Subgroups — C₄×#41×C₅⋊D₅ #72221046

Order 3200.

6912 conjugacy classes of subgroups.

The subgroup lattice has 423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅²×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	#41×#1039	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#87904	C₂	1	2	yes	maximal, complemented
5	C₄×Q₈×C₅⋊D₅	C₂	1	2	yes	maximal, complemented
6	C₄×#87902	C₂	1	6	yes	maximal, complemented
7	C₄×D₄×C₅⋊D₅	C₂	1	6	yes	maximal, complemented
8	#13107053	C₂	1	3	yes	maximal, complemented
9	#117×C₅⋊D₅	C₂	1	3	yes	maximal, complemented
10	C₄×#87900	C₂	1	3	yes	maximal, complemented
11	C₂×C₄²×C₅⋊D₅	C₂	1	3	yes	maximal, complemented
12	C₂×C₅²×#41	C₂²	1	1	yes	characteristic
13	#41×C₅⋊D₅	C₄	1	16	yes	direct product factor
14	C₂×#87904	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₅⋊D₅	C₂²	1	1	yes	characteristic
16	C₂×#87902	C₂²	1	3	yes	—
17	C₂×D₄×C₅⋊D₅	C₂²	1	3	yes	—
18	C₂×#87900	C₂²	1	3	yes	—
19	C₂²×C₄×C₅⋊D₅	C₂²	1	6	yes	—
20	C₂²×C₄×C₅⋊D₅	C₂²	1	3	yes	—
21	C₄×C₅²×Q₈	C₂²	1	2	yes	complemented
22	C₄×C₅²×D₄	C₂²	1	6	yes	complemented
23	C₅²×#117	C₂²	1	3	yes	complemented
24	C₂×C₄²×C₅²	C₂²	1	3	yes	complemented
25	Q₈×#1039	C₂²	1	2	yes	complemented
26	D₄×#1039	C₂²	1	6	yes	complemented
27	C₄×C₂²⋊(C₅⋊D₅)	C₂²	1	12	yes	complemented
28	#11717246	C₂²	1	3	yes	complemented
29	C₂×C₄×#1039	C₂²	1	3	yes	complemented
30	C₂×C₄×#1039	C₂²	1	6	yes	complemented
31	#11717213	C₂²	1	6	yes	complemented
32	#11717212	C₂²	1	6	yes	complemented
33	C₄⋊C₄×C₅⋊D₅	C₂²	1	6	yes	—
34	#11717207	C₂²	1	6	yes	complemented
35	#11717201	C₂²	1	12	yes	complemented
36	C₂²⋊C₄×C₅⋊D₅	C₂²	1	6	yes	—
37	#11717197	C₂²	1	6	yes	complemented
38	C₄×C₄⋊(C₅⋊D₅)	C₂²	1	6	yes	complemented
39	#11717192	C₂²	1	6	yes	complemented
40	C₄²×C₅⋊D₅	C₂²	1	1	yes	characteristic
41	C₄²×C₅⋊D₅	C₂²	1	3	yes	—
42	C₄²×C₅⋊D₅	C₂²	1	6	yes	—
43	C₄²×C₅⋊D₅	C₂²	1	3	yes	complemented
44	C₄²×C₅⋊D₅	C₂²	1	3	yes	complemented
45	C₄²×C₅⋊D₅	C₂²	1	6	yes	complemented
46	C₄×#6045	C₂²	1	6	yes	complemented
47	C₄×D₅×#41	—	5	6	no	maximal
48	C₂³×C₅⋊D₅	C₂³	1	3	yes	—
49	C₅²×#41	C₂×C₄	1	8	yes	complemented
50	C₂×C₅²×Q₈	C₂³	1	1	yes	characteristic
51	C₂×C₅²×D₄	C₂³	1	3	yes	—
52	C₂²×C₄×C₅²	C₂³	1	6	yes	—
53	C₂²×C₄×C₅²	C₂³	1	3	yes	—
54	C₂×C₂²⋊(C₅⋊D₅)	C₂³	1	6	yes	—
55	C₂²×#1039	C₂³	1	6	yes	—
56	C₂²×#1039	C₂³	1	3	yes	—
57	#87904	C₂×C₄	1	8	yes	complemented
58	Q₈×C₅⋊D₅	C₂×C₄	1	8	yes	complemented
59	#87902	C₂×C₄	1	24	yes	complemented
60	D₄×C₅⋊D₅	C₂×C₄	1	24	yes	complemented
61	#87900	C₂×C₄	1	24	yes	complemented
62	C₂×C₄⋊(C₅⋊D₅)	C₂³	1	3	yes	—
63	C₂×C₄×C₅⋊D₅	—	2	24	no	—
64	C₂×C₄×C₅⋊D₅	C₂×C₄	1	24	yes	complemented
65	C₂×C₄×C₅⋊D₅	C₂³	1	6	yes	—
66	C₂×C₄×C₅⋊D₅	C₂³	1	6	yes	—
67	C₂×C₄×C₅⋊D₅	C₂³	1	6	yes	—
68	C₂×C₄×C₅⋊D₅	C₂³	1	1	yes	characteristic
69	C₂×C₄×C₅⋊D₅	C₂³	1	3	yes	—
70	C₂×C₄×C₅⋊D₅	C₂³	1	3	yes	—
71	C₂×C₄×C₅⋊D₅	C₂³	1	3	yes	—
72	C₂×C₄×C₅⋊D₅	C₂³	1	2	yes	—
73	C₂×#6045	C₂³	1	3	yes	—
74	C₅²×C₄⋊C₄	C₂³	1	6	yes	—
75	C₅²×C₂²⋊C₄	C₂³	1	6	yes	—
76	C₄²×C₅²	C₂³	1	6	yes	—
77	C₄²×C₅²	C₂³	1	1	yes	characteristic
78	C₄²×C₅²	C₂³	1	3	yes	—
79	C₂²⋊#1039	C₂³	1	6	yes	—
80	#87808	C₂³	1	12	yes	—
81	C₄⋊#1039	C₂³	1	6	yes	—
82	#87806	C₂³	1	12	yes	—
83	C₄×#1039	C₂³	1	6	yes	—
84	C₄×#1039	C₂³	1	2	yes	—
85	C₄×#1039	C₂³	1	1	yes	characteristic
86	C₄×#1039	C₂³	1	3	yes	—
87	C₄×#1039	C₂³	1	6	yes	—
88	C₄×#1039	C₂³	1	6	yes	—
89	C₄×#1039	C₂³	1	6	yes	—
90	C₂×D₅×#41	—	5	6	no	—
91	C₄×C₅×#41	D₅	1	6	yes	complemented
92	#41×Dic₅	—	5	6	no	—
93	C₄×#713	—	5	12	no	—
94	C₄×Q₈×D₅	—	5	12	no	—
95	C₄×D₄×D₅	—	5	36	no	—
96	C₄×#711	—	5	36	no	—
97	#65856	—	5	18	no	—
98	D₅×#117	—	5	18	no	—
99	C₄×#709	—	5	18	no	—
100	C₂×C₄²×D₅	—	5	18	no	—
101	C₂³×C₅²	C₂⁴	1	3	yes	—
102	C₂²×C₅⋊D₅	—	2	12	no	—
103	C₂²×C₅⋊D₅	C₂²×C₄	1	12	yes	—
104	C₂²×C₅⋊D₅	C₂⁴	1	3	yes	—
105	C₂²×C₅⋊D₅	C₂⁴	1	1	yes	characteristic
106	C₅²×Q₈	C₂²×C₄	1	4	yes	complemented
107	C₅²×D₄	C₂²×C₄	1	12	yes	complemented
108	C₂×C₄×C₅²	—	2	12	no	—
109	C₂×C₄×C₅²	C₂²×C₄	1	12	yes	complemented
110	C₂×C₄×C₅²	C₂⁴	1	6	yes	—
111	C₂×C₄×C₅²	C₂⁴	1	1	yes	characteristic
112	C₂×C₄×C₅²	C₂⁴	1	3	yes	—
113	C₂×C₄×C₅²	C₂⁴	1	2	yes	—
114	C₂²⋊(C₅⋊D₅)	C₂²×C₄	1	24	yes	complemented
115	C₂×#1039	—	2	12	no	—
116	C₂×#1039	C₂²×C₄	1	12	yes	complemented
117	C₂×#1039	C₂⁴	1	6	yes	—
118	C₂×#1039	C₂⁴	1	3	yes	—
119	C₂×#1039	C₂⁴	1	1	yes	characteristic
120	C₂×#1039	C₂⁴	1	2	yes	—
121	C₄⋊(C₅⋊D₅)	C₂²×C₄	1	12	yes	complemented
122	C₄×C₅⋊D₅	—	2	12	no	—
123	C₄×C₅⋊D₅	—	2	12	no	—
124	C₄×C₅⋊D₅	—	2	12	no	—
125	C₄×C₅⋊D₅	C₂²×C₄	1	4	yes	—
126	C₄×C₅⋊D₅	C₂²×C₄	1	12	yes	—
127	C₄×C₅⋊D₅	C₂²×C₄	1	12	yes	complemented
128	C₄×C₅⋊D₅	C₂²×C₄	1	12	yes	complemented
129	C₄×C₅⋊D₅	#41	1	8	yes	direct product factor
130	#6045	C₂²×C₄	1	12	yes	complemented
131	C₂×C₅×#41	C₂×D₅	1	6	yes	—
132	D₅×#41	—	5	96	no	—
133	C₂×#713	—	5	6	no	—
134	C₂×Q₈×D₅	—	5	6	no	—
135	C₂×#711	—	5	18	no	—
136	C₂×D₄×D₅	—	5	18	no	—
137	C₂×#709	—	5	18	no	—
138	C₂²×C₄×D₅	—	5	18	no	—
139	C₂²×C₄×D₅	—	5	36	no	—
140	C₄×C₅×Q₈	C₂×D₅	1	12	yes	complemented
141	C₄×C₅×D₄	C₂×D₅	1	36	yes	complemented
142	C₅×#117	C₂×D₅	1	18	yes	complemented
143	C₂×C₄²×C₅	C₂×D₅	1	18	yes	complemented
144	Q₈×Dic₅	—	5	12	no	—
145	D₄×Dic₅	—	5	36	no	—
146	C₄×C₂²⋊D₅	—	5	72	no	—
147	#4072	—	5	18	no	—
148	C₂×C₄×Dic₅	—	5	18	no	—
149	C₂×C₄×Dic₅	—	5	36	no	—
150	#4039	—	5	36	no	—
151	#4038	—	5	36	no	—
152	D₅×C₄⋊C₄	—	5	36	no	—
153	#4033	—	5	36	no	—
154	#4027	—	5	72	no	—
155	D₅×C₂²⋊C₄	—	5	36	no	—
156	#4023	—	5	36	no	—
157	C₄×D₂₀	—	5	36	no	—
158	#4018	—	5	36	no	—
159	C₄²×D₅	—	5	6	no	—
160	C₄²×D₅	—	5	18	no	—
161	C₄²×D₅	—	5	18	no	—
162	C₄²×D₅	—	5	18	no	—
163	C₄²×D₅	—	5	36	no	—
164	C₄²×D₅	—	5	36	no	—
165	C₄×Dic₁₀	—	5	36	no	—
166	C₂×C₄×#41	—	25	1	no	Sylow
167	C₂²×C₅²	—	2	6	no	—
168	C₂²×C₅²	C₂³×C₄	1	6	yes	—
169	C₂²×C₅²	C₂⁵	1	1	yes	characteristic
170	C₂×C₅⋊D₅	—	2	6	no	—
171	C₂×C₅⋊D₅	—	2	24	no	—
172	C₂×C₅⋊D₅	C₂³×C₄	1	6	yes	—
173	C₂×C₅⋊D₅	C₂³×C₄	1	2	yes	—
174	C₂×C₅⋊D₅	C₂×#41	1	4	yes	—
175	C₄×C₅²	—	2	6	no	—
176	C₄×C₅²	C₂³×C₄	1	6	yes	—
177	C₄×C₅²	C₂³×C₄	1	2	yes	—
178	C₄×C₅²	C₂×#41	1	4	yes	complemented
179	#1039	—	2	6	no	—
180	#1039	C₂³×C₄	1	6	yes	—
181	#1039	C₂³×C₄	1	2	yes	—
182	#1039	C₂×#41	1	4	yes	complemented
183	C₂³×D₅	—	5	18	no	—
184	C₅×#41	C₄×D₅	1	48	yes	complemented
185	C₂×C₅×Q₈	C₂²×D₅	1	6	yes	—
186	C₂×C₅×D₄	C₂²×D₅	1	18	yes	—
187	C₂²×C₄×C₅	C₂²×D₅	1	36	yes	—
188	C₂²×C₄×C₅	C₂²×D₅	1	18	yes	—
189	C₂×C₂²⋊D₅	—	5	36	no	—
190	C₂²×Dic₅	—	5	18	no	—
191	C₂²×Dic₅	—	5	36	no	—
192	#713	—	5	48	no	—
193	Q₈×D₅	—	5	48	no	—
194	#711	—	5	144	no	—
195	D₄×D₅	—	5	144	no	—
196	#709	—	5	144	no	—
197	C₂×D₂₀	—	5	18	no	—
198	C₂×C₄×D₅	—	5	144	no	—
199	C₂×C₄×D₅	—	5	6	no	—
200	C₂×C₄×D₅	—	5	12	no	—
201	C₂×C₄×D₅	—	5	18	no	—
202	C₂×C₄×D₅	—	5	18	no	—
203	C₂×C₄×D₅	—	5	18	no	—
204	C₂×C₄×D₅	—	5	36	no	—
205	C₂×C₄×D₅	—	5	36	no	—
206	C₂×C₄×D₅	—	5	36	no	—
207	C₂×C₄×D₅	—	10	144	no	—
208	C₂×Dic₁₀	—	5	18	no	—
209	C₅×C₄⋊C₄	C₂²×D₅	1	36	yes	—
210	C₅×C₂²⋊C₄	C₂²×D₅	1	36	yes	—
211	C₄²×C₅	C₂²×D₅	1	18	yes	—
212	C₄²×C₅	C₂²×D₅	1	36	yes	—
213	C₄²×C₅	C₂²×D₅	1	6	yes	—
214	C₂²⋊Dic₅	—	5	36	no	—
215	#685	—	5	72	no	—
216	C₄⋊Dic₅	—	5	36	no	—
217	#683	—	5	72	no	—
218	C₄×Dic₅	—	5	36	no	—
219	C₄×Dic₅	—	5	6	no	—
220	C₄×Dic₅	—	5	12	no	—
221	C₄×Dic₅	—	5	18	no	—
222	C₄×Dic₅	—	5	36	no	—
223	C₄×Dic₅	—	5	36	no	—
224	C₄×Dic₅	—	5	36	no	—
225	C₂²×#41	—	25	1	no	—
226	C₄×#41	—	25	1	no	—
227	C₄×#41	—	25	2	no	—
228	C₄×#41	—	25	6	no	—
229	C₄×#41	—	25	3	no	—
230	C₄×#41	—	25	3	no	—
231	C₄×#41	C₅⋊D₅	1	1	yes	characteristic, direct product factor
232	C₂×C₄×Q₈	—	25	2	no	—
233	C₂×C₄×D₄	—	25	6	no	—
234	C₂×#117	—	25	3	no	—
235	C₂²×C₄²	—	25	3	no	—
236	C₂×C₅²	—	2	6	no	—
237	C₂×C₅²	C₂⁴×C₄	1	1	yes	characteristic
238	C₂×C₅²	C₂²×#41	1	2	yes	—
239	C₅⋊D₅	—	2	6	no	—
240	C₅⋊D₅	C₄×#41	1	4	yes	direct product factor
241	C₂³×C₅	C₂³×D₅	1	18	yes	—
242	C₂²×D₅	—	5	6	no	—
243	C₂²×D₅	—	5	72	no	—
244	C₂²×D₅	—	5	18	no	—
245	C₂²×D₅	—	10	72	no	—
246	C₅×Q₈	C₂×C₄×D₅	1	24	yes	complemented
247	C₅×D₄	C₂×C₄×D₅	1	72	yes	complemented
248	C₂×C₄×C₅	—	2	72	no	—
249	C₂×C₄×C₅	C₂×C₄×D₅	1	72	yes	complemented
250	C₂×C₄×C₅	C₂³×D₅	1	36	yes	—
251	C₂×C₄×C₅	C₂³×D₅	1	6	yes	—
252	C₂×C₄×C₅	C₂³×D₅	1	18	yes	—
253	C₂×C₄×C₅	C₂³×D₅	1	12	yes	—
254	C₂²⋊D₅	—	5	144	no	—
255	C₂×Dic₅	—	5	72	no	—
256	C₂×Dic₅	—	5	6	no	—
257	C₂×Dic₅	—	5	12	no	—
258	C₂×Dic₅	—	5	18	no	—
259	C₂×Dic₅	—	5	36	no	—
260	C₂×Dic₅	—	10	72	no	—
261	D₂₀	—	5	72	no	—
262	C₄×D₅	—	5	24	no	—
263	C₄×D₅	—	5	72	no	—
264	C₄×D₅	—	5	72	no	—
265	C₄×D₅	—	5	72	no	—
266	C₄×D₅	—	5	48	no	—
267	C₄×D₅	—	10	72	no	—
268	C₄×D₅	—	10	72	no	—
269	C₄×D₅	—	10	72	no	—
270	Dic₁₀	—	5	72	no	—
271	C₂×#41	—	25	16	no	—
272	C₂×#41	—	25	1	no	—
273	C₂×#41	—	25	3	no	—
274	C₂×#41	—	25	3	no	—
275	C₂×#41	C₂×C₅⋊D₅	1	1	yes	characteristic
276	C₂²×Q₈	—	25	1	no	—
277	C₂²×D₄	—	25	3	no	—
278	C₂³×C₄	—	25	3	no	—
279	C₂³×C₄	—	25	6	no	—
280	C₄×Q₈	—	25	2	no	—
281	C₄×Q₈	—	25	6	no	—
282	C₄×Q₈	—	25	6	no	—
283	C₄×Q₈	C₂×C₅⋊D₅	1	2	yes	complemented
284	C₄×D₄	—	25	6	no	—
285	C₄×D₄	—	25	12	no	—
286	C₄×D₄	—	25	6	no	—
287	C₄×D₄	—	25	12	no	—
288	C₄×D₄	—	25	6	no	—
289	C₄×D₄	C₂×C₅⋊D₅	1	6	yes	complemented
290	#117	—	25	3	no	—
291	#117	—	25	6	no	—
292	#117	—	25	6	no	—
293	#117	—	25	6	no	—
294	#117	C₂×C₅⋊D₅	1	3	yes	complemented
295	C₂×C₄⋊C₄	—	25	6	no	—
296	C₂×C₂²⋊C₄	—	25	6	no	—
297	C₂×C₄²	—	25	6	no	—
298	C₂×C₄²	—	25	3	no	—
299	C₂×C₄²	—	25	3	no	—
300	C₂×C₄²	—	25	6	no	—
301	C₂×C₄²	—	25	6	no	—
302	C₂×C₄²	—	25	3	no	—
303	C₂×C₄²	—	25	3	no	—
304	C₂×C₄²	—	25	1	no	—
305	C₂×C₄²	C₂×C₅⋊D₅	1	3	yes	complemented
306	C₅²	C₂×C₄×#41	1	1	yes	characteristic, complemented, Sylow
307	C₂²×C₅	—	2	36	no	—
308	C₂²×C₅	C₂²×C₄×D₅	1	36	yes	—
309	C₂²×C₅	C₂⁴×D₅	1	6	yes	—
310	C₂×D₅	—	5	12	no	—
311	C₂×D₅	—	5	24	no	—
312	C₂×D₅	—	5	36	no	—
313	C₂×D₅	—	10	144	no	—
314	C₂×D₅	—	10	36	no	—
315	C₄×C₅	—	2	36	no	—
316	C₄×C₅	C₂²×C₄×D₅	1	36	yes	—
317	C₄×C₅	C₂²×C₄×D₅	1	12	yes	—
318	C₄×C₅	D₅×#41	1	24	yes	complemented
319	Dic₅	—	5	36	no	—
320	Dic₅	—	5	12	no	—
321	Dic₅	—	5	24	no	—
322	Dic₅	—	10	36	no	—
323	C₂⁴	—	25	3	no	—
324	#41	—	25	8	no	—
325	#41	—	25	24	no	—
326	#41	—	25	24	no	—
327	#41	C₄×C₅⋊D₅	1	8	yes	direct product factor
328	C₂×Q₈	—	25	8	no	—
329	C₂×Q₈	—	25	3	no	—
330	C₂×Q₈	C₂²×C₅⋊D₅	1	1	yes	characteristic
331	C₂×D₄	—	25	6	no	—
332	C₂×D₄	—	25	24	no	—
333	C₂×D₄	—	25	3	no	—
334	C₂×D₄	C₂²×C₅⋊D₅	1	3	yes	—
335	C₂²×C₄	—	25	3	no	—
336	C₂²×C₄	—	25	24	no	—
337	C₂²×C₄	—	25	1	no	—
338	C₂²×C₄	—	25	2	no	—
339	C₂²×C₄	—	25	3	no	—
340	C₂²×C₄	—	25	3	no	—
341	C₂²×C₄	—	25	3	no	—
342	C₂²×C₄	—	25	6	no	—
343	C₂²×C₄	—	25	6	no	—
344	C₂²×C₄	—	25	6	no	—
345	C₂²×C₄	—	25	6	no	—
346	C₂²×C₄	—	50	24	no	—
347	C₂²×C₄	C₂²×C₅⋊D₅	1	6	yes	—
348	C₂²×C₄	C₂²×C₅⋊D₅	1	3	yes	—
349	C₄⋊C₄	—	25	12	no	—
350	C₄⋊C₄	—	25	6	no	—
351	C₄⋊C₄	C₂²×C₅⋊D₅	1	6	yes	—
352	C₂²⋊C₄	—	25	6	no	—
353	C₂²⋊C₄	—	25	12	no	—
354	C₂²⋊C₄	C₂²×C₅⋊D₅	1	6	yes	—
355	C₄²	—	25	1	no	—
356	C₄²	—	25	2	no	—
357	C₄²	—	25	6	no	—
358	C₄²	—	25	3	no	—
359	C₄²	—	25	6	no	—
360	C₄²	—	25	6	no	—
361	C₄²	—	25	6	no	—
362	C₄²	C₂²×C₅⋊D₅	1	3	yes	—
363	C₄²	C₂²×C₅⋊D₅	1	6	yes	—
364	C₄²	C₂²×C₅⋊D₅	1	1	yes	characteristic
365	C₂×C₅	—	2	36	no	—
366	C₂×C₅	C₂³×C₄×D₅	1	6	yes	—
367	C₂×C₅	C₂×D₅×#41	1	12	yes	—
368	D₅	—	5	24	no	—
369	D₅	—	10	36	no	—
370	C₂³	—	25	1	no	—
371	C₂³	—	25	12	no	—
372	C₂³	—	25	3	no	—
373	C₂³	—	50	12	no	—
374	C₂³	C₂³×C₅⋊D₅	1	3	yes	—
375	Q₈	—	25	12	no	—
376	Q₈	C₂×C₄×C₅⋊D₅	1	4	yes	complemented
377	D₄	—	25	24	no	—
378	D₄	—	25	12	no	—
379	D₄	C₂×C₄×C₅⋊D₅	1	12	yes	complemented
380	C₂×C₄	—	2	12	no	—
381	C₂×C₄	—	25	12	no	—
382	C₂×C₄	—	25	1	no	—
383	C₂×C₄	—	25	2	no	—
384	C₂×C₄	—	25	3	no	—
385	C₂×C₄	—	25	4	no	—
386	C₂×C₄	—	25	12	no	—
387	C₂×C₄	—	25	12	no	—
388	C₂×C₄	—	25	12	no	—
389	C₂×C₄	—	25	8	no	—
390	C₂×C₄	—	25	6	no	—
391	C₂×C₄	—	50	12	no	—
392	C₂×C₄	—	50	12	no	—
393	C₂×C₄	—	50	12	no	—
394	C₂×C₄	—	50	12	no	—
395	C₂×C₄	C₂×C₄×C₅⋊D₅	1	12	yes	complemented
396	C₂×C₄	C₂³×C₅⋊D₅	1	6	yes	—
397	C₂×C₄	C₂³×C₅⋊D₅	1	1	yes	characteristic
398	C₂×C₄	C₂³×C₅⋊D₅	1	3	yes	—
399	C₂×C₄	C₂³×C₅⋊D₅	1	2	yes	—
400	C₅	C₄×D₅×#41	1	6	yes	complemented
401	C₂²	—	2	6	no	—
402	C₂²	—	25	2	no	—
403	C₂²	—	25	4	no	—
404	C₂²	—	25	6	no	—
405	C₂²	—	50	24	no	—
406	C₂²	—	50	6	no	—
407	C₂²	C₂²×C₄×C₅⋊D₅	1	6	yes	—
408	C₂²	C₂⁴×C₅⋊D₅	1	1	yes	characteristic
409	C₄	—	2	6	no	—
410	C₄	—	25	2	no	—
411	C₄	—	25	6	no	—
412	C₄	—	25	4	no	—
413	C₄	—	50	6	no	—
414	C₄	C₂²×C₄×C₅⋊D₅	1	2	yes	—
415	C₄	C₂²×C₄×C₅⋊D₅	1	6	yes	—
416	C₄	#41×C₅⋊D₅	1	4	yes	direct product factor
417	C₂	—	2	6	no	—
418	C₂	—	25	4	no	—
419	C₂	—	50	6	no	—
420	C₂	C₂³×C₄×C₅⋊D₅	1	1	yes	characteristic
421	C₂	C₂×#41×C₅⋊D₅	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂²×C₅⋊D₅
commutator	C₂×C₅²	C₂⁴×C₄
Frattini	C₂²	C₂⁴×C₅⋊D₅
Fitting	C₄×C₅²×#41	C₂
socle, cosocle	C₂²×C₅²	C₂⁵
prime radical	C₂×#41×C₅⋊D₅	C₂
hypercenter	C₄×#41	C₅⋊D₅
hypocenter	C₅²	C₂×C₄×#41
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₄² ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
2. C₄×C₅²×#41	C₂	semidirect
3. #41×#1039	C₂	semidirect
4. C₄×#87904	C₂	semidirect
5. C₄×Q₈×C₅⋊D₅	C₂	semidirect
6. C₄×#87902	C₂	semidirect
7. C₄×D₄×C₅⋊D₅	C₂	semidirect
8. #13107053	C₂	semidirect
9. #117×C₅⋊D₅	C₂	semidirect
10. C₄×#87900	C₂	semidirect
11. C₂×C₄²×C₅⋊D₅	C₂	semidirect
13. #41×C₅⋊D₅	C₄	direct (N × H)
21. C₄×C₅²×Q₈	C₂²	semidirect
22. C₄×C₅²×D₄	C₂²	semidirect
23. C₅²×#117	C₂²	semidirect
24. C₂×C₄²×C₅²	C₂²	semidirect
25. Q₈×#1039	C₂²	semidirect
26. D₄×#1039	C₂²	semidirect
27. C₄×C₂²⋊(C₅⋊D₅)	C₂²	semidirect
28. #11717246	C₂²	semidirect
29. C₂×C₄×#1039	C₂²	semidirect
30. C₂×C₄×#1039	C₂²	semidirect
31. #11717213	C₂²	semidirect
32. #11717212	C₂²	semidirect
34. #11717207	C₂²	semidirect
35. #11717201	C₂²	semidirect
37. #11717197	C₂²	semidirect
38. C₄×C₄⋊(C₅⋊D₅)	C₂²	semidirect
39. #11717192	C₂²	semidirect
43. C₄²×C₅⋊D₅	C₂²	semidirect
44. C₄²×C₅⋊D₅	C₂²	semidirect
45. C₄²×C₅⋊D₅	C₂²	semidirect
46. C₄×#6045	C₂²	semidirect
49. C₅²×#41	C₂×C₄	semidirect
57. #87904	C₂×C₄	semidirect
58. Q₈×C₅⋊D₅	C₂×C₄	semidirect
59. #87902	C₂×C₄	semidirect
60. D₄×C₅⋊D₅	C₂×C₄	semidirect
61. #87900	C₂×C₄	semidirect
64. C₂×C₄×C₅⋊D₅	C₂×C₄	semidirect
91. C₄×C₅×#41	D₅	semidirect
106. C₅²×Q₈	C₂²×C₄	semidirect
107. C₅²×D₄	C₂²×C₄	semidirect
109. C₂×C₄×C₅²	C₂²×C₄	semidirect
114. C₂²⋊(C₅⋊D₅)	C₂²×C₄	semidirect
116. C₂×#1039	C₂²×C₄	semidirect
121. C₄⋊(C₅⋊D₅)	C₂²×C₄	semidirect
127. C₄×C₅⋊D₅	C₂²×C₄	semidirect
128. C₄×C₅⋊D₅	C₂²×C₄	semidirect
129. C₄×C₅⋊D₅	#41	direct (N × H)
130. #6045	C₂²×C₄	semidirect
140. C₄×C₅×Q₈	C₂×D₅	semidirect
141. C₄×C₅×D₄	C₂×D₅	semidirect
142. C₅×#117	C₂×D₅	semidirect
143. C₂×C₄²×C₅	C₂×D₅	semidirect
178. C₄×C₅²	C₂×#41	semidirect
182. #1039	C₂×#41	semidirect
184. C₅×#41	C₄×D₅	semidirect
231. C₄×#41	C₅⋊D₅	direct (N × H)
240. C₅⋊D₅	C₄×#41	direct (N × H)
246. C₅×Q₈	C₂×C₄×D₅	semidirect
247. C₅×D₄	C₂×C₄×D₅	semidirect
249. C₂×C₄×C₅	C₂×C₄×D₅	semidirect
283. C₄×Q₈	C₂×C₅⋊D₅	semidirect
289. C₄×D₄	C₂×C₅⋊D₅	semidirect
294. #117	C₂×C₅⋊D₅	semidirect
305. C₂×C₄²	C₂×C₅⋊D₅	semidirect
306. C₅²	C₂×C₄×#41	semidirect
318. C₄×C₅	D₅×#41	semidirect
327. #41	C₄×C₅⋊D₅	direct (N × H)
376. Q₈	C₂×C₄×C₅⋊D₅	semidirect
379. D₄	C₂×C₄×C₅⋊D₅	semidirect
395. C₂×C₄	C₂×C₄×C₅⋊D₅	semidirect
400. C₅	C₄×D₅×#41	semidirect
416. C₄	#41×C₅⋊D₅	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×#41×C₅⋊D₅	2
C₄×C₅²×#41	2
#41×#1039	2
C₄×#87904	2
C₄×Q₈×C₅⋊D₅	2
C₄×#87902	2
C₄×D₄×C₅⋊D₅	2
#13107053	2
#117×C₅⋊D₅	2
C₄×#87900	2
C₂×C₄²×C₅⋊D₅	2
C₄×D₅×#41	5

Subgroups — C4×#41×C5⋊D5 #72221046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#41×C₅⋊D₅ #72221046