Subgroups — C₄×C₄₁×#525 #23810232

Order 10496.

3902 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₄²×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₂²⋊Q₈×C₄₁	C₂	1	4	yes	maximal, complemented
5	C₄×#123×C₄₁	C₂	1	4	yes	maximal, complemented
6	C₄×#121×C₄₁	C₂	1	4	yes	maximal, complemented
7	C₄×#120×C₄₁	C₂	1	4	yes	maximal, complemented
8	C₄₁×#2297	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#2296	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#2290	C₂	1	4	yes	maximal, complemented
11	C₄₁×#2280	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄²×D₄×C₄₁	C₂	1	4	yes	maximal, complemented
13	C₄×#117×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₄₁	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
17	C₄₁×#525	C₄	1	16	yes	direct product factor
18	C₂×#123×C₄₁	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
20	C₂×#121×C₄₁	C₂²	1	2	yes	—
21	C₂×#120×C₄₁	C₂²	1	2	yes	—
22	C₄×#41×C₄₁	—	2	8	no	—
23	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	complemented
24	C₂×C₄×D₄×C₄₁	C₂²	1	8	yes	—
25	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
28	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#117×C₄₁	C₂²	1	2	yes	complemented
32	C₂²×C₄²×C₄₁	—	2	8	no	—
33	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
34	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₄₁	C₂²	1	4	yes	—
36	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
37	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
38	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₄₁	C₂²	1	2	yes	complemented
40	C₄₁×#391	C₂²	1	2	yes	complemented
41	C₄₁×#390	C₂²	1	2	yes	complemented
42	C₄₁×#389	C₂²	1	4	yes	complemented
43	C₄₁×#388	C₂²	1	8	yes	complemented
44	C₄₁×#387	C₂²	1	8	yes	complemented
45	C₄₁×#386	C₂²	1	8	yes	—
46	C₄₁×#386	C₂²	1	4	yes	—
47	C₄₁×#385	C₂²	1	8	yes	—
48	C₄₁×#385	C₂²	1	4	yes	—
49	C₄₁×#381	C₂²	1	2	yes	—
50	C₄₁×#380	C₂²	1	4	yes	—
51	C₄₁×#379	C₂²	1	2	yes	—
52	C₄×C₄⋊C₄×C₄₁	C₂²	1	4	yes	complemented
53	C₄×C₄⋊C₄×C₄₁	C₂²	1	4	yes	complemented
54	C₄×C₄⋊C₄×C₄₁	C₂²	1	8	yes	complemented
55	C₄×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	—
56	C₄×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	—
57	C₄×C₂²⋊C₄×C₄₁	C₂²	1	8	yes	—
58	C₄×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	complemented
59	C₄×C₂²⋊C₄×C₄₁	C₂²	1	8	yes	complemented
60	C₄₁×#376	C₂²	1	2	yes	complemented
61	C₄³×C₄₁	C₂²	1	2	yes	complemented
62	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
63	C₂×#41×C₄₁	—	2	4	no	—
64	C₂×#41×C₄₁	—	2	4	no	—
65	C₂×#41×C₄₁	C₂×C₄	1	8	yes	complemented
66	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
68	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
69	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₄₁	—	2	8	no	—
71	C₂³×C₄×C₄₁	—	2	4	no	—
72	C₂³×C₄×C₄₁	—	2	4	no	—
73	C₂³×C₄×C₄₁	—	2	16	no	—
74	C₂³×C₄×C₄₁	C₂×C₄	1	8	yes	complemented
75	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
76	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
77	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
78	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
79	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
80	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
82	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
83	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
84	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
85	#123×C₄₁	C₂×C₄	1	16	yes	complemented
86	C₂²⋊Q₈×C₄₁	C₂×C₄	1	16	yes	complemented
87	#121×C₄₁	C₂×C₄	1	16	yes	complemented
88	#120×C₄₁	C₂×C₄	1	16	yes	complemented
89	C₄×Q₈×C₄₁	—	2	8	no	—
90	C₄×D₄×C₄₁	—	2	16	no	—
91	C₄×D₄×C₄₁	—	2	32	no	—
92	C₄×D₄×C₄₁	—	2	8	no	—
93	C₄×D₄×C₄₁	C₂×C₄	1	32	yes	complemented
94	#117×C₄₁	—	2	4	no	—
95	#117×C₄₁	—	2	4	no	—
96	#117×C₄₁	—	2	8	no	—
97	#117×C₄₁	C₂×C₄	1	8	yes	complemented
98	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
102	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
105	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
106	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
108	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
109	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
110	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
112	C₂×C₄²×C₄₁	—	2	8	no	—
113	C₂×C₄²×C₄₁	—	2	4	no	—
114	C₂×C₄²×C₄₁	—	2	8	no	—
115	C₂×C₄²×C₄₁	—	2	8	no	—
116	C₂×C₄²×C₄₁	—	2	16	no	—
117	C₂×C₄²×C₄₁	—	2	8	no	—
118	C₂×C₄²×C₄₁	D₄	1	8	yes	complemented
119	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
120	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
121	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
122	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
123	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
124	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
125	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
126	C₂×C₄²×C₄₁	C₂³	1	8	yes	—
127	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
128	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
130	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
131	#95×C₄₁	C₂³	1	8	yes	—
132	#95×C₄₁	C₂³	1	8	yes	—
133	#95×C₄₁	C₂³	1	8	yes	—
134	#95×C₄₁	C₂³	1	8	yes	—
135	C₂⁴×C₄₁	—	2	2	no	—
136	C₂⁴×C₄₁	—	2	8	no	—
137	C₂⁴×C₄₁	—	2	2	no	—
138	C₂⁴×C₄₁	C₂²×C₄	1	4	yes	—
139	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
140	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
141	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
142	#41×C₄₁	—	2	32	no	—
143	C₂×Q₈×C₄₁	—	2	2	no	—
144	C₂×Q₈×C₄₁	—	2	2	no	—
145	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	complemented
146	C₂×D₄×C₄₁	—	2	4	no	—
147	C₂×D₄×C₄₁	—	2	16	no	—
148	C₂×D₄×C₄₁	—	2	4	no	—
149	C₂×D₄×C₄₁	—	2	2	no	—
150	C₂×D₄×C₄₁	—	2	2	no	—
151	C₂×D₄×C₄₁	C₂²×C₄	1	16	yes	—
152	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
153	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	complemented
154	C₂²×C₄×C₄₁	—	2	64	no	—
155	C₂²×C₄×C₄₁	—	2	4	no	—
156	C₂²×C₄×C₄₁	—	2	2	no	—
157	C₂²×C₄×C₄₁	—	2	8	no	—
158	C₂²×C₄×C₄₁	—	2	2	no	—
159	C₂²×C₄×C₄₁	—	2	32	no	—
160	C₂²×C₄×C₄₁	—	2	8	no	—
161	C₂²×C₄×C₄₁	—	2	4	no	—
162	C₂²×C₄×C₄₁	—	2	4	no	—
163	C₂²×C₄×C₄₁	—	2	8	no	—
164	C₂²×C₄×C₄₁	—	2	4	no	—
165	C₂²×C₄×C₄₁	—	2	8	no	—
166	C₂²×C₄×C₄₁	—	2	8	no	—
167	C₂²×C₄×C₄₁	—	2	4	no	—
168	C₂²×C₄×C₄₁	—	2	4	no	—
169	C₂²×C₄×C₄₁	—	2	8	no	—
170	C₂²×C₄×C₄₁	—	2	8	no	—
171	C₂²×C₄×C₄₁	—	2	4	no	—
172	C₂²×C₄×C₄₁	—	2	8	no	—
173	C₂²×C₄×C₄₁	—	2	16	no	—
174	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
175	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
176	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
177	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
178	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	complemented
179	C₂²×C₄×C₄₁	C₂×D₄	1	8	yes	—
180	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₄₁	#41	1	4	yes	—
182	C₂²×C₄×C₄₁	#41	1	16	yes	complemented
183	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
193	C₄⋊C₄×C₄₁	—	2	8	no	—
194	C₄⋊C₄×C₄₁	—	2	4	no	—
195	C₄⋊C₄×C₄₁	—	2	4	no	—
196	C₄⋊C₄×C₄₁	—	2	16	no	—
197	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	complemented
198	C₄⋊C₄×C₄₁	C₂²×C₄	1	16	yes	complemented
199	C₂²⋊C₄×C₄₁	—	2	4	no	—
200	C₂²⋊C₄×C₄₁	—	2	4	no	—
201	C₂²⋊C₄×C₄₁	—	2	16	no	—
202	C₂²⋊C₄×C₄₁	—	2	8	no	—
203	C₂²⋊C₄×C₄₁	—	2	16	no	—
204	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
205	C₂²⋊C₄×C₄₁	C₂²×C₄	1	16	yes	—
206	C₂²⋊C₄×C₄₁	C₂²×C₄	1	16	yes	complemented
207	C₄²×C₄₁	—	2	8	no	—
208	C₄²×C₄₁	—	2	4	no	—
209	C₄²×C₄₁	—	2	4	no	—
210	C₄²×C₄₁	—	2	8	no	—
211	C₄²×C₄₁	—	2	4	no	—
212	C₄²×C₄₁	—	2	8	no	—
213	C₄²×C₄₁	—	2	4	no	—
214	C₄²×C₄₁	—	2	16	no	—
215	C₄²×C₄₁	C₂²×C₄	1	8	yes	complemented
216	C₄²×C₄₁	C₂×D₄	1	4	yes	—
217	C₄²×C₄₁	C₂×D₄	1	4	yes	—
218	C₄²×C₄₁	C₂×D₄	1	8	yes	—
219	C₂³×C₄₁	—	2	16	no	—
220	C₂³×C₄₁	—	2	16	no	—
221	C₂³×C₄₁	—	2	8	no	—
222	C₂³×C₄₁	—	2	16	no	—
223	C₂³×C₄₁	—	2	2	no	—
224	C₂³×C₄₁	—	2	2	no	—
225	C₂³×C₄₁	—	2	4	no	—
226	C₂³×C₄₁	—	2	4	no	—
227	C₂³×C₄₁	—	2	2	no	—
228	C₂³×C₄₁	—	2	8	no	—
229	C₂³×C₄₁	—	2	2	no	—
230	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
231	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
232	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
233	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
234	C₂³×C₄₁	C₂×#41	1	2	yes	—
235	C₂³×C₄₁	C₂×#41	1	8	yes	—
236	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
237	Q₈×C₄₁	—	2	8	no	—
238	D₄×C₄₁	—	2	16	no	—
239	D₄×C₄₁	—	2	32	no	—
240	D₄×C₄₁	—	2	8	no	—
241	C₂×C₄×C₄₁	—	2	32	no	—
242	C₂×C₄×C₄₁	—	2	16	no	—
243	C₂×C₄×C₄₁	—	2	8	no	—
244	C₂×C₄×C₄₁	—	2	2	no	—
245	C₂×C₄×C₄₁	—	2	4	no	—
246	C₂×C₄×C₄₁	—	2	2	no	—
247	C₂×C₄×C₄₁	—	2	8	no	—
248	C₂×C₄×C₄₁	—	2	2	no	—
249	C₂×C₄×C₄₁	—	2	4	no	—
250	C₂×C₄×C₄₁	—	2	4	no	—
251	C₂×C₄×C₄₁	—	2	2	no	—
252	C₂×C₄×C₄₁	—	2	16	no	—
253	C₂×C₄×C₄₁	—	2	16	no	—
254	C₂×C₄×C₄₁	—	2	16	no	—
255	C₂×C₄×C₄₁	—	2	16	no	—
256	C₂×C₄×C₄₁	—	2	32	no	—
257	C₂×C₄×C₄₁	—	2	4	no	—
258	C₂×C₄×C₄₁	—	2	8	no	—
259	C₂×C₄×C₄₁	—	2	4	no	—
260	C₂×C₄×C₄₁	—	2	8	no	—
261	C₂×C₄×C₄₁	—	4	16	no	—
262	C₂×C₄×C₄₁	C₄×D₄	1	16	yes	complemented
263	C₂×C₄×C₄₁	C₂³×C₄	1	8	yes	—
264	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
265	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
266	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
267	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
268	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
269	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
271	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
272	C₂×C₄×C₄₁	C₂×#41	1	8	yes	—
273	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
274	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
275	C₂×C₄×C₄₁	C₂×#41	1	8	yes	—
276	C₄×#525	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂²×C₄₁	—	2	32	no	—
278	C₂²×C₄₁	—	2	4	no	—
279	C₂²×C₄₁	—	2	4	no	—
280	C₂²×C₄₁	—	2	4	no	—
281	C₂²×C₄₁	—	2	4	no	—
282	C₂²×C₄₁	—	2	8	no	—
283	C₂²×C₄₁	—	2	4	no	—
284	C₂²×C₄₁	—	2	8	no	—
285	C₂²×C₄₁	—	2	4	no	—
286	C₂²×C₄₁	—	2	8	no	—
287	C₂²×C₄₁	—	4	4	no	—
288	C₂²×C₄₁	—	4	4	no	—
289	C₂²×C₄₁	C₂×C₄×D₄	1	4	yes	—
290	C₂²×C₄₁	C₄×#41	1	8	yes	complemented
291	C₂²×C₄₁	C₂⁴×C₄	1	1	yes	characteristic
292	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
293	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
294	C₂²×C₄₁	C₂²×#41	1	4	yes	—
295	C₄×C₄₁	—	2	4	no	—
296	C₄×C₄₁	—	2	4	no	—
297	C₄×C₄₁	—	2	8	no	—
298	C₄×C₄₁	—	2	4	no	—
299	C₄×C₄₁	—	2	8	no	—
300	C₄×C₄₁	—	4	4	no	—
301	C₄×C₄₁	—	4	4	no	—
302	C₄×C₄₁	C₂×C₄×D₄	1	4	yes	—
303	C₄×C₄₁	C₂×C₄×D₄	1	4	yes	—
304	C₄×C₄₁	#525	1	8	yes	direct product factor
305	C₂×#525	C₂×C₄₁	1	1	yes	characteristic
306	C₂×C₄×#41	C₂×C₄₁	1	1	yes	characteristic, complemented
307	C₂³×C₄²	C₂×C₄₁	1	1	yes	characteristic, complemented
308	C₄×C₂²⋊Q₈	C₂×C₄₁	1	4	yes	complemented
309	C₄×#123	C₂×C₄₁	1	4	yes	complemented
310	C₄×#121	C₂×C₄₁	1	4	yes	complemented
311	C₄×#120	C₂×C₄₁	1	4	yes	complemented
312	#2297	C₂×C₄₁	1	1	yes	characteristic, complemented
313	#2296	C₂×C₄₁	1	1	yes	characteristic, complemented
314	#2290	C₂×C₄₁	1	4	yes	complemented
315	#2280	C₂×C₄₁	1	1	yes	characteristic, complemented
316	C₄²×D₄	C₂×C₄₁	1	4	yes	complemented
317	C₄×#117	C₂×C₄₁	1	1	yes	characteristic, complemented
318	C₂×C₄₁	—	2	4	no	—
319	C₂×C₄₁	—	2	8	no	—
320	C₂×C₄₁	—	4	4	no	—
321	C₂×C₄₁	C₂²×C₄×D₄	1	1	yes	characteristic
322	C₂×C₄₁	C₂×C₄×#41	1	2	yes	—
323	C₂×C₄₁	C₂×#525	1	2	yes	—
324	C₂×C₄₁	#3444	1	2	yes	—
325	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
326	C₂⁴×C₄	C₂²×C₄₁	1	2	yes	—
327	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
328	#525	C₄×C₄₁	1	16	yes	direct product factor
329	C₂×#123	C₂²×C₄₁	1	2	yes	—
330	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
331	C₂×#121	C₂²×C₄₁	1	2	yes	—
332	C₂×#120	C₂²×C₄₁	1	2	yes	—
333	C₄×#41	—	2	8	no	—
334	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	complemented
335	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
336	C₂×C₄×D₄	C₂²×C₄₁	1	8	yes	—
337	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
338	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
339	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
340	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
341	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
342	C₂×#117	C₂²×C₄₁	1	2	yes	complemented
343	C₂²×C₄²	—	2	8	no	—
344	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
345	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
346	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
347	C₂²×C₄²	C₂²×C₄₁	1	4	yes	—
348	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
349	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
350	C₂²×C₄²	C₂²×C₄₁	1	2	yes	complemented
351	#391	C₂²×C₄₁	1	2	yes	complemented
352	#390	C₂²×C₄₁	1	2	yes	complemented
353	#389	C₂²×C₄₁	1	4	yes	complemented
354	#388	C₂²×C₄₁	1	8	yes	complemented
355	#387	C₂²×C₄₁	1	8	yes	complemented
356	#386	C₂²×C₄₁	1	8	yes	—
357	#386	C₂²×C₄₁	1	4	yes	—
358	#385	C₂²×C₄₁	1	8	yes	—
359	#385	C₂²×C₄₁	1	4	yes	—
360	#381	C₂²×C₄₁	1	2	yes	—
361	#380	C₂²×C₄₁	1	4	yes	—
362	#379	C₂²×C₄₁	1	2	yes	—
363	C₄×C₄⋊C₄	C₂²×C₄₁	1	4	yes	complemented
364	C₄×C₄⋊C₄	C₂²×C₄₁	1	4	yes	complemented
365	C₄×C₄⋊C₄	C₂²×C₄₁	1	8	yes	complemented
366	C₄×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	—
367	C₄×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	—
368	C₄×C₂²⋊C₄	C₂²×C₄₁	1	8	yes	—
369	C₄×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	complemented
370	C₄×C₂²⋊C₄	C₂²×C₄₁	1	8	yes	complemented
371	#376	C₂²×C₄₁	1	2	yes	complemented
372	C₄³	C₂²×C₄₁	1	2	yes	complemented
373	C₄₁	C₄×#525	1	1	yes	characteristic, direct product factor, Sylow
374	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
375	C₂×#41	—	2	4	no	—
376	C₂×#41	—	2	4	no	—
377	C₂×#41	C₂×C₄×C₄₁	1	8	yes	complemented
378	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
379	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
380	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
381	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
382	C₂³×C₄	—	2	8	no	—
383	C₂³×C₄	—	2	4	no	—
384	C₂³×C₄	—	2	4	no	—
385	C₂³×C₄	—	2	16	no	—
386	C₂³×C₄	C₂×C₄×C₄₁	1	8	yes	complemented
387	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
388	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
389	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
390	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
391	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
392	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
394	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
395	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
396	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
397	#123	C₂×C₄×C₄₁	1	16	yes	complemented
398	C₂²⋊Q₈	C₂×C₄×C₄₁	1	16	yes	complemented
399	#121	C₂×C₄×C₄₁	1	16	yes	complemented
400	#120	C₂×C₄×C₄₁	1	16	yes	complemented
401	C₄×Q₈	—	2	8	no	—
402	C₄×D₄	—	2	16	no	—
403	C₄×D₄	—	2	32	no	—
404	C₄×D₄	—	2	8	no	—
405	C₄×D₄	C₂×C₄×C₄₁	1	32	yes	complemented
406	#117	—	2	4	no	—
407	#117	—	2	4	no	—
408	#117	—	2	8	no	—
409	#117	C₂×C₄×C₄₁	1	8	yes	complemented
410	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
413	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
414	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
415	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
424	C₂×C₄²	—	2	8	no	—
425	C₂×C₄²	—	2	4	no	—
426	C₂×C₄²	—	2	8	no	—
427	C₂×C₄²	—	2	8	no	—
428	C₂×C₄²	—	2	8	no	—
429	C₂×C₄²	—	2	16	no	—
430	C₂×C₄²	D₄×C₄₁	1	8	yes	complemented
431	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
432	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
433	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
434	C₂×C₄²	C₂³×C₄₁	1	8	yes	—
435	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
436	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
437	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
438	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
439	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
440	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
442	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
443	#95	C₂³×C₄₁	1	8	yes	—
444	#95	C₂³×C₄₁	1	8	yes	—
445	#95	C₂³×C₄₁	1	8	yes	—
446	#95	C₂³×C₄₁	1	8	yes	—
447	C₂⁴	—	2	2	no	—
448	C₂⁴	—	2	8	no	—
449	C₂⁴	—	2	2	no	—
450	C₂⁴	C₂²×C₄×C₄₁	1	4	yes	—
451	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
452	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
453	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
454	#41	—	2	32	no	—
455	C₂×Q₈	—	2	2	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	complemented
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	2	16	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	C₂²×C₄×C₄₁	1	16	yes	—
464	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
465	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	complemented
466	C₂²×C₄	—	2	64	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	8	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	32	no	—
472	C₂²×C₄	—	2	8	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	8	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	8	no	—
478	C₂²×C₄	—	2	8	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	8	no	—
482	C₂²×C₄	—	2	8	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	8	no	—
485	C₂²×C₄	—	2	16	no	—
486	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
487	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
488	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
489	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
490	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	complemented
491	C₂²×C₄	C₂×D₄×C₄₁	1	8	yes	—
492	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
493	C₂²×C₄	#41×C₄₁	1	4	yes	—
494	C₂²×C₄	#41×C₄₁	1	16	yes	complemented
495	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
497	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
500	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
502	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
503	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
504	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
505	C₄⋊C₄	—	2	8	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	16	no	—
509	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	complemented
510	C₄⋊C₄	C₂²×C₄×C₄₁	1	16	yes	complemented
511	C₂²⋊C₄	—	2	4	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	2	16	no	—
514	C₂²⋊C₄	—	2	8	no	—
515	C₂²⋊C₄	—	2	16	no	—
516	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
517	C₂²⋊C₄	C₂²×C₄×C₄₁	1	16	yes	—
518	C₂²⋊C₄	C₂²×C₄×C₄₁	1	16	yes	complemented
519	C₄²	—	2	8	no	—
520	C₄²	—	2	4	no	—
521	C₄²	—	2	4	no	—
522	C₄²	—	2	8	no	—
523	C₄²	—	2	4	no	—
524	C₄²	—	2	8	no	—
525	C₄²	—	2	4	no	—
526	C₄²	—	2	16	no	—
527	C₄²	C₂²×C₄×C₄₁	1	8	yes	complemented
528	C₄²	C₂×D₄×C₄₁	1	4	yes	—
529	C₄²	C₂×D₄×C₄₁	1	4	yes	—
530	C₄²	C₂×D₄×C₄₁	1	8	yes	—
531	C₂³	—	2	16	no	—
532	C₂³	—	2	16	no	—
533	C₂³	—	2	8	no	—
534	C₂³	—	2	16	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	8	no	—
541	C₂³	—	2	2	no	—
542	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
543	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
544	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
545	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
546	C₂³	C₂×#41×C₄₁	1	2	yes	—
547	C₂³	C₂×#41×C₄₁	1	8	yes	—
548	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
549	Q₈	—	2	8	no	—
550	D₄	—	2	16	no	—
551	D₄	—	2	32	no	—
552	D₄	—	2	8	no	—
553	C₂×C₄	—	2	32	no	—
554	C₂×C₄	—	2	16	no	—
555	C₂×C₄	—	2	8	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	8	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	16	no	—
565	C₂×C₄	—	2	16	no	—
566	C₂×C₄	—	2	16	no	—
567	C₂×C₄	—	2	16	no	—
568	C₂×C₄	—	2	32	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	8	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	4	16	no	—
574	C₂×C₄	C₄×D₄×C₄₁	1	16	yes	complemented
575	C₂×C₄	C₂³×C₄×C₄₁	1	8	yes	—
576	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
577	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
578	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
579	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
580	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
581	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
582	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
583	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
584	C₂×C₄	C₂×#41×C₄₁	1	8	yes	—
585	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
586	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
587	C₂×C₄	C₂×#41×C₄₁	1	8	yes	—
588	C₂²	—	2	32	no	—
589	C₂²	—	2	4	no	—
590	C₂²	—	2	4	no	—
591	C₂²	—	2	4	no	—
592	C₂²	—	2	4	no	—
593	C₂²	—	2	8	no	—
594	C₂²	—	2	4	no	—
595	C₂²	—	2	8	no	—
596	C₂²	—	2	4	no	—
597	C₂²	—	2	8	no	—
598	C₂²	—	4	4	no	—
599	C₂²	—	4	4	no	—
600	C₂²	C₂×C₄×D₄×C₄₁	1	4	yes	—
601	C₂²	C₄×#41×C₄₁	1	8	yes	complemented
602	C₂²	C₂⁴×C₄×C₄₁	1	1	yes	characteristic
603	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
604	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
605	C₂²	C₂²×#41×C₄₁	1	4	yes	—
606	C₄	—	2	4	no	—
607	C₄	—	2	4	no	—
608	C₄	—	2	8	no	—
609	C₄	—	2	4	no	—
610	C₄	—	2	8	no	—
611	C₄	—	4	4	no	—
612	C₄	—	4	4	no	—
613	C₄	C₂×C₄×D₄×C₄₁	1	4	yes	—
614	C₄	C₂×C₄×D₄×C₄₁	1	4	yes	—
615	C₄	C₄₁×#525	1	8	yes	direct product factor
616	C₂	—	2	4	no	—
617	C₂	—	2	8	no	—
618	C₂	—	4	4	no	—
619	C₂	C₂²×C₄×D₄×C₄₁	1	1	yes	characteristic
620	C₂	C₂×C₄×#41×C₄₁	1	2	yes	—
621	C₂	C₂×C₄₁×#525	1	2	yes	—
622	C₂	C₄₁×#3444	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²×C₄₁	C₂³
commutator	C₂²	C₂⁴×C₄×C₄₁
Frattini, cosocle	C₂³	C₂⁵×C₄₁
socle	C₂³×C₄₁	C₂⁵
prime radical	C₂×C₄₁×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#41×C₄₁	C₂	semidirect
3. C₂³×C₄²×C₄₁	C₂	semidirect
4. C₄×C₂²⋊Q₈×C₄₁	C₂	semidirect
5. C₄×#123×C₄₁	C₂	semidirect
6. C₄×#121×C₄₁	C₂	semidirect
7. C₄×#120×C₄₁	C₂	semidirect
8. C₄₁×#2297	C₂	semidirect
9. C₄₁×#2296	C₂	semidirect
10. C₄₁×#2290	C₂	semidirect
11. C₄₁×#2280	C₂	semidirect
12. C₄²×D₄×C₄₁	C₂	semidirect
13. C₄×#117×C₄₁	C₂	semidirect
17. C₄₁×#525	C₄	direct (N × H)
23. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
27. C₂×C₄×D₄×C₄₁	C₂²	semidirect
31. C₂×#117×C₄₁	C₂²	semidirect
39. C₂²×C₄²×C₄₁	C₂²	semidirect
40. C₄₁×#391	C₂²	semidirect
41. C₄₁×#390	C₂²	semidirect
42. C₄₁×#389	C₂²	semidirect
43. C₄₁×#388	C₂²	semidirect
44. C₄₁×#387	C₂²	semidirect
52. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
53. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
54. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
58. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
59. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
60. C₄₁×#376	C₂²	semidirect
61. C₄³×C₄₁	C₂²	semidirect
65. C₂×#41×C₄₁	C₂×C₄	semidirect
74. C₂³×C₄×C₄₁	C₂×C₄	semidirect
85. #123×C₄₁	C₂×C₄	semidirect
86. C₂²⋊Q₈×C₄₁	C₂×C₄	semidirect
87. #121×C₄₁	C₂×C₄	semidirect
88. #120×C₄₁	C₂×C₄	semidirect
93. C₄×D₄×C₄₁	C₂×C₄	semidirect
97. #117×C₄₁	C₂×C₄	semidirect
118. C₂×C₄²×C₄₁	D₄	semidirect
145. C₂×Q₈×C₄₁	C₂²×C₄	semidirect
153. C₂×D₄×C₄₁	C₂²×C₄	semidirect
178. C₂²×C₄×C₄₁	C₂²×C₄	semidirect
182. C₂²×C₄×C₄₁	#41	semidirect
197. C₄⋊C₄×C₄₁	C₂²×C₄	semidirect
198. C₄⋊C₄×C₄₁	C₂²×C₄	semidirect
206. C₂²⋊C₄×C₄₁	C₂²×C₄	semidirect
215. C₄²×C₄₁	C₂²×C₄	semidirect
262. C₂×C₄×C₄₁	C₄×D₄	semidirect
276. C₄×#525	C₄₁	direct (N × H)
290. C₂²×C₄₁	C₄×#41	semidirect
304. C₄×C₄₁	#525	direct (N × H)
306. C₂×C₄×#41	C₂×C₄₁	semidirect
307. C₂³×C₄²	C₂×C₄₁	semidirect
308. C₄×C₂²⋊Q₈	C₂×C₄₁	semidirect
309. C₄×#123	C₂×C₄₁	semidirect
310. C₄×#121	C₂×C₄₁	semidirect
311. C₄×#120	C₂×C₄₁	semidirect
312. #2297	C₂×C₄₁	semidirect
313. #2296	C₂×C₄₁	semidirect
314. #2290	C₂×C₄₁	semidirect
315. #2280	C₂×C₄₁	semidirect
316. C₄²×D₄	C₂×C₄₁	semidirect
317. C₄×#117	C₂×C₄₁	semidirect
328. #525	C₄×C₄₁	direct (N × H)
334. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
338. C₂×C₄×D₄	C₂²×C₄₁	semidirect
342. C₂×#117	C₂²×C₄₁	semidirect
350. C₂²×C₄²	C₂²×C₄₁	semidirect
351. #391	C₂²×C₄₁	semidirect
352. #390	C₂²×C₄₁	semidirect
353. #389	C₂²×C₄₁	semidirect
354. #388	C₂²×C₄₁	semidirect
355. #387	C₂²×C₄₁	semidirect
363. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
364. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
365. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
369. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
370. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
371. #376	C₂²×C₄₁	semidirect
372. C₄³	C₂²×C₄₁	semidirect
373. C₄₁	C₄×#525	direct (N × H)
377. C₂×#41	C₂×C₄×C₄₁	semidirect
386. C₂³×C₄	C₂×C₄×C₄₁	semidirect
397. #123	C₂×C₄×C₄₁	semidirect
398. C₂²⋊Q₈	C₂×C₄×C₄₁	semidirect
399. #121	C₂×C₄×C₄₁	semidirect
400. #120	C₂×C₄×C₄₁	semidirect
405. C₄×D₄	C₂×C₄×C₄₁	semidirect
409. #117	C₂×C₄×C₄₁	semidirect
430. C₂×C₄²	D₄×C₄₁	semidirect
457. C₂×Q₈	C₂²×C₄×C₄₁	semidirect
465. C₂×D₄	C₂²×C₄×C₄₁	semidirect
490. C₂²×C₄	C₂²×C₄×C₄₁	semidirect
494. C₂²×C₄	#41×C₄₁	semidirect
509. C₄⋊C₄	C₂²×C₄×C₄₁	semidirect
510. C₄⋊C₄	C₂²×C₄×C₄₁	semidirect
518. C₂²⋊C₄	C₂²×C₄×C₄₁	semidirect
527. C₄²	C₂²×C₄×C₄₁	semidirect
574. C₂×C₄	C₄×D₄×C₄₁	semidirect
601. C₂²	C₄×#41×C₄₁	semidirect
615. C₄	C₄₁×#525	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×C₄₁×#525	2
C₂×C₄×#41×C₄₁	2
C₂³×C₄²×C₄₁	2
C₄×C₂²⋊Q₈×C₄₁	2
C₄×#123×C₄₁	2
C₄×#121×C₄₁	2
C₄×#120×C₄₁	2
C₄₁×#2297	2
C₄₁×#2296	2
C₄₁×#2290	2
C₄₁×#2280	2
C₄²×D₄×C₄₁	2
C₄×#117×C₄₁	2
C₄×#525	41

Subgroups — C4×C41×#525 #23810232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄₁×#525 #23810232