Subgroups — C₅×D₄×C₂²⋊D₅ #13106957

Order 1600.

1092 conjugacy classes of subgroups.

The subgroup lattice has 443 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4099	C₂	1	2	yes	maximal, complemented
5	C₅×#4086	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4085	C₂	1	2	yes	maximal, complemented
7	C₅×#4084	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4083	C₂	1	2	yes	maximal, complemented
9	C₅×D₄×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4076	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₅²	C₂²	1	2	yes	complemented
13	C₂³×C₅×D₅	C₂²	1	2	yes	complemented
14	C₂×C₅²×D₄	—	2	4	no	—
15	C₂×C₅²×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₅²×D₄	C₂²	1	2	yes	complemented
17	C₂×C₅²×D₄	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₄×C₅²	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₅×C₂²⋊D₅	—	2	8	no	—
20	C₂×C₅×C₂²⋊D₅	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
22	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
23	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
24	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
25	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
26	C₂²×C₅×Dic₅	C₂²	1	2	yes	complemented
27	C₅×D₄×D₅	—	2	4	no	—
28	C₂×C₅×D₂₀	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic, complemented
30	C₅×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
31	C₅×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
32	C₅×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
33	C₅×#685	C₂²	1	1	yes	characteristic, complemented
34	C₅×#685	C₂²	1	2	yes	complemented
35	C₅×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
36	C₅×#683	C₂²	1	1	yes	characteristic, complemented
37	C₄×C₅×Dic₅	C₂²	1	1	yes	characteristic, complemented
38	C₅×D₄²	—	5	1	no	maximal
39	D₄×C₂²⋊D₅	C₅	1	1	yes	maximal, characteristic, direct product factor
40	C₂³×C₅²	—	2	4	no	—
41	C₂³×C₅²	—	2	4	no	—
42	C₂³×C₅²	—	4	2	no	—
43	C₂³×C₅²	C₂³	1	2	yes	—
44	C₂³×C₅²	C₂³	1	2	yes	—
45	C₂³×C₅²	C₂³	1	1	yes	characteristic
46	C₂²×C₅×D₅	—	2	4	no	—
47	C₂²×C₅×D₅	—	2	4	no	—
48	C₂²×C₅×D₅	—	4	2	no	—
49	C₂²×C₅×D₅	C₂³	1	2	yes	—
50	C₂²×C₅×D₅	C₂³	1	1	yes	characteristic
51	C₅²×D₄	—	2	4	no	—
52	C₅²×D₄	—	2	2	no	—
53	C₅²×D₄	D₄	1	4	yes	complemented
54	C₂×C₄×C₅²	—	2	2	no	—
55	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
56	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
57	C₅×C₂²⋊D₅	—	2	4	no	—
58	C₅×C₂²⋊D₅	—	2	4	no	—
59	C₅×C₂²⋊D₅	—	2	4	no	—
60	C₅×C₂²⋊D₅	—	2	4	no	—
61	C₅×C₂²⋊D₅	—	4	2	no	—
62	C₅×C₂²⋊D₅	D₄	1	4	yes	direct product factor
63	C₂×C₅×Dic₅	—	2	4	no	—
64	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
65	C₂×C₅×Dic₅	C₂³	1	2	yes	—
66	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
67	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
68	C₅×D₂₀	—	2	2	no	—
69	C₄×C₅×D₅	—	2	2	no	—
70	C₂²×C₅×D₄	—	2	2	no	—
71	C₂²×C₅×D₄	—	5	2	no	—
72	C₂²×C₅×D₄	—	5	1	no	—
73	C₂²×C₅×D₄	D₅	1	1	yes	characteristic, complemented
74	C₂²×C₅×D₄	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂²×C₂²⋊D₅	C₂×C₅	1	2	yes	complemented
76	C₂×D₄×D₅	C₂×C₅	1	1	yes	characteristic, complemented
77	C₅×#127	—	5	1	no	—
78	C₅×#121	—	5	1	no	—
79	C₅×#121	—	5	2	no	—
80	C₅×#121	—	5	1	no	—
81	C₅×#120	—	5	2	no	—
82	C₅×#120	—	5	2	no	—
83	C₄×C₅×D₄	—	5	1	no	—
84	C₄×C₅×D₄	—	5	1	no	—
85	#4099	C₂×C₅	1	2	yes	complemented
86	#4086	C₂×C₅	1	1	yes	characteristic, complemented
87	#4085	C₂×C₅	1	2	yes	complemented
88	#4084	C₂×C₅	1	1	yes	characteristic, complemented
89	#4083	C₂×C₅	1	2	yes	complemented
90	D₄×Dic₅	C₂×C₅	1	1	yes	characteristic, complemented
91	#4076	C₂×C₅	1	1	yes	characteristic, complemented
92	C₄×C₂²⋊D₅	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂²×C₅²	—	2	1	no	—
94	C₂²×C₅²	—	2	2	no	—
95	C₂²×C₅²	—	2	1	no	—
96	C₂²×C₅²	—	2	2	no	—
97	C₂²×C₅²	—	2	2	no	—
98	C₂²×C₅²	—	2	2	no	—
99	C₂²×C₅²	—	2	2	no	—
100	C₂²×C₅²	—	4	8	no	—
101	C₂²×C₅²	C₂×D₄	1	2	yes	complemented
102	C₂²×C₅²	C₂×D₄	1	4	yes	complemented
103	C₂²×C₅²	C₂⁴	1	1	yes	characteristic
104	C₂×C₅×D₅	—	2	1	no	—
105	C₂×C₅×D₅	—	2	2	no	—
106	C₂×C₅×D₅	—	2	2	no	—
107	C₂×C₅×D₅	—	2	1	no	—
108	C₂×C₅×D₅	—	2	2	no	—
109	C₂×C₅×D₅	—	4	8	no	—
110	C₂×C₅×D₅	C₂×D₄	1	2	yes	complemented
111	C₄×C₅²	—	2	1	no	—
112	C₄×C₅²	C₂×D₄	1	2	yes	complemented
113	C₅×Dic₅	—	2	1	no	—
114	C₅×Dic₅	—	2	2	no	—
115	C₅×Dic₅	—	2	1	no	—
116	C₅×Dic₅	C₂×D₄	1	2	yes	complemented
117	C₂⁴×C₅	—	2	4	no	—
118	C₂⁴×C₅	—	5	2	no	—
119	C₂⁴×C₅	C₂×D₅	1	2	yes	complemented
120	C₂⁴×C₅	C₂²×C₅	1	2	yes	complemented
121	C₂³×D₅	C₂²×C₅	1	2	yes	complemented
122	C₂×C₅×D₄	—	2	16	no	—
123	C₂×C₅×D₄	—	2	4	no	—
124	C₂×C₅×D₄	—	2	4	no	—
125	C₂×C₅×D₄	—	2	2	no	—
126	C₂×C₅×D₄	—	2	4	no	—
127	C₂×C₅×D₄	—	2	2	no	—
128	C₂×C₅×D₄	—	5	1	no	—
129	C₂×C₅×D₄	—	5	2	no	—
130	C₂×C₅×D₄	—	5	2	no	—
131	C₂×C₅×D₄	—	5	2	no	—
132	C₂×C₅×D₄	—	5	2	no	—
133	C₂×C₅×D₄	—	5	2	no	—
134	C₂×C₅×D₄	—	5	1	no	—
135	C₂×C₅×D₄	—	10	8	no	—
136	C₂×C₅×D₄	—	10	4	no	—
137	C₂×C₅×D₄	C₂×D₅	1	1	yes	characteristic
138	C₂×C₅×D₄	C₂×D₅	1	2	yes	complemented
139	C₂×C₅×D₄	C₂×D₅	1	1	yes	characteristic, complemented
140	C₂×C₅×D₄	C₂²×C₅	1	1	yes	characteristic
141	C₂×C₅×D₄	C₂²×C₅	1	2	yes	complemented
142	C₂×C₅×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
143	C₂²×C₄×C₅	—	2	2	no	—
144	C₂²×C₄×C₅	—	5	2	no	—
145	C₂²×C₄×C₅	—	5	1	no	—
146	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic, complemented
147	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic, complemented
148	C₂×C₂²⋊D₅	—	2	8	no	—
149	C₂×C₂²⋊D₅	C₂²×C₅	1	1	yes	characteristic
150	C₂×C₂²⋊D₅	C₂²×C₅	1	2	yes	complemented
151	C₂×C₂²⋊D₅	C₂²×C₅	1	2	yes	complemented
152	C₂×C₂²⋊D₅	C₂²×C₅	1	2	yes	complemented
153	C₂×C₂²⋊D₅	C₂²×C₅	1	2	yes	complemented
154	C₂×C₂²⋊D₅	C₂²×C₅	1	2	yes	complemented
155	C₂²×Dic₅	C₂²×C₅	1	2	yes	complemented
156	D₄×D₅	—	2	4	no	—
157	C₂×D₂₀	C₂²×C₅	1	1	yes	characteristic, complemented
158	C₂×C₄×D₅	C₂²×C₅	1	1	yes	characteristic, complemented
159	C₅×C₄⋊C₄	—	5	1	no	—
160	C₅×C₄⋊C₄	—	5	1	no	—
161	C₅×C₂²⋊C₄	—	5	1	no	—
162	C₅×C₂²⋊C₄	—	5	2	no	—
163	C₅×C₂²⋊C₄	—	5	2	no	—
164	C₅×C₂²⋊C₄	—	5	1	no	—
165	C₅×C₂²⋊C₄	—	5	2	no	—
166	C₄²×C₅	—	5	1	no	—
167	C₂²⋊Dic₅	C₂²×C₅	1	1	yes	characteristic, complemented
168	C₂²⋊Dic₅	C₂²×C₅	1	2	yes	complemented
169	C₂²⋊Dic₅	C₂²×C₅	1	2	yes	complemented
170	#685	C₂²×C₅	1	1	yes	characteristic, complemented
171	#685	C₂²×C₅	1	2	yes	complemented
172	C₄⋊Dic₅	C₂²×C₅	1	1	yes	characteristic, complemented
173	#683	C₂²×C₅	1	1	yes	characteristic, complemented
174	C₄×Dic₅	C₂²×C₅	1	1	yes	characteristic, complemented
175	D₄²	—	5	1	no	Sylow
176	C₂×C₅²	—	2	2	no	—
177	C₂×C₅²	—	2	4	no	—
178	C₂×C₅²	—	4	2	no	—
179	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₅²	H(5,𝔽₂)	1	1	yes	characteristic
182	C₅×D₅	—	2	2	no	—
183	C₅×D₅	—	4	2	no	—
184	C₂³×C₅	—	2	16	no	—
185	C₂³×C₅	—	2	4	no	—
186	C₂³×C₅	—	2	4	no	—
187	C₂³×C₅	—	2	4	no	—
188	C₂³×C₅	—	2	4	no	—
189	C₂³×C₅	—	2	2	no	—
190	C₂³×C₅	—	2	4	no	—
191	C₂³×C₅	—	2	4	no	—
192	C₂³×C₅	—	4	8	no	—
193	C₂³×C₅	—	4	2	no	—
194	C₂³×C₅	—	4	2	no	—
195	C₂³×C₅	—	4	8	no	—
196	C₂³×C₅	—	5	1	no	—
197	C₂³×C₅	—	5	2	no	—
198	C₂³×C₅	—	10	4	no	—
199	C₂³×C₅	—	10	4	no	—
200	C₂³×C₅	—	20	2	no	—
201	C₂³×C₅	C₂²×D₅	1	2	yes	—
202	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
203	C₂³×C₅	C₂²×D₅	1	2	yes	—
204	C₂³×C₅	C₂³×C₅	1	2	yes	—
205	C₂³×C₅	C₂³×C₅	1	2	yes	—
206	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
207	C₂²×D₅	—	2	4	no	—
208	C₂²×D₅	—	2	4	no	—
209	C₂²×D₅	—	4	2	no	—
210	C₂²×D₅	C₂³×C₅	1	2	yes	—
211	C₂²×D₅	C₂³×C₅	1	1	yes	characteristic
212	C₅×D₄	—	2	16	no	—
213	C₅×D₄	—	2	8	no	—
214	C₅×D₄	—	2	4	no	—
215	C₅×D₄	—	2	4	no	—
216	C₅×D₄	—	2	2	no	—
217	C₅×D₄	—	2	2	no	—
218	C₅×D₄	—	2	8	no	—
219	C₅×D₄	—	5	4	no	—
220	C₅×D₄	—	10	4	no	—
221	C₅×D₄	—	10	4	no	—
222	C₅×D₄	—	10	4	no	—
223	C₅×D₄	—	10	4	no	—
224	C₅×D₄	—	10	2	no	—
225	C₅×D₄	—	20	2	no	—
226	C₅×D₄	C₂²⋊D₅	1	4	yes	direct product factor
227	C₅×D₄	C₅×D₄	1	4	yes	complemented
228	C₂×C₄×C₅	—	2	8	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	5	1	no	—
234	C₂×C₄×C₅	—	5	1	no	—
235	C₂×C₄×C₅	—	5	2	no	—
236	C₂×C₄×C₅	—	5	1	no	—
237	C₂×C₄×C₅	—	10	4	no	—
238	C₂×C₄×C₅	—	10	2	no	—
239	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
243	C₂²⋊D₅	—	2	4	no	—
244	C₂²⋊D₅	—	2	4	no	—
245	C₂²⋊D₅	—	2	4	no	—
246	C₂²⋊D₅	—	2	4	no	—
247	C₂²⋊D₅	—	4	2	no	—
248	C₂²⋊D₅	C₅×D₄	1	4	yes	direct product factor
249	C₂×Dic₅	—	2	4	no	—
250	C₂×Dic₅	C₂³×C₅	1	1	yes	characteristic
251	C₂×Dic₅	C₂³×C₅	1	1	yes	characteristic
252	C₂×Dic₅	C₂³×C₅	1	2	yes	—
253	C₂×Dic₅	C₂³×C₅	1	1	yes	characteristic
254	D₂₀	—	2	2	no	—
255	C₄×D₅	—	2	2	no	—
256	C₂²×D₄	—	5	2	no	—
257	C₂²×D₄	—	5	1	no	—
258	C₂²×D₄	C₅×D₅	1	1	yes	characteristic, complemented
259	#127	—	5	1	no	—
260	#121	—	5	1	no	—
261	#121	—	5	2	no	—
262	#121	—	5	1	no	—
263	#120	—	5	2	no	—
264	#120	—	5	2	no	—
265	C₄×D₄	—	5	1	no	—
266	C₄×D₄	—	5	1	no	—
267	C₅²	D₄²	1	1	yes	characteristic, complemented, Sylow
268	C₂²×C₅	—	2	4	no	—
269	C₂²×C₅	—	2	4	no	—
270	C₂²×C₅	—	2	2	no	—
271	C₂²×C₅	—	2	1	no	—
272	C₂²×C₅	—	2	2	no	—
273	C₂²×C₅	—	2	1	no	—
274	C₂²×C₅	—	2	2	no	—
275	C₂²×C₅	—	2	1	no	—
276	C₂²×C₅	—	2	2	no	—
277	C₂²×C₅	—	2	1	no	—
278	C₂²×C₅	—	2	8	no	—
279	C₂²×C₅	—	2	2	no	—
280	C₂²×C₅	—	2	2	no	—
281	C₂²×C₅	—	2	2	no	—
282	C₂²×C₅	—	2	2	no	—
283	C₂²×C₅	—	2	2	no	—
284	C₂²×C₅	—	2	2	no	—
285	C₂²×C₅	—	2	4	no	—
286	C₂²×C₅	—	2	8	no	—
287	C₂²×C₅	—	2	2	no	—
288	C₂²×C₅	—	4	4	no	—
289	C₂²×C₅	—	4	4	no	—
290	C₂²×C₅	—	4	4	no	—
291	C₂²×C₅	—	4	4	no	—
292	C₂²×C₅	—	4	8	no	—
293	C₂²×C₅	—	4	8	no	—
294	C₂²×C₅	—	4	32	no	—
295	C₂²×C₅	—	5	2	no	—
296	C₂²×C₅	—	10	1	no	—
297	C₂²×C₅	—	10	1	no	—
298	C₂²×C₅	—	10	2	no	—
299	C₂²×C₅	—	10	2	no	—
300	C₂²×C₅	—	10	2	no	—
301	C₂²×C₅	—	20	8	no	—
302	C₂²×C₅	D₄×D₅	1	2	yes	complemented
303	C₂²×C₅	C₂×C₂²⋊D₅	1	4	yes	complemented
304	C₂²×C₅	C₂×C₅×D₄	1	2	yes	complemented
305	C₂²×C₅	C₂×C₅×D₄	1	4	yes	complemented
306	C₂²×C₅	C₂³×D₅	1	1	yes	characteristic
307	C₂²×C₅	C₂⁴×C₅	1	1	yes	characteristic
308	C₂×D₅	—	2	1	no	—
309	C₂×D₅	—	2	1	no	—
310	C₂×D₅	—	2	2	no	—
311	C₂×D₅	—	2	2	no	—
312	C₂×D₅	—	2	2	no	—
313	C₂×D₅	—	4	8	no	—
314	C₂×D₅	C₂×C₅×D₄	1	2	yes	complemented
315	C₄×C₅	—	2	4	no	—
316	C₄×C₅	—	2	1	no	—
317	C₄×C₅	—	2	1	no	—
318	C₄×C₅	—	2	4	no	—
319	C₄×C₅	—	5	2	no	—
320	C₄×C₅	—	10	2	no	—
321	C₄×C₅	—	10	1	no	—
322	C₄×C₅	—	10	1	no	—
323	C₄×C₅	C₂×C₂²⋊D₅	1	2	yes	complemented
324	C₄×C₅	C₂×C₅×D₄	1	2	yes	complemented
325	Dic₅	—	2	1	no	—
326	Dic₅	—	2	2	no	—
327	Dic₅	—	2	1	no	—
328	Dic₅	C₂×C₅×D₄	1	2	yes	complemented
329	C₂⁴	—	5	2	no	—
330	C₂⁴	C₂×C₅×D₅	1	2	yes	complemented
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	5	1	no	—
333	C₂×D₄	—	5	2	no	—
334	C₂×D₄	—	5	2	no	—
335	C₂×D₄	—	5	2	no	—
336	C₂×D₄	—	5	2	no	—
337	C₂×D₄	—	5	2	no	—
338	C₂×D₄	—	5	1	no	—
339	C₂×D₄	—	10	8	no	—
340	C₂×D₄	—	10	4	no	—
341	C₂×D₄	C₂×C₅×D₅	1	1	yes	characteristic
342	C₂×D₄	C₂×C₅×D₅	1	2	yes	complemented
343	C₂×D₄	C₂×C₅×D₅	1	1	yes	characteristic, complemented
344	C₂²×C₄	—	5	2	no	—
345	C₂²×C₄	—	5	1	no	—
346	C₂²×C₄	C₂×C₅×D₅	1	1	yes	characteristic, complemented
347	C₄⋊C₄	—	5	1	no	—
348	C₄⋊C₄	—	5	1	no	—
349	C₂²⋊C₄	—	5	1	no	—
350	C₂²⋊C₄	—	5	2	no	—
351	C₂²⋊C₄	—	5	2	no	—
352	C₂²⋊C₄	—	5	1	no	—
353	C₂²⋊C₄	—	5	2	no	—
354	C₄²	—	5	1	no	—
355	C₂×C₅	—	2	8	no	—
356	C₂×C₅	—	2	2	no	—
357	C₂×C₅	—	2	4	no	—
358	C₂×C₅	—	2	4	no	—
359	C₂×C₅	—	2	2	no	—
360	C₂×C₅	—	2	2	no	—
361	C₂×C₅	—	2	2	no	—
362	C₂×C₅	—	2	2	no	—
363	C₂×C₅	—	4	8	no	—
364	C₂×C₅	—	4	8	no	—
365	C₂×C₅	—	4	2	no	—
366	C₂×C₅	—	4	2	no	—
367	C₂×C₅	—	10	2	no	—
368	C₂×C₅	—	20	2	no	—
369	C₂×C₅	C₂×D₄×D₅	1	1	yes	characteristic
370	C₂×C₅	#4144	1	1	yes	characteristic
371	C₂×C₅	C₂²×C₂²⋊D₅	1	1	yes	characteristic
372	C₂×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
373	C₂×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
374	C₂×C₅	C₅×H(5,𝔽₂)	1	1	yes	characteristic
375	D₅	—	2	2	no	—
376	D₅	—	4	2	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	5	1	no	—
381	C₂³	—	5	2	no	—
382	C₂³	—	10	4	no	—
383	C₂³	—	10	4	no	—
384	C₂³	—	20	2	no	—
385	C₂³	C₂²×C₅×D₅	1	2	yes	—
386	C₂³	C₂²×C₅×D₅	1	1	yes	characteristic
387	C₂³	C₂²×C₅×D₅	1	2	yes	—
388	D₄	—	2	4	no	—
389	D₄	—	2	2	no	—
390	D₄	—	5	4	no	—
391	D₄	—	10	4	no	—
392	D₄	—	10	4	no	—
393	D₄	—	10	4	no	—
394	D₄	—	10	4	no	—
395	D₄	—	10	2	no	—
396	D₄	—	20	2	no	—
397	D₄	C₅×C₂²⋊D₅	1	4	yes	direct product factor
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	5	1	no	—
400	C₂×C₄	—	5	1	no	—
401	C₂×C₄	—	5	2	no	—
402	C₂×C₄	—	5	1	no	—
403	C₂×C₄	—	10	4	no	—
404	C₂×C₄	—	10	2	no	—
405	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
407	C₅	—	2	2	no	—
408	C₅	D₄×C₂²⋊D₅	1	1	yes	characteristic, direct product factor
409	C₅	C₅×D₄²	1	1	yes	characteristic, complemented
410	C₂²	—	2	2	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	4	8	no	—
418	C₂²	—	5	2	no	—
419	C₂²	—	10	1	no	—
420	C₂²	—	10	1	no	—
421	C₂²	—	10	2	no	—
422	C₂²	—	10	2	no	—
423	C₂²	—	10	2	no	—
424	C₂²	—	20	8	no	—
425	C₂²	C₅×D₄×D₅	1	2	yes	complemented
426	C₂²	C₂×C₅×C₂²⋊D₅	1	4	yes	complemented
427	C₂²	C₂³×C₅×D₅	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	5	2	no	—
430	C₄	—	10	2	no	—
431	C₄	—	10	1	no	—
432	C₄	—	10	1	no	—
433	C₄	C₂×C₅×C₂²⋊D₅	1	2	yes	complemented
434	C₂	—	2	2	no	—
435	C₂	—	2	4	no	—
436	C₂	—	4	2	no	—
437	C₂	—	10	2	no	—
438	C₂	—	20	2	no	—
439	C₂	C₂×C₅×D₄×D₅	1	1	yes	characteristic
440	C₂	C₅×#4144	1	1	yes	characteristic
441	C₂	C₂²×C₅×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁴×C₅
Frattini	C₂²	C₂³×C₅×D₅
Fitting	C₂²×C₅²×D₄	C₂
socle	C₂²×C₅²	C₂⁴
hypercenter	C₂²×C₅×D₄	D₅
hypocenter	C₅	C₅×D₄²
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅²×D₄	C₂	semidirect
2. C₂²×C₅×C₂²⋊D₅	C₂	semidirect
3. C₂×C₅×D₄×D₅	C₂	semidirect
4. C₅×#4099	C₂	semidirect
5. C₅×#4086	C₂	semidirect
6. C₅×#4085	C₂	semidirect
7. C₅×#4084	C₂	semidirect
8. C₅×#4083	C₂	semidirect
9. C₅×D₄×Dic₅	C₂	semidirect
10. C₅×#4076	C₂	semidirect
11. C₄×C₅×C₂²⋊D₅	C₂	semidirect
12. C₂⁴×C₅²	C₂²	semidirect
13. C₂³×C₅×D₅	C₂²	semidirect
16. C₂×C₅²×D₄	C₂²	semidirect
17. C₂×C₅²×D₄	C₂²	semidirect
18. C₂²×C₄×C₅²	C₂²	semidirect
21. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
22. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
23. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
24. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
25. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
26. C₂²×C₅×Dic₅	C₂²	semidirect
28. C₂×C₅×D₂₀	C₂²	semidirect
29. C₂×C₄×C₅×D₅	C₂²	semidirect
30. C₅×C₂²⋊Dic₅	C₂²	semidirect
31. C₅×C₂²⋊Dic₅	C₂²	semidirect
32. C₅×C₂²⋊Dic₅	C₂²	semidirect
33. C₅×#685	C₂²	semidirect
34. C₅×#685	C₂²	semidirect
35. C₅×C₄⋊Dic₅	C₂²	semidirect
36. C₅×#683	C₂²	semidirect
37. C₄×C₅×Dic₅	C₂²	semidirect
39. D₄×C₂²⋊D₅	C₅	direct (N × H)
53. C₅²×D₄	D₄	semidirect
62. C₅×C₂²⋊D₅	D₄	direct (N × H)
73. C₂²×C₅×D₄	D₅	semidirect
74. C₂²×C₅×D₄	C₂×C₅	semidirect
75. C₂²×C₂²⋊D₅	C₂×C₅	semidirect
76. C₂×D₄×D₅	C₂×C₅	semidirect
85. #4099	C₂×C₅	semidirect
86. #4086	C₂×C₅	semidirect
87. #4085	C₂×C₅	semidirect
88. #4084	C₂×C₅	semidirect
89. #4083	C₂×C₅	semidirect
90. D₄×Dic₅	C₂×C₅	semidirect
91. #4076	C₂×C₅	semidirect
92. C₄×C₂²⋊D₅	C₂×C₅	semidirect
101. C₂²×C₅²	C₂×D₄	semidirect
102. C₂²×C₅²	C₂×D₄	semidirect
110. C₂×C₅×D₅	C₂×D₄	semidirect
112. C₄×C₅²	C₂×D₄	semidirect
116. C₅×Dic₅	C₂×D₄	semidirect
119. C₂⁴×C₅	C₂×D₅	semidirect
120. C₂⁴×C₅	C₂²×C₅	semidirect
121. C₂³×D₅	C₂²×C₅	semidirect
138. C₂×C₅×D₄	C₂×D₅	semidirect
139. C₂×C₅×D₄	C₂×D₅	semidirect
141. C₂×C₅×D₄	C₂²×C₅	semidirect
142. C₂×C₅×D₄	C₂²×C₅	semidirect
146. C₂²×C₄×C₅	C₂×D₅	semidirect
147. C₂²×C₄×C₅	C₂²×C₅	semidirect
150. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
151. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
152. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
153. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
154. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
155. C₂²×Dic₅	C₂²×C₅	semidirect
157. C₂×D₂₀	C₂²×C₅	semidirect
158. C₂×C₄×D₅	C₂²×C₅	semidirect
167. C₂²⋊Dic₅	C₂²×C₅	semidirect
168. C₂²⋊Dic₅	C₂²×C₅	semidirect
169. C₂²⋊Dic₅	C₂²×C₅	semidirect
170. #685	C₂²×C₅	semidirect
171. #685	C₂²×C₅	semidirect
172. C₄⋊Dic₅	C₂²×C₅	semidirect
173. #683	C₂²×C₅	semidirect
174. C₄×Dic₅	C₂²×C₅	semidirect
226. C₅×D₄	C₂²⋊D₅	direct (N × H)
227. C₅×D₄	C₅×D₄	semidirect
248. C₂²⋊D₅	C₅×D₄	direct (N × H)
258. C₂²×D₄	C₅×D₅	semidirect
267. C₅²	D₄²	semidirect
302. C₂²×C₅	D₄×D₅	semidirect
303. C₂²×C₅	C₂×C₂²⋊D₅	semidirect
304. C₂²×C₅	C₂×C₅×D₄	semidirect
305. C₂²×C₅	C₂×C₅×D₄	semidirect
314. C₂×D₅	C₂×C₅×D₄	semidirect
323. C₄×C₅	C₂×C₂²⋊D₅	semidirect
324. C₄×C₅	C₂×C₅×D₄	semidirect
328. Dic₅	C₂×C₅×D₄	semidirect
330. C₂⁴	C₂×C₅×D₅	semidirect
342. C₂×D₄	C₂×C₅×D₅	semidirect
343. C₂×D₄	C₂×C₅×D₅	semidirect
346. C₂²×C₄	C₂×C₅×D₅	semidirect
397. D₄	C₅×C₂²⋊D₅	direct (N × H)
408. C₅	D₄×C₂²⋊D₅	direct (N × H)
409. C₅	C₅×D₄²	semidirect
425. C₂²	C₅×D₄×D₅	semidirect
426. C₂²	C₂×C₅×C₂²⋊D₅	semidirect
433. C₄	C₂×C₅×C₂²⋊D₅	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅²×D₄	2
C₂²×C₅×C₂²⋊D₅	2
C₂×C₅×D₄×D₅	2
C₅×#4099	2
C₅×#4086	2
C₅×#4085	2
C₅×#4084	2
C₅×#4083	2
C₅×D₄×Dic₅	2
C₅×#4076	2
C₄×C₅×C₂²⋊D₅	2
C₅×D₄²	5
D₄×C₂²⋊D₅	5

Subgroups — C5×D4×C22⋊D5 #13106957

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₄×C₂²⋊D₅ #13106957