Subgroups — C₂×C₅×#5228 #14423352

Order 1920.

1480 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#216	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#924	C₂	1	1	yes	maximal, characteristic
4	C₅×#5228	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#835	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#830	C₂	1	1	yes	maximal, characteristic
7	C₂×C₅×#451	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×Q₈	—	2	8	no	—
9	C₂²×C₃×C₅×Q₈	—	2	1	no	—
10	C₂²×C₃×C₅×Q₈	—	2	2	no	—
11	C₂²×C₃×C₅×Q₈	C₂²	1	4	yes	—
12	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
13	C₂³×C₃×C₄×C₅	—	2	1	no	—
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
16	C₂×C₅×#217	—	2	1	no	—
17	C₂×C₅×#216	—	2	8	no	—
18	C₂×C₅×#216	C₂²	1	8	yes	complemented
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₅×#924	—	2	2	no	—
21	C₅×#924	C₂²	1	4	yes	—
22	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
23	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
24	C₅×#835	C₂²	1	8	yes	complemented
25	C₅×#830	C₂²	1	4	yes	—
26	C₂×#5228	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂³×C₅×Q₈	D₃	1	1	yes	characteristic
28	C₂²×C₅×Q₁₆	—	3	2	no	—
29	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
30	C₅×#451	—	3	8	no	—
31	C₂×C₅×#103	—	3	2	no	—
32	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
33	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
34	C₂×C₃×C₅×Q₈	—	2	16	no	—
35	C₂×C₃×C₅×Q₈	—	2	8	no	—
36	C₂×C₃×C₅×Q₈	—	2	16	no	—
37	C₂×C₃×C₅×Q₈	—	2	4	no	—
38	C₂×C₃×C₅×Q₈	—	2	4	no	—
39	C₂×C₃×C₅×Q₈	—	2	2	no	—
40	C₂×C₃×C₅×Q₈	D₄	1	8	yes	—
41	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
42	C₂²×C₃×C₄×C₅	—	2	8	no	—
43	C₂²×C₃×C₄×C₅	—	2	4	no	—
44	C₂²×C₃×C₄×C₅	—	2	2	no	—
45	C₂²×C₃×C₄×C₅	—	2	4	no	—
46	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₅×Dic₃	—	2	1	no	—
51	C₂²×C₅×Dic₃	—	2	1	no	—
52	C₂×C₅×Dic₆	—	2	4	no	—
53	C₂×C₅×Dic₆	—	2	1	no	—
54	C₂×C₅×Dic₆	C₂³	1	2	yes	—
55	C₅×#217	—	2	4	no	—
56	C₅×#216	—	2	16	no	—
57	C₅×C₄⋊Dic₃	—	2	1	no	—
58	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
59	C₅×Dic₃⋊C₄	—	2	4	no	—
60	C₂×C₅×C₃⋊C₈	—	2	4	no	—
61	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
62	C₂³×C₃×Q₈	C₂×C₅	1	1	yes	characteristic
63	C₂²×#216	C₂×C₅	1	2	yes	complemented
64	C₂×#924	C₂×C₅	1	1	yes	characteristic
65	#5228	C₂×C₅	1	8	yes	direct product factor
66	C₂×#835	C₂×C₅	1	2	yes	complemented
67	C₂×#830	C₂×C₅	1	1	yes	characteristic
68	C₂²×C₅×Q₈	—	2	8	no	—
69	C₂²×C₅×Q₈	—	2	2	no	—
70	C₂²×C₅×Q₈	—	2	1	no	—
71	C₂²×C₅×Q₈	—	3	1	no	—
72	C₂²×C₅×Q₈	C₂×D₃	1	4	yes	—
73	C₂²×C₅×Q₈	C₂×D₃	1	2	yes	—
74	C₂³×C₄×C₅	—	2	1	no	—
75	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
76	C₂×C₅×Q₁₆	—	3	8	no	—
77	C₂×C₅×Q₁₆	—	6	8	no	—
78	C₂²×C₅×C₈	—	3	2	no	—
79	C₅×C₂²⋊Q₈	—	3	4	no	—
80	C₅×C₂²⋊Q₈	—	6	2	no	—
81	C₂×C₅×C₄⋊C₄	—	3	1	no	—
82	C₂×C₅×C₄⋊C₄	—	6	1	no	—
83	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
84	C₅×#103	—	3	8	no	—
85	C₅×C₂²⋊C₈	—	3	4	no	—
86	C₂×#451	—	3	1	no	Sylow
87	C₂³×C₃×C₅	—	2	2	no	—
88	C₂³×C₃×C₅	—	2	2	no	—
89	C₂³×C₃×C₅	Q₁₆	1	4	yes	complemented
90	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
91	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
92	C₃×C₅×Q₈	—	2	16	no	—
93	C₃×C₅×Q₈	—	2	8	no	—
94	C₃×C₅×Q₈	—	2	4	no	—
95	C₃×C₅×Q₈	C₂×D₄	1	8	yes	—
96	C₂×C₃×C₄×C₅	—	2	16	no	—
97	C₂×C₃×C₄×C₅	—	2	8	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	—	2	4	no	—
102	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
105	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
106	C₂×C₅×Dic₃	—	2	2	no	—
107	C₂×C₅×Dic₃	—	2	2	no	—
108	C₂×C₅×Dic₃	—	4	2	no	—
109	C₂×C₅×Dic₃	—	4	2	no	—
110	C₅×Dic₆	—	2	4	no	—
111	C₅×Dic₆	—	4	2	no	—
112	C₅×C₃⋊C₈	—	2	4	no	—
113	C₂²×C₃×Q₈	—	2	8	no	—
114	C₂²×C₃×Q₈	—	2	1	no	—
115	C₂²×C₃×Q₈	—	2	2	no	—
116	C₂²×C₃×Q₈	C₂²×C₅	1	4	yes	—
117	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
118	C₂³×C₃×C₄	—	2	1	no	—
119	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
120	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
121	C₂×#217	—	2	1	no	—
122	C₂×#216	—	2	8	no	—
123	C₂×#216	C₂²×C₅	1	8	yes	complemented
124	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
125	#924	—	2	2	no	—
126	#924	C₂²×C₅	1	4	yes	—
127	C₂×Dic₃⋊C₄	—	2	1	no	—
128	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
129	#835	C₂²×C₅	1	8	yes	complemented
130	#830	C₂²×C₅	1	4	yes	—
131	C₂⁴×C₅	#67	1	1	yes	characteristic
132	C₂×C₅×Q₈	—	2	16	no	—
133	C₂×C₅×Q₈	—	2	8	no	—
134	C₂×C₅×Q₈	—	2	16	no	—
135	C₂×C₅×Q₈	—	2	4	no	—
136	C₂×C₅×Q₈	—	2	4	no	—
137	C₂×C₅×Q₈	—	2	2	no	—
138	C₂×C₅×Q₈	—	3	2	no	—
139	C₂×C₅×Q₈	—	6	1	no	—
140	C₂×C₅×Q₈	—	6	4	no	—
141	C₂×C₅×Q₈	#67	1	8	yes	—
142	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
143	C₂²×C₄×C₅	—	2	8	no	—
144	C₂²×C₄×C₅	—	2	4	no	—
145	C₂²×C₄×C₅	—	2	2	no	—
146	C₂²×C₄×C₅	—	2	4	no	—
147	C₂²×C₄×C₅	—	6	1	no	—
148	C₂²×C₄×C₅	—	6	1	no	—
149	C₂²×C₄×C₅	#67	1	2	yes	—
150	C₂²×C₄×C₅	#67	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
152	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
153	C₅×Q₁₆	—	6	16	no	—
154	C₂×C₅×C₈	—	3	4	no	—
155	C₂×C₅×C₈	—	6	4	no	—
156	C₅×C₄⋊C₄	—	3	2	no	—
157	C₅×C₄⋊C₄	—	6	1	no	—
158	C₅×C₄⋊C₄	—	6	4	no	—
159	C₅×C₂²⋊C₄	—	6	4	no	—
160	C₂³×Q₈	C₅×D₃	1	1	yes	characteristic
161	C₂²×Q₁₆	—	3	2	no	—
162	C₂×C₂²⋊Q₈	—	3	1	no	—
163	#451	—	3	8	no	—
164	C₂×#103	—	3	2	no	—
165	C₂×C₂²⋊C₈	—	3	1	no	—
166	C₂²×C₃×C₅	—	2	2	no	—
167	C₂²×C₃×C₅	—	2	2	no	—
168	C₂²×C₃×C₅	—	2	8	no	—
169	C₂²×C₃×C₅	#120	1	2	yes	—
170	C₂²×C₃×C₅	C₂×Q₁₆	1	2	yes	—
171	C₂²×C₃×C₅	C₂×Q₁₆	1	4	yes	complemented
172	C₂²×C₃×C₅	#137	1	2	yes	—
173	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
174	C₃×C₄×C₅	—	2	8	no	—
175	C₃×C₄×C₅	—	2	2	no	—
176	C₃×C₄×C₅	#120	1	2	yes	—
177	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
178	C₅×Dic₃	—	4	2	no	—
179	C₅×Dic₃	—	4	2	no	—
180	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
181	C₂×C₃×Q₈	—	2	16	no	—
182	C₂×C₃×Q₈	—	2	8	no	—
183	C₂×C₃×Q₈	—	2	16	no	—
184	C₂×C₃×Q₈	—	2	4	no	—
185	C₂×C₃×Q₈	—	2	4	no	—
186	C₂×C₃×Q₈	—	2	2	no	—
187	C₂×C₃×Q₈	C₅×D₄	1	8	yes	—
188	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
189	C₂²×C₃×C₄	—	2	8	no	—
190	C₂²×C₃×C₄	—	2	4	no	—
191	C₂²×C₃×C₄	—	2	2	no	—
192	C₂²×C₃×C₄	—	2	4	no	—
193	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
195	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
196	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
197	C₂²×Dic₃	—	2	1	no	—
198	C₂²×Dic₃	—	2	1	no	—
199	C₂×Dic₆	—	2	4	no	—
200	C₂×Dic₆	—	2	1	no	—
201	C₂×Dic₆	C₂³×C₅	1	2	yes	—
202	#217	—	2	4	no	—
203	#216	—	2	16	no	—
204	C₄⋊Dic₃	—	2	1	no	—
205	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
206	Dic₃⋊C₄	—	2	4	no	—
207	C₂×C₃⋊C₈	—	2	4	no	—
208	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
209	C₂³×C₅	—	2	2	no	—
210	C₂³×C₅	—	2	2	no	—
211	C₂³×C₅	#216	1	4	yes	complemented
212	C₂³×C₅	C₂×#67	1	2	yes	—
213	C₂³×C₅	C₂×#67	1	1	yes	characteristic
214	C₅×Q₈	—	2	16	no	—
215	C₅×Q₈	—	2	8	no	—
216	C₅×Q₈	—	2	4	no	—
217	C₅×Q₈	—	6	4	no	—
218	C₅×Q₈	—	12	2	no	—
219	C₅×Q₈	C₂×#67	1	8	yes	—
220	C₂×C₄×C₅	—	2	16	no	—
221	C₂×C₄×C₅	—	2	8	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	4	no	—
224	C₂×C₄×C₅	—	2	4	no	—
225	C₂×C₄×C₅	—	2	4	no	—
226	C₂×C₄×C₅	—	6	2	no	—
227	C₂×C₄×C₅	—	6	2	no	—
228	C₂×C₄×C₅	—	12	2	no	—
229	C₂×C₄×C₅	—	12	2	no	—
230	C₂×C₄×C₅	C₂×#67	1	2	yes	—
231	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂×#67	1	4	yes	—
233	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
234	C₅×C₈	—	6	4	no	—
235	C₂²×Q₈	—	2	8	no	—
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×Q₈	—	2	2	no	—
238	C₂²×Q₈	—	3	1	no	—
239	C₂²×Q₈	C₂×C₅×D₃	1	4	yes	—
240	C₂²×Q₈	C₂×C₅×D₃	1	2	yes	—
241	C₂³×C₄	—	2	1	no	—
242	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
243	C₂×Q₁₆	—	3	8	no	—
244	C₂×Q₁₆	—	6	8	no	—
245	C₂²×C₈	—	3	2	no	—
246	C₂²⋊Q₈	—	3	4	no	—
247	C₂²⋊Q₈	—	6	2	no	—
248	C₂×C₄⋊C₄	—	3	1	no	—
249	C₂×C₄⋊C₄	—	6	1	no	—
250	C₂×C₂²⋊C₄	—	6	1	no	—
251	#103	—	3	8	no	—
252	C₂²⋊C₈	—	3	4	no	—
253	C₂×C₃×C₅	—	2	4	no	—
254	C₂×C₃×C₅	#451	1	4	yes	complemented
255	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
256	C₂×C₃×C₅	C₂²×Q₁₆	1	1	yes	characteristic
257	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
258	C₂³×C₃	—	2	2	no	—
259	C₂³×C₃	—	2	2	no	—
260	C₂³×C₃	C₅×Q₁₆	1	4	yes	complemented
261	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
262	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
263	C₃×Q₈	—	2	16	no	—
264	C₃×Q₈	—	2	8	no	—
265	C₃×Q₈	—	2	4	no	—
266	C₃×Q₈	C₂×C₅×D₄	1	8	yes	—
267	C₂×C₃×C₄	—	2	16	no	—
268	C₂×C₃×C₄	—	2	8	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	4	no	—
271	C₂×C₃×C₄	—	2	4	no	—
272	C₂×C₃×C₄	—	2	4	no	—
273	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
274	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
276	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
277	C₂×Dic₃	—	2	2	no	—
278	C₂×Dic₃	—	2	2	no	—
279	C₂×Dic₃	—	4	2	no	—
280	C₂×Dic₃	—	4	2	no	—
281	Dic₆	—	2	4	no	—
282	Dic₆	—	4	2	no	—
283	C₃⋊C₈	—	2	4	no	—
284	C₂²×C₅	—	2	8	no	—
285	C₂²×C₅	—	2	2	no	—
286	C₂²×C₅	—	2	2	no	—
287	C₂²×C₅	#942	1	2	yes	—
288	C₂²×C₅	C₂×#216	1	2	yes	—
289	C₂²×C₅	C₂×#216	1	4	yes	complemented
290	C₂²×C₅	#953	1	2	yes	—
291	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
292	C₄×C₅	—	2	8	no	—
293	C₄×C₅	—	2	2	no	—
294	C₄×C₅	—	12	2	no	—
295	C₄×C₅	—	12	2	no	—
296	C₄×C₅	#953	1	2	yes	—
297	C₄×C₅	C₂²×#67	1	2	yes	—
298	C₂⁴	C₅×#67	1	1	yes	characteristic
299	C₂×Q₈	—	2	16	no	—
300	C₂×Q₈	—	2	8	no	—
301	C₂×Q₈	—	2	16	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	3	2	no	—
306	C₂×Q₈	—	6	1	no	—
307	C₂×Q₈	—	6	4	no	—
308	C₂×Q₈	C₅×#67	1	8	yes	—
309	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	6	1	no	—
315	C₂²×C₄	—	6	1	no	—
316	C₂²×C₄	C₅×#67	1	1	yes	characteristic
317	C₂²×C₄	C₅×#67	1	2	yes	—
318	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
319	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
320	Q₁₆	—	6	16	no	—
321	C₂×C₈	—	3	4	no	—
322	C₂×C₈	—	6	4	no	—
323	C₄⋊C₄	—	3	2	no	—
324	C₄⋊C₄	—	6	1	no	—
325	C₄⋊C₄	—	6	4	no	—
326	C₂²⋊C₄	—	6	4	no	—
327	C₃×C₅	C₂×#451	1	1	yes	characteristic, complemented, Hall
328	C₂²×C₃	—	2	8	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	2	2	no	—
331	C₂²×C₃	C₅×#120	1	2	yes	—
332	C₂²×C₃	C₂×C₅×Q₁₆	1	2	yes	—
333	C₂²×C₃	C₂×C₅×Q₁₆	1	4	yes	complemented
334	C₂²×C₃	C₅×#137	1	2	yes	—
335	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
336	C₃×C₄	—	2	8	no	—
337	C₃×C₄	—	2	2	no	—
338	C₃×C₄	C₅×#120	1	2	yes	—
339	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
340	Dic₃	—	4	2	no	—
341	Dic₃	—	4	2	no	—
342	C₂×C₅	—	2	4	no	—
343	C₂×C₅	#5228	1	4	yes	direct product factor
344	C₂×C₅	C₂×#942	1	1	yes	characteristic
345	C₂×C₅	C₂²×#216	1	1	yes	characteristic
346	C₂×C₅	C₂×#953	1	1	yes	characteristic
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	C₅×#216	1	4	yes	complemented
350	C₂³	C₂×C₅×#67	1	2	yes	—
351	C₂³	C₂×C₅×#67	1	1	yes	characteristic
352	Q₈	—	2	16	no	—
353	Q₈	—	2	8	no	—
354	Q₈	—	2	4	no	—
355	Q₈	—	6	4	no	—
356	Q₈	—	12	2	no	—
357	Q₈	C₂×C₅×#67	1	8	yes	—
358	C₂×C₄	—	2	16	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	6	2	no	—
365	C₂×C₄	—	6	2	no	—
366	C₂×C₄	—	12	2	no	—
367	C₂×C₄	—	12	2	no	—
368	C₂×C₄	C₂×C₅×#67	1	2	yes	—
369	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
370	C₂×C₄	C₂×C₅×#67	1	4	yes	—
371	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
372	C₈	—	6	4	no	—
373	C₂×C₃	—	2	4	no	—
374	C₂×C₃	C₅×#451	1	4	yes	complemented
375	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
376	C₂×C₃	C₂²×C₅×Q₁₆	1	1	yes	characteristic
377	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
378	C₅	C₂×#5228	1	1	yes	characteristic, direct product factor, Sylow
379	C₂²	—	2	8	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	C₅×#942	1	2	yes	—
383	C₂²	C₂×C₅×#216	1	2	yes	—
384	C₂²	C₂×C₅×#216	1	4	yes	complemented
385	C₂²	C₅×#953	1	2	yes	—
386	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
387	C₄	—	2	8	no	—
388	C₄	—	2	2	no	—
389	C₄	—	12	2	no	—
390	C₄	—	12	2	no	—
391	C₄	C₅×#953	1	2	yes	—
392	C₄	C₂²×C₅×#67	1	2	yes	—
393	C₃	C₂×C₅×#451	1	1	yes	characteristic, complemented, Sylow
394	C₂	—	2	4	no	—
395	C₂	C₅×#5228	1	4	yes	direct product factor
396	C₂	C₂×C₅×#942	1	1	yes	characteristic
397	C₂	C₂²×C₅×#216	1	1	yes	characteristic
398	C₂	C₂×C₅×#953	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂³×C₃×C₅×Q₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂⁴×C₃×C₅	D₄
hypercenter	C₂³×C₅×Q₈	D₃
hypocenter	C₃	C₂×C₅×#451
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×#216	C₂	semidirect
4. C₅×#5228	C₂	direct (N × H)
5. C₂×C₅×#835	C₂	semidirect
18. C₂×C₅×#216	C₂²	semidirect
24. C₅×#835	C₂²	semidirect
26. C₂×#5228	C₅	direct (N × H)
63. C₂²×#216	C₂×C₅	semidirect
65. #5228	C₂×C₅	direct (N × H)
66. C₂×#835	C₂×C₅	semidirect
89. C₂³×C₃×C₅	Q₁₆	semidirect
123. C₂×#216	C₂²×C₅	semidirect
129. #835	C₂²×C₅	semidirect
171. C₂²×C₃×C₅	C₂×Q₁₆	semidirect
211. C₂³×C₅	#216	semidirect
254. C₂×C₃×C₅	#451	semidirect
260. C₂³×C₃	C₅×Q₁₆	semidirect
289. C₂²×C₅	C₂×#216	semidirect
327. C₃×C₅	C₂×#451	semidirect
333. C₂²×C₃	C₂×C₅×Q₁₆	semidirect
343. C₂×C₅	#5228	direct (N × H)
349. C₂³	C₅×#216	semidirect
374. C₂×C₃	C₅×#451	semidirect
378. C₅	C₂×#5228	direct (N × H)
384. C₂²	C₂×C₅×#216	semidirect
393. C₃	C₂×C₅×#451	semidirect
395. C₂	C₅×#5228	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×C₃×C₅×Q₈	2
C₂²×C₅×#216	2
C₂×C₅×#924	2
C₅×#5228	2
C₂×C₅×#835	2
C₂×C₅×#830	2
C₂×C₅×#451	3
C₂×#5228	5

Subgroups — C2×C5×#5228 #14423352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5228 #14423352