Subgroups — C₅×#71678 #14300733

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#832	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#830	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4529	C₂	1	2	yes	maximal, complemented
6	C₅×#1875	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₅×D₄	—	2	1	no	—
8	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₃×C₅×#121	—	2	2	no	—
11	C₃×C₅×#121	C₄	1	4	yes	complemented
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
14	C₂×C₅×#217	—	2	1	no	—
15	C₅×#926	—	2	4	no	—
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
17	C₂×C₄×C₅×Dic₃	—	2	1	no	—
18	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
19	C₅×#832	—	2	4	no	—
20	C₅×#830	—	2	2	no	—
21	#71678	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×#121	D₃	1	1	yes	characteristic
23	C₂×C₅×#117	—	3	1	no	—
24	C₂×C₅×#102	—	3	2	no	—
25	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
26	C₅×#340	—	3	2	no	—
27	C₂⁴×C₃×C₅	—	2	1	no	—
28	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
29	C₂×C₃×C₅×D₄	—	2	4	no	—
30	C₂×C₃×C₅×D₄	—	2	2	no	—
31	C₂×C₃×C₅×D₄	—	2	1	no	—
32	C₂×C₃×C₅×D₄	—	2	2	no	—
33	C₂×C₃×C₅×D₄	—	4	4	no	—
34	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
35	C₂²×C₃×C₄×C₅	—	2	2	no	—
36	C₂²×C₃×C₄×C₅	—	2	2	no	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₅×Dic₃	—	2	2	no	—
43	C₃×C₅×C₄⋊C₄	—	2	1	no	—
44	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
45	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
46	C₅×#217	—	2	4	no	—
47	C₅×C₄⋊Dic₃	—	2	2	no	—
48	C₅×C₄⋊Dic₃	D₄	1	4	yes	complemented
49	C₄×C₅×Dic₃	—	2	4	no	—
50	C₂×C₅×C₃⋊C₈	—	2	2	no	—
51	C₂×C₅×C₃⋊C₈	—	2	2	no	—
52	C₂×C₅×C₃⋊C₈	—	2	2	no	—
53	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic
54	C₂×#926	C₂×C₅	1	1	yes	characteristic, complemented
55	C₂×#832	C₂×C₅	1	2	yes	complemented
56	C₂×#830	C₂×C₅	1	1	yes	characteristic, complemented
57	#4529	C₂×C₅	1	2	yes	complemented
58	C₂²×C₅×D₄	—	2	1	no	—
59	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
60	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
61	C₂²×C₅×C₈	—	3	2	no	—
62	C₅×#121	—	2	2	no	—
63	C₅×#121	Dic₃	1	4	yes	complemented
64	C₅×#117	—	6	4	no	—
65	C₂×C₅×C₄⋊C₄	—	3	2	no	—
66	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
67	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
69	C₂×C₄²×C₅	—	6	1	no	—
70	C₅×#102	—	6	4	no	—
71	C₅×C₂²⋊C₈	—	6	2	no	—
72	#1875	—	3	1	no	Sylow
73	C₂³×C₃×C₅	—	2	1	no	—
74	C₂³×C₃×C₅	—	2	1	no	—
75	C₂³×C₃×C₅	—	2	2	no	—
76	C₂³×C₃×C₅	—	2	2	no	—
77	C₂³×C₃×C₅	—	2	2	no	—
78	C₂³×C₃×C₅	—	4	1	no	—
79	C₂³×C₃×C₅	—	4	1	no	—
80	C₂³×C₃×C₅	—	4	2	no	—
81	C₂³×C₃×C₅	—	4	2	no	—
82	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
83	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
84	C₃×C₅×D₄	—	2	4	no	—
85	C₃×C₅×D₄	—	4	8	no	—
86	C₃×C₅×D₄	—	4	2	no	—
87	C₂×C₃×C₄×C₅	—	2	1	no	—
88	C₂×C₃×C₄×C₅	—	2	1	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	4	2	no	—
93	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	#41	1	2	yes	—
98	C₂×C₅×Dic₃	—	2	4	no	—
99	C₂×C₅×Dic₃	—	4	2	no	—
100	C₂×C₅×Dic₃	—	4	2	no	—
101	C₅×C₃⋊C₈	—	4	2	no	—
102	C₂²×C₃×D₄	—	2	1	no	—
103	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
104	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
105	C₃×#121	—	2	2	no	—
106	C₃×#121	C₄×C₅	1	4	yes	complemented
107	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
108	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
109	C₂×#217	—	2	1	no	—
110	#926	—	2	4	no	—
111	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
112	C₂×C₄×Dic₃	—	2	1	no	—
113	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
114	#832	—	2	4	no	—
115	#830	—	2	2	no	—
116	C₂⁴×C₅	—	2	1	no	—
117	C₂⁴×C₅	#67	1	1	yes	characteristic
118	C₂×C₅×D₄	—	2	4	no	—
119	C₂×C₅×D₄	—	2	2	no	—
120	C₂×C₅×D₄	—	2	2	no	—
121	C₂×C₅×D₄	—	2	1	no	—
122	C₂×C₅×D₄	—	4	4	no	—
123	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	6	2	no	—
128	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
129	C₂²×C₄×C₅	#67	1	1	yes	characteristic
130	C₂²×C₄×C₅	#67	1	2	yes	—
131	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
132	C₂×C₅×C₈	—	6	2	no	—
133	C₂×C₅×C₈	—	6	2	no	—
134	C₂×C₅×C₈	—	6	2	no	—
135	C₅×C₄⋊C₄	—	2	1	no	—
136	C₅×C₄⋊C₄	—	3	4	no	—
137	C₅×C₄⋊C₄	—	6	2	no	—
138	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
139	C₅×C₂²⋊C₄	—	2	4	no	—
140	C₅×C₂²⋊C₄	—	6	4	no	—
141	C₄²×C₅	—	6	4	no	—
142	C₂×#121	C₅×D₃	1	1	yes	characteristic
143	C₂×#117	—	3	1	no	—
144	C₂×#102	—	3	2	no	—
145	C₂×C₂²⋊C₈	—	3	1	no	—
146	#340	—	3	2	no	—
147	C₂²×C₃×C₅	—	2	2	no	—
148	C₂²×C₃×C₅	—	2	2	no	—
149	C₂²×C₃×C₅	—	2	2	no	—
150	C₂²×C₃×C₅	—	4	2	no	—
151	C₂²×C₃×C₅	—	4	2	no	—
152	C₂²×C₃×C₅	—	4	2	no	—
153	C₂²×C₃×C₅	—	4	2	no	—
154	C₂²×C₃×C₅	—	4	2	no	—
155	C₂²×C₃×C₅	—	8	2	no	—
156	C₂²×C₃×C₅	—	8	2	no	—
157	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₃×C₅	#120	1	1	yes	characteristic
159	C₂²×C₃×C₅	#123	1	1	yes	characteristic
160	C₂²×C₃×C₅	#135	1	2	yes	—
161	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
162	C₃×C₄×C₅	—	2	2	no	—
163	C₃×C₄×C₅	—	4	2	no	—
164	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
165	C₃×C₄×C₅	#121	1	2	yes	—
166	C₅×Dic₃	—	4	4	no	—
167	C₂⁴×C₃	—	2	1	no	—
168	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
169	C₂×C₃×D₄	—	2	4	no	—
170	C₂×C₃×D₄	—	2	2	no	—
171	C₂×C₃×D₄	—	2	1	no	—
172	C₂×C₃×D₄	—	2	2	no	—
173	C₂×C₃×D₄	—	4	4	no	—
174	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
175	C₂²×C₃×C₄	—	2	2	no	—
176	C₂²×C₃×C₄	—	2	2	no	—
177	C₂²×C₃×C₄	—	2	1	no	—
178	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
179	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
181	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
182	C₂²×Dic₃	—	2	2	no	—
183	C₃×C₄⋊C₄	—	2	1	no	—
184	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
185	C₃×C₂²⋊C₄	—	2	4	no	—
186	#217	—	2	4	no	—
187	C₄⋊Dic₃	—	2	2	no	—
188	C₄⋊Dic₃	C₅×D₄	1	4	yes	complemented
189	C₄×Dic₃	—	2	4	no	—
190	C₂×C₃⋊C₈	—	2	2	no	—
191	C₂×C₃⋊C₈	—	2	2	no	—
192	C₂×C₃⋊C₈	—	2	2	no	—
193	C₂³×C₅	—	2	2	no	—
194	C₂³×C₅	—	2	1	no	—
195	C₂³×C₅	—	2	1	no	—
196	C₂³×C₅	—	2	2	no	—
197	C₂³×C₅	—	2	2	no	—
198	C₂³×C₅	—	4	2	no	—
199	C₂³×C₅	—	4	1	no	—
200	C₂³×C₅	—	4	1	no	—
201	C₂³×C₅	—	4	2	no	—
202	C₂³×C₅	#217	1	2	yes	—
203	C₂³×C₅	C₂×#67	1	1	yes	characteristic
204	C₅×D₄	—	2	4	no	—
205	C₅×D₄	—	4	8	no	—
206	C₅×D₄	—	4	2	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	—	2	4	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	4	2	no	—
213	C₂×C₄×C₅	—	6	4	no	—
214	C₂×C₄×C₅	—	12	2	no	—
215	C₂×C₄×C₅	—	12	2	no	—
216	C₂×C₄×C₅	#217	1	2	yes	—
217	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
218	C₂×C₄×C₅	#237	1	2	yes	—
219	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
221	C₅×C₈	—	12	2	no	—
222	C₂²×D₄	—	2	1	no	—
223	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
224	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
225	C₂²×C₈	—	3	2	no	—
226	#121	—	2	2	no	—
227	#121	C₅×Dic₃	1	4	yes	complemented
228	#117	—	6	4	no	—
229	C₂×C₄⋊C₄	—	3	2	no	—
230	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
231	C₂×C₂²⋊C₄	—	2	1	no	—
232	C₂×C₂²⋊C₄	—	6	1	no	—
233	C₂×C₄²	—	6	1	no	—
234	#102	—	6	4	no	—
235	C₂²⋊C₈	—	6	2	no	—
236	C₂×C₃×C₅	—	4	2	no	—
237	C₂×C₃×C₅	—	8	2	no	—
238	C₂×C₃×C₅	#386	1	1	yes	characteristic
239	C₂×C₃×C₅	#416	1	1	yes	characteristic
240	C₂×C₃×C₅	#418	1	1	yes	characteristic
241	C₂×C₃×C₅	#449	1	2	yes	—
242	C₂×C₃×C₅	#482	1	2	yes	—
243	C₂³×C₃	—	2	1	no	—
244	C₂³×C₃	—	2	1	no	—
245	C₂³×C₃	—	2	2	no	—
246	C₂³×C₃	—	2	2	no	—
247	C₂³×C₃	—	2	2	no	—
248	C₂³×C₃	—	4	1	no	—
249	C₂³×C₃	—	4	1	no	—
250	C₂³×C₃	—	4	2	no	—
251	C₂³×C₃	—	4	2	no	—
252	C₂³×C₃	C₅×C₂²⋊C₄	1	2	yes	—
253	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
254	C₃×D₄	—	2	4	no	—
255	C₃×D₄	—	4	8	no	—
256	C₃×D₄	—	4	2	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	4	2	no	—
263	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
264	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
266	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
267	C₂×C₃×C₄	C₅×#41	1	2	yes	—
268	C₂×Dic₃	—	2	4	no	—
269	C₂×Dic₃	—	4	2	no	—
270	C₂×Dic₃	—	4	2	no	—
271	C₃⋊C₈	—	4	2	no	—
272	C₂²×C₅	—	2	2	no	—
273	C₂²×C₅	—	2	2	no	—
274	C₂²×C₅	—	2	2	no	—
275	C₂²×C₅	—	4	2	no	—
276	C₂²×C₅	—	4	2	no	—
277	C₂²×C₅	—	4	2	no	—
278	C₂²×C₅	—	4	2	no	—
279	C₂²×C₅	—	4	2	no	—
280	C₂²×C₅	—	8	2	no	—
281	C₂²×C₅	—	8	2	no	—
282	C₂²×C₅	#932	1	2	yes	—
283	C₂²×C₅	#935	1	1	yes	characteristic
284	C₂²×C₅	#937	1	1	yes	characteristic
285	C₂²×C₅	#950	1	2	yes	—
286	C₂²×C₅	C₂×#217	1	1	yes	characteristic
287	C₄×C₅	—	2	2	no	—
288	C₄×C₅	—	4	2	no	—
289	C₄×C₅	—	12	4	no	—
290	C₄×C₅	D₄×Dic₃	1	2	yes	—
291	C₄×C₅	#939	1	2	yes	—
292	C₂⁴	—	2	1	no	—
293	C₂⁴	C₅×#67	1	1	yes	characteristic
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	4	4	no	—
299	C₂×D₄	C₂×C₅×Dic₃	1	2	yes	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	6	2	no	—
304	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
305	C₂²×C₄	C₅×#67	1	1	yes	characteristic
306	C₂²×C₄	C₅×#67	1	2	yes	—
307	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
308	C₂×C₈	—	6	2	no	—
309	C₂×C₈	—	6	2	no	—
310	C₂×C₈	—	6	2	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	3	4	no	—
313	C₄⋊C₄	—	6	2	no	—
314	C₄⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
315	C₂²⋊C₄	—	2	4	no	—
316	C₂²⋊C₄	—	6	4	no	—
317	C₄²	—	6	4	no	—
318	C₃×C₅	#1875	1	1	yes	characteristic, complemented, Hall
319	C₂²×C₃	—	2	2	no	—
320	C₂²×C₃	—	2	2	no	—
321	C₂²×C₃	—	2	2	no	—
322	C₂²×C₃	—	4	2	no	—
323	C₂²×C₃	—	4	2	no	—
324	C₂²×C₃	—	4	2	no	—
325	C₂²×C₃	—	4	2	no	—
326	C₂²×C₃	—	4	2	no	—
327	C₂²×C₃	—	8	2	no	—
328	C₂²×C₃	—	8	2	no	—
329	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
330	C₂²×C₃	C₅×#120	1	1	yes	characteristic
331	C₂²×C₃	C₅×#123	1	1	yes	characteristic
332	C₂²×C₃	C₅×#135	1	2	yes	—
333	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
334	C₃×C₄	—	2	2	no	—
335	C₃×C₄	—	4	2	no	—
336	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
337	C₃×C₄	C₅×#121	1	2	yes	—
338	Dic₃	—	4	4	no	—
339	C₂×C₅	—	4	2	no	—
340	C₂×C₅	—	8	2	no	—
341	C₂×C₅	#5035	1	2	yes	—
342	C₂×C₅	#5037	1	2	yes	—
343	C₂×C₅	#5215	1	1	yes	characteristic
344	C₂×C₅	#5220	1	1	yes	characteristic
345	C₂×C₅	#5233	1	1	yes	characteristic
346	C₂³	—	2	2	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	1	no	—
353	C₂³	—	4	1	no	—
354	C₂³	—	4	2	no	—
355	C₂³	C₅×#217	1	2	yes	—
356	C₂³	C₂×C₅×#67	1	1	yes	characteristic
357	D₄	—	2	4	no	—
358	D₄	—	4	8	no	—
359	D₄	—	4	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	6	4	no	—
367	C₂×C₄	—	12	2	no	—
368	C₂×C₄	—	12	2	no	—
369	C₂×C₄	C₅×#217	1	2	yes	—
370	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
371	C₂×C₄	C₅×#237	1	2	yes	—
372	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
373	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
374	C₈	—	12	2	no	—
375	C₂×C₃	—	4	2	no	—
376	C₂×C₃	—	8	2	no	—
377	C₂×C₃	C₅×#386	1	1	yes	characteristic
378	C₂×C₃	C₅×#416	1	1	yes	characteristic
379	C₂×C₃	C₅×#418	1	1	yes	characteristic
380	C₂×C₃	C₅×#449	1	2	yes	—
381	C₂×C₃	C₅×#482	1	2	yes	—
382	C₅	#71678	1	1	yes	characteristic, direct product factor, Sylow
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	C₅×#932	1	2	yes	—
394	C₂²	C₅×#935	1	1	yes	characteristic
395	C₂²	C₅×#937	1	1	yes	characteristic
396	C₂²	C₅×#950	1	2	yes	—
397	C₂²	C₂×C₅×#217	1	1	yes	characteristic
398	C₄	—	2	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	12	4	no	—
401	C₄	C₅×D₄×Dic₃	1	2	yes	—
402	C₄	C₅×#939	1	2	yes	—
403	C₃	C₅×#1875	1	1	yes	characteristic, complemented, Sylow
404	C₂	—	4	2	no	—
405	C₂	—	8	2	no	—
406	C₂	C₅×#5035	1	2	yes	—
407	C₂	C₅×#5037	1	2	yes	—
408	C₂	C₅×#5215	1	1	yes	characteristic
409	C₂	C₅×#5220	1	1	yes	characteristic
410	C₂	C₅×#5233	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting, prime radical	C₂×C₃×C₅×#121	C₂
socle	C₂³×C₃×C₅	C₂×D₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×#121	D₃
hypocenter	C₃	C₅×#1875
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂×C₅×#121

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#926	C₂	semidirect
3. C₂×C₅×#832	C₂	semidirect
4. C₂×C₅×#830	C₂	semidirect
5. C₅×#4529	C₂	semidirect
11. C₃×C₅×#121	C₄	semidirect
21. #71678	C₅	direct (N × H)
48. C₅×C₄⋊Dic₃	D₄	semidirect
54. C₂×#926	C₂×C₅	semidirect
55. C₂×#832	C₂×C₅	semidirect
56. C₂×#830	C₂×C₅	semidirect
57. #4529	C₂×C₅	semidirect
63. C₅×#121	Dic₃	semidirect
106. C₃×#121	C₄×C₅	semidirect
188. C₄⋊Dic₃	C₅×D₄	semidirect
227. #121	C₅×Dic₃	semidirect
318. C₃×C₅	#1875	semidirect
382. C₅	#71678	direct (N × H)
403. C₃	C₅×#1875	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#121	2
C₂×C₅×#926	2
C₂×C₅×#832	2
C₂×C₅×#830	2
C₅×#4529	2
C₅×#1875	3
#71678	5

Subgroups — C5×#71678 #14300733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71678 #14300733