Subgroups — #41×C₄⋊#261 #16807576

Order 3328.

3250 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×#261	C₂	1	2	yes	maximal
2	#13131351	C₂	1	2	yes	maximal, complemented
3	Q₈×C₄⋊#261	C₂	1	2	yes	maximal, complemented
4	#13131349	C₂	1	6	yes	maximal, complemented
5	D₄×C₄⋊#261	C₂	1	6	yes	maximal, complemented
6	#13131296	C₂	1	6	yes	maximal, complemented
7	#13131285	C₂	1	3	yes	maximal, complemented
8	C₂×C₄×C₄⋊#261	C₂	1	3	yes	maximal, complemented
9	C₄×#41×D₁₃	C₂	1	1	yes	maximal, characteristic
10	C₂×#41×D₁₃	C₂²	1	1	yes	characteristic
11	#41×#261	—	2	16	no	—
12	C₂×Q₈×#261	C₂²	1	4	yes	—
13	C₂×D₄×#261	C₂²	1	12	yes	—
14	C₂×#88237	C₂²	1	6	yes	—
15	C₂²×C₄⋊#261	C₂²	1	6	yes	—
16	C₂²×C₄×#261	C₂²	1	6	yes	—
17	C₄×C₁₃×#41	C₄	1	1	yes	characteristic, complemented
18	#41×Dic₁₃	C₄	1	1	yes	characteristic, complemented
19	C₄×#6131	C₄	1	1	yes	characteristic, complemented
20	C₄×#6131	C₄	1	1	yes	characteristic, complemented
21	C₄×Q₈×D₁₃	C₂²	1	1	yes	characteristic
22	C₄×Q₈×D₁₃	C₂²	1	1	yes	characteristic
23	C₄×D₄×D₁₃	C₂²	1	3	yes	—
24	C₄×D₄×D₁₃	C₂²	1	3	yes	—
25	C₄×#6129	C₄	1	3	yes	complemented
26	C₄×#6129	C₄	1	3	yes	complemented
27	#11719227	C₄	1	3	yes	complemented
28	D₁₃×#117	C₂²	1	3	yes	—
29	C₄×#6127	C₄	1	3	yes	complemented
30	C₂×C₄²×D₁₃	C₂²	1	3	yes	—
31	#11719136	C₂²	1	6	yes	—
32	#11719136	C₂²	1	6	yes	—
33	C₂×(C₂×#261)⋊C₄	C₂²	1	6	yes	—
34	#11719083	C₂²	1	12	yes	—
35	#11719083	C₂²	1	12	yes	—
36	#11719070	C₂²	1	24	yes	—
37	#11719060	C₂²	1	6	yes	—
38	#11719059	C₂²	1	6	yes	—
39	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊#261	C₂²	1	3	yes	—
41	C₄×C₄⋊#261	C₂²	1	6	yes	—
42	C₄×C₄⋊#261	C₂²	1	6	yes	—
43	C₄×C₄⋊#261	C₂²	1	6	yes	—
44	C₄×C₄⋊#261	C₂²	1	6	yes	—
45	C₂³×#261	C₂³	1	12	yes	—
46	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
47	#41×D₁₃	D₄	1	8	yes	—
48	#41×D₁₃	Q₈	1	8	yes	—
49	C₂×#6131	C₂×C₄	1	1	yes	characteristic
50	C₂×Q₈×D₁₃	C₂³	1	1	yes	characteristic
51	C₂×#6129	C₂×C₄	1	3	yes	—
52	C₂×D₄×D₁₃	C₂³	1	3	yes	—
53	C₂×#6127	C₂×C₄	1	3	yes	—
54	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
55	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
56	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
57	C₂×C₂²⋊#261	C₂³	1	12	yes	—
58	Q₈×#261	—	2	16	no	—
59	D₄×#261	—	2	48	no	—
60	#88237	—	2	24	no	—
61	C₂×C₄⋊#261	—	2	24	no	—
62	C₂×C₄⋊#261	C₂³	1	6	yes	—
63	C₂×C₄⋊#261	C₂³	1	12	yes	—
64	C₂×C₄⋊#261	C₂³	1	12	yes	—
65	C₂×C₄⋊#261	C₂³	1	12	yes	—
66	C₂×C₄⋊#261	C₂³	1	2	yes	—
67	C₂×C₄×#261	—	2	24	no	—
68	C₂×C₄×#261	C₂³	1	2	yes	—
69	C₂×C₄×#261	C₂³	1	6	yes	—
70	C₂×C₄×#261	C₂³	1	12	yes	—
71	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
72	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
73	C₄×D₄×C₁₃	C₂×C₄	1	3	yes	complemented
74	C₄×D₄×C₁₃	C₂×C₄	1	3	yes	complemented
75	C₁₃×#117	C₂×C₄	1	3	yes	complemented
76	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	complemented
77	Q₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic, complemented
78	Q₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic, complemented
79	D₄×Dic₁₃	C₂×C₄	1	3	yes	complemented
80	D₄×Dic₁₃	C₂×C₄	1	3	yes	complemented
81	C₄×C₂²⋊D₁₃	C₂×C₄	1	6	yes	complemented
82	C₄×C₂²⋊D₁₃	C₂×C₄	1	6	yes	complemented
83	#88180	C₂×C₄	1	3	yes	complemented
84	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	complemented
85	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	complemented
86	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	complemented
87	#88147	C₂×C₄	1	3	yes	complemented
88	#88147	C₂×C₄	1	3	yes	complemented
89	#88146	C₂×C₄	1	3	yes	complemented
90	#88146	C₂×C₄	1	3	yes	complemented
91	C₄⋊C₄×D₁₃	C₂³	1	3	yes	—
92	C₄⋊C₄×D₁₃	C₂³	1	3	yes	—
93	#88141	C₂×C₄	1	3	yes	complemented
94	#88141	C₂×C₄	1	3	yes	complemented
95	#88135	C₂×C₄	1	6	yes	complemented
96	#88135	C₂×C₄	1	6	yes	complemented
97	C₂²⋊C₄×D₁₃	C₂³	1	6	yes	—
98	#88131	C₂×C₄	1	6	yes	complemented
99	C₄×D₅₂	C₂×C₄	1	3	yes	complemented
100	C₄×D₅₂	C₂×C₄	1	3	yes	complemented
101	#88126	C₂×C₄	1	6	yes	complemented
102	C₄²×D₁₃	C₂×C₄	1	3	yes	complemented
103	C₄²×D₁₃	C₂×C₄	1	3	yes	complemented
104	C₄²×D₁₃	C₂×C₄	1	3	yes	complemented
105	C₄²×D₁₃	C₂×C₄	1	3	yes	complemented
106	C₄²×D₁₃	C₂³	1	1	yes	characteristic
107	C₄²×D₁₃	C₂³	1	3	yes	—
108	C₄²×D₁₃	C₂³	1	3	yes	—
109	C₄²×D₁₃	C₂³	1	3	yes	—
110	C₄×Dic₂₆	C₂×C₄	1	3	yes	complemented
111	C₄×Dic₂₆	C₂×C₄	1	3	yes	complemented
112	(C₂×#261)⋊C₄	C₂³	1	2	yes	—
113	(C₂×#261)⋊C₄	C₂³	1	6	yes	—
114	(C₂×#261)⋊C₄	C₂³	1	12	yes	—
115	(C₂×#261)⋊C₄	C₂³	1	12	yes	—
116	C₄⋊C₄×#41	—	13	1	no	maximal, Sylow
117	C₂³×D₁₃	C₂⁴	1	3	yes	—
118	C₂²×#261	—	2	24	no	—
119	C₂²×#261	—	2	24	no	—
120	C₂²×#261	—	4	12	no	—
121	C₂²×#261	C₂⁴	1	12	yes	—
122	C₂²×#261	C₂⁴	1	4	yes	—
123	C₁₃×#41	C₄⋊C₄	1	8	yes	complemented
124	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×D₄×C₁₃	C₂²×C₄	1	3	yes	—
126	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
127	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
128	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
129	C₂×C₂²⋊D₁₃	C₂²×C₄	1	6	yes	—
130	C₂²×Dic₁₃	C₂²×C₄	1	3	yes	—
131	C₂²×Dic₁₃	C₂²×C₄	1	3	yes	—
132	C₂²×Dic₁₃	C₂²×C₄	1	3	yes	—
133	#6131	C₄⋊C₄	1	8	yes	complemented
134	Q₈×D₁₃	C₂×D₄	1	4	yes	—
135	Q₈×D₁₃	C₂×Q₈	1	4	yes	—
136	#6129	C₄⋊C₄	1	24	yes	complemented
137	D₄×D₁₃	C₂×D₄	1	12	yes	—
138	D₄×D₁₃	C₂×Q₈	1	12	yes	—
139	#6127	C₄⋊C₄	1	24	yes	complemented
140	C₂×D₅₂	C₂²×C₄	1	3	yes	—
141	C₂×C₄×D₁₃	—	2	12	no	—
142	C₂×C₄×D₁₃	—	4	6	no	—
143	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
144	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
145	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
146	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
147	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
148	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
149	C₂×C₄×D₁₃	C₂×D₄	1	12	yes	—
150	C₂×C₄×D₁₃	C₂×Q₈	1	12	yes	—
151	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
152	C₂×C₄×D₁₃	C₂⁴	1	3	yes	—
153	C₂×C₄×D₁₃	C₂⁴	1	3	yes	—
154	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
155	C₂×C₄×D₁₃	C₂⁴	1	3	yes	—
156	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
157	C₂×Dic₂₆	C₂²×C₄	1	3	yes	—
158	C₂²⋊#261	—	2	24	no	—
159	C₄⋊#261	—	2	24	no	—
160	C₄⋊#261	—	2	24	no	—
161	C₄⋊#261	—	2	12	no	—
162	C₄⋊#261	—	4	12	no	—
163	C₄⋊#261	#41	1	8	yes	direct product factor
164	C₄×#261	—	2	4	no	—
165	C₄×#261	—	2	12	no	—
166	C₄×#261	—	2	24	no	—
167	C₁₃×C₄⋊C₄	C₂²×C₄	1	3	yes	—
168	C₁₃×C₄⋊C₄	C₂²×C₄	1	3	yes	—
169	C₁₃×C₂²⋊C₄	C₂²×C₄	1	6	yes	—
170	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
171	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
172	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
174	C₂²⋊Dic₁₃	C₂²×C₄	1	6	yes	—
175	#6103	C₂²×C₄	1	6	yes	—
176	#6103	C₂²×C₄	1	6	yes	—
177	C₄⋊Dic₁₃	C₂²×C₄	1	3	yes	—
178	C₄⋊Dic₁₃	C₂²×C₄	1	3	yes	—
179	#6101	C₂²×C₄	1	6	yes	—
180	#6101	C₂²×C₄	1	6	yes	—
181	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
182	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
183	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
184	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
185	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
186	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
187	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
188	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
189	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
190	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
191	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
192	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
193	C₂×C₄×#41	—	13	1	no	—
194	C₂×C₄×#41	—	13	2	no	—
195	#2351	—	13	2	no	—
196	Q₈×C₄⋊C₄	—	13	2	no	—
197	#2349	—	13	6	no	—
198	D₄×C₄⋊C₄	—	13	6	no	—
199	#2296	—	13	6	no	—
200	#2285	—	13	3	no	—
201	C₂×C₄×C₄⋊C₄	—	13	3	no	—
202	C₂³×C₁₃	C₂³×C₄	1	3	yes	—
203	C₂²×D₁₃	—	2	6	no	—
204	C₂²×D₁₃	—	2	6	no	—
205	C₂²×D₁₃	C₂³×C₄	1	3	yes	—
206	C₂²×D₁₃	C₂²×D₄	1	6	yes	—
207	C₂²×D₁₃	C₂²×Q₈	1	6	yes	—
208	C₂²×D₁₃	C₂⁵	1	1	yes	characteristic
209	C₂×#261	—	2	4	no	—
210	C₂×#261	—	2	4	no	—
211	C₂×#261	—	2	12	no	—
212	C₂×#261	—	2	12	no	—
213	C₂×#261	—	2	12	no	—
214	C₂×#261	—	4	48	no	—
215	C₂×#261	C₂×#41	1	8	yes	—
216	Q₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	complemented
217	D₄×C₁₃	C₂×C₄⋊C₄	1	12	yes	complemented
218	C₂×C₄×C₁₃	—	2	6	no	—
219	C₂×C₄×C₁₃	—	4	3	no	—
220	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	12	yes	complemented
221	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂³×C₄	1	3	yes	—
223	C₂×C₄×C₁₃	C₂³×C₄	1	3	yes	—
224	C₂×C₄×C₁₃	C₂³×C₄	1	3	yes	—
225	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
227	C₂²⋊D₁₃	C₂×C₄⋊C₄	1	24	yes	complemented
228	C₂×Dic₁₃	—	2	6	no	—
229	C₂×Dic₁₃	—	4	3	no	—
230	C₂×Dic₁₃	C₂×C₄⋊C₄	1	12	yes	complemented
231	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
232	C₂×Dic₁₃	C₂³×C₄	1	3	yes	—
233	C₂×Dic₁₃	C₂³×C₄	1	3	yes	—
234	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
235	C₂×Dic₁₃	C₂³×C₄	1	3	yes	—
236	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
237	D₅₂	C₂×C₄⋊C₄	1	12	yes	complemented
238	C₄×D₁₃	—	2	6	no	—
239	C₄×D₁₃	—	2	6	no	—
240	C₄×D₁₃	—	2	2	no	—
241	C₄×D₁₃	—	2	6	no	—
242	C₄×D₁₃	—	2	6	no	—
243	C₄×D₁₃	—	4	3	no	—
244	C₄×D₁₃	—	4	3	no	—
245	C₄×D₁₃	C₂×C₄⋊C₄	1	12	yes	complemented
246	C₄×D₁₃	C₂×C₄⋊C₄	1	12	yes	complemented
247	C₄×D₁₃	C₂²×D₄	1	2	yes	—
248	C₄×D₁₃	C₂²×D₄	1	6	yes	—
249	C₄×D₁₃	C₂²×Q₈	1	2	yes	—
250	C₄×D₁₃	C₂²×Q₈	1	6	yes	—
251	C₄×D₁₃	C₂×#41	1	4	yes	—
252	Dic₂₆	C₂×C₄⋊C₄	1	12	yes	complemented
253	C₂²×#41	—	13	1	no	—
254	C₄×#41	—	13	1	no	—
255	C₄×#41	—	13	1	no	—
256	C₄×#41	—	13	1	no	—
257	C₄×#41	—	13	3	no	—
258	C₄×#41	—	13	3	no	—
259	C₄×#41	—	13	3	no	—
260	C₄×#41	—	13	3	no	—
261	C₄×#41	—	26	16	no	—
262	C₄×#41	#261	1	1	yes	characteristic, complemented
263	C₂×C₄×Q₈	—	13	1	no	—
264	C₂×C₄×Q₈	—	13	1	no	—
265	C₂×C₄×Q₈	—	13	4	no	—
266	C₂×C₄×D₄	—	13	3	no	—
267	C₂×C₄×D₄	—	13	3	no	—
268	C₂×C₄×D₄	—	13	12	no	—
269	C₂×#117	—	13	3	no	—
270	C₂×#117	—	13	6	no	—
271	C₂²×C₄⋊C₄	—	13	6	no	—
272	C₂²×C₄²	—	13	3	no	—
273	C₂²×C₄²	—	13	6	no	—
274	#389	—	13	12	no	—
275	#389	—	13	12	no	—
276	#385	—	13	24	no	—
277	#384	—	13	6	no	—
278	#382	—	13	6	no	—
279	#380	—	13	6	no	—
280	#380	—	13	6	no	—
281	C₄×C₄⋊C₄	—	13	6	no	—
282	C₄×C₄⋊C₄	—	13	6	no	—
283	C₄×C₄⋊C₄	—	13	1	no	—
284	C₄×C₄⋊C₄	—	13	3	no	—
285	C₄×C₄⋊C₄	—	13	6	no	—
286	C₄×C₄⋊C₄	—	13	6	no	—
287	C₂×#95	—	13	6	no	—
288	C₂²×C₁₃	—	2	3	no	—
289	C₂²×C₁₃	—	2	3	no	—
290	C₂²×C₁₃	C₂²×C₄⋊C₄	1	6	yes	—
291	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
292	C₂×D₁₃	—	2	3	no	—
293	C₂×D₁₃	—	2	3	no	—
294	C₂×D₁₃	—	2	12	no	—
295	C₂×D₁₃	—	2	12	no	—
296	C₂×D₁₃	C₂²×C₄⋊C₄	1	6	yes	—
297	C₂×D₁₃	C₂³×D₄	1	1	yes	characteristic
298	C₂×D₁₃	C₂³×Q₈	1	1	yes	characteristic
299	C₂×D₁₃	C₂²×#41	1	2	yes	—
300	C₂×D₁₃	#585	1	2	yes	—
301	#261	—	2	8	no	—
302	#261	—	4	12	no	—
303	C₄×C₁₃	—	2	3	no	—
304	C₄×C₁₃	—	2	1	no	—
305	C₄×C₁₃	—	2	3	no	—
306	C₄×C₁₃	C₂²×C₄⋊C₄	1	6	yes	—
307	C₄×C₁₃	C₂²×C₄⋊C₄	1	2	yes	—
308	C₄×C₁₃	C₄×#41	1	2	yes	complemented
309	Dic₁₃	—	2	3	no	—
310	Dic₁₃	—	2	1	no	—
311	Dic₁₃	—	2	3	no	—
312	Dic₁₃	C₂²×C₄⋊C₄	1	6	yes	—
313	Dic₁₃	C₂²×C₄⋊C₄	1	2	yes	—
314	Dic₁₃	C₄×#41	1	2	yes	complemented
315	C₂×#41	—	13	8	no	—
316	C₂×#41	—	13	8	no	—
317	C₂×#41	—	13	1	no	—
318	C₂×#41	—	13	3	no	—
319	C₂×#41	—	13	3	no	—
320	C₂×#41	C₂×#261	1	1	yes	characteristic
321	C₂²×Q₈	—	13	1	no	—
322	C₂²×D₄	—	13	3	no	—
323	C₂³×C₄	—	13	3	no	—
324	C₂³×C₄	—	13	3	no	—
325	C₂³×C₄	—	13	3	no	—
326	C₂³×C₄	—	13	12	no	—
327	C₄×Q₈	—	13	1	no	—
328	C₄×Q₈	—	13	1	no	—
329	C₄×Q₈	—	13	3	no	—
330	C₄×Q₈	—	13	3	no	—
331	C₄×Q₈	—	13	3	no	—
332	C₄×Q₈	—	13	3	no	—
333	C₄×Q₈	—	26	16	no	—
334	C₄×Q₈	C₂×#261	1	1	yes	characteristic, complemented
335	C₄×Q₈	C₂×#261	1	1	yes	characteristic, complemented
336	C₄×D₄	—	13	3	no	—
337	C₄×D₄	—	13	3	no	—
338	C₄×D₄	—	13	6	no	—
339	C₄×D₄	—	13	6	no	—
340	C₄×D₄	—	13	3	no	—
341	C₄×D₄	—	13	3	no	—
342	C₄×D₄	—	13	6	no	—
343	C₄×D₄	—	13	6	no	—
344	C₄×D₄	—	13	3	no	—
345	C₄×D₄	—	13	3	no	—
346	C₄×D₄	—	26	48	no	—
347	C₄×D₄	C₂×#261	1	3	yes	complemented
348	C₄×D₄	C₂×#261	1	3	yes	complemented
349	#117	—	13	3	no	—
350	#117	—	13	3	no	—
351	#117	—	13	3	no	—
352	#117	—	13	6	no	—
353	#117	—	13	6	no	—
354	#117	—	26	24	no	—
355	#117	C₂×#261	1	3	yes	complemented
356	C₂×C₄⋊C₄	—	13	2	no	—
357	C₂×C₄⋊C₄	—	13	3	no	—
358	C₂×C₄⋊C₄	—	13	3	no	—
359	C₂×C₄⋊C₄	—	13	6	no	—
360	C₂×C₄⋊C₄	—	13	12	no	—
361	C₂×C₄⋊C₄	—	13	12	no	—
362	C₂×C₄⋊C₄	—	13	12	no	—
363	C₂×C₄⋊C₄	—	26	24	no	—
364	C₂×C₂²⋊C₄	—	13	6	no	—
365	C₂×C₂²⋊C₄	—	13	12	no	—
366	C₂×C₄²	—	13	3	no	—
367	C₂×C₄²	—	13	3	no	—
368	C₂×C₄²	—	13	3	no	—
369	C₂×C₄²	—	13	3	no	—
370	C₂×C₄²	—	13	3	no	—
371	C₂×C₄²	—	13	3	no	—
372	C₂×C₄²	—	13	3	no	—
373	C₂×C₄²	—	13	3	no	—
374	C₂×C₄²	—	13	3	no	—
375	C₂×C₄²	—	13	3	no	—
376	C₂×C₄²	—	13	1	no	—
377	C₂×C₄²	—	13	6	no	—
378	C₂×C₄²	—	13	12	no	—
379	C₂×C₄²	—	13	2	no	—
380	C₂×C₄²	—	26	24	no	—
381	C₂×C₄²	C₂×#261	1	3	yes	complemented
382	#95	—	13	2	no	—
383	#95	—	13	6	no	—
384	#95	—	13	12	no	—
385	#95	—	13	12	no	—
386	C₂×C₁₃	—	2	6	no	—
387	C₂×C₁₃	C₂³×C₄⋊C₄	1	1	yes	characteristic
388	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
389	C₂×C₁₃	#3428	1	1	yes	characteristic
390	D₁₃	—	2	6	no	—
391	D₁₃	D₄×#41	1	2	yes	—
392	D₁₃	Q₈×#41	1	2	yes	—
393	C₂⁴	—	13	3	no	—
394	#41	—	13	8	no	—
395	#41	—	13	24	no	—
396	#41	—	13	24	no	—
397	#41	C₄⋊#261	1	8	yes	direct product factor
398	C₂×Q₈	—	13	4	no	—
399	C₂×Q₈	—	13	4	no	—
400	C₂×Q₈	—	13	3	no	—
401	C₂×Q₈	C₂²×#261	1	1	yes	characteristic
402	C₂×D₄	—	13	6	no	—
403	C₂×D₄	—	13	12	no	—
404	C₂×D₄	—	13	12	no	—
405	C₂×D₄	—	13	3	no	—
406	C₂×D₄	C₂²×#261	1	3	yes	—
407	C₂²×C₄	—	13	3	no	—
408	C₂²×C₄	—	13	12	no	—
409	C₂²×C₄	—	13	12	no	—
410	C₂²×C₄	—	13	3	no	—
411	C₂²×C₄	—	13	1	no	—
412	C₂²×C₄	—	13	3	no	—
413	C₂²×C₄	—	13	1	no	—
414	C₂²×C₄	—	13	3	no	—
415	C₂²×C₄	—	13	4	no	—
416	C₂²×C₄	—	13	3	no	—
417	C₂²×C₄	—	13	3	no	—
418	C₂²×C₄	—	13	1	no	—
419	C₂²×C₄	—	13	3	no	—
420	C₂²×C₄	—	13	3	no	—
421	C₂²×C₄	—	13	3	no	—
422	C₂²×C₄	—	13	3	no	—
423	C₂²×C₄	—	13	3	no	—
424	C₂²×C₄	—	13	3	no	—
425	C₂²×C₄	—	13	12	no	—
426	C₂²×C₄	—	26	12	no	—
427	C₂²×C₄	—	26	24	no	—
428	C₂²×C₄	—	26	24	no	—
429	C₂²×C₄	—	52	6	no	—
430	C₂²×C₄	—	52	12	no	—
431	C₂²×C₄	C₂²×#261	1	3	yes	—
432	C₂²×C₄	C₂²×#261	1	3	yes	—
433	C₂²×C₄	C₂²×#261	1	3	yes	—
434	C₄⋊C₄	—	13	8	no	—
435	C₄⋊C₄	—	13	6	no	—
436	C₄⋊C₄	—	13	6	no	—
437	C₄⋊C₄	—	13	3	no	—
438	C₄⋊C₄	—	13	3	no	—
439	C₄⋊C₄	—	26	12	no	—
440	C₄⋊C₄	—	26	24	no	—
441	C₄⋊C₄	—	26	24	no	—
442	C₄⋊C₄	—	52	12	no	—
443	C₄⋊C₄	C₂²×#261	1	3	yes	—
444	C₄⋊C₄	C₂²×#261	1	3	yes	—
445	C₂²⋊C₄	—	13	6	no	—
446	C₂²⋊C₄	—	13	6	no	—
447	C₂²⋊C₄	—	13	6	no	—
448	C₂²⋊C₄	—	26	24	no	—
449	C₂²⋊C₄	C₂²×#261	1	6	yes	—
450	C₄²	—	13	1	no	—
451	C₄²	—	13	1	no	—
452	C₄²	—	13	3	no	—
453	C₄²	—	13	3	no	—
454	C₄²	—	13	3	no	—
455	C₄²	—	13	3	no	—
456	C₄²	—	13	3	no	—
457	C₄²	—	13	3	no	—
458	C₄²	—	13	3	no	—
459	C₄²	—	13	3	no	—
460	C₄²	—	13	1	no	—
461	C₄²	—	13	3	no	—
462	C₄²	—	26	4	no	—
463	C₄²	—	26	12	no	—
464	C₄²	—	26	24	no	—
465	C₄²	C₂²×#261	1	3	yes	—
466	C₄²	C₂²×#261	1	3	yes	—
467	C₄²	C₂²×#261	1	1	yes	characteristic
468	C₄²	C₂²×#261	1	3	yes	—
469	C₁₃	C₄⋊C₄×#41	1	1	yes	characteristic, complemented, Sylow
470	C₂³	—	13	1	no	—
471	C₂³	—	13	6	no	—
472	C₂³	—	13	6	no	—
473	C₂³	—	13	3	no	—
474	C₂³	—	26	6	no	—
475	C₂³	—	26	6	no	—
476	C₂³	C₂³×#261	1	3	yes	—
477	Q₈	—	13	12	no	—
478	Q₈	C₂×C₄⋊#261	1	4	yes	complemented
479	D₄	—	13	24	no	—
480	D₄	—	13	12	no	—
481	D₄	C₂×C₄⋊#261	1	12	yes	complemented
482	C₂×C₄	—	2	6	no	—
483	C₂×C₄	—	4	3	no	—
484	C₂×C₄	—	13	12	no	—
485	C₂×C₄	—	13	1	no	—
486	C₂×C₄	—	13	1	no	—
487	C₂×C₄	—	13	3	no	—
488	C₂×C₄	—	13	2	no	—
489	C₂×C₄	—	13	6	no	—
490	C₂×C₄	—	13	12	no	—
491	C₂×C₄	—	13	12	no	—
492	C₂×C₄	—	13	2	no	—
493	C₂×C₄	—	13	6	no	—
494	C₂×C₄	—	13	4	no	—
495	C₂×C₄	—	13	8	no	—
496	C₂×C₄	—	13	1	no	—
497	C₂×C₄	—	13	3	no	—
498	C₂×C₄	—	13	3	no	—
499	C₂×C₄	—	26	6	no	—
500	C₂×C₄	—	26	6	no	—
501	C₂×C₄	—	26	6	no	—
502	C₂×C₄	—	26	2	no	—
503	C₂×C₄	—	26	6	no	—
504	C₂×C₄	—	26	4	no	—
505	C₂×C₄	—	26	4	no	—
506	C₂×C₄	—	26	6	no	—
507	C₂×C₄	—	26	12	no	—
508	C₂×C₄	—	26	12	no	—
509	C₂×C₄	—	26	12	no	—
510	C₂×C₄	—	52	3	no	—
511	C₂×C₄	—	52	3	no	—
512	C₂×C₄	—	52	3	no	—
513	C₂×C₄	—	52	48	no	—
514	C₂×C₄	C₂×C₄⋊#261	1	12	yes	complemented
515	C₂×C₄	C₂³×#261	1	1	yes	characteristic
516	C₂×C₄	C₂³×#261	1	3	yes	—
517	C₂×C₄	C₂³×#261	1	3	yes	—
518	C₂×C₄	C₂³×#261	1	3	yes	—
519	C₂×C₄	C₂³×#261	1	1	yes	characteristic
520	C₂×C₄	C₂³×#261	1	1	yes	characteristic
521	C₂²	—	2	3	no	—
522	C₂²	—	2	3	no	—
523	C₂²	—	13	1	no	—
524	C₂²	—	13	1	no	—
525	C₂²	—	13	2	no	—
526	C₂²	—	13	2	no	—
527	C₂²	—	13	6	no	—
528	C₂²	—	26	12	no	—
529	C₂²	—	26	12	no	—
530	C₂²	—	26	3	no	—
531	C₂²	—	26	3	no	—
532	C₂²	C₂²×C₄⋊#261	1	6	yes	—
533	C₂²	C₂⁴×#261	1	1	yes	characteristic
534	C₄	—	2	3	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	3	no	—
537	C₄	—	13	2	no	—
538	C₄	—	13	6	no	—
539	C₄	—	13	2	no	—
540	C₄	—	26	8	no	—
541	C₄	—	26	3	no	—
542	C₄	—	26	3	no	—
543	C₄	—	26	1	no	—
544	C₄	—	52	12	no	—
545	C₄	C₂²×C₄⋊#261	1	2	yes	—
546	C₄	C₂²×C₄⋊#261	1	6	yes	—
547	C₄	#41×#261	1	2	yes	complemented
548	C₂	—	2	6	no	—
549	C₂	—	13	2	no	—
550	C₂	—	13	2	no	—
551	C₂	—	26	6	no	—
552	C₂	C₂³×C₄⋊#261	1	1	yes	characteristic
553	C₂	C₂×#41×#261	1	1	yes	characteristic
554	C₂	#13131816	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂⁴×C₄
Frattini	C₂²	C₂⁴×#261
Fitting	C₄×C₁₃×#41	C₄
prime radical	C₂×#41×D₁₃	C₂²
cosocle	C₂²×D₁₃	C₂⁵
hypercenter	C₄×#41	#261
hypocenter	C₁₃	C₄⋊C₄×#41
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
2. #13131351	C₂	semidirect
3. Q₈×C₄⋊#261	C₂	semidirect
4. #13131349	C₂	semidirect
5. D₄×C₄⋊#261	C₂	semidirect
6. #13131296	C₂	semidirect
7. #13131285	C₂	semidirect
8. C₂×C₄×C₄⋊#261	C₂	semidirect
17. C₄×C₁₃×#41	C₄	semidirect
18. #41×Dic₁₃	C₄	semidirect
19. C₄×#6131	C₄	semidirect
20. C₄×#6131	C₄	semidirect
25. C₄×#6129	C₄	semidirect
26. C₄×#6129	C₄	semidirect
27. #11719227	C₄	semidirect
29. C₄×#6127	C₄	semidirect
71. C₄×Q₈×C₁₃	C₂×C₄	semidirect
72. C₄×Q₈×C₁₃	C₂×C₄	semidirect
73. C₄×D₄×C₁₃	C₂×C₄	semidirect
74. C₄×D₄×C₁₃	C₂×C₄	semidirect
75. C₁₃×#117	C₂×C₄	semidirect
76. C₂×C₄²×C₁₃	C₂×C₄	semidirect
77. Q₈×Dic₁₃	C₂×C₄	semidirect
78. Q₈×Dic₁₃	C₂×C₄	semidirect
79. D₄×Dic₁₃	C₂×C₄	semidirect
80. D₄×Dic₁₃	C₂×C₄	semidirect
81. C₄×C₂²⋊D₁₃	C₂×C₄	semidirect
82. C₄×C₂²⋊D₁₃	C₂×C₄	semidirect
83. #88180	C₂×C₄	semidirect
84. C₂×C₄×Dic₁₃	C₂×C₄	semidirect
85. C₂×C₄×Dic₁₃	C₂×C₄	semidirect
86. C₂×C₄×Dic₁₃	C₂×C₄	semidirect
87. #88147	C₂×C₄	semidirect
88. #88147	C₂×C₄	semidirect
89. #88146	C₂×C₄	semidirect
90. #88146	C₂×C₄	semidirect
93. #88141	C₂×C₄	semidirect
94. #88141	C₂×C₄	semidirect
95. #88135	C₂×C₄	semidirect
96. #88135	C₂×C₄	semidirect
98. #88131	C₂×C₄	semidirect
99. C₄×D₅₂	C₂×C₄	semidirect
100. C₄×D₅₂	C₂×C₄	semidirect
101. #88126	C₂×C₄	semidirect
102. C₄²×D₁₃	C₂×C₄	semidirect
103. C₄²×D₁₃	C₂×C₄	semidirect
104. C₄²×D₁₃	C₂×C₄	semidirect
105. C₄²×D₁₃	C₂×C₄	semidirect
110. C₄×Dic₂₆	C₂×C₄	semidirect
111. C₄×Dic₂₆	C₂×C₄	semidirect
123. C₁₃×#41	C₄⋊C₄	semidirect
133. #6131	C₄⋊C₄	semidirect
136. #6129	C₄⋊C₄	semidirect
139. #6127	C₄⋊C₄	semidirect
163. C₄⋊#261	#41	direct (N × H)
216. Q₈×C₁₃	C₂×C₄⋊C₄	semidirect
217. D₄×C₁₃	C₂×C₄⋊C₄	semidirect
220. C₂×C₄×C₁₃	C₂×C₄⋊C₄	semidirect
227. C₂²⋊D₁₃	C₂×C₄⋊C₄	semidirect
230. C₂×Dic₁₃	C₂×C₄⋊C₄	semidirect
237. D₅₂	C₂×C₄⋊C₄	semidirect
245. C₄×D₁₃	C₂×C₄⋊C₄	semidirect
246. C₄×D₁₃	C₂×C₄⋊C₄	semidirect
252. Dic₂₆	C₂×C₄⋊C₄	semidirect
262. C₄×#41	#261	semidirect
308. C₄×C₁₃	C₄×#41	semidirect
314. Dic₁₃	C₄×#41	semidirect
334. C₄×Q₈	C₂×#261	semidirect
335. C₄×Q₈	C₂×#261	semidirect
347. C₄×D₄	C₂×#261	semidirect
348. C₄×D₄	C₂×#261	semidirect
355. #117	C₂×#261	semidirect
381. C₂×C₄²	C₂×#261	semidirect
397. #41	C₄⋊#261	direct (N × H)
469. C₁₃	C₄⋊C₄×#41	semidirect
478. Q₈	C₂×C₄⋊#261	semidirect
481. D₄	C₂×C₄⋊#261	semidirect
514. C₂×C₄	C₂×C₄⋊#261	semidirect
547. C₄	#41×#261	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×#261	2
#13131351	2
Q₈×C₄⋊#261	2
#13131349	2
D₄×C₄⋊#261	2
#13131296	2
#13131285	2
C₂×C₄×C₄⋊#261	2
C₄×#41×D₁₃	2
C₄⋊C₄×#41	13

Subgroups — #41×C4⋊#261 #16807576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #41×C₄⋊#261 #16807576