Subgroups — C₅×#68232 #14281809

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5578	C₂	1	1	yes	maximal, characteristic
2	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#4685	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4535	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4484	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4456	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1481	—	3	1	no	maximal, Hall
9	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₅×#946	C₄	1	1	yes	characteristic
11	C₅×#944	C₄	1	1	yes	characteristic
12	C₂×C₅×D₃×C₈	—	2	1	no	—
13	C₅×#897	C₄	1	1	yes	characteristic
14	C₅×#896	—	2	1	no	—
15	C₅×#889	—	2	1	no	—
16	C₅×#888	C₄	1	1	yes	characteristic
17	C₅×#872	—	2	1	no	—
18	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₄×C₅×Dic₆	—	2	1	no	—
20	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
24	C₅×Dic₃⋊C₈	—	2	1	no	—
25	C₅×Dic₃⋊C₈	—	2	1	no	—
26	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
27	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	#68232	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₅×#533	—	3	1	no	—
30	C₅×#431	—	3	1	no	—
31	C₂×C₅×C₄⋊C₈	—	3	1	no	—
32	C₅×Q₈⋊C₈	—	3	1	no	—
33	C₅×Q₈⋊C₈	—	3	1	no	—
34	C₅×Q₈⋊C₈	—	3	1	no	—
35	C₅×Q₈⋊C₈	D₃	1	1	yes	characteristic, complemented
36	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
39	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
40	C₂×C₅×Dic₆	—	2	1	no	—
41	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃×C₅×C₈	—	2	1	no	—
43	C₂×C₃×C₅×C₈	—	2	1	no	—
44	C₃×C₅×C₄⋊C₄	—	2	1	no	—
45	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
46	C₃×C₄²×C₅	—	2	1	no	—
47	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
48	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
49	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
50	C₅×C₄⋊Dic₃	—	2	1	no	—
51	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
52	C₅×Dic₃⋊C₄	—	2	1	no	—
53	C₅×Dic₃⋊C₄	—	2	1	no	—
54	C₅×Dic₃⋊C₄	—	2	1	no	—
55	C₅×Dic₃⋊C₄	—	2	1	no	—
56	C₅×Dic₃⋊C₄	—	2	1	no	—
57	C₄×C₅×Dic₃	—	2	1	no	—
58	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
59	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
60	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
61	C₂×C₅×C₃⋊C₈	—	2	1	no	—
62	C₂×C₅×C₃⋊C₈	—	2	1	no	—
63	C₅×D₃×C₈	—	4	2	no	—
64	#5578	C₂×C₅	1	1	yes	characteristic
65	D₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
66	#4685	C₂×C₅	1	1	yes	characteristic
67	C₃×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
68	#4535	C₂×C₅	1	1	yes	characteristic, complemented
69	#4484	C₂×C₅	1	1	yes	characteristic, complemented
70	#4456	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂²×C₅×C₈	—	6	1	no	—
72	C₅×C₄⋊Q₈	—	3	1	no	—
73	C₅×C₄⋊Q₈	—	3	1	no	—
74	C₅×#125	—	6	1	no	—
75	C₅×C₂²⋊Q₈	—	3	1	no	—
76	C₅×C₂²⋊Q₈	—	3	1	no	—
77	C₅×C₂²⋊Q₈	—	6	1	no	—
78	C₄×C₅×Q₈	—	3	1	no	—
79	C₄×C₅×Q₈	—	6	1	no	—
80	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
81	C₅×#117	—	6	1	no	—
82	C₂×C₄²×C₅	—	3	1	no	—
83	C₅×C₄⋊C₈	—	3	1	no	—
84	C₅×C₄⋊C₈	—	6	1	no	—
85	C₅×C₄⋊C₈	—	6	1	no	—
86	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
87	C₅×C₂²⋊C₈	—	6	1	no	—
88	C₄×C₅×C₈	—	3	1	no	—
89	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
90	#1481	—	3	1	no	Sylow
91	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₃×C₅×Q₈	—	2	1	no	—
93	C₃×C₅×Q₈	—	2	1	no	—
94	C₂×C₃×C₄×C₅	—	2	1	no	—
95	C₂×C₃×C₄×C₅	—	2	1	no	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₅×Dic₃	—	2	1	no	—
100	C₂×C₅×Dic₃	—	2	1	no	—
101	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₄×C₅×D₃	—	2	1	no	—
105	C₄×C₅×D₃	—	2	1	no	—
106	C₄×C₅×D₃	—	4	1	no	—
107	C₄×C₅×D₃	SD₁₆	1	2	yes	—
108	C₄×C₅×D₃	Q₁₆	1	2	yes	—
109	C₅×Dic₆	—	2	1	no	—
110	C₅×Dic₆	—	2	1	no	—
111	C₅×Dic₆	—	4	2	no	—
112	C₃×C₅×C₈	—	4	1	no	—
113	C₃×C₅×C₈	—	4	1	no	—
114	C₅×C₃⋊C₈	—	4	1	no	—
115	C₅×C₃⋊C₈	—	4	1	no	—
116	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
117	#946	C₄×C₅	1	1	yes	characteristic
118	#944	C₄×C₅	1	1	yes	characteristic
119	C₂×D₃×C₈	—	2	1	no	—
120	#897	C₄×C₅	1	1	yes	characteristic
121	#896	—	2	1	no	—
122	#889	—	2	1	no	—
123	#888	C₄×C₅	1	1	yes	characteristic
124	#872	—	2	1	no	—
125	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
126	C₄×Dic₆	—	2	1	no	—
127	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
128	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
129	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
130	(C₂×D₃)⋊C₈	—	2	1	no	—
131	Dic₃⋊C₈	—	2	1	no	—
132	Dic₃⋊C₈	—	2	1	no	—
133	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
134	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₅×Q₈	—	3	1	no	—
136	C₂×C₅×Q₈	—	6	1	no	—
137	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
138	C₂²×C₄×C₅	—	3	1	no	—
139	C₂²×C₄×C₅	—	3	1	no	—
140	C₂²×C₄×C₅	—	3	1	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	6	1	no	—
144	C₂×C₅×C₈	—	6	1	no	—
145	C₂×C₅×C₈	—	12	2	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	3	1	no	—
148	C₅×C₄⋊C₄	—	6	1	no	—
149	C₅×C₄⋊C₄	—	6	1	no	—
150	C₅×C₄⋊C₄	—	6	1	no	—
151	C₅×C₄⋊C₄	—	6	1	no	—
152	C₅×C₄⋊C₄	—	6	1	no	—
153	C₅×C₄⋊C₄	—	6	1	no	—
154	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
155	C₅×C₂²⋊C₄	—	6	1	no	—
156	C₅×C₂²⋊C₄	—	6	1	no	—
157	C₄²×C₅	—	2	1	no	—
158	C₄²×C₅	—	3	1	no	—
159	C₄²×C₅	—	3	1	no	—
160	C₄²×C₅	—	3	1	no	—
161	C₄²×C₅	—	6	1	no	—
162	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
163	#533	—	3	1	no	—
164	#431	—	3	1	no	—
165	C₂×C₄⋊C₈	—	3	1	no	—
166	Q₈⋊C₈	—	3	1	no	—
167	Q₈⋊C₈	—	3	1	no	—
168	Q₈⋊C₈	—	3	1	no	—
169	Q₈⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
170	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₅×D₃	—	2	1	no	—
172	C₂×C₅×D₃	—	2	1	no	—
173	C₂×C₅×D₃	#103	1	2	yes	—
174	C₃×C₄×C₅	—	2	1	no	—
175	C₃×C₄×C₅	—	4	1	no	—
176	C₃×C₄×C₅	—	4	1	no	—
177	C₃×C₄×C₅	#131	1	1	yes	characteristic
178	C₃×C₄×C₅	#131	1	1	yes	characteristic
179	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
180	C₃×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
181	C₅×Dic₃	—	2	1	no	—
182	C₅×Dic₃	—	2	1	no	—
183	C₅×Dic₃	—	4	1	no	—
184	C₅×Dic₃	—	4	1	no	—
185	C₅×Dic₃	#103	1	2	yes	—
186	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
187	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
188	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
189	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
190	C₂×Dic₆	—	2	1	no	—
191	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
192	C₂×C₃×C₈	—	2	1	no	—
193	C₂×C₃×C₈	—	2	1	no	—
194	C₃×C₄⋊C₄	—	2	1	no	—
195	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
196	C₃×C₄²	—	2	1	no	—
197	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
198	(C₂×D₃)⋊C₄	—	2	1	no	—
199	(C₂×D₃)⋊C₄	—	2	1	no	—
200	C₄⋊Dic₃	—	2	1	no	—
201	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
202	Dic₃⋊C₄	—	2	1	no	—
203	Dic₃⋊C₄	—	2	1	no	—
204	Dic₃⋊C₄	—	2	1	no	—
205	Dic₃⋊C₄	—	2	1	no	—
206	Dic₃⋊C₄	—	2	1	no	—
207	C₄×Dic₃	—	2	1	no	—
208	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
209	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
210	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
211	C₂×C₃⋊C₈	—	2	1	no	—
212	C₂×C₃⋊C₈	—	2	1	no	—
213	D₃×C₈	—	4	2	no	—
214	C₂³×C₅	—	3	1	no	—
215	C₅×Q₈	—	2	1	no	—
216	C₅×Q₈	—	2	1	no	—
217	C₅×Q₈	—	6	1	no	—
218	C₅×Q₈	—	6	1	no	—
219	C₅×Q₈	—	12	2	no	—
220	C₂×C₄×C₅	—	2	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	3	1	no	—
223	C₂×C₄×C₅	—	3	2	no	—
224	C₂×C₄×C₅	—	3	2	no	—
225	C₂×C₄×C₅	—	3	1	no	—
226	C₂×C₄×C₅	—	3	1	no	—
227	C₂×C₄×C₅	—	6	1	no	—
228	C₂×C₄×C₅	—	6	1	no	—
229	C₂×C₄×C₅	—	6	1	no	—
230	C₂×C₄×C₅	—	6	1	no	—
231	C₂×C₄×C₅	—	12	1	no	—
232	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
233	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
235	C₅×C₈	—	4	1	no	—
236	C₅×C₈	—	4	1	no	—
237	C₅×C₈	—	12	1	no	—
238	C₅×C₈	—	12	1	no	—
239	C₂²×C₈	—	6	1	no	—
240	C₄⋊Q₈	—	3	1	no	—
241	C₄⋊Q₈	—	3	1	no	—
242	#125	—	6	1	no	—
243	C₂²⋊Q₈	—	3	1	no	—
244	C₂²⋊Q₈	—	3	1	no	—
245	C₂²⋊Q₈	—	6	1	no	—
246	C₄×Q₈	—	3	1	no	—
247	C₄×Q₈	—	6	1	no	—
248	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
249	#117	—	6	1	no	—
250	C₂×C₄²	—	3	1	no	—
251	C₄⋊C₈	—	3	1	no	—
252	C₄⋊C₈	—	6	1	no	—
253	C₄⋊C₈	—	6	1	no	—
254	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
255	C₂²⋊C₈	—	6	1	no	—
256	C₄×C₈	—	3	1	no	—
257	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
258	C₂×C₃×C₅	#408	1	1	yes	characteristic
259	C₂×C₃×C₅	C₂×#103	1	1	yes	characteristic
260	C₂×C₃×C₅	#421	1	1	yes	characteristic
261	C₅×D₃	—	2	2	no	—
262	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
263	C₃×Q₈	—	2	1	no	—
264	C₃×Q₈	—	2	1	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
270	C₂×Dic₃	—	2	1	no	—
271	C₂×Dic₃	—	2	1	no	—
272	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
275	C₄×D₃	—	2	1	no	—
276	C₄×D₃	—	2	1	no	—
277	C₄×D₃	—	4	1	no	—
278	C₄×D₃	C₅×SD₁₆	1	2	yes	—
279	C₄×D₃	C₅×Q₁₆	1	2	yes	—
280	Dic₆	—	2	1	no	—
281	Dic₆	—	2	1	no	—
282	Dic₆	—	4	2	no	—
283	C₃×C₈	—	4	1	no	—
284	C₃×C₈	—	4	1	no	—
285	C₃⋊C₈	—	4	1	no	—
286	C₃⋊C₈	—	4	1	no	—
287	C₂²×C₅	—	3	2	no	—
288	C₂²×C₅	—	6	1	no	—
289	C₂²×C₅	—	6	1	no	—
290	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
291	C₄×C₅	—	2	1	no	—
292	C₄×C₅	—	3	2	no	—
293	C₄×C₅	—	4	1	no	—
294	C₄×C₅	—	4	1	no	—
295	C₄×C₅	—	6	1	no	—
296	C₄×C₅	—	6	1	no	—
297	C₄×C₅	—	12	1	no	—
298	C₄×C₅	—	12	1	no	—
299	C₄×C₅	#901	1	1	yes	characteristic
300	C₄×C₅	#907	1	1	yes	characteristic
301	C₄×C₅	D₃×SD₁₆	1	1	yes	characteristic
302	C₄×C₅	D₃×Q₁₆	1	1	yes	characteristic
303	C₂×Q₈	—	3	1	no	—
304	C₂×Q₈	—	6	1	no	—
305	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
306	C₂²×C₄	—	3	1	no	—
307	C₂²×C₄	—	3	1	no	—
308	C₂²×C₄	—	3	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	6	1	no	—
312	C₂×C₈	—	6	1	no	—
313	C₂×C₈	—	12	2	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	3	1	no	—
316	C₄⋊C₄	—	6	1	no	—
317	C₄⋊C₄	—	6	1	no	—
318	C₄⋊C₄	—	6	1	no	—
319	C₄⋊C₄	—	6	1	no	—
320	C₄⋊C₄	—	6	1	no	—
321	C₄⋊C₄	—	6	1	no	—
322	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
323	C₂²⋊C₄	—	6	1	no	—
324	C₂²⋊C₄	—	6	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	3	1	no	—
327	C₄²	—	3	1	no	—
328	C₄²	—	3	1	no	—
329	C₄²	—	6	1	no	—
330	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
331	C₃×C₅	#1481	1	1	yes	characteristic, complemented, Hall
332	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
333	C₂×D₃	—	2	1	no	—
334	C₂×D₃	—	2	1	no	—
335	C₂×D₃	C₅×#103	1	2	yes	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	4	1	no	—
338	C₃×C₄	—	4	1	no	—
339	C₃×C₄	C₅×#131	1	1	yes	characteristic
340	C₃×C₄	C₅×#131	1	1	yes	characteristic
341	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
342	C₃×C₄	C₂×C₅×Q₁₆	1	1	yes	characteristic
343	Dic₃	—	2	1	no	—
344	Dic₃	—	2	1	no	—
345	Dic₃	—	4	1	no	—
346	Dic₃	—	4	1	no	—
347	Dic₃	C₅×#103	1	2	yes	—
348	C₂×C₅	—	6	2	no	—
349	C₂×C₅	#4727	1	1	yes	characteristic
350	C₂×C₅	D₃×#103	1	1	yes	characteristic
351	C₂×C₅	#4821	1	1	yes	characteristic
352	C₂³	—	3	1	no	—
353	Q₈	—	2	1	no	—
354	Q₈	—	2	1	no	—
355	Q₈	—	6	1	no	—
356	Q₈	—	6	1	no	—
357	Q₈	—	12	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	3	1	no	—
361	C₂×C₄	—	3	2	no	—
362	C₂×C₄	—	3	2	no	—
363	C₂×C₄	—	3	1	no	—
364	C₂×C₄	—	3	1	no	—
365	C₂×C₄	—	6	1	no	—
366	C₂×C₄	—	6	1	no	—
367	C₂×C₄	—	6	1	no	—
368	C₂×C₄	—	6	1	no	—
369	C₂×C₄	—	12	1	no	—
370	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
371	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
372	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
373	C₈	—	4	1	no	—
374	C₈	—	4	1	no	—
375	C₈	—	12	1	no	—
376	C₈	—	12	1	no	—
377	C₂×C₃	C₅×#408	1	1	yes	characteristic
378	C₂×C₃	C₂×C₅×#103	1	1	yes	characteristic
379	C₂×C₃	C₅×#421	1	1	yes	characteristic
380	D₃	—	2	2	no	—
381	C₅	#68232	1	1	yes	characteristic, direct product factor, Sylow
382	C₂²	—	3	2	no	—
383	C₂²	—	6	1	no	—
384	C₂²	—	6	1	no	—
385	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	3	2	no	—
388	C₄	—	4	1	no	—
389	C₄	—	4	1	no	—
390	C₄	—	6	1	no	—
391	C₄	—	6	1	no	—
392	C₄	—	12	1	no	—
393	C₄	—	12	1	no	—
394	C₄	C₅×#901	1	1	yes	characteristic
395	C₄	C₅×#907	1	1	yes	characteristic
396	C₄	C₅×D₃×SD₁₆	1	1	yes	characteristic
397	C₄	C₅×D₃×Q₁₆	1	1	yes	characteristic
398	C₃	C₅×#1481	1	1	yes	characteristic, complemented, Sylow
399	C₂	—	6	2	no	—
400	C₂	C₅×#4727	1	1	yes	characteristic
401	C₂	C₅×D₃×#103	1	1	yes	characteristic
402	C₂	C₅×#4821	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×Q₈⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂²×C₅×D₃	C₂²⋊C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×Q₈⋊C₈	D₃
hypocenter	C₃	C₅×#1481
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄²×C₅ ◁ C₅×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×Q₈⋊C₈	C₂	semidirect
5. C₅×#4535	C₂	semidirect
6. C₅×#4484	C₂	semidirect
7. C₅×#4456	C₂	semidirect
28. #68232	C₅	direct (N × H)
35. C₅×Q₈⋊C₈	D₃	semidirect
67. C₃×Q₈⋊C₈	C₂×C₅	semidirect
68. #4535	C₂×C₅	semidirect
69. #4484	C₂×C₅	semidirect
70. #4456	C₂×C₅	semidirect
169. Q₈⋊C₈	C₅×D₃	semidirect
331. C₃×C₅	#1481	semidirect
381. C₅	#68232	direct (N × H)
398. C₃	C₅×#1481	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5578	2
C₅×D₃×C₄⋊C₈	2
C₅×#4685	2
C₃×C₅×Q₈⋊C₈	2
C₅×#4535	2
C₅×#4484	2
C₅×#4456	2
C₅×#1481	3
#68232	5

Subgroups — C5×#68232 #14281809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68232 #14281809