Subgroups — C₅×#68231 #14281723

Order 1920.

496 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×#4833	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×#1479	—	3	1	no	maximal, Hall
9	C₂×C₅×D₃×Q₈	C₄	1	1	yes	characteristic
10	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₅×Q₈×Dic₃	C₄	1	1	yes	characteristic
12	C₅×D₃×C₄⋊C₄	—	2	1	no	—
13	C₅×D₃×C₄⋊C₄	C₄	1	1	yes	characteristic
14	C₅×#887	—	2	1	no	—
15	C₅×#887	C₄	1	1	yes	characteristic
16	C₄²×C₅×D₃	—	2	1	no	—
17	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₄×C₅×Dic₆	—	2	1	no	—
19	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
23	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
24	C₅×Dic₃⋊C₈	—	2	1	no	—
25	C₅×C₈×Dic₃	—	2	1	no	—
26	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
27	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	#68231	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₄×C₅×Q₈	—	3	1	no	—
30	C₅×#431	—	3	1	no	—
31	C₅×#431	—	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	C₅×D₃×Q₈	—	2	2	no	—
38	C₅×D₃×Q₈	C₈	1	4	yes	complemented
39	C₂×C₄×C₅×D₃	—	2	1	no	—
40	C₂×C₄×C₅×D₃	—	2	1	no	—
41	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
43	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
44	C₂×C₅×Dic₆	—	2	1	no	—
45	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
52	C₅×C₄⋊Dic₃	—	2	1	no	—
53	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
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	—	2	1	no	—
59	C₄×C₅×Dic₃	—	2	1	no	—
60	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
61	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
62	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
63	C₂×C₅×C₃⋊C₈	—	2	1	no	—
64	C₂×C₅×C₃⋊C₈	—	2	1	no	—
65	C₄×D₃×Q₈	C₂×C₅	1	1	yes	characteristic
66	#4833	C₂×C₅	1	1	yes	characteristic
67	#4685	C₂×C₅	1	1	yes	characteristic
68	C₃×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
69	#4535	C₂×C₅	1	1	yes	characteristic, complemented
70	#4484	C₂×C₅	1	1	yes	characteristic, complemented
71	#4456	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂²×C₅×Q₈	—	3	1	no	—
73	C₄×C₅×Q₈	—	3	1	no	—
74	C₄×C₅×Q₈	—	3	1	no	—
75	C₄×C₅×Q₈	—	3	1	no	—
76	C₄×C₅×Q₈	—	6	1	no	—
77	C₄×C₅×Q₈	—	6	1	no	—
78	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	—	3	1	no	—
80	C₂×C₅×C₄⋊C₄	—	6	1	no	—
81	C₂×C₄²×C₅	—	3	1	no	—
82	C₂×C₄²×C₅	—	6	1	no	—
83	C₅×C₄⋊C₈	—	3	1	no	—
84	C₅×C₄⋊C₈	—	6	1	no	—
85	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
86	C₅×C₂²⋊C₈	—	6	1	no	—
87	C₅×C₂²⋊C₈	—	6	1	no	—
88	C₄×C₅×C₈	—	3	1	no	—
89	C₄×C₅×C₈	—	6	1	no	—
90	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
91	#1479	—	3	1	no	Sylow
92	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
93	C₃×C₅×Q₈	—	2	1	no	—
94	C₃×C₅×Q₈	C₂×C₈	1	2	yes	—
95	C₂×C₃×C₄×C₅	—	2	1	no	—
96	C₂×C₃×C₄×C₅	—	2	1	no	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₅×Dic₃	—	2	1	no	—
101	C₂×C₅×Dic₃	—	2	1	no	—
102	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₄×C₅×D₃	—	2	4	no	—
106	C₄×C₅×D₃	—	2	1	no	—
107	C₄×C₅×D₃	—	2	1	no	—
108	C₄×C₅×D₃	—	4	1	no	—
109	C₄×C₅×D₃	—	4	2	no	—
110	C₄×C₅×D₃	C₂×C₈	1	2	yes	—
111	C₄×C₅×D₃	M₁₆	1	2	yes	—
112	C₅×Dic₆	—	2	1	no	—
113	C₅×Dic₆	—	2	4	no	—
114	C₅×Dic₆	C₂×C₈	1	2	yes	—
115	C₃×C₅×C₈	—	4	1	no	—
116	C₃×C₅×C₈	—	4	1	no	—
117	C₅×C₃⋊C₈	—	4	1	no	—
118	C₅×C₃⋊C₈	—	4	1	no	—
119	C₂×D₃×Q₈	C₄×C₅	1	1	yes	characteristic
120	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
121	Q₈×Dic₃	C₄×C₅	1	1	yes	characteristic
122	D₃×C₄⋊C₄	—	2	1	no	—
123	D₃×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
124	#887	—	2	1	no	—
125	#887	C₄×C₅	1	1	yes	characteristic
126	C₄²×D₃	—	2	1	no	—
127	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
128	C₄×Dic₆	—	2	1	no	—
129	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
130	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
131	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
132	(C₂×D₃)⋊C₈	—	2	1	no	—
133	(C₂×D₃)⋊C₈	—	2	1	no	—
134	Dic₃⋊C₈	—	2	1	no	—
135	C₈×Dic₃	—	2	1	no	—
136	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
137	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
138	C₂×C₅×Q₈	—	3	4	no	—
139	C₂×C₅×Q₈	—	3	1	no	—
140	C₂×C₅×Q₈	—	6	1	no	—
141	C₂×C₅×Q₈	—	6	2	no	—
142	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
143	C₂²×C₄×C₅	—	3	1	no	—
144	C₂²×C₄×C₅	—	3	1	no	—
145	C₂²×C₄×C₅	—	3	1	no	—
146	C₂²×C₄×C₅	—	6	1	no	—
147	C₂²×C₄×C₅	—	6	1	no	—
148	C₂×C₅×C₈	—	2	1	no	—
149	C₂×C₅×C₈	—	2	1	no	—
150	C₂×C₅×C₈	—	6	1	no	—
151	C₂×C₅×C₈	—	6	1	no	—
152	C₅×C₄⋊C₄	—	2	1	no	—
153	C₅×C₄⋊C₄	—	3	1	no	—
154	C₅×C₄⋊C₄	—	6	1	no	—
155	C₅×C₄⋊C₄	—	6	1	no	—
156	C₅×C₄⋊C₄	—	6	1	no	—
157	C₅×C₄⋊C₄	—	6	1	no	—
158	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
159	C₄²×C₅	—	2	1	no	—
160	C₄²×C₅	—	3	1	no	—
161	C₄²×C₅	—	3	1	no	—
162	C₄²×C₅	—	3	1	no	—
163	C₄²×C₅	—	6	1	no	—
164	C₄²×C₅	—	6	1	no	—
165	C₄²×C₅	—	6	1	no	—
166	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
167	C₂×C₄×Q₈	—	3	1	no	—
168	#431	—	3	1	no	—
169	#431	—	3	1	no	—
170	Q₈⋊C₈	—	3	1	no	—
171	Q₈⋊C₈	—	3	1	no	—
172	Q₈⋊C₈	—	3	1	no	—
173	Q₈⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
174	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₅×D₃	—	2	1	no	—
176	C₂×C₅×D₃	—	2	1	no	—
177	C₂×C₅×D₃	C₂²⋊C₈	1	2	yes	—
178	C₃×C₄×C₅	—	2	2	no	—
179	C₃×C₄×C₅	—	2	1	no	—
180	C₃×C₄×C₅	—	4	1	no	—
181	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
182	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
183	C₃×C₄×C₅	#137	1	1	yes	characteristic
184	C₃×C₄×C₅	#137	1	1	yes	characteristic
185	C₅×Dic₃	—	2	2	no	—
186	C₅×Dic₃	—	2	1	no	—
187	C₅×Dic₃	—	2	1	no	—
188	C₅×Dic₃	—	4	1	no	—
189	C₅×Dic₃	C₂²⋊C₈	1	2	yes	—
190	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
191	D₃×Q₈	—	2	2	no	—
192	D₃×Q₈	C₅×C₈	1	4	yes	complemented
193	C₂×C₄×D₃	—	2	1	no	—
194	C₂×C₄×D₃	—	2	1	no	—
195	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
196	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
197	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
198	C₂×Dic₆	—	2	1	no	—
199	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
200	C₂×C₃×C₈	—	2	1	no	—
201	C₂×C₃×C₈	—	2	1	no	—
202	C₃×C₄⋊C₄	—	2	1	no	—
203	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
204	C₃×C₄²	—	2	1	no	—
205	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
206	C₄⋊Dic₃	—	2	1	no	—
207	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
208	Dic₃⋊C₄	—	2	1	no	—
209	Dic₃⋊C₄	—	2	1	no	—
210	Dic₃⋊C₄	—	2	1	no	—
211	C₄×Dic₃	—	2	1	no	—
212	C₄×Dic₃	—	2	1	no	—
213	C₄×Dic₃	—	2	1	no	—
214	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
215	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
216	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
217	C₂×C₃⋊C₈	—	2	1	no	—
218	C₂×C₃⋊C₈	—	2	1	no	—
219	C₂³×C₅	—	3	1	no	—
220	C₅×Q₈	—	2	1	no	—
221	C₅×Q₈	—	3	2	no	—
222	C₅×Q₈	—	6	4	no	—
223	C₅×Q₈	—	6	1	no	—
224	C₅×Q₈	D₃×C₈	1	2	yes	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	3	1	no	—
228	C₂×C₄×C₅	—	3	2	no	—
229	C₂×C₄×C₅	—	3	2	no	—
230	C₂×C₄×C₅	—	3	1	no	—
231	C₂×C₄×C₅	—	3	1	no	—
232	C₂×C₄×C₅	—	6	4	no	—
233	C₂×C₄×C₅	—	6	1	no	—
234	C₂×C₄×C₅	—	6	1	no	—
235	C₂×C₄×C₅	—	6	1	no	—
236	C₂×C₄×C₅	—	6	1	no	—
237	C₂×C₄×C₅	—	12	1	no	—
238	C₂×C₄×C₅	—	12	2	no	—
239	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
240	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
241	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
242	C₅×C₈	—	4	1	no	—
243	C₅×C₈	—	4	1	no	—
244	C₅×C₈	—	12	1	no	—
245	C₅×C₈	—	12	1	no	—
246	C₂²×Q₈	—	3	1	no	—
247	C₄×Q₈	—	3	1	no	—
248	C₄×Q₈	—	3	1	no	—
249	C₄×Q₈	—	3	1	no	—
250	C₄×Q₈	—	6	1	no	—
251	C₄×Q₈	—	6	1	no	—
252	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
253	C₂×C₄⋊C₄	—	3	1	no	—
254	C₂×C₄⋊C₄	—	6	1	no	—
255	C₂×C₄²	—	3	1	no	—
256	C₂×C₄²	—	6	1	no	—
257	C₄⋊C₈	—	3	1	no	—
258	C₄⋊C₈	—	6	1	no	—
259	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
260	C₂²⋊C₈	—	6	1	no	—
261	C₂²⋊C₈	—	6	1	no	—
262	C₄×C₈	—	3	1	no	—
263	C₄×C₈	—	6	1	no	—
264	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
265	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
266	C₂×C₃×C₅	#419	1	1	yes	characteristic
267	C₂×C₃×C₅	#421	1	1	yes	characteristic
268	C₅×D₃	—	2	2	no	—
269	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
270	C₃×Q₈	—	2	1	no	—
271	C₃×Q₈	C₂×C₅×C₈	1	2	yes	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	2	1	no	—
274	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
277	C₂×Dic₃	—	2	1	no	—
278	C₂×Dic₃	—	2	1	no	—
279	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
281	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
282	C₄×D₃	—	2	4	no	—
283	C₄×D₃	—	2	1	no	—
284	C₄×D₃	—	2	1	no	—
285	C₄×D₃	—	4	1	no	—
286	C₄×D₃	—	4	2	no	—
287	C₄×D₃	C₂×C₅×C₈	1	2	yes	—
288	C₄×D₃	C₅×M₁₆	1	2	yes	—
289	Dic₆	—	2	1	no	—
290	Dic₆	—	2	4	no	—
291	Dic₆	C₂×C₅×C₈	1	2	yes	—
292	C₃×C₈	—	4	1	no	—
293	C₃×C₈	—	4	1	no	—
294	C₃⋊C₈	—	4	1	no	—
295	C₃⋊C₈	—	4	1	no	—
296	C₂²×C₅	—	3	2	no	—
297	C₂²×C₅	—	6	1	no	—
298	C₂²×C₅	—	6	1	no	—
299	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
300	C₄×C₅	—	2	2	no	—
301	C₄×C₅	—	2	1	no	—
302	C₄×C₅	—	3	2	no	—
303	C₄×C₅	—	4	1	no	—
304	C₄×C₅	—	6	2	no	—
305	C₄×C₅	—	6	1	no	—
306	C₄×C₅	—	6	1	no	—
307	C₄×C₅	—	12	1	no	—
308	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
309	C₄×C₅	D₃×M₁₆	1	1	yes	characteristic
310	C₄×C₅	#915	1	1	yes	characteristic
311	C₄×C₅	#918	1	1	yes	characteristic
312	C₂×Q₈	—	3	4	no	—
313	C₂×Q₈	—	3	1	no	—
314	C₂×Q₈	—	6	1	no	—
315	C₂×Q₈	—	6	2	no	—
316	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
317	C₂²×C₄	—	3	1	no	—
318	C₂²×C₄	—	3	1	no	—
319	C₂²×C₄	—	3	1	no	—
320	C₂²×C₄	—	6	1	no	—
321	C₂²×C₄	—	6	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	6	1	no	—
325	C₂×C₈	—	6	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	3	1	no	—
328	C₄⋊C₄	—	6	1	no	—
329	C₄⋊C₄	—	6	1	no	—
330	C₄⋊C₄	—	6	1	no	—
331	C₄⋊C₄	—	6	1	no	—
332	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
333	C₄²	—	2	1	no	—
334	C₄²	—	3	1	no	—
335	C₄²	—	3	1	no	—
336	C₄²	—	3	1	no	—
337	C₄²	—	6	1	no	—
338	C₄²	—	6	1	no	—
339	C₄²	—	6	1	no	—
340	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
341	C₃×C₅	#1479	1	1	yes	characteristic, complemented, Hall
342	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
343	C₂×D₃	—	2	1	no	—
344	C₂×D₃	—	2	1	no	—
345	C₂×D₃	C₅×C₂²⋊C₈	1	2	yes	—
346	C₃×C₄	—	2	2	no	—
347	C₃×C₄	—	2	1	no	—
348	C₃×C₄	—	4	1	no	—
349	C₃×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
350	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
351	C₃×C₄	C₅×#137	1	1	yes	characteristic
352	C₃×C₄	C₅×#137	1	1	yes	characteristic
353	Dic₃	—	2	2	no	—
354	Dic₃	—	2	1	no	—
355	Dic₃	—	2	1	no	—
356	Dic₃	—	4	1	no	—
357	Dic₃	C₅×C₂²⋊C₈	1	2	yes	—
358	C₂×C₅	—	6	2	no	—
359	C₂×C₅	D₃×C₂²⋊C₈	1	1	yes	characteristic
360	C₂×C₅	#4802	1	1	yes	characteristic
361	C₂×C₅	#4821	1	1	yes	characteristic
362	C₂³	—	3	1	no	—
363	Q₈	—	2	1	no	—
364	Q₈	—	3	2	no	—
365	Q₈	—	6	4	no	—
366	Q₈	—	6	1	no	—
367	Q₈	C₅×D₃×C₈	1	2	yes	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	3	1	no	—
371	C₂×C₄	—	3	2	no	—
372	C₂×C₄	—	3	2	no	—
373	C₂×C₄	—	3	1	no	—
374	C₂×C₄	—	3	1	no	—
375	C₂×C₄	—	6	4	no	—
376	C₂×C₄	—	6	1	no	—
377	C₂×C₄	—	6	1	no	—
378	C₂×C₄	—	6	1	no	—
379	C₂×C₄	—	6	1	no	—
380	C₂×C₄	—	12	1	no	—
381	C₂×C₄	—	12	2	no	—
382	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
383	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
384	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
385	C₈	—	4	1	no	—
386	C₈	—	4	1	no	—
387	C₈	—	12	1	no	—
388	C₈	—	12	1	no	—
389	C₂×C₃	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
390	C₂×C₃	C₅×#419	1	1	yes	characteristic
391	C₂×C₃	C₅×#421	1	1	yes	characteristic
392	D₃	—	2	2	no	—
393	C₅	#68231	1	1	yes	characteristic, direct product factor, Sylow
394	C₂²	—	3	2	no	—
395	C₂²	—	6	1	no	—
396	C₂²	—	6	1	no	—
397	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
398	C₄	—	2	2	no	—
399	C₄	—	2	1	no	—
400	C₄	—	3	2	no	—
401	C₄	—	4	1	no	—
402	C₄	—	6	2	no	—
403	C₄	—	6	1	no	—
404	C₄	—	6	1	no	—
405	C₄	—	12	1	no	—
406	C₄	C₂×C₅×D₃×C₈	1	1	yes	characteristic
407	C₄	C₅×D₃×M₁₆	1	1	yes	characteristic
408	C₄	C₅×#915	1	1	yes	characteristic
409	C₄	C₅×#918	1	1	yes	characteristic
410	C₃	C₅×#1479	1	1	yes	characteristic, complemented, Sylow
411	C₂	—	6	2	no	—
412	C₂	C₅×D₃×C₂²⋊C₈	1	1	yes	characteristic
413	C₂	C₅×#4802	1	1	yes	characteristic
414	C₂	C₅×#4821	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₃×C₄	C₂²×C₅×C₈
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×#1479
LCS	G ▷ 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. #68231	C₅	direct (N × H)
35. C₅×Q₈⋊C₈	D₃	semidirect
38. C₅×D₃×Q₈	C₈	semidirect
68. C₃×Q₈⋊C₈	C₂×C₅	semidirect
69. #4535	C₂×C₅	semidirect
70. #4484	C₂×C₅	semidirect
71. #4456	C₂×C₅	semidirect
173. Q₈⋊C₈	C₅×D₃	semidirect
192. D₃×Q₈	C₅×C₈	semidirect
341. C₃×C₅	#1479	semidirect
393. C₅	#68231	direct (N × H)
410. C₃	C₅×#1479	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×D₃×Q₈	2
C₅×#4833	2
C₅×#4685	2
C₃×C₅×Q₈⋊C₈	2
C₅×#4535	2
C₅×#4484	2
C₅×#4456	2
C₅×#1479	3
#68231	5

Subgroups — C5×#68231 #14281723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68231 #14281723