Subgroups — C₅×#70370 #14296005

Order 1920.

584 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#948	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#104	C₂	1	1	yes	maximal, characteristic
3	C₅×#5233	C₂	1	1	yes	maximal, characteristic
4	C₅×#5122	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4558	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4523	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1765	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₅×#948	—	2	2	no	—
13	C₅×#948	C₄	1	4	yes	complemented
14	C₅×#926	C₂²	1	1	yes	characteristic
15	C₂×C₅×#208	—	2	1	no	—
16	C₂×C₅×#208	C₂²	1	1	yes	characteristic
17	C₂²×C₅×C₃⋊C₈	—	2	1	no	—
18	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₃×C₅×#104	C₄	1	4	yes	complemented
21	C₅×#835	C₄	1	2	yes	complemented
22	C₅×#832	C₄	1	2	yes	complemented
23	C₅×#815	—	2	1	no	—
24	C₅×C₈×Dic₃	—	2	1	no	—
25	C₅×#803	—	2	2	no	—
26	#70370	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₅×#131	—	3	1	no	—
28	C₂×C₅×#104	D₃	1	1	yes	characteristic
29	C₅×#416	—	3	1	no	—
30	C₅×#405	—	3	1	no	—
31	C₂×C₅×#97	—	3	1	no	—
32	C₅×#341	—	3	1	no	—
33	C₅×#339	—	3	1	no	—
34	C₃×C₅×#41	—	2	1	no	—
35	C₃×C₅×#41	—	2	1	no	—
36	C₃×C₅×#41	C₂×C₄	1	2	yes	—
37	C₃×C₅×#41	C₂×C₄	1	2	yes	—
38	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃×C₅×D₄	—	2	1	no	—
40	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₃×C₅×M₁₆	—	2	1	no	—
45	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	—
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₃×C₄²×C₅	—	2	1	no	—
48	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
49	C₅×#217	—	2	1	no	—
50	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
51	C₄×C₅×Dic₃	—	2	1	no	—
52	C₅×#208	—	2	1	no	—
53	C₅×#208	—	2	4	no	—
54	C₅×#208	C₂×C₄	1	2	yes	—
55	C₂×C₅×C₃⋊C₈	—	2	1	no	—
56	C₂×C₅×C₃⋊C₈	—	2	1	no	—
57	C₂×C₅×C₃⋊C₈	—	2	1	no	—
58	C₂×C₅×C₃⋊C₈	—	2	4	no	—
59	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
60	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
61	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
62	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
63	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
64	C₂×#948	C₂×C₅	1	1	yes	characteristic
65	C₂×C₃×#104	C₂×C₅	1	1	yes	characteristic
66	#5233	C₂×C₅	1	1	yes	characteristic
67	#5122	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×#803	C₂×C₅	1	1	yes	characteristic, complemented
69	#4558	C₂×C₅	1	1	yes	characteristic, complemented
70	#4523	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
72	C₅×#131	—	3	4	no	—
73	C₅×#131	—	6	2	no	—
74	C₂×C₅×M₁₆	—	3	1	no	—
75	C₂×C₅×M₁₆	—	6	1	no	—
76	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
77	C₂²×C₅×C₈	—	3	1	no	—
78	C₂²×C₅×C₈	—	3	1	no	—
79	C₂²×C₅×C₈	—	6	1	no	—
80	C₅×#117	—	3	1	no	—
81	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
82	C₅×#104	Dic₃	1	4	yes	complemented
83	C₅×#103	—	3	2	no	—
84	C₅×#102	—	3	2	no	—
85	C₅×#97	—	6	2	no	—
86	C₅×#97	—	6	1	no	—
87	C₄×C₅×C₈	—	6	1	no	—
88	#1765	—	3	1	no	Sylow
89	C₂³×C₃×C₅	—	2	1	no	—
90	C₂³×C₃×C₅	#41	1	1	yes	characteristic
91	C₃×C₅×Q₈	—	2	1	no	—
92	C₃×C₅×Q₈	C₄²	1	2	yes	—
93	C₃×C₅×D₄	—	2	2	no	—
94	C₃×C₅×D₄	—	2	2	no	—
95	C₃×C₅×D₄	—	2	1	no	—
96	C₃×C₅×D₄	C₄²	1	2	yes	—
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	4	2	no	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
108	C₂×C₅×Dic₃	—	2	2	no	—
109	C₃×C₅×C₈	—	2	2	no	—
110	C₅×C₃⋊C₈	—	2	2	no	—
111	C₅×C₃⋊C₈	—	2	2	no	—
112	C₅×C₃⋊C₈	C₂²⋊C₄	1	2	yes	—
113	C₅×C₃⋊C₈	C₂²⋊C₄	1	2	yes	—
114	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
115	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
116	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
117	#948	—	2	2	no	—
118	#948	C₄×C₅	1	4	yes	complemented
119	#926	C₂²×C₅	1	1	yes	characteristic
120	C₂×#208	—	2	1	no	—
121	C₂×#208	C₂²×C₅	1	1	yes	characteristic
122	C₂²×C₃⋊C₈	—	2	1	no	—
123	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
124	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
125	C₃×#104	C₄×C₅	1	4	yes	complemented
126	#835	C₄×C₅	1	2	yes	complemented
127	#832	C₄×C₅	1	2	yes	complemented
128	#815	—	2	1	no	—
129	C₈×Dic₃	—	2	1	no	—
130	#803	—	2	2	no	—
131	C₅×#41	—	2	1	no	—
132	C₅×#41	—	2	1	no	—
133	C₅×#41	C₄×D₃	1	2	yes	—
134	C₅×#41	C₂×Dic₃	1	2	yes	—
135	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
136	C₂×C₅×D₄	—	2	1	no	—
137	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
138	C₂²×C₄×C₅	—	2	1	no	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
141	C₅×M₁₆	—	2	1	no	—
142	C₅×M₁₆	—	3	2	no	—
143	C₅×M₁₆	—	6	4	no	—
144	C₅×M₁₆	—	6	1	no	—
145	C₅×M₁₆	C₂×Dic₃	1	2	yes	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	3	2	no	—
148	C₂×C₅×C₈	—	3	2	no	—
149	C₂×C₅×C₈	—	3	1	no	—
150	C₂×C₅×C₈	—	3	1	no	—
151	C₂×C₅×C₈	—	3	2	no	—
152	C₂×C₅×C₈	—	6	4	no	—
153	C₂×C₅×C₈	—	6	1	no	—
154	C₂×C₅×C₈	—	6	1	no	—
155	C₂×C₅×C₈	—	6	1	no	—
156	C₅×C₄⋊C₄	—	3	2	no	—
157	C₅×C₂²⋊C₄	—	6	1	no	—
158	C₄²×C₅	—	2	1	no	—
159	C₄²×C₅	—	6	1	no	—
160	C₄²×C₅	C₂×Dic₃	1	2	yes	—
161	C₂×#131	—	3	1	no	—
162	C₂×#104	C₅×D₃	1	1	yes	characteristic
163	#416	—	3	1	no	—
164	#405	—	3	1	no	—
165	C₂×#97	—	3	1	no	—
166	#341	—	3	1	no	—
167	#339	—	3	1	no	—
168	C₂²×C₃×C₅	—	2	2	no	—
169	C₂²×C₃×C₅	—	2	2	no	—
170	C₂²×C₃×C₅	—	4	2	no	—
171	C₂²×C₃×C₅	#117	1	1	yes	characteristic
172	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
173	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
174	C₃×C₄×C₅	—	2	2	no	—
175	C₃×C₄×C₅	—	4	2	no	—
176	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
177	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
179	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
180	C₅×Dic₃	—	4	2	no	—
181	C₃×#41	—	2	1	no	—
182	C₃×#41	—	2	1	no	—
183	C₃×#41	C₂×C₄×C₅	1	2	yes	—
184	C₃×#41	C₂×C₄×C₅	1	2	yes	—
185	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
186	C₂×C₃×D₄	—	2	1	no	—
187	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
188	C₂²×C₃×C₄	—	2	1	no	—
189	C₂²×C₃×C₄	—	2	1	no	—
190	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
191	C₃×M₁₆	—	2	1	no	—
192	C₃×M₁₆	C₂×C₄×C₅	1	2	yes	—
193	C₂×C₃×C₈	—	2	1	no	—
194	C₃×C₄²	—	2	1	no	—
195	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
196	#217	—	2	1	no	—
197	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
198	C₄×Dic₃	—	2	1	no	—
199	#208	—	2	1	no	—
200	#208	—	2	4	no	—
201	#208	C₂×C₄×C₅	1	2	yes	—
202	C₂×C₃⋊C₈	—	2	1	no	—
203	C₂×C₃⋊C₈	—	2	1	no	—
204	C₂×C₃⋊C₈	—	2	1	no	—
205	C₂×C₃⋊C₈	—	2	4	no	—
206	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
207	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
208	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
209	C₂×C₃⋊C₈	C₅×D₄	1	1	yes	characteristic
210	C₂×C₃⋊C₈	C₅×D₄	1	1	yes	characteristic
211	C₂³×C₅	—	2	1	no	—
212	C₂³×C₅	#237	1	1	yes	characteristic
213	C₅×Q₈	—	2	1	no	—
214	C₅×Q₈	C₄×Dic₃	1	2	yes	—
215	C₅×D₄	—	2	2	no	—
216	C₅×D₄	—	2	2	no	—
217	C₅×D₄	—	2	1	no	—
218	C₅×D₄	C₄×Dic₃	1	2	yes	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	4	2	no	—
224	C₂×C₄×C₅	—	6	2	no	—
225	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
227	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
228	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅	#237	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
231	C₅×C₈	—	2	2	no	—
232	C₅×C₈	—	3	2	no	—
233	C₅×C₈	—	3	2	no	—
234	C₅×C₈	—	6	2	no	—
235	C₅×C₈	—	6	2	no	—
236	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
237	#131	—	3	4	no	—
238	#131	—	6	2	no	—
239	C₂×M₁₆	—	3	1	no	—
240	C₂×M₁₆	—	6	1	no	—
241	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
242	C₂²×C₈	—	3	1	no	—
243	C₂²×C₈	—	3	1	no	—
244	C₂²×C₈	—	6	1	no	—
245	#117	—	3	1	no	—
246	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
247	#104	C₅×Dic₃	1	4	yes	complemented
248	#103	—	3	2	no	—
249	#102	—	3	2	no	—
250	#97	—	6	2	no	—
251	#97	—	6	1	no	—
252	C₄×C₈	—	6	1	no	—
253	C₂×C₃×C₅	—	2	1	no	—
254	C₂×C₃×C₅	—	2	1	no	—
255	C₂×C₃×C₅	—	4	2	no	—
256	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×C₃×C₅	#444	1	2	yes	—
258	C₂³×C₃	—	2	1	no	—
259	C₂³×C₃	C₅×#41	1	1	yes	characteristic
260	C₃×Q₈	—	2	1	no	—
261	C₃×Q₈	C₄²×C₅	1	2	yes	—
262	C₃×D₄	—	2	2	no	—
263	C₃×D₄	—	2	2	no	—
264	C₃×D₄	—	2	1	no	—
265	C₃×D₄	C₄²×C₅	1	2	yes	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	4	2	no	—
271	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
276	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
277	C₂×Dic₃	—	2	2	no	—
278	C₃×C₈	—	2	2	no	—
279	C₃⋊C₈	—	2	2	no	—
280	C₃⋊C₈	—	2	2	no	—
281	C₃⋊C₈	C₅×C₂²⋊C₄	1	2	yes	—
282	C₃⋊C₈	C₅×C₂²⋊C₄	1	2	yes	—
283	C₂²×C₅	—	2	2	no	—
284	C₂²×C₅	—	2	2	no	—
285	C₂²×C₅	—	4	2	no	—
286	C₂²×C₅	#877	1	1	yes	characteristic
287	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
288	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
289	C₄×C₅	—	2	2	no	—
290	C₄×C₅	—	4	2	no	—
291	C₄×C₅	—	12	2	no	—
292	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
293	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
294	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
295	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
296	#41	—	2	1	no	—
297	#41	—	2	1	no	—
298	#41	C₄×C₅×D₃	1	2	yes	—
299	#41	C₂×C₅×Dic₃	1	2	yes	—
300	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
306	M₁₆	—	2	1	no	—
307	M₁₆	—	3	2	no	—
308	M₁₆	—	6	4	no	—
309	M₁₆	—	6	1	no	—
310	M₁₆	C₂×C₅×Dic₃	1	2	yes	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	3	2	no	—
313	C₂×C₈	—	3	1	no	—
314	C₂×C₈	—	3	1	no	—
315	C₂×C₈	—	3	2	no	—
316	C₂×C₈	—	3	2	no	—
317	C₂×C₈	—	6	4	no	—
318	C₂×C₈	—	6	1	no	—
319	C₂×C₈	—	6	1	no	—
320	C₂×C₈	—	6	1	no	—
321	C₄⋊C₄	—	3	2	no	—
322	C₂²⋊C₄	—	6	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	6	1	no	—
325	C₄²	C₂×C₅×Dic₃	1	2	yes	—
326	C₃×C₅	#1765	1	1	yes	characteristic, complemented, Hall
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	4	2	no	—
330	C₂²×C₃	C₅×#117	1	1	yes	characteristic
331	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
332	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
333	C₃×C₄	—	2	2	no	—
334	C₃×C₄	—	4	2	no	—
335	C₃×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
336	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
337	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
338	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
339	Dic₃	—	4	2	no	—
340	C₂×C₅	—	2	1	no	—
341	C₂×C₅	—	2	1	no	—
342	C₂×C₅	—	4	2	no	—
343	C₂×C₅	#4823	1	2	yes	—
344	C₂×C₅	Dic₃×C₂²⋊C₄	1	1	yes	characteristic
345	C₂³	—	2	1	no	—
346	C₂³	C₅×#237	1	1	yes	characteristic
347	Q₈	—	2	1	no	—
348	Q₈	C₄×C₅×Dic₃	1	2	yes	—
349	D₄	—	2	2	no	—
350	D₄	—	2	2	no	—
351	D₄	—	2	1	no	—
352	D₄	C₄×C₅×Dic₃	1	2	yes	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	6	2	no	—
359	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
361	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
362	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
363	C₂×C₄	C₅×#237	1	1	yes	characteristic
364	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
365	C₈	—	2	2	no	—
366	C₈	—	3	2	no	—
367	C₈	—	3	2	no	—
368	C₈	—	6	2	no	—
369	C₈	—	6	2	no	—
370	C₂×C₃	—	2	1	no	—
371	C₂×C₃	—	2	1	no	—
372	C₂×C₃	—	4	2	no	—
373	C₂×C₃	C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
374	C₂×C₃	C₅×#444	1	2	yes	—
375	C₅	#70370	1	1	yes	characteristic, direct product factor, Sylow
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	C₅×#877	1	1	yes	characteristic
380	C₂²	C₅×#67⋊C₄	1	1	yes	characteristic
381	C₂²	C₅×D₄×Dic₃	1	1	yes	characteristic
382	C₄	—	2	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	12	2	no	—
385	C₄	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
386	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
387	C₄	C₂×C₄×C₅×Dic₃	1	1	yes	characteristic
388	C₄	C₅×D₄×Dic₃	1	1	yes	characteristic
389	C₃	C₅×#1765	1	1	yes	characteristic, complemented, Sylow
390	C₂	—	2	1	no	—
391	C₂	—	2	1	no	—
392	C₂	—	4	2	no	—
393	C₂	C₅×#4823	1	2	yes	—
394	C₂	C₅×Dic₃×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₃×C₄	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×#104	C₂
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×#104	D₃
hypocenter	C₃	C₅×#1765
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#104

Complements

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

N	H ≅ G/N	type
4. C₅×#5122	C₂	semidirect
5. C₂×C₅×#803	C₂	semidirect
6. C₅×#4558	C₂	semidirect
7. C₅×#4523	C₂	semidirect
13. C₅×#948	C₄	semidirect
20. C₃×C₅×#104	C₄	semidirect
21. C₅×#835	C₄	semidirect
22. C₅×#832	C₄	semidirect
26. #70370	C₅	direct (N × H)
67. #5122	C₂×C₅	semidirect
68. C₂×#803	C₂×C₅	semidirect
69. #4558	C₂×C₅	semidirect
70. #4523	C₂×C₅	semidirect
82. C₅×#104	Dic₃	semidirect
118. #948	C₄×C₅	semidirect
125. C₃×#104	C₄×C₅	semidirect
126. #835	C₄×C₅	semidirect
127. #832	C₄×C₅	semidirect
247. #104	C₅×Dic₃	semidirect
326. C₃×C₅	#1765	semidirect
375. C₅	#70370	direct (N × H)
389. C₃	C₅×#1765	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#948	2
C₂×C₃×C₅×#104	2
C₅×#5233	2
C₅×#5122	2
C₂×C₅×#803	2
C₅×#4558	2
C₅×#4523	2
C₅×#1765	3
#70370	5

Subgroups — C5×#70370 #14296005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70370 #14296005