Subgroups — C₂×C₅×D₃×C₂²⋊D₅ #72231130

Order 2400.

1212 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅²×D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₃×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#1220	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×D₃×C₂²⋊D₅	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#1203	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#1201	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×D₃×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₅×C₂²⋊D₅	—	3	1	no	maximal, Hall
10	C₂³×C₃×C₅²	C₂²	1	1	yes	characteristic, complemented
11	C₂²×C₅×D₁₅	C₂²	1	1	yes	characteristic, complemented
12	C₂²×C₅²×D₃	—	2	4	no	—
13	C₂²×C₅²×D₃	C₂²	1	1	yes	characteristic
14	C₂²×C₅²×D₃	C₂²	1	4	yes	complemented
15	C₂²×C₅²×D₃	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₅×D₅	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₅×D₃×D₅	—	2	4	no	—
18	C₂×C₅×D₃×D₅	C₂²	1	4	yes	complemented
19	C₅×#1220	C₂²	1	4	yes	complemented
20	C₂×C₅×Dic₁₅	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₅×C₂²⋊D₅	C₂²	1	4	yes	complemented
22	C₂×C₃×C₅×Dic₅	C₂²	1	1	yes	characteristic, complemented
23	C₅×#1203	C₂²	1	4	yes	complemented
24	C₅×#1201	C₂²	1	4	yes	complemented
25	C₅×D₃×Dic₅	C₂²	1	4	yes	complemented
26	C₂×C₅×D₃×D₄	—	5	1	no	maximal
27	C₂×D₃×C₂²⋊D₅	C₅	1	1	yes	maximal, characteristic, direct product factor
28	C₂⁴×C₅²	—	3	1	no	—
29	C₂³×C₅×D₅	—	3	1	no	—
30	C₂×C₅×C₂²⋊D₅	—	3	1	no	—
31	C₂×C₅×C₂²⋊D₅	—	3	1	no	—
32	C₂×C₅×C₂²⋊D₅	—	3	8	no	—
33	C₂×C₅×C₂²⋊D₅	—	3	1	no	—
34	C₂×C₅×C₂²⋊D₅	D₃	1	1	yes	characteristic, direct product factor
35	C₂²×C₅×Dic₅	—	3	1	no	—
36	C₂²×C₃×C₅²	—	2	2	no	—
37	C₂²×C₃×C₅²	C₂³	1	1	yes	characteristic
38	C₂²×C₃×C₅²	C₂³	1	2	yes	complemented
39	C₂×C₅×D₁₅	—	2	2	no	—
40	C₂×C₅×D₁₅	C₂³	1	2	yes	complemented
41	C₂×C₅²×D₃	—	2	2	no	—
42	C₂×C₅²×D₃	—	2	8	no	—
43	C₂×C₅²×D₃	D₄	1	4	yes	complemented
44	C₂×C₅²×D₃	C₂³	1	2	yes	—
45	C₂×C₅²×D₃	C₂³	1	2	yes	complemented
46	C₂×C₃×C₅×D₅	—	2	2	no	—
47	C₂×C₃×C₅×D₅	C₂³	1	2	yes	complemented
48	C₅×D₃×D₅	—	2	8	no	—
49	C₅×Dic₁₅	C₂³	1	2	yes	complemented
50	C₃×C₅×Dic₅	C₂³	1	2	yes	complemented
51	C₂³×C₅×D₃	—	2	2	no	—
52	C₂³×C₅×D₃	—	5	1	no	—
53	C₂³×C₅×D₃	D₅	1	1	yes	characteristic, complemented
54	C₂³×C₅×D₃	C₂×C₅	1	1	yes	characteristic, complemented
55	C₂²×D₃×D₅	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂×C₃×C₅×D₄	—	5	1	no	—
57	C₂×#1220	C₂×C₅	1	1	yes	characteristic, complemented
58	C₂×C₅×#67	—	5	1	no	—
59	C₂×C₅×#67	—	5	1	no	—
60	C₅×D₃×D₄	—	5	8	no	—
61	C₂×C₅×D₁₂	—	5	1	no	—
62	C₂×C₄×C₅×D₃	—	5	1	no	—
63	C₂×C₃×C₂²⋊D₅	C₂×C₅	1	1	yes	characteristic, complemented
64	D₃×C₂²⋊D₅	C₂×C₅	1	8	yes	direct product factor
65	C₂×#1203	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂×#1201	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂×D₃×Dic₅	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂³×C₅²	—	3	1	no	—
69	C₂³×C₅²	—	3	1	no	—
70	C₂³×C₅²	—	3	4	no	—
71	C₂³×C₅²	—	6	4	no	—
72	C₂³×C₅²	C₂×D₃	1	1	yes	characteristic, complemented
73	C₂²×C₅×D₅	—	3	1	no	—
74	C₂²×C₅×D₅	—	3	4	no	—
75	C₂²×C₅×D₅	—	6	4	no	—
76	C₂²×C₅×D₅	C₂×D₃	1	1	yes	characteristic, complemented
77	C₅×C₂²⋊D₅	—	3	4	no	—
78	C₅×C₂²⋊D₅	—	3	4	no	—
79	C₅×C₂²⋊D₅	—	3	4	no	—
80	C₅×C₂²⋊D₅	C₂×D₃	1	4	yes	direct product factor
81	C₂×C₅×Dic₅	—	3	1	no	—
82	C₂×C₅×Dic₅	—	3	4	no	—
83	C₂×C₅×Dic₅	C₂×D₃	1	1	yes	characteristic, complemented
84	C₂²×C₅×D₄	—	15	1	no	—
85	C₂²×C₂²⋊D₅	—	3	1	no	—
86	C₂×C₃×C₅²	—	2	2	no	—
87	C₂×C₃×C₅²	C₂×D₄	1	2	yes	complemented
88	C₂×C₃×C₅²	C₂⁴	1	1	yes	characteristic
89	C₅×D₁₅	—	2	2	no	—
90	C₅²×D₃	—	2	2	no	—
91	C₅²×D₃	C₂×D₄	1	4	yes	complemented
92	C₃×C₅×D₅	—	2	2	no	—
93	C₂³×C₃×C₅	—	2	2	no	—
94	C₂³×C₃×C₅	—	5	1	no	—
95	C₂³×C₃×C₅	C₂×D₅	1	1	yes	characteristic, complemented
96	C₂³×C₃×C₅	C₂²×C₅	1	1	yes	characteristic, complemented
97	C₂²×D₁₅	C₂²×C₅	1	1	yes	characteristic, complemented
98	C₂²×C₅×D₃	—	2	8	no	—
99	C₂²×C₅×D₃	—	2	8	no	—
100	C₂²×C₅×D₃	—	2	2	no	—
101	C₂²×C₅×D₃	—	2	4	no	—
102	C₂²×C₅×D₃	—	2	4	no	—
103	C₂²×C₅×D₃	—	2	8	no	—
104	C₂²×C₅×D₃	—	2	2	no	—
105	C₂²×C₅×D₃	—	5	1	no	—
106	C₂²×C₅×D₃	—	5	4	no	—
107	C₂²×C₅×D₃	—	10	4	no	—
108	C₂²×C₅×D₃	C₂×D₅	1	1	yes	characteristic
109	C₂²×C₅×D₃	C₂×D₅	1	4	yes	complemented
110	C₂²×C₅×D₃	C₂×D₅	1	1	yes	characteristic, complemented
111	C₂²×C₅×D₃	C₂²×C₅	1	1	yes	characteristic
112	C₂²×C₅×D₃	C₂²×C₅	1	4	yes	complemented
113	C₂²×C₅×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
114	C₂²×C₃×D₅	C₂²×C₅	1	1	yes	characteristic, complemented
115	C₂×D₃×D₅	—	2	4	no	—
116	C₂×D₃×D₅	C₂²×C₅	1	4	yes	complemented
117	C₃×C₅×D₄	—	5	4	no	—
118	C₂×C₃×C₄×C₅	—	5	1	no	—
119	#1220	C₂²×C₅	1	4	yes	complemented
120	C₂×Dic₁₅	C₂²×C₅	1	1	yes	characteristic, complemented
121	C₅×#67	—	5	4	no	—
122	C₅×#67	—	5	4	no	—
123	C₂×C₅×Dic₃	—	5	1	no	—
124	C₅×D₁₂	—	5	4	no	—
125	C₄×C₅×D₃	—	5	4	no	—
126	C₃×C₂²⋊D₅	C₂²×C₅	1	4	yes	complemented
127	C₂×C₃×Dic₅	C₂²×C₅	1	1	yes	characteristic, complemented
128	#1203	C₂²×C₅	1	4	yes	complemented
129	#1201	C₂²×C₅	1	4	yes	complemented
130	D₃×Dic₅	C₂²×C₅	1	4	yes	complemented
131	C₂²×C₅²	—	2	2	no	—
132	C₂²×C₅²	—	3	4	no	—
133	C₂²×C₅²	—	3	2	no	—
134	C₂²×C₅²	—	3	2	no	—
135	C₂²×C₅²	—	6	8	no	—
136	C₂²×C₅²	—	6	2	no	—
137	C₂²×C₅²	C₂²×D₃	1	1	yes	characteristic
138	C₂²×C₅²	C₂²×D₃	1	2	yes	complemented
139	C₂×C₅×D₅	—	2	2	no	—
140	C₂×C₅×D₅	—	3	2	no	—
141	C₂×C₅×D₅	—	6	8	no	—
142	C₂×C₅×D₅	—	6	2	no	—
143	C₂×C₅×D₅	C₂²×D₃	1	2	yes	complemented
144	C₅×Dic₅	—	3	2	no	—
145	C₅×Dic₅	C₂²×D₃	1	2	yes	complemented
146	C₂×D₃×D₄	—	5	1	no	Hall
147	C₂⁴×C₅	—	3	1	no	—
148	C₂⁴×C₅	—	3	1	no	—
149	C₂⁴×C₅	—	6	2	no	—
150	C₂⁴×C₅	—	15	1	no	—
151	C₂³×D₅	—	3	1	no	—
152	C₂×C₅×D₄	—	5	1	no	—
153	C₂×C₅×D₄	—	15	1	no	—
154	C₂×C₅×D₄	—	15	8	no	—
155	C₂×C₅×D₄	—	15	1	no	—
156	C₂×C₅×D₄	—	15	1	no	—
157	C₂²×C₄×C₅	—	15	1	no	—
158	C₂×C₂²⋊D₅	—	3	1	no	—
159	C₂×C₂²⋊D₅	—	3	1	no	—
160	C₂×C₂²⋊D₅	—	3	8	no	—
161	C₂×C₂²⋊D₅	—	3	1	no	—
162	C₂×C₂²⋊D₅	C₅×D₃	1	1	yes	characteristic, direct product factor
163	C₂²×Dic₅	—	3	1	no	—
164	C₃×C₅²	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
165	C₂²×C₃×C₅	—	2	4	no	—
166	C₂²×C₃×C₅	—	2	4	no	—
167	C₂²×C₃×C₅	—	2	2	no	—
168	C₂²×C₃×C₅	—	2	2	no	—
169	C₂²×C₃×C₅	—	2	2	no	—
170	C₂²×C₃×C₅	—	2	4	no	—
171	C₂²×C₃×C₅	—	5	2	no	—
172	C₂²×C₃×C₅	—	10	2	no	—
173	C₂²×C₃×C₅	C₂²×D₅	1	1	yes	characteristic
174	C₂²×C₃×C₅	C₂²×D₅	1	2	yes	complemented
175	C₂²×C₃×C₅	C₂³×C₅	1	1	yes	characteristic
176	C₂²×C₃×C₅	C₂³×C₅	1	2	yes	complemented
177	C₂×D₁₅	—	2	2	no	—
178	C₂×D₁₅	C₂³×C₅	1	2	yes	complemented
179	C₂×C₅×D₃	—	2	4	no	—
180	C₂×C₅×D₃	—	2	16	no	—
181	C₂×C₅×D₃	—	2	4	no	—
182	C₂×C₅×D₃	—	2	16	no	—
183	C₂×C₅×D₃	—	2	2	no	—
184	C₂×C₅×D₃	—	2	2	no	—
185	C₂×C₅×D₃	—	2	8	no	—
186	C₂×C₅×D₃	—	2	8	no	—
187	C₂×C₅×D₃	—	2	8	no	—
188	C₂×C₅×D₃	—	2	4	no	—
189	C₂×C₅×D₃	—	2	4	no	—
190	C₂×C₅×D₃	—	5	2	no	—
191	C₂×C₅×D₃	—	10	2	no	—
192	C₂×C₅×D₃	—	10	8	no	—
193	C₂×C₅×D₃	C₂²⋊D₅	1	4	yes	direct product factor
194	C₂×C₅×D₃	C₅×D₄	1	4	yes	complemented
195	C₂×C₅×D₃	C₂²×D₅	1	2	yes	—
196	C₂×C₅×D₃	C₂²×D₅	1	2	yes	complemented
197	C₂×C₅×D₃	C₂³×C₅	1	2	yes	—
198	C₂×C₅×D₃	C₂³×C₅	1	2	yes	complemented
199	C₂×C₃×D₅	—	2	2	no	—
200	C₂×C₃×D₅	C₂³×C₅	1	2	yes	complemented
201	D₃×D₅	—	2	8	no	—
202	C₃×C₄×C₅	—	5	2	no	—
203	Dic₁₅	C₂³×C₅	1	2	yes	complemented
204	C₃×Dic₅	C₂³×C₅	1	2	yes	complemented
205	C₅×Dic₃	—	5	2	no	—
206	C₂×C₅²	—	2	2	no	—
207	C₂×C₅²	—	3	4	no	—
208	C₂×C₅²	—	6	2	no	—
209	C₂×C₅²	D₃×D₄	1	2	yes	complemented
210	C₂×C₅²	C₂³×D₃	1	1	yes	characteristic
211	C₅×D₅	—	2	2	no	—
212	C₅×D₅	—	6	2	no	—
213	C₂³×D₃	—	5	1	no	—
214	C₂³×D₃	C₅×D₅	1	1	yes	characteristic, complemented
215	C₂×C₃×D₄	—	5	1	no	—
216	C₂×#67	—	5	1	no	—
217	C₂×#67	—	5	1	no	—
218	D₃×D₄	—	5	8	no	—
219	C₂×D₁₂	—	5	1	no	—
220	C₂×C₄×D₃	—	5	1	no	—
221	C₂³×C₅	—	2	2	no	—
222	C₂³×C₅	—	3	1	no	—
223	C₂³×C₅	—	3	1	no	—
224	C₂³×C₅	—	3	1	no	—
225	C₂³×C₅	—	3	4	no	—
226	C₂³×C₅	—	3	1	no	—
227	C₂³×C₅	—	3	4	no	—
228	C₂³×C₅	—	5	1	no	—
229	C₂³×C₅	—	6	2	no	—
230	C₂³×C₅	—	6	8	no	—
231	C₂³×C₅	—	6	2	no	—
232	C₂³×C₅	—	6	4	no	—
233	C₂³×C₅	—	6	4	no	—
234	C₂³×C₅	—	6	8	no	—
235	C₂³×C₅	—	6	8	no	—
236	C₂³×C₅	—	15	4	no	—
237	C₂³×C₅	—	15	1	no	—
238	C₂³×C₅	—	30	4	no	—
239	C₂³×C₅	D₃×D₅	1	1	yes	characteristic, complemented
240	C₂³×C₅	C₂×C₅×D₃	1	1	yes	characteristic, complemented
241	C₂²×D₅	—	3	1	no	—
242	C₂²×D₅	—	3	4	no	—
243	C₂²×D₅	—	6	4	no	—
244	C₂²×D₅	C₂×C₅×D₃	1	1	yes	characteristic, complemented
245	C₅×D₄	—	5	4	no	—
246	C₅×D₄	—	15	4	no	—
247	C₅×D₄	—	15	4	no	—
248	C₅×D₄	—	15	4	no	—
249	C₂×C₄×C₅	—	5	1	no	—
250	C₂×C₄×C₅	—	15	4	no	—
251	C₂×C₄×C₅	—	15	1	no	—
252	C₂²⋊D₅	—	3	4	no	—
253	C₂²⋊D₅	—	3	4	no	—
254	C₂²⋊D₅	—	3	4	no	—
255	C₂²⋊D₅	C₂×C₅×D₃	1	4	yes	direct product factor
256	C₂×Dic₅	—	3	1	no	—
257	C₂×Dic₅	—	3	4	no	—
258	C₂×Dic₅	C₂×C₅×D₃	1	1	yes	characteristic, complemented
259	C₂²×D₄	—	15	1	no	Sylow
260	C₂×C₃×C₅	—	2	4	no	—
261	C₂×C₃×C₅	—	2	4	no	—
262	C₂×C₃×C₅	—	2	2	no	—
263	C₂×C₃×C₅	—	2	2	no	—
264	C₂×C₃×C₅	—	2	4	no	—
265	C₂×C₃×C₅	—	2	2	no	—
266	C₂×C₃×C₅	—	10	2	no	—
267	C₂×C₃×C₅	C₂×C₂²⋊D₅	1	2	yes	complemented
268	C₂×C₃×C₅	C₂×C₅×D₄	1	2	yes	complemented
269	C₂×C₃×C₅	C₂³×D₅	1	1	yes	characteristic
270	C₂×C₃×C₅	C₂⁴×C₅	1	1	yes	characteristic
271	D₁₅	—	2	2	no	—
272	C₃×D₅	—	2	2	no	—
273	C₅×D₃	—	2	4	no	—
274	C₅×D₃	—	2	4	no	—
275	C₅×D₃	—	2	2	no	—
276	C₅×D₃	—	2	2	no	—
277	C₅×D₃	—	2	8	no	—
278	C₅×D₃	—	10	2	no	—
279	C₅×D₃	C₂×C₂²⋊D₅	1	4	yes	direct product factor
280	C₅×D₃	C₂×C₅×D₄	1	4	yes	complemented
281	C₅²	C₂×D₃×D₄	1	1	yes	characteristic, complemented, Sylow
282	C₂³×C₃	—	5	1	no	—
283	C₂³×C₃	C₂×C₅×D₅	1	1	yes	characteristic, complemented
284	C₂²×D₃	—	2	4	no	—
285	C₂²×D₃	—	5	1	no	—
286	C₂²×D₃	—	5	4	no	—
287	C₂²×D₃	—	10	4	no	—
288	C₂²×D₃	C₂×C₅×D₅	1	1	yes	characteristic
289	C₂²×D₃	C₂×C₅×D₅	1	4	yes	complemented
290	C₂²×D₃	C₂×C₅×D₅	1	1	yes	characteristic, complemented
291	C₃×D₄	—	5	4	no	—
292	C₂×C₃×C₄	—	5	1	no	—
293	#67	—	5	4	no	—
294	#67	—	5	4	no	—
295	C₂×Dic₃	—	5	1	no	—
296	D₁₂	—	5	4	no	—
297	C₄×D₃	—	5	4	no	—
298	C₂²×C₅	—	2	4	no	—
299	C₂²×C₅	—	2	4	no	—
300	C₂²×C₅	—	2	2	no	—
301	C₂²×C₅	—	2	2	no	—
302	C₂²×C₅	—	2	2	no	—
303	C₂²×C₅	—	2	4	no	—
304	C₂²×C₅	—	3	4	no	—
305	C₂²×C₅	—	3	4	no	—
306	C₂²×C₅	—	3	2	no	—
307	C₂²×C₅	—	3	2	no	—
308	C₂²×C₅	—	3	2	no	—
309	C₂²×C₅	—	3	2	no	—
310	C₂²×C₅	—	5	2	no	—
311	C₂²×C₅	—	6	4	no	—
312	C₂²×C₅	—	6	4	no	—
313	C₂²×C₅	—	6	8	no	—
314	C₂²×C₅	—	6	8	no	—
315	C₂²×C₅	—	6	8	no	—
316	C₂²×C₅	—	6	16	no	—
317	C₂²×C₅	—	6	4	no	—
318	C₂²×C₅	—	6	16	no	—
319	C₂²×C₅	—	6	4	no	—
320	C₂²×C₅	—	6	2	no	—
321	C₂²×C₅	—	6	2	no	—
322	C₂²×C₅	—	10	2	no	—
323	C₂²×C₅	—	15	2	no	—
324	C₂²×C₅	—	30	8	no	—
325	C₂²×C₅	—	30	2	no	—
326	C₂²×C₅	C₂×D₃×D₅	1	1	yes	characteristic
327	C₂²×C₅	C₂×D₃×D₅	1	2	yes	complemented
328	C₂²×C₅	C₂²×C₅×D₃	1	1	yes	characteristic
329	C₂²×C₅	C₂²×C₅×D₃	1	2	yes	complemented
330	C₂×D₅	—	2	2	no	—
331	C₂×D₅	—	3	2	no	—
332	C₂×D₅	—	6	8	no	—
333	C₂×D₅	—	6	2	no	—
334	C₂×D₅	C₂²×C₅×D₃	1	2	yes	complemented
335	C₄×C₅	—	5	2	no	—
336	C₄×C₅	—	15	2	no	—
337	Dic₅	—	3	2	no	—
338	Dic₅	C₂²×C₅×D₃	1	2	yes	complemented
339	C₂⁴	—	3	1	no	—
340	C₂⁴	—	15	1	no	—
341	C₂×D₄	—	5	1	no	—
342	C₂×D₄	—	15	1	no	—
343	C₂×D₄	—	15	8	no	—
344	C₂×D₄	—	15	1	no	—
345	C₂×D₄	—	15	1	no	—
346	C₂²×C₄	—	15	1	no	—
347	C₃×C₅	—	2	2	no	—
348	C₃×C₅	C₂²×C₂²⋊D₅	1	1	yes	characteristic, complemented
349	C₃×C₅	C₂²×C₅×D₄	1	1	yes	characteristic, complemented
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	—	5	2	no	—
352	C₂²×C₃	—	10	2	no	—
353	C₂²×C₃	C₂²×C₅×D₅	1	1	yes	characteristic
354	C₂²×C₃	C₂²×C₅×D₅	1	2	yes	complemented
355	C₂×D₃	—	2	2	no	—
356	C₂×D₃	—	2	8	no	—
357	C₂×D₃	—	5	2	no	—
358	C₂×D₃	—	10	2	no	—
359	C₂×D₃	—	10	8	no	—
360	C₂×D₃	C₅×C₂²⋊D₅	1	4	yes	direct product factor
361	C₂×D₃	C₂²×C₅×D₅	1	2	yes	—
362	C₂×D₃	C₂²×C₅×D₅	1	2	yes	complemented
363	C₃×C₄	—	5	2	no	—
364	Dic₃	—	5	2	no	—
365	C₂×C₅	—	2	4	no	—
366	C₂×C₅	—	2	4	no	—
367	C₂×C₅	—	2	2	no	—
368	C₂×C₅	—	2	2	no	—
369	C₂×C₅	—	2	2	no	—
370	C₂×C₅	—	2	4	no	—
371	C₂×C₅	—	3	4	no	—
372	C₂×C₅	—	3	4	no	—
373	C₂×C₅	—	6	8	no	—
374	C₂×C₅	—	6	4	no	—
375	C₂×C₅	—	6	4	no	—
376	C₂×C₅	—	6	2	no	—
377	C₂×C₅	—	6	2	no	—
378	C₂×C₅	—	10	2	no	—
379	C₂×C₅	—	30	2	no	—
380	C₂×C₅	D₃×C₂²⋊D₅	1	2	yes	direct product factor
381	C₂×C₅	C₅×D₃×D₄	1	2	yes	complemented
382	C₂×C₅	C₂²×D₃×D₅	1	1	yes	characteristic
383	C₂×C₅	C₂³×C₅×D₃	1	1	yes	characteristic
384	D₅	—	2	2	no	—
385	D₅	—	6	2	no	—
386	C₂³	—	3	1	no	—
387	C₂³	—	3	1	no	—
388	C₂³	—	3	4	no	—
389	C₂³	—	5	1	no	—
390	C₂³	—	6	4	no	—
391	C₂³	—	15	4	no	—
392	C₂³	—	15	1	no	—
393	C₂³	—	30	4	no	—
394	C₂³	C₅×D₃×D₅	1	1	yes	characteristic, complemented
395	D₄	—	5	4	no	—
396	D₄	—	15	4	no	—
397	D₄	—	15	4	no	—
398	D₄	—	15	4	no	—
399	C₂×C₄	—	5	1	no	—
400	C₂×C₄	—	15	4	no	—
401	C₂×C₄	—	15	1	no	—
402	C₂×C₃	—	2	2	no	—
403	C₂×C₃	—	10	2	no	—
404	C₂×C₃	C₂×C₅×C₂²⋊D₅	1	2	yes	complemented
405	C₂×C₃	C₂³×C₅×D₅	1	1	yes	characteristic
406	D₃	—	2	2	no	—
407	D₃	—	10	2	no	—
408	D₃	C₂×C₅×C₂²⋊D₅	1	4	yes	direct product factor
409	C₅	—	2	2	no	—
410	C₅	C₂×D₃×C₂²⋊D₅	1	1	yes	characteristic, direct product factor
411	C₅	C₂×C₅×D₃×D₄	1	1	yes	characteristic, complemented
412	C₂²	—	2	2	no	—
413	C₂²	—	3	2	no	—
414	C₂²	—	3	4	no	—
415	C₂²	—	3	2	no	—
416	C₂²	—	5	2	no	—
417	C₂²	—	6	8	no	—
418	C₂²	—	6	2	no	—
419	C₂²	—	10	2	no	—
420	C₂²	—	15	2	no	—
421	C₂²	—	30	8	no	—
422	C₂²	—	30	2	no	—
423	C₂²	C₂×C₅×D₃×D₅	1	1	yes	characteristic
424	C₂²	C₂×C₅×D₃×D₅	1	2	yes	complemented
425	C₄	—	5	2	no	—
426	C₄	—	15	2	no	—
427	C₃	C₂²×C₅×C₂²⋊D₅	1	1	yes	characteristic, complemented, Sylow
428	C₂	—	2	2	no	—
429	C₂	—	3	4	no	—
430	C₂	—	6	2	no	—
431	C₂	—	10	2	no	—
432	C₂	—	30	2	no	—
433	C₂	C₅×D₃×C₂²⋊D₅	1	2	yes	direct product factor
434	C₂	C₂²×C₅×D₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₅
commutator, cosocle	C₂×C₃×C₅	C₂⁴×C₅
Frattini	C₂	C₂²×C₅×D₃×D₅
Fitting	C₂³×C₃×C₅²	C₂²
socle	C₂²×C₃×C₅²	C₂³
hypercenter	C₂³×C₅	D₃×D₅
hypocenter	C₃×C₅	C₂²×C₅×D₄
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₅

Complements

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

N	H ≅ G/N	type
1. C₂³×C₅²×D₃	C₂	semidirect
2. C₂²×C₅×D₃×D₅	C₂	semidirect
3. C₂×C₅×#1220	C₂	semidirect
4. C₂×C₃×C₅×C₂²⋊D₅	C₂	semidirect
5. C₅×D₃×C₂²⋊D₅	C₂	direct (N × H)
6. C₂×C₅×#1203	C₂	semidirect
7. C₂×C₅×#1201	C₂	semidirect
8. C₂×C₅×D₃×Dic₅	C₂	semidirect
10. C₂³×C₃×C₅²	C₂²	semidirect
11. C₂²×C₅×D₁₅	C₂²	semidirect
14. C₂²×C₅²×D₃	C₂²	semidirect
15. C₂²×C₅²×D₃	C₂²	semidirect
16. C₂²×C₃×C₅×D₅	C₂²	semidirect
18. C₂×C₅×D₃×D₅	C₂²	semidirect
19. C₅×#1220	C₂²	semidirect
20. C₂×C₅×Dic₁₅	C₂²	semidirect
21. C₃×C₅×C₂²⋊D₅	C₂²	semidirect
22. C₂×C₃×C₅×Dic₅	C₂²	semidirect
23. C₅×#1203	C₂²	semidirect
24. C₅×#1201	C₂²	semidirect
25. C₅×D₃×Dic₅	C₂²	semidirect
27. C₂×D₃×C₂²⋊D₅	C₅	direct (N × H)
34. C₂×C₅×C₂²⋊D₅	D₃	direct (N × H)
38. C₂²×C₃×C₅²	C₂³	semidirect
40. C₂×C₅×D₁₅	C₂³	semidirect
43. C₂×C₅²×D₃	D₄	semidirect
45. C₂×C₅²×D₃	C₂³	semidirect
47. C₂×C₃×C₅×D₅	C₂³	semidirect
49. C₅×Dic₁₅	C₂³	semidirect
50. C₃×C₅×Dic₅	C₂³	semidirect
53. C₂³×C₅×D₃	D₅	semidirect
54. C₂³×C₅×D₃	C₂×C₅	semidirect
55. C₂²×D₃×D₅	C₂×C₅	semidirect
57. C₂×#1220	C₂×C₅	semidirect
63. C₂×C₃×C₂²⋊D₅	C₂×C₅	semidirect
64. D₃×C₂²⋊D₅	C₂×C₅	direct (N × H)
65. C₂×#1203	C₂×C₅	semidirect
66. C₂×#1201	C₂×C₅	semidirect
67. C₂×D₃×Dic₅	C₂×C₅	semidirect
72. C₂³×C₅²	C₂×D₃	semidirect
76. C₂²×C₅×D₅	C₂×D₃	semidirect
80. C₅×C₂²⋊D₅	C₂×D₃	direct (N × H)
83. C₂×C₅×Dic₅	C₂×D₃	semidirect
87. C₂×C₃×C₅²	C₂×D₄	semidirect
91. C₅²×D₃	C₂×D₄	semidirect
95. C₂³×C₃×C₅	C₂×D₅	semidirect
96. C₂³×C₃×C₅	C₂²×C₅	semidirect
97. C₂²×D₁₅	C₂²×C₅	semidirect
109. C₂²×C₅×D₃	C₂×D₅	semidirect
110. C₂²×C₅×D₃	C₂×D₅	semidirect
112. C₂²×C₅×D₃	C₂²×C₅	semidirect
113. C₂²×C₅×D₃	C₂²×C₅	semidirect
114. C₂²×C₃×D₅	C₂²×C₅	semidirect
116. C₂×D₃×D₅	C₂²×C₅	semidirect
119. #1220	C₂²×C₅	semidirect
120. C₂×Dic₁₅	C₂²×C₅	semidirect
126. C₃×C₂²⋊D₅	C₂²×C₅	semidirect
127. C₂×C₃×Dic₅	C₂²×C₅	semidirect
128. #1203	C₂²×C₅	semidirect
129. #1201	C₂²×C₅	semidirect
130. D₃×Dic₅	C₂²×C₅	semidirect
138. C₂²×C₅²	C₂²×D₃	semidirect
143. C₂×C₅×D₅	C₂²×D₃	semidirect
145. C₅×Dic₅	C₂²×D₃	semidirect
162. C₂×C₂²⋊D₅	C₅×D₃	direct (N × H)
164. C₃×C₅²	C₂²×D₄	semidirect
174. C₂²×C₃×C₅	C₂²×D₅	semidirect
176. C₂²×C₃×C₅	C₂³×C₅	semidirect
178. C₂×D₁₅	C₂³×C₅	semidirect
193. C₂×C₅×D₃	C₂²⋊D₅	direct (N × H)
194. C₂×C₅×D₃	C₅×D₄	semidirect
196. C₂×C₅×D₃	C₂²×D₅	semidirect
198. C₂×C₅×D₃	C₂³×C₅	semidirect
200. C₂×C₃×D₅	C₂³×C₅	semidirect
203. Dic₁₅	C₂³×C₅	semidirect
204. C₃×Dic₅	C₂³×C₅	semidirect
209. C₂×C₅²	D₃×D₄	semidirect
214. C₂³×D₃	C₅×D₅	semidirect
239. C₂³×C₅	D₃×D₅	semidirect
240. C₂³×C₅	C₂×C₅×D₃	semidirect
244. C₂²×D₅	C₂×C₅×D₃	semidirect
255. C₂²⋊D₅	C₂×C₅×D₃	direct (N × H)
258. C₂×Dic₅	C₂×C₅×D₃	semidirect
267. C₂×C₃×C₅	C₂×C₂²⋊D₅	semidirect
268. C₂×C₃×C₅	C₂×C₅×D₄	semidirect
279. C₅×D₃	C₂×C₂²⋊D₅	direct (N × H)
280. C₅×D₃	C₂×C₅×D₄	semidirect
281. C₅²	C₂×D₃×D₄	semidirect
283. C₂³×C₃	C₂×C₅×D₅	semidirect
289. C₂²×D₃	C₂×C₅×D₅	semidirect
290. C₂²×D₃	C₂×C₅×D₅	semidirect
327. C₂²×C₅	C₂×D₃×D₅	semidirect
329. C₂²×C₅	C₂²×C₅×D₃	semidirect
334. C₂×D₅	C₂²×C₅×D₃	semidirect
338. Dic₅	C₂²×C₅×D₃	semidirect
348. C₃×C₅	C₂²×C₂²⋊D₅	semidirect
349. C₃×C₅	C₂²×C₅×D₄	semidirect
354. C₂²×C₃	C₂²×C₅×D₅	semidirect
360. C₂×D₃	C₅×C₂²⋊D₅	direct (N × H)
362. C₂×D₃	C₂²×C₅×D₅	semidirect
380. C₂×C₅	D₃×C₂²⋊D₅	direct (N × H)
381. C₂×C₅	C₅×D₃×D₄	semidirect
394. C₂³	C₅×D₃×D₅	semidirect
404. C₂×C₃	C₂×C₅×C₂²⋊D₅	semidirect
408. D₃	C₂×C₅×C₂²⋊D₅	direct (N × H)
410. C₅	C₂×D₃×C₂²⋊D₅	direct (N × H)
411. C₅	C₂×C₅×D₃×D₄	semidirect
424. C₂²	C₂×C₅×D₃×D₅	semidirect
427. C₃	C₂²×C₅×C₂²⋊D₅	semidirect
433. C₂	C₅×D₃×C₂²⋊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
C₂³×C₅²×D₃	2
C₂²×C₅×D₃×D₅	2
C₂×C₅×#1220	2
C₂×C₃×C₅×C₂²⋊D₅	2
C₅×D₃×C₂²⋊D₅	2
C₂×C₅×#1203	2
C₂×C₅×#1201	2
C₂×C₅×D₃×Dic₅	2
C₂²×C₅×C₂²⋊D₅	3
C₂×C₅×D₃×D₄	5
C₂×D₃×C₂²⋊D₅	5

Subgroups — C2×C5×D3×C22⋊D5 #72231130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₃×C₂²⋊D₅ #72231130