2	yes	—
58	C₂×C₄×#261	C₂×C₄	1	4	yes	—
59	C₂×C₄×#261	C₂×C₄	1	2	yes	—
60	C₂×C₄×#261	C₂³	1	1	yes	characteristic
61	C₂×C₄×#261	C₂³	1	2	yes	—
62	C₂×C₄×#261	C₂³	1	1	yes	characteristic
63	C₂×D₁₃⋊C₈	—	2	4	no	—
64	C₂×D₁₃⋊C₈	—	2	4	no	—
65	C₂×D₁₃⋊C₈	C₂×C₄	1	4	yes	complemented
66	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
67	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
68	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	complemented
70	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
71	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
72	C₄×C₂²⋊D₁₃	C₂×C₄	1	2	yes	—
73	C₂²×#1055	C₂×C₄	1	2	yes	complemented
74	C₂×C₈×D₁₃	—	2	4	no	—
75	C₂×C₈×D₁₃	—	2	4	no	—
76	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	complemented
77	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	complemented
78	C₂×C₈×D₁₃	C₂³	1	2	yes	—
79	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
80	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
81	#88147	C₂×C₄	1	1	yes	characteristic
82	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
83	#88135	C₂×C₄	1	2	yes	—
84	C₂²⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
85	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
86	C₄²×D₁₃	C₂³	1	1	yes	characteristic
87	C₂²⋊#1057	C₂×C₄	1	4	yes	complemented
88	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
89	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
90	#88112	C₂×C₄	1	2	yes	complemented
91	#88111	C₂×C₄	1	4	yes	complemented
92	C₄⋊#1057	C₂×C₄	1	2	yes	complemented
93	C₄×#1057	C₂×C₄	1	2	yes	complemented
94	C₄×#1057	C₂×C₄	1	2	yes	complemented
95	C₈×#261	—	2	4	no	—
96	C₈×#261	—	2	2	no	—
97	C₈×#261	—	2	4	no	—
98	C₈×#261	—	2	2	no	—
99	C₈×#261	—	2	4	no	—
100	C₈×#261	—	2	2	no	—
101	C₈×#261	D₄	1	4	yes	direct product factor
102	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic, complemented
103	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	complemented
104	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
105	C₂²⋊#1055	C₂×C₄	1	2	yes	complemented
106	#88060	C₂×C₄	1	2	yes	complemented
107	#88060	C₂×C₄	1	2	yes	complemented
108	#88054	C₂×C₄	1	2	yes	complemented
109	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic, complemented
110	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic, complemented
111	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic, complemented
112	C₄×#1055	C₂×C₄	1	1	yes	characteristic, complemented
113	C₄×C₈×D₄	—	13	1	no	maximal, Sylow
114	C₂³×D₁₃	C₂²×C₄	1	2	yes	—
115	C₂²×#261	—	2	8	no	—
116	C₂²×#261	—	2	8	no	—
117	C₂²×#261	C₂×C₈	1	16	yes	complemented
118	C₂²×#261	C₂²×C₄	1	2	yes	—
119	C₂²×#261	C₂²×C₄	1	4	yes	—
120	C₂²×#261	C₂²×C₄	1	2	yes	—
121	C₂×D₄×C₁₃	C₄²	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
123	C₂×C₂²⋊D₁₃	C₄²	1	2	yes	—
124	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
125	D₄×D₁₃	C₂×C₈	1	8	yes	—
126	C₂×D₅₂	C₄²	1	1	yes	characteristic
127	C₂×C₄×D₁₃	—	2	2	no	—
128	C₂×C₄×D₁₃	—	2	2	no	—
129	C₂×C₄×D₁₃	—	2	2	no	—
130	C₂×C₄×D₁₃	—	2	2	no	—
131	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
133	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
134	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
135	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
137	C₂²⋊#261	C₂×C₈	1	16	yes	complemented
138	C₂×#1057	—	2	8	no	—
139	C₂×#1057	C₂²×C₄	1	2	yes	—
140	C₂×#1057	C₂²×C₄	1	4	yes	—
141	C₂×#1057	C₂²×C₄	1	2	yes	—
142	C₄⋊#261	C₂×C₈	1	8	yes	complemented
143	C₄×#261	—	2	8	no	—
144	C₄×#261	—	2	4	no	—
145	C₄×#261	—	2	2	no	—
146	C₄×#261	—	2	1	no	—
147	C₄×#261	—	2	1	no	—
148	C₄×#261	—	2	2	no	—
149	C₄×#261	C₂×C₈	1	8	yes	complemented
150	C₄×#261	C₂×D₄	1	2	yes	—
151	C₄×#261	#41	1	2	yes	—
152	D₁₃⋊C₈	—	2	2	no	—
153	D₁₃⋊C₈	—	2	1	no	—
154	D₁₃⋊C₈	—	2	1	no	—
155	D₁₃⋊C₈	—	2	2	no	—
156	D₁₃⋊C₈	—	2	8	no	—
157	D₁₃⋊C₈	C₂×D₄	1	2	yes	—
158	D₁₃⋊C₈	#41	1	2	yes	—
159	C₂×C₈×C₁₃	—	2	4	no	—
160	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
162	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
163	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
164	C₁₃×C₂²⋊C₄	C₄²	1	2	yes	—
165	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
166	C₂²⋊Dic₁₃	C₄²	1	2	yes	—
167	#6103	C₄²	1	2	yes	—
168	#6103	C₄²	1	2	yes	—
169	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
170	#6101	C₄²	1	2	yes	—
171	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
172	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
173	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
174	C₂×#1055	—	2	4	no	—
175	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
176	C₂×#1055	C₂²×C₄	1	2	yes	—
177	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
178	C₈×D₁₃	—	2	2	no	—
179	C₈×D₁₃	—	2	1	no	—
180	C₈×D₁₃	—	2	1	no	—
181	C₈×D₁₃	—	2	2	no	—
182	C₈×D₁₃	—	2	4	no	—
183	C₈×D₁₃	—	2	4	no	—
184	C₈×D₁₃	C₂×D₄	1	2	yes	—
185	C₈×D₁₃	#41	1	2	yes	—
186	C₂×C₈×D₄	—	13	1	no	—
187	C₂×C₈×D₄	—	13	1	no	—
188	C₂²×C₄×C₈	—	13	2	no	—
189	C₄²×D₄	—	13	1	no	—
190	C₈×C₄⋊C₄	—	13	1	no	—
191	C₈×C₄⋊C₄	—	13	1	no	—
192	C₄×C₄⋊C₈	—	13	1	no	—
193	C₈×C₂²⋊C₄	—	13	2	no	—
194	C₈×C₂²⋊C₄	—	13	2	no	—
195	C₄×C₂²⋊C₈	—	13	2	no	—
196	C₄²×C₈	—	13	1	no	—
197	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
198	C₂²×D₁₃	—	2	2	no	—
199	C₂²×D₁₃	—	2	2	no	—
200	C₂²×D₁₃	—	2	4	no	—
201	C₂²×D₁₃	C₂×C₄²	1	2	yes	—
202	C₂²×D₁₃	C₂²×C₈	1	8	yes	—
203	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
204	C₂×#261	—	2	4	no	—
205	C₂×#261	—	2	2	no	—
206	C₂×#261	—	2	2	no	—
207	C₂×#261	—	2	4	no	—
208	C₂×#261	—	2	32	no	—
209	C₂×#261	C₄×D₄	1	4	yes	—
210	C₂×#261	C₂²×C₈	1	4	yes	—
211	C₂×#261	C₂²×C₈	1	8	yes	—
212	C₂×#261	C₂²×C₈	1	4	yes	—
213	C₂×#261	#131	1	4	yes	—
214	D₄×C₁₃	C₄×C₈	1	4	yes	complemented
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
219	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
221	C₂²⋊D₁₃	C₄×C₈	1	8	yes	complemented
222	C₂×Dic₁₃	—	2	2	no	—
223	C₂×Dic₁₃	—	2	2	no	—
224	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
225	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
226	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
227	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
228	D₅₂	C₄×C₈	1	4	yes	complemented
229	C₄×D₁₃	—	2	2	no	—
230	C₄×D₁₃	—	2	2	no	—
231	C₄×D₁₃	—	2	2	no	—
232	C₄×D₁₃	—	2	2	no	—
233	C₄×D₁₃	—	2	2	no	—
234	C₄×D₁₃	—	2	2	no	—
235	C₄×D₁₃	—	2	2	no	—
236	C₄×D₁₃	C₂²×C₈	1	4	yes	—
237	C₄×D₁₃	C₂²×D₄	1	1	yes	characteristic
238	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
239	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
240	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
241	#1057	—	2	4	no	—
242	#1057	—	2	2	no	—
243	#1057	C₄×D₄	1	4	yes	complemented
244	C₈×C₁₃	—	2	2	no	—
245	C₈×C₁₃	—	2	1	no	—
246	C₈×C₁₃	C₄×D₄	1	2	yes	complemented
247	#1055	—	2	2	no	—
248	#1055	—	2	1	no	—
249	#1055	C₄×D₄	1	2	yes	complemented
250	C₂³×C₈	—	13	2	no	—
251	C₂³×C₈	—	13	2	no	—
252	C₂×C₄×D₄	—	13	2	no	—
253	C₂×C₄×D₄	—	13	1	no	—
254	C₂²×C₄²	—	13	2	no	—
255	C₈×D₄	—	13	4	no	—
256	C₈×D₄	—	13	2	no	—
257	C₈×D₄	—	13	2	no	—
258	C₈×D₄	—	13	2	no	—
259	C₈×D₄	—	13	1	no	—
260	C₈×D₄	—	13	1	no	—
261	C₈×D₄	—	13	2	no	—
262	C₈×D₄	—	13	1	no	—
263	C₈×D₄	#261	1	1	yes	characteristic, direct product factor
264	C₂×C₄⋊C₈	—	13	1	no	—
265	C₂×C₄⋊C₈	—	13	1	no	—
266	C₂×C₂²⋊C₈	—	13	2	no	—
267	C₂×C₂²⋊C₈	—	13	2	no	—
268	C₂×C₄×C₈	—	13	1	no	—
269	C₂×C₄×C₈	—	13	1	no	—
270	C₂×C₄×C₈	—	13	1	no	—
271	C₂×C₄×C₈	—	13	2	no	—
272	C₂×C₄×C₈	—	13	2	no	—
273	C₂×C₄×C₈	—	13	2	no	—
274	C₂×C₄×C₈	—	13	1	no	—
275	C₂×C₄×C₈	—	13	1	no	—
276	C₂×C₄×C₈	—	13	1	no	—
277	C₂×C₄×C₈	—	26	8	no	—
278	C₄×C₄⋊C₄	—	13	1	no	—
279	C₄×C₄⋊C₄	—	13	2	no	—
280	C₄×C₂²⋊C₄	—	13	4	no	—
281	C₄×C₂²⋊C₄	—	13	2	no	—
282	C₄³	—	13	1	no	—
283	#336	—	13	2	no	—
284	#336	—	13	2	no	—
285	#336	—	13	2	no	—
286	C₂²×C₁₃	—	2	2	no	—
287	C₂²×C₁₃	—	2	2	no	—
288	C₂²×C₁₃	C₂×C₄×C₈	1	4	yes	complemented
289	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
290	C₂×D₁₃	—	2	2	no	—
291	C₂×D₁₃	—	2	2	no	—
292	C₂×D₁₃	—	2	8	no	—
293	C₂×D₁₃	—	2	8	no	—
294	C₂×D₁₃	C₂×C₄×C₈	1	4	yes	complemented
295	C₂×D₁₃	C₂×C₄×D₄	1	1	yes	characteristic
296	C₂×D₁₃	C₄×#41	1	1	yes	characteristic
297	C₂×D₁₃	C₂³×C₈	1	2	yes	—
298	C₂×D₁₃	C₂×#131	1	2	yes	—
299	#261	—	2	8	no	—
300	#261	—	2	4	no	—
301	#261	C₈×D₄	1	8	yes	direct product factor
302	C₄×C₁₃	—	2	1	no	—
303	C₄×C₁₃	—	2	2	no	—
304	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	complemented
305	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
306	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
307	Dic₁₃	—	2	1	no	—
308	Dic₁₃	—	2	2	no	—
309	Dic₁₃	C₂×C₄×C₈	1	2	yes	complemented
310	Dic₁₃	C₂×C₄×D₄	1	1	yes	characteristic
311	Dic₁₃	C₄×#41	1	1	yes	characteristic
312	C₂²×D₄	—	13	1	no	—
313	C₂³×C₄	—	13	4	no	—
314	C₂³×C₄	—	13	2	no	—
315	C₂²×C₈	—	13	1	no	—
316	C₂²×C₈	—	13	1	no	—
317	C₂²×C₈	—	13	2	no	—
318	C₂²×C₈	—	13	4	no	—
319	C₂²×C₈	—	13	4	no	—
320	C₂²×C₈	—	13	1	no	—
321	C₂²×C₈	—	13	2	no	—
322	C₂²×C₈	—	13	2	no	—
323	C₂²×C₈	—	13	2	no	—
324	C₂²×C₈	—	13	1	no	—
325	C₂²×C₈	—	13	2	no	—
326	C₂²×C₈	—	26	4	no	—
327	C₂²×C₈	—	26	4	no	—
328	C₂²×C₈	—	26	4	no	—
329	C₂²×C₈	—	26	4	no	—
330	C₂²×C₈	C₂×#261	1	2	yes	complemented
331	C₄×D₄	—	13	16	no	—
332	C₄×D₄	—	13	1	no	—
333	C₄×D₄	—	13	2	no	—
334	C₄×D₄	—	13	1	no	—
335	C₄×D₄	—	13	2	no	—
336	C₄×D₄	—	13	1	no	—
337	C₄×D₄	C₂×#261	1	1	yes	characteristic
338	C₂×C₄⋊C₄	—	13	2	no	—
339	C₂×C₄⋊C₄	—	13	1	no	—
340	C₂×C₂²⋊C₄	—	13	4	no	—
341	C₂×C₂²⋊C₄	—	13	2	no	—
342	C₂×C₄²	—	13	2	no	—
343	C₂×C₄²	—	13	1	no	—
344	C₂×C₄²	—	13	1	no	—
345	C₂×C₄²	—	13	1	no	—
346	C₂×C₄²	—	13	2	no	—
347	C₂×C₄²	—	13	2	no	—
348	C₂×C₄²	—	13	4	no	—
349	C₂×C₄²	—	26	4	no	—
350	C₂×C₄²	—	26	4	no	—
351	C₄⋊C₈	—	13	2	no	—
352	C₄⋊C₈	—	13	2	no	—
353	C₄⋊C₈	—	13	2	no	—
354	C₄⋊C₈	—	13	1	no	—
355	C₄⋊C₈	C₂×#261	1	1	yes	characteristic, complemented
356	C₂²⋊C₈	—	13	4	no	—
357	C₂²⋊C₈	—	13	4	no	—
358	C₂²⋊C₈	—	13	2	no	—
359	C₂²⋊C₈	—	13	2	no	—
360	C₂²⋊C₈	—	13	2	no	—
361	C₂²⋊C₈	C₂×#261	1	2	yes	complemented
362	C₄×C₈	—	13	4	no	—
363	C₄×C₈	—	13	2	no	—
364	C₄×C₈	—	13	2	no	—
365	C₄×C₈	—	13	1	no	—
366	C₄×C₈	—	13	1	no	—
367	C₄×C₈	—	13	1	no	—
368	C₄×C₈	—	26	2	no	—
369	C₄×C₈	—	26	4	no	—
370	C₄×C₈	—	26	2	no	—
371	C₄×C₈	—	26	2	no	—
372	C₄×C₈	—	26	4	no	—
373	C₄×C₈	—	26	4	no	—
374	C₄×C₈	C₂×#261	1	1	yes	characteristic, complemented
375	#95	—	13	4	no	—
376	#95	—	13	2	no	—
377	C₂×C₁₃	—	2	4	no	—
378	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
379	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
380	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
381	D₁₃	—	2	4	no	—
382	D₁₃	C₂×C₈×D₄	1	2	yes	—
383	D₁₃	C₈×#41	1	2	yes	—
384	C₂⁴	—	13	2	no	—
385	C₂×D₄	—	13	2	no	—
386	C₂×D₄	—	13	8	no	—
387	C₂×D₄	—	13	1	no	—
388	C₂×D₄	C₄×#261	1	1	yes	characteristic
389	C₂²×C₄	—	13	2	no	—
390	C₂²×C₄	—	13	1	no	—
391	C₂²×C₄	—	13	1	no	—
392	C₂²×C₄	—	13	2	no	—
393	C₂²×C₄	—	13	4	no	—
394	C₂²×C₄	—	13	16	no	—
395	C₂²×C₄	—	13	2	no	—
396	C₂²×C₄	—	13	1	no	—
397	C₂²×C₄	—	13	2	no	—
398	C₂²×C₄	—	13	2	no	—
399	C₂²×C₄	—	13	2	no	—
400	C₂²×C₄	—	26	2	no	—
401	C₂²×C₄	—	26	2	no	—
402	C₂²×C₄	—	26	2	no	—
403	C₂²×C₄	—	26	2	no	—
404	C₂²×C₄	—	26	8	no	—
405	C₂²×C₄	—	26	8	no	—
406	C₂²×C₄	C₂²×#261	1	2	yes	—
407	C₂×C₈	—	2	4	no	—
408	C₂×C₈	—	13	2	no	—
409	C₂×C₈	—	13	2	no	—
410	C₂×C₈	—	13	2	no	—
411	C₂×C₈	—	13	1	no	—
412	C₂×C₈	—	13	2	no	—
413	C₂×C₈	—	13	2	no	—
414	C₂×C₈	—	13	2	no	—
415	C₂×C₈	—	13	4	no	—
416	C₂×C₈	—	13	1	no	—
417	C₂×C₈	—	13	2	no	—
418	C₂×C₈	—	26	4	no	—
419	C₂×C₈	—	26	2	no	—
420	C₂×C₈	—	26	1	no	—
421	C₂×C₈	—	26	1	no	—
422	C₂×C₈	—	26	2	no	—
423	C₂×C₈	—	26	4	no	—
424	C₂×C₈	—	26	8	no	—
425	C₂×C₈	—	26	8	no	—
426	C₂×C₈	—	26	2	no	—
427	C₂×C₈	—	26	1	no	—
428	C₂×C₈	—	26	1	no	—
429	C₂×C₈	—	26	2	no	—
430	C₂×C₈	—	26	4	no	—
431	C₂×C₈	C₂²×#261	1	1	yes	characteristic
432	C₂×C₈	C₂²×#261	1	2	yes	—
433	C₂×C₈	C₂²×#261	1	1	yes	characteristic
434	C₄⋊C₄	—	13	8	no	—
435	C₄⋊C₄	—	13	2	no	—
436	C₄⋊C₄	—	13	1	no	—
437	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
438	C₂²⋊C₄	—	13	16	no	—
439	C₂²⋊C₄	—	13	2	no	—
440	C₂²⋊C₄	—	13	2	no	—
441	C₂²⋊C₄	—	13	2	no	—
442	C₂²⋊C₄	C₄×#261	1	2	yes	—
443	C₄²	—	13	2	no	—
444	C₄²	—	13	2	no	—
445	C₄²	—	13	8	no	—
446	C₄²	—	13	1	no	—
447	C₄²	—	13	1	no	—
448	C₄²	—	13	1	no	—
449	C₄²	—	26	2	no	—
450	C₄²	—	26	1	no	—
451	C₄²	—	26	1	no	—
452	C₄²	—	26	8	no	—
453	C₄²	—	26	2	no	—
454	C₄²	—	26	4	no	—
455	C₄²	C₂²×#261	1	1	yes	characteristic
456	C₁₃	C₄×C₈×D₄	1	1	yes	characteristic, complemented, Sylow
457	C₂³	—	13	1	no	—
458	C₂³	—	13	8	no	—
459	C₂³	—	13	2	no	—
460	C₂³	—	26	2	no	—
461	C₂³	—	26	2	no	—
462	C₂³	—	26	4	no	—
463	C₂³	C₂×C₄×#261	1	2	yes	—
464	D₄	—	13	8	no	—
465	D₄	—	13	4	no	—
466	D₄	C₈×#261	1	4	yes	direct product factor
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	13	4	no	—
470	C₂×C₄	—	13	4	no	—
471	C₂×C₄	—	13	4	no	—
472	C₂×C₄	—	13	1	no	—
473	C₂×C₄	—	13	1	no	—
474	C₂×C₄	—	13	4	no	—
475	C₂×C₄	—	13	1	no	—
476	C₂×C₄	—	13	1	no	—
477	C₂×C₄	—	13	1	no	—
478	C₂×C₄	—	13	1	no	—
479	C₂×C₄	—	13	4	no	—
480	C₂×C₄	—	13	8	no	—
481	C₂×C₄	—	13	1	no	—
482	C₂×C₄	—	13	2	no	—
483	C₂×C₄	—	26	2	no	—
484	C₂×C₄	—	26	2	no	—
485	C₂×C₄	—	26	2	no	—
486	C₂×C₄	—	26	2	no	—
487	C₂×C₄	—	26	2	no	—
488	C₂×C₄	—	26	2	no	—
489	C₂×C₄	—	26	2	no	—
490	C₂×C₄	—	26	32	no	—
491	C₂×C₄	—	26	4	no	—
492	C₂×C₄	—	26	2	no	—
493	C₂×C₄	—	26	2	no	—
494	C₂×C₄	—	26	4	no	—
495	C₂×C₄	—	26	2	no	—
496	C₂×C₄	—	26	2	no	—
497	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
498	C₂×C₄	C₂×C₄×#261	1	2	yes	—
499	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
500	C₂×C₄	C₂³×#261	1	1	yes	characteristic
501	C₈	—	2	2	no	—
502	C₈	—	2	1	no	—
503	C₈	—	13	4	no	—
504	C₈	—	13	2	no	—
505	C₈	—	26	4	no	—
506	C₈	—	26	2	no	—
507	C₈	—	26	2	no	—
508	C₈	—	26	1	no	—
509	C₈	D₄×#261	1	2	yes	direct product factor
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	13	1	no	—
513	C₂²	—	13	1	no	—
514	C₂²	—	13	2	no	—
515	C₂²	—	13	2	no	—
516	C₂²	—	13	4	no	—
517	C₂²	—	26	8	no	—
518	C₂²	—	26	8	no	—
519	C₂²	—	26	2	no	—
520	C₂²	—	26	2	no	—
521	C₂²	C₂×C₈×#261	1	4	yes	complemented
522	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
523	C₄	—	2	2	no	—
524	C₄	—	2	1	no	—
525	C₄	—	13	8	no	—
526	C₄	—	13	1	no	—
527	C₄	—	13	1	no	—
528	C₄	—	13	2	no	—
529	C₄	—	26	4	no	—
530	C₄	—	26	8	no	—
531	C₄	—	26	2	no	—
532	C₄	—	26	1	no	—
533	C₄	C₂×C₈×#261	1	2	yes	complemented
534	C₄	C₂×D₄×#261	1	1	yes	characteristic
535	C₄	#41×#261	1	1	yes	characteristic
536	C₂	—	2	4	no	—
537	C₂	—	13	2	no	—
538	C₂	—	13	2	no	—
539	C₂	—	26	4	no	—
540	C₂	C₄×D₄×#261	1	1	yes	characteristic
541	C₂	C₂²×C₈×#261	1	1	yes	characteristic
542	C₂	#131×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×#261
commutator	C₂×C₁₃	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂³×#261
Fitting	C₈×D₄×C₁₃	C₄
socle	C₂²×C₁₃	C₂²×C₄²
prime radical	C₂×D₄×D₁₃	C₂×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₈×D₄	#261
hypocenter	C₁₃	C₄×C₈×D₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₈×#261	C₂	semidirect
4. #13130629	C₂	semidirect
5. C₈×C₄⋊#261	C₂	semidirect
6. C₄⋊C₈×#261	C₂	semidirect
7. #13130571	C₂	semidirect
8. C₈×C₂²⋊#261	C₂	semidirect
9. C₂²⋊C₈×#261	C₂	semidirect
10. C₄×C₈×#261	C₂	semidirect
17. D₄×#1057	C₄	semidirect
29. #11719073	C₄	semidirect
31. #11719063	C₄	semidirect
36. C₈×D₄×C₁₃	C₄	semidirect
37. C₈×C₂²⋊D₁₃	C₄	semidirect
38. D₄×#1055	C₄	semidirect
39. #11718495	C₄	semidirect
41. #11718386	C₄	semidirect
43. C₈×D₅₂	C₄	semidirect
52. C₂²×#1057	C₂×C₄	semidirect
53. D₄×#261	C₈	direct (N × H)
65. C₂×D₁₃⋊C₈	C₂×C₄	semidirect
69. C₂²×C₈×C₁₃	C₂×C₄	semidirect
73. C₂²×#1055	C₂×C₄	semidirect
76. C₂×C₈×D₁₃	C₂×C₄	semidirect
77. C₂×C₈×D₁₃	C₂×C₄	semidirect
87. C₂²⋊#1057	C₂×C₄	semidirect
90. #88112	C₂×C₄	semidirect
91. #88111	C₂×C₄	semidirect
92. C₄⋊#1057	C₂×C₄	semidirect
93. C₄×#1057	C₂×C₄	semidirect
94. C₄×#1057	C₂×C₄	semidirect
101. C₈×#261	D₄	direct (N × H)
102. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
103. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
104. C₄×C₈×C₁₃	C₂×C₄	semidirect
105. C₂²⋊#1055	C₂×C₄	semidirect
106. #88060	C₂×C₄	semidirect
107. #88060	C₂×C₄	semidirect
108. #88054	C₂×C₄	semidirect
109. C₈×Dic₁₃	C₂×C₄	semidirect
110. C₈×Dic₁₃	C₂×C₄	semidirect
111. C₄⋊#1055	C₂×C₄	semidirect
112. C₄×#1055	C₂×C₄	semidirect
117. C₂²×#261	C₂×C₈	semidirect
137. C₂²⋊#261	C₂×C₈	semidirect
142. C₄⋊#261	C₂×C₈	semidirect
149. C₄×#261	C₂×C₈	semidirect
214. D₄×C₁₃	C₄×C₈	semidirect
221. C₂²⋊D₁₃	C₄×C₈	semidirect
228. D₅₂	C₄×C₈	semidirect
243. #1057	C₄×D₄	semidirect
246. C₈×C₁₃	C₄×D₄	semidirect
249. #1055	C₄×D₄	semidirect
263. C₈×D₄	#261	direct (N × H)
288. C₂²×C₁₃	C₂×C₄×C₈	semidirect
294. C₂×D₁₃	C₂×C₄×C₈	semidirect
301. #261	C₈×D₄	direct (N × H)
304. C₄×C₁₃	C₂×C₄×C₈	semidirect
309. Dic₁₃	C₂×C₄×C₈	semidirect
330. C₂²×C₈	C₂×#261	semidirect
355. C₄⋊C₈	C₂×#261	semidirect
361. C₂²⋊C₈	C₂×#261	semidirect
374. C₄×C₈	C₂×#261	semidirect
456. C₁₃	C₄×C₈×D₄	semidirect
466. D₄	C₈×#261	direct (N × H)
509. C₈	D₄×#261	direct (N × H)
521. C₂²	C₂×C₈×#261	semidirect
533. C₄	C₂×C₈×#261	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₄×D₁₃⋊C₈	2
C₂²×C₈×#261	2
C₄×D₄×#261	2
#13130629	2
C₈×C₄⋊#261	2
C₄⋊C₈×#261	2
#13130571	2
C₈×C₂²⋊#261	2
C₂²⋊C₈×#261	2
C₄×C₈×#261	2
C₈×D₄×D₁₃	2
C₄×C₈×D₄	13

Subgroups — C8×D4×#261 #16797335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×D₄×#261 #16797335