Subgroups — C₂×C₄₁×#1740 #23796554

Order 10496.

2350 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#117×C₄₁	C₂	1	2	yes	maximal
2	C₂²×#117×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#1740	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄₁×#342	C₂	1	4	yes	maximal
5	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
6	C₂×#117×C₄₁	—	2	8	no	—
7	C₂×#117×C₄₁	—	2	2	no	—
8	C₂×#117×C₄₁	—	2	4	no	—
9	C₂×#117×C₄₁	—	2	2	no	—
10	C₂×#117×C₄₁	—	2	4	no	—
11	C₂×#117×C₄₁	C₄	1	16	yes	complemented
12	C₂×#117×C₄₁	C₄	1	4	yes	complemented
13	C₂×#117×C₄₁	C₂²	1	8	yes	—
14	C₂×#117×C₄₁	C₂²	1	4	yes	—
15	C₂²×C₄⋊C₄×C₄₁	—	2	2	no	—
16	C₂²×C₄⋊C₄×C₄₁	C₄	1	2	yes	complemented
17	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	—
19	C₂²×C₄²×C₄₁	—	2	2	no	—
20	C₂²×C₄²×C₄₁	C₄	1	2	yes	complemented
21	C₄₁×#342	C₂²	1	16	yes	—
22	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
23	C₂³×C₄×C₄₁	—	2	4	no	—
24	C₂³×C₄×C₄₁	C₂×C₄	1	4	yes	—
25	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₄₁	C₂×C₄	1	8	yes	—
27	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₄₁	D₄	1	2	yes	—
30	C₂³×C₄×C₄₁	D₄	1	4	yes	—
31	C₂³×C₄×C₄₁	D₄	1	4	yes	—
32	C₂³×C₄×C₄₁	D₄	1	2	yes	—
33	C₂³×C₄×C₄₁	Q₈	1	4	yes	—
34	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
35	#117×C₄₁	—	2	32	no	—
36	#117×C₄₁	—	2	8	no	—
37	#117×C₄₁	—	2	8	no	—
38	#117×C₄₁	—	2	16	no	—
39	#117×C₄₁	—	2	8	no	—
40	#117×C₄₁	—	2	8	no	—
41	#117×C₄₁	C₂×C₄	1	32	yes	complemented
42	C₂×C₄⋊C₄×C₄₁	—	2	16	no	—
43	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
44	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
45	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
46	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	8	yes	complemented
47	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
48	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
49	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
50	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
51	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
52	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	16	yes	—
53	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
54	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
55	C₂×C₄²×C₄₁	—	2	16	no	—
56	C₂×C₄²×C₄₁	—	2	2	no	—
57	C₂×C₄²×C₄₁	—	2	4	no	—
58	C₂×C₄²×C₄₁	—	2	2	no	—
59	C₂×C₄²×C₄₁	—	2	8	no	—
60	C₂×C₄²×C₄₁	C₂×C₄	1	8	yes	complemented
61	C₂⁴×C₄₁	—	4	4	no	—
62	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
63	C₂⁴×C₄₁	C₂²×C₄	1	4	yes	—
64	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
65	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
66	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
67	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
68	C₂⁴×C₄₁	C₂×Q₈	1	2	yes	—
69	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
70	C₂²×C₄×C₄₁	—	2	4	no	—
71	C₂²×C₄×C₄₁	—	2	4	no	—
72	C₂²×C₄×C₄₁	—	2	16	no	—
73	C₂²×C₄×C₄₁	—	2	8	no	—
74	C₂²×C₄×C₄₁	—	4	16	no	—
75	C₂²×C₄×C₄₁	—	4	8	no	—
76	C₂²×C₄×C₄₁	C₄²	1	4	yes	—
77	C₂²×C₄×C₄₁	C₄²	1	8	yes	—
78	C₂²×C₄×C₄₁	C₄²	1	4	yes	—
79	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
81	C₂²×C₄×C₄₁	C₂²⋊C₄	1	8	yes	—
82	C₂²×C₄×C₄₁	C₂²⋊C₄	1	8	yes	—
83	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
84	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
85	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
86	C₂²×C₄×C₄₁	C₂²⋊C₄	1	16	yes	—
87	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
88	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₁	C₄⋊C₄	1	4	yes	—
90	C₂²×C₄×C₄₁	C₄⋊C₄	1	8	yes	—
91	C₂²×C₄×C₄₁	C₄⋊C₄	1	8	yes	—
92	C₂²×C₄×C₄₁	C₄⋊C₄	1	16	yes	—
93	C₂²×C₄×C₄₁	C₄⋊C₄	1	8	yes	—
94	C₂²×C₄×C₄₁	C₄⋊C₄	1	4	yes	—
95	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
96	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
99	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₄₁	C₂×Q₈	1	4	yes	—
103	C₄⋊C₄×C₄₁	—	2	32	no	—
104	C₄⋊C₄×C₄₁	—	2	16	no	—
105	C₂²⋊C₄×C₄₁	—	2	8	no	—
106	C₂²⋊C₄×C₄₁	—	2	16	no	—
107	C₂²⋊C₄×C₄₁	—	2	8	no	—
108	C₂²⋊C₄×C₄₁	—	2	8	no	—
109	C₂²⋊C₄×C₄₁	C₂²×C₄	1	16	yes	—
110	C₄²×C₄₁	—	2	32	no	—
111	C₄²×C₄₁	—	2	8	no	—
112	C₄²×C₄₁	—	2	8	no	—
113	C₂³×C₄₁	—	2	4	no	—
114	C₂³×C₄₁	—	2	8	no	—
115	C₂³×C₄₁	—	4	2	no	—
116	C₂³×C₄₁	—	4	8	no	—
117	C₂³×C₄₁	—	4	4	no	—
118	C₂³×C₄₁	—	4	4	no	—
119	C₂³×C₄₁	—	4	4	no	—
120	C₂³×C₄₁	—	4	2	no	—
121	C₂³×C₄₁	C₂×C₄²	1	2	yes	—
122	C₂³×C₄₁	C₂×C₄²	1	2	yes	—
123	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
124	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂³×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
126	C₂³×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
127	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	C₂³×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
129	C₂³×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
130	C₂³×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
131	C₂³×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
132	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
133	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
134	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
135	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
136	C₂³×C₄₁	C₂²×Q₈	1	1	yes	characteristic
137	C₂×C₄×C₄₁	—	2	8	no	—
138	C₂×C₄×C₄₁	—	2	16	no	—
139	C₂×C₄×C₄₁	—	4	16	no	—
140	C₂×C₄×C₄₁	—	4	32	no	—
141	C₂×C₄×C₄₁	—	4	8	no	—
142	C₂×C₄×C₄₁	—	4	8	no	—
143	C₂×C₄×C₄₁	—	4	8	no	—
144	C₂×C₄×C₄₁	#95	1	8	yes	—
145	C₂×C₄×C₄₁	#95	1	16	yes	—
146	C₂×C₄×C₄₁	#95	1	8	yes	—
147	C₂×C₄×C₄₁	#95	1	16	yes	—
148	C₂×C₄×C₄₁	#95	1	8	yes	—
149	C₂×C₄×C₄₁	#95	1	4	yes	—
150	C₂×C₄×C₄₁	#95	1	4	yes	—
151	C₂×C₄×C₄₁	C₂×C₄²	1	4	yes	—
152	C₂×C₄×C₄₁	C₂×C₄²	1	4	yes	—
153	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	8	yes	—
154	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	8	yes	—
157	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
158	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
159	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
160	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	8	yes	—
161	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	8	yes	—
162	C₂×#1740	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂²×C₄₁	—	2	2	no	—
164	C₂²×C₄₁	—	2	2	no	—
165	C₂²×C₄₁	—	2	4	no	—
166	C₂²×C₄₁	—	2	4	no	—
167	C₂²×C₄₁	—	2	8	no	—
168	C₂²×C₄₁	—	2	4	no	—
169	C₂²×C₄₁	—	2	4	no	—
170	C₂²×C₄₁	—	2	8	no	—
171	C₂²×C₄₁	—	4	2	no	—
172	C₂²×C₄₁	—	4	4	no	—
173	C₂²×C₄₁	—	4	2	no	—
174	C₂²×C₄₁	—	4	4	no	—
175	C₂²×C₄₁	—	4	2	no	—
176	C₂²×C₄₁	—	4	1	no	—
177	C₂²×C₄₁	—	4	1	no	—
178	C₂²×C₄₁	C₂×#95	1	2	yes	—
179	C₂²×C₄₁	C₂×#95	1	4	yes	—
180	C₂²×C₄₁	C₂×#95	1	2	yes	—
181	C₂²×C₄₁	#410	1	4	yes	—
182	C₂²×C₄₁	C₂²×C₄²	1	1	yes	characteristic
183	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	2	yes	—
184	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
185	C₂²×C₄₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
186	C₂²×C₄₁	C₂²×C₄⋊C₄	1	2	yes	—
187	C₄×C₄₁	—	4	16	no	—
188	C₄×C₄₁	—	4	8	no	—
189	C₄×C₄₁	C₂×#95	1	4	yes	—
190	C₄×C₄₁	C₂×#95	1	8	yes	—
191	C₄×C₄₁	C₂×#95	1	4	yes	—
192	C₂²×#117	C₂×C₄₁	1	2	yes	—
193	C₂²×#117	C₂×C₄₁	1	1	yes	characteristic
194	#1740	C₂×C₄₁	1	8	yes	direct product factor
195	C₂×#342	C₂×C₄₁	1	4	yes	—
196	C₂×C₄₁	—	2	2	no	—
197	C₂×C₄₁	—	2	1	no	—
198	C₂×C₄₁	—	2	2	no	—
199	C₂×C₄₁	—	2	2	no	—
200	C₂×C₄₁	—	2	4	no	—
201	C₂×C₄₁	—	2	1	no	—
202	C₂×C₄₁	#1740	1	4	yes	direct product factor
203	C₂×C₄₁	C₂²×#95	1	1	yes	characteristic
204	C₂×C₄₁	C₂×#410	1	2	yes	—
205	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
206	C₂×#117	—	2	2	no	—
207	C₂×#117	—	2	4	no	—
208	C₂×#117	—	2	2	no	—
209	C₂×#117	—	2	8	no	—
210	C₂×#117	—	2	4	no	—
211	C₂×#117	C₄×C₄₁	1	16	yes	complemented
212	C₂×#117	C₄×C₄₁	1	4	yes	complemented
213	C₂×#117	C₂²×C₄₁	1	8	yes	—
214	C₂×#117	C₂²×C₄₁	1	4	yes	—
215	C₂²×C₄⋊C₄	—	2	2	no	—
216	C₂²×C₄⋊C₄	C₄×C₄₁	1	2	yes	complemented
217	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
218	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	—
219	C₂²×C₄²	—	2	2	no	—
220	C₂²×C₄²	C₄×C₄₁	1	2	yes	complemented
221	#342	C₂²×C₄₁	1	16	yes	—
222	C₄₁	C₂×#1740	1	1	yes	characteristic, direct product factor, Sylow
223	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
224	C₂³×C₄	—	2	4	no	—
225	C₂³×C₄	C₂×C₄×C₄₁	1	4	yes	—
226	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
227	C₂³×C₄	C₂×C₄×C₄₁	1	8	yes	—
228	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
229	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
230	C₂³×C₄	D₄×C₄₁	1	2	yes	—
231	C₂³×C₄	D₄×C₄₁	1	4	yes	—
232	C₂³×C₄	D₄×C₄₁	1	4	yes	—
233	C₂³×C₄	D₄×C₄₁	1	2	yes	—
234	C₂³×C₄	Q₈×C₄₁	1	4	yes	—
235	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
236	#117	—	2	32	no	—
237	#117	—	2	8	no	—
238	#117	—	2	8	no	—
239	#117	—	2	16	no	—
240	#117	—	2	8	no	—
241	#117	—	2	8	no	—
242	#117	C₂×C₄×C₄₁	1	32	yes	complemented
243	C₂×C₄⋊C₄	—	2	16	no	—
244	C₂×C₄⋊C₄	—	2	4	no	—
245	C₂×C₄⋊C₄	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	8	no	—
247	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	8	yes	complemented
248	C₂×C₂²⋊C₄	—	2	4	no	—
249	C₂×C₂²⋊C₄	—	2	4	no	—
250	C₂×C₂²⋊C₄	—	2	4	no	—
251	C₂×C₂²⋊C₄	—	2	8	no	—
252	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
253	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	16	yes	—
254	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
255	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
256	C₂×C₄²	—	2	4	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	—	2	16	no	—
260	C₂×C₄²	—	2	8	no	—
261	C₂×C₄²	C₂×C₄×C₄₁	1	8	yes	complemented
262	C₂⁴	—	4	4	no	—
263	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
264	C₂⁴	C₂²×C₄×C₄₁	1	4	yes	—
265	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
266	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
267	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
268	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
269	C₂⁴	C₂×Q₈×C₄₁	1	2	yes	—
270	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	16	no	—
274	C₂²×C₄	—	2	8	no	—
275	C₂²×C₄	—	4	16	no	—
276	C₂²×C₄	—	4	8	no	—
277	C₂²×C₄	C₄²×C₄₁	1	4	yes	—
278	C₂²×C₄	C₄²×C₄₁	1	4	yes	—
279	C₂²×C₄	C₄²×C₄₁	1	8	yes	—
280	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
281	C₂²×C₄	C₂²⋊C₄×C₄₁	1	8	yes	—
282	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
283	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
284	C₂²×C₄	C₂²⋊C₄×C₄₁	1	8	yes	—
285	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
286	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
287	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
288	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
289	C₂²×C₄	C₂²⋊C₄×C₄₁	1	16	yes	—
290	C₂²×C₄	C₄⋊C₄×C₄₁	1	4	yes	—
291	C₂²×C₄	C₄⋊C₄×C₄₁	1	8	yes	—
292	C₂²×C₄	C₄⋊C₄×C₄₁	1	8	yes	—
293	C₂²×C₄	C₄⋊C₄×C₄₁	1	4	yes	—
294	C₂²×C₄	C₄⋊C₄×C₄₁	1	8	yes	—
295	C₂²×C₄	C₄⋊C₄×C₄₁	1	16	yes	—
296	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
297	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
298	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
300	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
301	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
302	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
303	C₂²×C₄	C₂×Q₈×C₄₁	1	4	yes	—
304	C₄⋊C₄	—	2	32	no	—
305	C₄⋊C₄	—	2	16	no	—
306	C₂²⋊C₄	—	2	8	no	—
307	C₂²⋊C₄	—	2	16	no	—
308	C₂²⋊C₄	—	2	8	no	—
309	C₂²⋊C₄	—	2	8	no	—
310	C₂²⋊C₄	C₂²×C₄×C₄₁	1	16	yes	—
311	C₄²	—	2	32	no	—
312	C₄²	—	2	8	no	—
313	C₄²	—	2	8	no	—
314	C₂³	—	2	4	no	—
315	C₂³	—	2	8	no	—
316	C₂³	—	4	2	no	—
317	C₂³	—	4	8	no	—
318	C₂³	—	4	4	no	—
319	C₂³	—	4	4	no	—
320	C₂³	—	4	4	no	—
321	C₂³	—	4	2	no	—
322	C₂³	C₂×C₄²×C₄₁	1	2	yes	—
323	C₂³	C₂×C₄²×C₄₁	1	2	yes	—
324	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
325	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
326	C₂³	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
327	C₂³	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
328	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
329	C₂³	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
330	C₂³	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
331	C₂³	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
332	C₂³	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
333	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
334	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
335	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
336	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
337	C₂³	C₂²×Q₈×C₄₁	1	1	yes	characteristic
338	C₂×C₄	—	2	8	no	—
339	C₂×C₄	—	2	16	no	—
340	C₂×C₄	—	4	16	no	—
341	C₂×C₄	—	4	32	no	—
342	C₂×C₄	—	4	8	no	—
343	C₂×C₄	—	4	8	no	—
344	C₂×C₄	—	4	8	no	—
345	C₂×C₄	#95×C₄₁	1	8	yes	—
346	C₂×C₄	#95×C₄₁	1	16	yes	—
347	C₂×C₄	#95×C₄₁	1	8	yes	—
348	C₂×C₄	#95×C₄₁	1	16	yes	—
349	C₂×C₄	#95×C₄₁	1	4	yes	—
350	C₂×C₄	#95×C₄₁	1	8	yes	—
351	C₂×C₄	#95×C₄₁	1	4	yes	—
352	C₂×C₄	C₂×C₄²×C₄₁	1	4	yes	—
353	C₂×C₄	C₂×C₄²×C₄₁	1	4	yes	—
354	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	8	yes	—
355	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
356	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
357	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	8	yes	—
358	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
359	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
360	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
361	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	8	yes	—
362	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	8	yes	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	4	no	—
367	C₂²	—	2	8	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	2	8	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	C₂×#95×C₄₁	1	2	yes	—
379	C₂²	C₂×#95×C₄₁	1	4	yes	—
380	C₂²	C₂×#95×C₄₁	1	2	yes	—
381	C₂²	C₄₁×#410	1	4	yes	—
382	C₂²	C₂²×C₄²×C₄₁	1	1	yes	characteristic
383	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	2	yes	—
384	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
385	C₂²	C₂²×C₄⋊C₄×C₄₁	1	1	yes	characteristic
386	C₂²	C₂²×C₄⋊C₄×C₄₁	1	2	yes	—
387	C₄	—	4	16	no	—
388	C₄	—	4	8	no	—
389	C₄	C₂×#95×C₄₁	1	4	yes	—
390	C₄	C₂×#95×C₄₁	1	4	yes	—
391	C₄	C₂×#95×C₄₁	1	8	yes	—
392	C₂	—	2	2	no	—
393	C₂	—	2	1	no	—
394	C₂	—	2	1	no	—
395	C₂	—	2	2	no	—
396	C₂	—	2	2	no	—
397	C₂	—	2	4	no	—
398	C₂	C₄₁×#1740	1	4	yes	direct product factor
399	C₂	C₂²×#95×C₄₁	1	1	yes	characteristic
400	C₂	C₂×C₄₁×#410	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₄₁×#1740	C₂	direct (N × H)
11. C₂×#117×C₄₁	C₄	semidirect
12. C₂×#117×C₄₁	C₄	semidirect
16. C₂²×C₄⋊C₄×C₄₁	C₄	semidirect
20. C₂²×C₄²×C₄₁	C₄	semidirect
41. #117×C₄₁	C₂×C₄	semidirect
46. C₂×C₄⋊C₄×C₄₁	C₂×C₄	semidirect
60. C₂×C₄²×C₄₁	C₂×C₄	semidirect
162. C₂×#1740	C₄₁	direct (N × H)
194. #1740	C₂×C₄₁	direct (N × H)
202. C₂×C₄₁	#1740	direct (N × H)
211. C₂×#117	C₄×C₄₁	semidirect
212. C₂×#117	C₄×C₄₁	semidirect
216. C₂²×C₄⋊C₄	C₄×C₄₁	semidirect
220. C₂²×C₄²	C₄×C₄₁	semidirect
222. C₄₁	C₂×#1740	direct (N × H)
242. #117	C₂×C₄×C₄₁	semidirect
247. C₂×C₄⋊C₄	C₂×C₄×C₄₁	semidirect
261. C₂×C₄²	C₂×C₄×C₄₁	semidirect
398. C₂	C₄₁×#1740	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#117×C₄₁	2
C₄₁×#1740	2
C₂×C₄₁×#342	2
C₂×#1740	41

Subgroups — C2×C41×#1740 #23796554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1740 #23796554