Subgroups — C₂×C₈×C₄⋊#261 #16797116

Order 3328.

1438 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃⋊(C₄⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×#261	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊#261	C₂	1	1	yes	maximal, characteristic
4	C₈×C₄⋊#261	C₂	1	8	yes	maximal, direct product factor
5	C₂×(C₂×#261)⋊C₈	C₂	1	2	yes	maximal
6	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄⋊#261	C₄	1	2	yes	—
8	C₂²×C₄×#261	C₂²	1	2	yes	—
9	C₂²×D₁₃⋊C₈	C₂²	1	2	yes	—
10	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
13	C₂×(C₂×#261)⋊C₄	C₄	1	2	yes	—
14	C₂×#88112	C₄	1	2	yes	complemented
15	C₂×C₄⋊#1057	C₄	1	2	yes	complemented
16	C₂×C₈×#261	—	2	8	no	—
17	C₂×C₈×#261	C₂²	1	8	yes	—
18	C₄×C₄⋊#261	C₄	1	4	yes	—
19	C₄×C₄⋊#261	C₂²	1	4	yes	—
20	D₁₃⋊(C₄⋊C₈)	C₄	1	4	yes	complemented
21	D₁₃⋊(C₄⋊C₈)	C₂²	1	4	yes	—
22	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
23	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic, complemented
24	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic, complemented
25	C₂×C₄×#1055	C₄	1	1	yes	characteristic, complemented
26	C₄×C₈×D₁₃	C₄	1	4	yes	complemented
27	C₄×C₈×D₁₃	C₂²	1	4	yes	—
28	(C₂×#261)⋊C₈	C₂²	1	8	yes	—
29	C₂³×#261	C₂×C₄	1	4	yes	—
30	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
33	C₂²×#1057	C₂×C₄	1	4	yes	—
34	C₂×C₄⋊#261	C₈	1	16	yes	direct product factor
35	C₂×C₄⋊#261	C₂×C₄	1	8	yes	—
36	C₂×C₄×#261	—	2	4	no	—
37	C₂×C₄×#261	—	2	4	no	—
38	C₂×C₄×#261	C₂×C₄	1	4	yes	—
39	C₂×C₄×#261	C₂³	1	4	yes	—
40	C₂×D₁₃⋊C₈	—	2	4	no	—
41	C₂×D₁₃⋊C₈	—	2	4	no	—
42	C₂×D₁₃⋊C₈	C₂×C₄	1	4	yes	—
43	C₂×D₁₃⋊C₈	C₂³	1	4	yes	—
44	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
51	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₁₃	—	2	2	no	—
53	C₂×C₈×D₁₃	—	2	2	no	—
54	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
55	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
56	C₂×C₈×D₁₃	D₄	1	4	yes	—
57	C₂×C₈×D₁₃	Q₈	1	4	yes	—
58	C₂×C₈×D₁₃	C₂³	1	2	yes	—
59	C₂×C₈×D₁₃	C₂³	1	2	yes	—
60	C₄²×D₁₃	C₂×C₄	1	2	yes	—
61	C₄²×D₁₃	C₂×C₄	1	2	yes	—
62	C₄²×D₁₃	C₂×C₄	1	2	yes	—
63	C₄²×D₁₃	C₂³	1	2	yes	—
64	(C₂×#261)⋊C₄	C₂×C₄	1	8	yes	—
65	#88112	C₂×C₄	1	8	yes	complemented
66	C₄⋊#1057	C₂×C₄	1	8	yes	complemented
67	C₈×#261	—	2	16	no	—
68	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
69	C₈×Dic₁₃	C₂×C₄	1	4	yes	complemented
70	C₈×Dic₁₃	C₂×C₄	1	4	yes	complemented
71	C₄×#1055	C₂×C₄	1	4	yes	complemented
72	C₂×C₈×C₄⋊C₄	—	13	1	no	maximal, Sylow
73	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
74	C₂²×#261	—	2	8	no	—
75	C₂²×#261	—	2	8	no	—
76	C₂²×#261	C₂×C₈	1	16	yes	—
77	C₂²×#261	C₂²×C₄	1	8	yes	—
78	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
82	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
83	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
84	C₂×C₄×D₁₃	—	2	4	no	—
85	C₂×C₄×D₁₃	C₄²	1	2	yes	—
86	C₂×C₄×D₁₃	C₄²	1	2	yes	—
87	C₂×C₄×D₁₃	C₂×C₈	1	8	yes	—
88	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
89	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
93	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
94	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
95	C₂×C₄×D₁₃	#41	1	2	yes	—
96	C₂×C₄×D₁₃	#41	1	2	yes	—
97	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
98	C₂×#1057	—	2	8	no	—
99	C₂×#1057	C₂²×C₄	1	8	yes	—
100	C₄⋊#261	C₂×C₈	1	32	yes	direct product factor
101	C₄×#261	—	2	8	no	—
102	C₄×#261	—	2	4	no	—
103	C₄×#261	—	2	4	no	—
104	D₁₃⋊C₈	—	2	8	no	—
105	D₁₃⋊C₈	—	2	4	no	—
106	D₁₃⋊C₈	—	2	4	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	complemented
109	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
111	C₄²×C₁₃	C₄²	1	2	yes	—
112	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
113	C₄×Dic₁₃	C₄²	1	2	yes	—
114	C₄×Dic₁₃	C₄²	1	2	yes	—
115	C₄×Dic₁₃	C₄²	1	2	yes	—
116	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
117	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
118	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
119	C₂×#1055	—	2	2	no	—
120	C₂×#1055	C₄⋊C₄	1	4	yes	complemented
121	C₂×#1055	C₂²×C₄	1	2	yes	—
122	C₂×#1055	C₂²×C₄	1	2	yes	—
123	C₈×D₁₃	—	2	4	no	—
124	C₈×D₁₃	—	2	2	no	—
125	C₈×D₁₃	—	2	2	no	—
126	C₈×D₁₃	C₄⋊C₄	1	8	yes	complemented
127	C₈×D₁₃	C₂×D₄	1	4	yes	—
128	C₈×D₁₃	C₂×Q₈	1	4	yes	—
129	C₂²×C₄⋊C₈	—	13	1	no	—
130	C₂²×C₄×C₈	—	13	1	no	—
131	C₂²×C₄×C₈	—	13	2	no	—
132	C₂×C₄×C₄⋊C₄	—	13	1	no	—
133	C₈×C₄⋊C₄	—	13	8	no	—
134	C₂×#336	—	13	2	no	—
135	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
136	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
137	C₂²×D₁₃	C₄×D₄	1	2	yes	—
138	C₂²×D₁₃	C₄×Q₈	1	2	yes	—
139	C₂²×D₁₃	C₂²×C₈	1	4	yes	—
140	C₂²×D₁₃	#131	1	4	yes	—
141	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
142	C₂×#261	—	2	8	no	—
143	C₂×#261	—	2	8	no	—
144	C₂×#261	—	2	32	no	—
145	C₂×#261	C₂²×C₈	1	16	yes	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	C₄×C₈	1	4	yes	complemented
148	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
149	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
151	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
152	C₂×C₄×C₁₃	#117	1	2	yes	—
153	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
154	C₂×Dic₁₃	—	2	2	no	—
155	C₂×Dic₁₃	C₄×C₈	1	4	yes	complemented
156	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
157	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
158	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
159	C₂×Dic₁₃	C₄×D₄	1	2	yes	—
160	C₂×Dic₁₃	C₄×Q₈	1	2	yes	—
161	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
162	C₄×D₁₃	—	2	4	no	—
163	C₄×D₁₃	—	2	4	no	—
164	C₄×D₁₃	C₄×C₈	1	8	yes	complemented
165	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
166	C₄×D₁₃	#117	1	2	yes	—
167	C₄×D₁₃	C₄×D₄	1	2	yes	—
168	C₄×D₁₃	C₄×D₄	1	2	yes	—
169	C₄×D₁₃	C₄×Q₈	1	2	yes	—
170	C₄×D₁₃	C₄×Q₈	1	2	yes	—
171	C₄×D₁₃	C₂²×C₈	1	8	yes	—
172	C₄×D₁₃	C₂²×D₄	1	1	yes	characteristic
173	C₄×D₁₃	C₂²×Q₈	1	1	yes	characteristic
174	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
175	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
176	#1057	—	2	8	no	—
177	C₈×C₁₃	—	2	2	no	—
178	C₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	complemented
179	#1055	—	2	2	no	—
180	#1055	C₂×C₄⋊C₄	1	4	yes	complemented
181	C₂³×C₈	—	13	1	no	—
182	C₂³×C₈	—	13	2	no	—
183	C₂³×C₈	—	13	1	no	—
184	C₂²×C₄⋊C₄	—	13	2	no	—
185	C₂²×C₄²	—	13	1	no	—
186	C₂²×C₄²	—	13	2	no	—
187	C₂×C₄⋊C₈	—	13	4	no	—
188	C₂×C₄⋊C₈	—	13	4	no	—
189	C₂×C₄⋊C₈	—	13	2	no	—
190	C₂×C₄⋊C₈	—	13	2	no	—
191	C₂×C₄×C₈	—	13	1	no	—
192	C₂×C₄×C₈	—	13	1	no	—
193	C₂×C₄×C₈	—	13	1	no	—
194	C₂×C₄×C₈	—	13	4	no	—
195	C₂×C₄×C₈	—	13	4	no	—
196	C₂×C₄×C₈	—	13	8	no	—
197	C₂×C₄×C₈	—	26	8	no	—
198	C₂×C₄×C₈	#261	1	1	yes	characteristic, complemented
199	C₄×C₄⋊C₄	—	13	4	no	—
200	C₄×C₄⋊C₄	—	13	4	no	—
201	C₂×#95	—	13	2	no	—
202	#336	—	13	8	no	—
203	C₂²×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
204	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
205	C₂²×C₁₃	#405	1	2	yes	—
206	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
207	C₂×D₁₃	C₄×C₄⋊C₄	1	2	yes	—
208	C₂×D₁₃	C₂×C₄×C₈	1	2	yes	—
209	C₂×D₁₃	#405	1	2	yes	—
210	C₂×D₁₃	C₈×D₄	1	8	yes	—
211	C₂×D₁₃	C₈×Q₈	1	8	yes	—
212	C₂×D₁₃	C₂×C₄×D₄	1	1	yes	characteristic
213	C₂×D₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
214	C₂×D₁₃	C₂³×C₈	1	2	yes	—
215	C₂×D₁₃	C₂×#131	1	2	yes	—
216	#261	—	2	16	no	—
217	C₄×C₁₃	—	2	2	no	—
218	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
219	C₄×C₁₃	C₂×C₄×C₈	1	4	yes	complemented
220	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
221	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
222	Dic₁₃	—	2	2	no	—
223	Dic₁₃	C₄×C₄⋊C₄	1	2	yes	—
224	Dic₁₃	C₂×C₄×C₈	1	4	yes	complemented
225	Dic₁₃	C₂×C₄×D₄	1	1	yes	characteristic
226	Dic₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
227	C₂³×C₄	—	13	1	no	—
228	C₂³×C₄	—	13	1	no	—
229	C₂³×C₄	—	13	4	no	—
230	C₂³×C₄	—	13	1	no	—
231	C₂²×C₈	—	13	1	no	—
232	C₂²×C₈	—	13	4	no	—
233	C₂²×C₈	—	13	4	no	—
234	C₂²×C₈	—	13	2	no	—
235	C₂²×C₈	—	13	2	no	—
236	C₂²×C₈	—	13	4	no	—
237	C₂²×C₈	—	13	4	no	—
238	C₂²×C₈	—	13	4	no	—
239	C₂²×C₈	—	13	1	no	—
240	C₂²×C₈	—	13	2	no	—
241	C₂²×C₈	—	13	2	no	—
242	C₂²×C₈	—	26	2	no	—
243	C₂²×C₈	—	26	2	no	—
244	C₂²×C₈	—	26	4	no	—
245	C₂²×C₈	—	26	4	no	—
246	C₂²×C₈	C₂×#261	1	1	yes	characteristic
247	C₂²×C₈	C₂×#261	1	1	yes	characteristic
248	C₂×C₄⋊C₄	—	13	8	no	—
249	C₂×C₄⋊C₄	—	13	16	no	—
250	C₂×C₄²	—	13	1	no	—
251	C₂×C₄²	—	13	1	no	—
252	C₂×C₄²	—	13	1	no	—
253	C₂×C₄²	—	13	2	no	—
254	C₂×C₄²	—	13	2	no	—
255	C₂×C₄²	—	13	2	no	—
256	C₂×C₄²	—	13	2	no	—
257	C₂×C₄²	—	13	4	no	—
258	C₂×C₄²	—	13	4	no	—
259	C₂×C₄²	—	26	4	no	—
260	C₂×C₄²	—	26	4	no	—
261	C₂×C₄²	C₂×#261	1	1	yes	characteristic
262	C₄⋊C₈	—	13	8	no	—
263	C₄⋊C₈	—	13	8	no	—
264	C₄×C₈	—	13	4	no	—
265	C₄×C₈	—	13	4	no	—
266	C₄×C₈	—	13	4	no	—
267	C₄×C₈	—	26	16	no	—
268	C₄×C₈	C₂×#261	1	4	yes	complemented
269	#95	—	13	8	no	—
270	C₂×C₁₃	C₈×C₄⋊C₄	1	4	yes	complemented
271	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
272	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
273	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
274	D₁₃	C₈×C₄⋊C₄	1	4	yes	complemented
275	D₁₃	C₂×C₈×D₄	1	2	yes	—
276	D₁₃	C₂×C₈×Q₈	1	2	yes	—
277	C₂⁴	—	13	1	no	—
278	C₂²×C₄	—	13	1	no	—
279	C₂²×C₄	—	13	1	no	—
280	C₂²×C₄	—	13	8	no	—
281	C₂²×C₄	—	13	1	no	—
282	C₂²×C₄	—	13	2	no	—
283	C₂²×C₄	—	13	1	no	—
284	C₂²×C₄	—	13	2	no	—
285	C₂²×C₄	—	13	2	no	—
286	C₂²×C₄	—	13	2	no	—
287	C₂²×C₄	—	13	2	no	—
288	C₂²×C₄	—	13	2	no	—
289	C₂²×C₄	—	13	1	no	—
290	C₂²×C₄	—	13	1	no	—
291	C₂²×C₄	—	13	8	no	—
292	C₂²×C₄	—	13	16	no	—
293	C₂²×C₄	—	13	1	no	—
294	C₂²×C₄	—	13	2	no	—
295	C₂²×C₄	—	13	2	no	—
296	C₂²×C₄	—	26	4	no	—
297	C₂²×C₄	—	26	8	no	—
298	C₂²×C₄	—	26	8	no	—
299	C₂²×C₄	C₄×#261	1	1	yes	characteristic
300	C₂²×C₄	C₄×#261	1	1	yes	characteristic
301	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	13	4	no	—
304	C₂×C₈	—	13	2	no	—
305	C₂×C₈	—	13	4	no	—
306	C₂×C₈	—	13	8	no	—
307	C₂×C₈	—	13	4	no	—
308	C₂×C₈	—	13	8	no	—
309	C₂×C₈	—	13	2	no	—
310	C₂×C₈	—	26	2	no	—
311	C₂×C₈	—	26	2	no	—
312	C₂×C₈	—	26	4	no	—
313	C₂×C₈	—	26	4	no	—
314	C₂×C₈	—	26	8	no	—
315	C₂×C₈	—	26	4	no	—
316	C₂×C₈	—	26	8	no	—
317	C₂×C₈	—	26	2	no	—
318	C₂×C₈	C₄⋊#261	1	4	yes	direct product factor
319	C₂×C₈	C₂²×#261	1	2	yes	—
320	C₂×C₈	C₂²×#261	1	2	yes	—
321	C₄⋊C₄	—	13	32	no	—
322	C₄²	—	13	2	no	—
323	C₄²	—	13	2	no	—
324	C₄²	—	13	2	no	—
325	C₄²	—	13	2	no	—
326	C₄²	—	13	2	no	—
327	C₄²	—	13	2	no	—
328	C₄²	—	26	4	no	—
329	C₄²	—	26	8	no	—
330	C₄²	—	26	4	no	—
331	C₄²	C₄×#261	1	2	yes	—
332	C₄²	C₂²×#261	1	2	yes	—
333	C₁₃	C₂×C₈×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
334	C₂³	—	13	2	no	—
335	C₂³	—	13	2	no	—
336	C₂³	—	13	4	no	—
337	C₂³	—	13	4	no	—
338	C₂³	—	13	1	no	—
339	C₂³	—	13	1	no	—
340	C₂³	C₂×C₄×#261	1	1	yes	characteristic
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	13	2	no	—
343	C₂×C₄	—	13	2	no	—
344	C₂×C₄	—	13	4	no	—
345	C₂×C₄	—	13	1	no	—
346	C₂×C₄	—	13	1	no	—
347	C₂×C₄	—	13	2	no	—
348	C₂×C₄	—	13	2	no	—
349	C₂×C₄	—	13	2	no	—
350	C₂×C₄	—	13	2	no	—
351	C₂×C₄	—	13	2	no	—
352	C₂×C₄	—	13	8	no	—
353	C₂×C₄	—	13	8	no	—
354	C₂×C₄	—	13	1	no	—
355	C₂×C₄	—	13	2	no	—
356	C₂×C₄	—	13	1	no	—
357	C₂×C₄	—	13	1	no	—
358	C₂×C₄	—	13	1	no	—
359	C₂×C₄	—	13	2	no	—
360	C₂×C₄	—	13	16	no	—
361	C₂×C₄	—	13	2	no	—
362	C₂×C₄	—	26	4	no	—
363	C₂×C₄	—	26	4	no	—
364	C₂×C₄	—	26	8	no	—
365	C₂×C₄	—	26	32	no	—
366	C₂×C₄	—	26	8	no	—
367	C₂×C₄	—	26	2	no	—
368	C₂×C₄	C₈×#261	1	4	yes	complemented
369	C₂×C₄	C₂×C₄×#261	1	2	yes	—
370	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄×#261	1	2	yes	—
372	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
373	C₂×C₄	#88237	1	2	yes	—
374	C₂×C₄	C₂³×#261	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	13	4	no	—
377	C₈	—	26	8	no	—
378	C₈	—	26	2	no	—
379	C₈	C₂×C₄⋊#261	1	4	yes	direct product factor
380	C₂²	—	13	1	no	—
381	C₂²	—	13	1	no	—
382	C₂²	—	13	2	no	—
383	C₂²	—	13	2	no	—
384	C₂²	—	13	2	no	—
385	C₂²	—	13	8	no	—
386	C₂²	—	13	8	no	—
387	C₂²	—	13	2	no	—
388	C₂²	—	13	2	no	—
389	C₂²	C₄×C₄⋊#261	1	2	yes	—
390	C₂²	C₂×C₈×#261	1	2	yes	—
391	C₂²	#11719089	1	2	yes	—
392	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	13	1	no	—
395	C₄	—	13	1	no	—
396	C₄	—	13	2	no	—
397	C₄	—	13	4	no	—
398	C₄	—	26	16	no	—
399	C₄	—	26	2	no	—
400	C₄	C₄×C₄⋊#261	1	2	yes	—
401	C₄	C₂×C₈×#261	1	4	yes	complemented
402	C₄	C₂²×C₄⋊#261	1	1	yes	characteristic
403	C₄	C₂×#88237	1	1	yes	characteristic
404	C₂	—	13	2	no	—
405	C₂	—	13	2	no	—
406	C₂	—	13	4	no	—
407	C₂	C₈×C₄⋊#261	1	4	yes	direct product factor
408	C₂	C₂×C₄×C₄⋊#261	1	1	yes	characteristic
409	C₂	C₂²×C₈×#261	1	1	yes	characteristic
410	C₂	C₂×#11719089	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₈×C₄⋊#261	C₂	direct (N × H)
14. C₂×#88112	C₄	semidirect
15. C₂×C₄⋊#1057	C₄	semidirect
20. D₁₃⋊(C₄⋊C₈)	C₄	semidirect
22. C₂×C₄×C₈×C₁₃	C₄	semidirect
23. C₂×C₈×Dic₁₃	C₄	semidirect
24. C₂×C₈×Dic₁₃	C₄	semidirect
25. C₂×C₄×#1055	C₄	semidirect
26. C₄×C₈×D₁₃	C₄	semidirect
34. C₂×C₄⋊#261	C₈	direct (N × H)
65. #88112	C₂×C₄	semidirect
66. C₄⋊#1057	C₂×C₄	semidirect
68. C₄×C₈×C₁₃	C₂×C₄	semidirect
69. C₈×Dic₁₃	C₂×C₄	semidirect
70. C₈×Dic₁₃	C₂×C₄	semidirect
71. C₄×#1055	C₂×C₄	semidirect
100. C₄⋊#261	C₂×C₈	direct (N × H)
108. C₂×C₈×C₁₃	C₄⋊C₄	semidirect
120. C₂×#1055	C₄⋊C₄	semidirect
126. C₈×D₁₃	C₄⋊C₄	semidirect
147. C₂×C₄×C₁₃	C₄×C₈	semidirect
155. C₂×Dic₁₃	C₄×C₈	semidirect
164. C₄×D₁₃	C₄×C₈	semidirect
178. C₈×C₁₃	C₂×C₄⋊C₄	semidirect
180. #1055	C₂×C₄⋊C₄	semidirect
198. C₂×C₄×C₈	#261	semidirect
219. C₄×C₁₃	C₂×C₄×C₈	semidirect
224. Dic₁₃	C₂×C₄×C₈	semidirect
268. C₄×C₈	C₂×#261	semidirect
270. C₂×C₁₃	C₈×C₄⋊C₄	semidirect
274. D₁₃	C₈×C₄⋊C₄	semidirect
318. C₂×C₈	C₄⋊#261	direct (N × H)
333. C₁₃	C₂×C₈×C₄⋊C₄	semidirect
368. C₂×C₄	C₈×#261	semidirect
379. C₈	C₂×C₄⋊#261	direct (N × H)
401. C₄	C₂×C₈×#261	semidirect
407. C₂	C₈×C₄⋊#261	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×D₁₃⋊(C₄⋊C₈)	2
C₂²×C₈×#261	2
C₂×C₄×C₄⋊#261	2
C₈×C₄⋊#261	2
C₂×(C₂×#261)⋊C₈	2
C₂×C₄×C₈×D₁₃	2
C₂×C₈×C₄⋊C₄	13

Subgroups — C2×C8×C4⋊#261 #16797116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×C₄⋊#261 #16797116