Subgroups — C₅×#82269 #14322428

Order 1920.

2208 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×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4988	C₂	1	4	yes	maximal, complemented
5	C₅×#4955	C₂	1	4	yes	maximal, complemented
6	C₅×#4939	C₂	1	4	yes	maximal, complemented
7	C₅×#2309	—	3	1	no	maximal, Hall
8	C₂⁴×C₅×D₃	C₂²	1	2	yes	—
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂²×C₅×D₁₂	—	2	4	no	—
11	C₂²×C₅×D₁₂	—	2	4	no	—
12	C₂²×C₅×D₁₂	C₄	1	8	yes	complemented
13	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
14	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
15	C₃×C₅×#117	—	2	4	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
19	C₂×C₅×#217	C₂²	1	2	yes	—
20	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	16	yes	complemented
21	C₅×#926	—	2	4	no	—
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
23	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
24	#82269	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂³×C₅×D₄	—	3	1	no	—
26	C₂×C₅×#117	—	3	1	no	—
27	C₂×C₅×#117	D₃	1	1	yes	characteristic, complemented
28	C₅×#390	—	3	4	no	—
29	C₅×#390	—	3	4	no	—
30	C₅×#379	—	3	4	no	—
31	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
32	C₂³×C₅×D₃	—	2	4	no	—
33	C₂³×C₅×D₃	—	2	4	no	—
34	C₂³×C₅×D₃	—	4	8	no	—
35	C₂³×C₅×D₃	C₂×C₄	1	8	yes	—
36	C₂³×C₅×D₃	C₂³	1	4	yes	—
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
38	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
39	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
44	C₂×C₅×D₁₂	—	2	32	no	—
45	C₂×C₅×D₁₂	—	2	4	no	—
46	C₂×C₅×D₁₂	—	2	4	no	—
47	C₂×C₅×D₁₂	—	2	4	no	—
48	C₂×C₅×D₁₂	—	2	4	no	—
49	C₂×C₅×D₁₂	C₂×C₄	1	8	yes	—
50	C₂×C₅×D₁₂	C₂×C₄	1	8	yes	—
51	C₃×C₅×C₄⋊C₄	—	2	4	no	—
52	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
53	C₃×C₄²×C₅	—	2	4	no	—
54	C₅×#217	—	2	4	no	—
55	C₅×(C₂×D₃)⋊C₄	—	4	16	no	—
56	C₅×C₄⋊Dic₃	—	2	4	no	—
57	C₄×C₅×Dic₃	—	2	4	no	—
58	C₂³×D₁₂	C₂×C₅	1	1	yes	characteristic
59	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
60	C₂×#926	C₂×C₅	1	1	yes	characteristic, complemented
61	#4988	C₂×C₅	1	4	yes	complemented
62	#4955	C₂×C₅	1	4	yes	complemented
63	#4939	C₂×C₅	1	4	yes	complemented
64	C₂⁵×C₅	—	3	2	no	—
65	C₂²×C₅×D₄	—	3	8	no	—
66	C₂²×C₅×D₄	—	3	2	no	—
67	C₂²×C₅×D₄	—	3	2	no	—
68	C₂²×C₅×D₄	—	6	4	no	—
69	C₂²×C₅×D₄	—	6	4	no	—
70	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
71	C₅×#117	—	2	4	no	—
72	C₅×#117	—	6	4	no	—
73	C₂×C₅×C₄⋊C₄	—	3	2	no	—
74	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
75	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
76	C₂×C₅×C₂²⋊C₄	—	3	16	no	—
77	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
78	C₂×C₄²×C₅	—	3	2	no	—
79	C₂×C₄²×C₅	C₂×D₃	1	2	yes	complemented
80	#2309	—	3	1	no	Sylow
81	C₂³×C₃×C₅	—	2	4	no	—
82	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
83	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
84	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
85	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
86	C₂²×C₅×D₃	—	2	16	no	—
87	C₂²×C₅×D₃	—	2	4	no	—
88	C₂²×C₅×D₃	—	2	4	no	—
89	C₂²×C₅×D₃	—	2	16	no	—
90	C₂²×C₅×D₃	—	4	16	no	—
91	C₂²×C₅×D₃	—	4	16	no	—
92	C₂²×C₅×D₃	—	4	16	no	—
93	C₂²×C₅×D₃	C₂²×C₄	1	8	yes	—
94	C₂×C₃×C₄×C₅	—	2	4	no	—
95	C₂×C₃×C₄×C₅	—	2	8	no	—
96	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	16	yes	complemented
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
103	C₂×C₅×Dic₃	—	2	4	no	—
104	C₂×C₅×Dic₃	—	2	8	no	—
105	C₅×D₁₂	—	2	16	no	—
106	C₅×D₁₂	—	2	16	no	—
107	C₂⁴×D₃	C₂²×C₅	1	2	yes	—
108	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
109	C₂²×D₁₂	—	2	4	no	—
110	C₂²×D₁₂	—	2	4	no	—
111	C₂²×D₁₂	C₄×C₅	1	8	yes	complemented
112	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
113	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
114	C₃×#117	—	2	4	no	—
115	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
116	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
117	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	complemented
118	C₂×#217	C₂²×C₅	1	2	yes	—
119	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	16	yes	complemented
120	#926	—	2	4	no	—
121	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
122	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
123	C₂⁴×C₅	—	3	4	no	—
124	C₂⁴×C₅	—	3	8	no	—
125	C₂⁴×C₅	—	6	4	no	—
126	C₂⁴×C₅	—	6	4	no	—
127	C₂⁴×C₅	—	12	8	no	—
128	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
129	C₂×C₅×D₄	—	3	8	no	—
130	C₂×C₅×D₄	—	3	8	no	—
131	C₂×C₅×D₄	—	6	32	no	—
132	C₂×C₅×D₄	—	6	4	no	—
133	C₂×C₅×D₄	—	6	4	no	—
134	C₂×C₅×D₄	—	6	4	no	—
135	C₂×C₅×D₄	—	6	4	no	—
136	C₂²×C₄×C₅	—	3	4	no	—
137	C₂²×C₄×C₅	C₄×D₃	1	4	yes	—
138	C₂²×C₄×C₅	D₁₂	1	4	yes	—
139	C₂²×C₄×C₅	#67	1	4	yes	—
140	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
141	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
143	C₅×C₄⋊C₄	—	2	4	no	—
144	C₅×C₄⋊C₄	—	6	4	no	—
145	C₅×C₂²⋊C₄	—	2	4	no	—
146	C₅×C₂²⋊C₄	—	6	4	no	—
147	C₅×C₂²⋊C₄	—	12	16	no	—
148	C₄²×C₅	—	2	4	no	—
149	C₄²×C₅	—	6	4	no	—
150	C₂³×D₄	—	3	1	no	—
151	C₂×#117	—	3	1	no	—
152	C₂×#117	C₅×D₃	1	1	yes	characteristic, complemented
153	#390	—	3	4	no	—
154	#390	—	3	4	no	—
155	#379	—	3	4	no	—
156	C₂²×C₃×C₅	—	2	4	no	—
157	C₂²×C₃×C₅	—	2	4	no	—
158	C₂²×C₃×C₅	—	2	4	no	—
159	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
160	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
161	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
162	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
163	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
164	C₂×C₅×D₃	—	2	8	no	—
165	C₂×C₅×D₃	—	2	16	no	—
166	C₂×C₅×D₃	—	4	32	no	—
167	C₂×C₅×D₃	—	4	8	no	—
168	C₂×C₅×D₃	—	4	8	no	—
169	C₃×C₄×C₅	—	4	4	no	—
170	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
171	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
172	C₅×Dic₃	—	4	4	no	—
173	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
174	C₂³×D₃	—	2	4	no	—
175	C₂³×D₃	—	2	4	no	—
176	C₂³×D₃	—	4	8	no	—
177	C₂³×D₃	C₂×C₄×C₅	1	8	yes	—
178	C₂³×D₃	C₂³×C₅	1	4	yes	—
179	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
180	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
181	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
182	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
183	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
185	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
186	C₂×D₁₂	—	2	32	no	—
187	C₂×D₁₂	—	2	4	no	—
188	C₂×D₁₂	—	2	4	no	—
189	C₂×D₁₂	—	2	4	no	—
190	C₂×D₁₂	—	2	4	no	—
191	C₂×D₁₂	C₂×C₄×C₅	1	8	yes	—
192	C₂×D₁₂	C₂×C₄×C₅	1	8	yes	—
193	C₃×C₄⋊C₄	—	2	4	no	—
194	C₃×C₂²⋊C₄	—	2	4	no	—
195	C₃×C₄²	—	2	4	no	—
196	#217	—	2	4	no	—
197	(C₂×D₃)⋊C₄	—	4	16	no	—
198	C₄⋊Dic₃	—	2	4	no	—
199	C₄×Dic₃	—	2	4	no	—
200	C₂³×C₅	—	2	4	no	—
201	C₂³×C₅	—	3	8	no	—
202	C₂³×C₅	—	6	16	no	—
203	C₂³×C₅	—	6	4	no	—
204	C₂³×C₅	—	6	16	no	—
205	C₂³×C₅	—	6	4	no	—
206	C₂³×C₅	—	12	16	no	—
207	C₂³×C₅	—	12	16	no	—
208	C₂³×C₅	—	12	16	no	—
209	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
210	C₂³×C₅	C₂×D₁₂	1	2	yes	—
211	C₂³×C₅	C₂×#67	1	2	yes	—
212	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
213	C₅×D₄	—	6	16	no	—
214	C₅×D₄	—	6	16	no	—
215	C₂×C₄×C₅	—	2	8	no	—
216	C₂×C₄×C₅	—	2	4	no	—
217	C₂×C₄×C₅	—	6	4	no	—
218	C₂×C₄×C₅	—	6	8	no	—
219	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	16	yes	complemented
220	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
221	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
222	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
223	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
224	C₂×C₄×C₅	C₂×#67	1	2	yes	—
225	C₂×C₄×C₅	C₂×#67	1	2	yes	—
226	C₂⁵	—	3	2	no	—
227	C₂²×D₄	—	3	8	no	—
228	C₂²×D₄	—	3	2	no	—
229	C₂²×D₄	—	3	2	no	—
230	C₂²×D₄	—	6	4	no	—
231	C₂²×D₄	—	6	4	no	—
232	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
233	#117	—	2	4	no	—
234	#117	—	6	4	no	—
235	C₂×C₄⋊C₄	—	3	2	no	—
236	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
237	C₂×C₂²⋊C₄	—	3	2	no	—
238	C₂×C₂²⋊C₄	—	3	16	no	—
239	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
240	C₂×C₄²	—	3	2	no	—
241	C₂×C₄²	C₂×C₅×D₃	1	2	yes	complemented
242	C₂×C₃×C₅	—	2	4	no	—
243	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₃×C₅	#518	1	2	yes	—
245	C₂×C₃×C₅	#535	1	2	yes	—
246	C₂×C₃×C₅	#535	1	2	yes	—
247	C₅×D₃	—	4	8	no	—
248	C₂³×C₃	—	2	4	no	—
249	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
250	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
251	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
252	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
253	C₂²×D₃	—	2	16	no	—
254	C₂²×D₃	—	2	4	no	—
255	C₂²×D₃	—	2	4	no	—
256	C₂²×D₃	—	2	16	no	—
257	C₂²×D₃	—	4	16	no	—
258	C₂²×D₃	—	4	16	no	—
259	C₂²×D₃	—	4	16	no	—
260	C₂²×D₃	C₂²×C₄×C₅	1	8	yes	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	2	8	no	—
263	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	16	yes	complemented
264	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
265	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
266	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
267	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
268	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
269	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
270	C₂×Dic₃	—	2	4	no	—
271	C₂×Dic₃	—	2	8	no	—
272	D₁₂	—	2	16	no	—
273	D₁₂	—	2	16	no	—
274	C₂²×C₅	—	2	4	no	—
275	C₂²×C₅	—	2	4	no	—
276	C₂²×C₅	—	2	4	no	—
277	C₂²×C₅	—	6	16	no	—
278	C₂²×C₅	—	6	8	no	—
279	C₂²×C₅	—	12	32	no	—
280	C₂²×C₅	—	12	8	no	—
281	C₂²×C₅	—	12	8	no	—
282	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
283	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
284	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
285	C₂²×C₅	#1009	1	4	yes	—
286	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
287	C₄×C₅	—	4	4	no	—
288	C₄×C₅	—	12	4	no	—
289	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
290	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
291	C₂⁴	—	3	4	no	—
292	C₂⁴	—	3	8	no	—
293	C₂⁴	—	6	4	no	—
294	C₂⁴	—	6	4	no	—
295	C₂⁴	—	12	8	no	—
296	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
297	C₂×D₄	—	3	8	no	—
298	C₂×D₄	—	3	8	no	—
299	C₂×D₄	—	6	32	no	—
300	C₂×D₄	—	6	4	no	—
301	C₂×D₄	—	6	4	no	—
302	C₂×D₄	—	6	4	no	—
303	C₂×D₄	—	6	4	no	—
304	C₂²×C₄	—	3	4	no	—
305	C₂²×C₄	C₄×C₅×D₃	1	4	yes	—
306	C₂²×C₄	C₅×D₁₂	1	4	yes	—
307	C₂²×C₄	C₅×#67	1	4	yes	—
308	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
309	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	6	4	no	—
313	C₂²⋊C₄	—	2	4	no	—
314	C₂²⋊C₄	—	6	4	no	—
315	C₂²⋊C₄	—	12	16	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	6	4	no	—
318	C₃×C₅	#2309	1	1	yes	characteristic, complemented, Hall
319	C₂²×C₃	—	2	4	no	—
320	C₂²×C₃	—	2	4	no	—
321	C₂²×C₃	—	2	4	no	—
322	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
323	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
324	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
325	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
326	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
327	C₂×D₃	—	2	8	no	—
328	C₂×D₃	—	2	16	no	—
329	C₂×D₃	—	4	32	no	—
330	C₂×D₃	—	4	8	no	—
331	C₂×D₃	—	4	8	no	—
332	C₃×C₄	—	4	4	no	—
333	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
334	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
335	Dic₃	—	4	4	no	—
336	C₂×C₅	—	2	4	no	—
337	C₂×C₅	—	12	8	no	—
338	C₂×C₅	#5521	1	2	yes	—
339	C₂×C₅	#5525	1	2	yes	—
340	C₂×C₅	C₂²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
341	C₂×C₅	#5830	1	2	yes	—
342	C₂³	—	2	4	no	—
343	C₂³	—	3	8	no	—
344	C₂³	—	6	16	no	—
345	C₂³	—	6	4	no	—
346	C₂³	—	6	16	no	—
347	C₂³	—	6	4	no	—
348	C₂³	—	12	16	no	—
349	C₂³	—	12	16	no	—
350	C₂³	—	12	16	no	—
351	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
352	C₂³	C₂×C₅×D₁₂	1	2	yes	—
353	C₂³	C₂×C₅×#67	1	2	yes	—
354	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
355	D₄	—	6	16	no	—
356	D₄	—	6	16	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	6	4	no	—
360	C₂×C₄	—	6	8	no	—
361	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	16	yes	complemented
362	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
363	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
364	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
365	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
366	C₂×C₄	C₂×C₅×#67	1	2	yes	—
367	C₂×C₄	C₂×C₅×#67	1	2	yes	—
368	C₂×C₃	—	2	4	no	—
369	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
370	C₂×C₃	C₅×#518	1	2	yes	—
371	C₂×C₃	C₅×#535	1	2	yes	—
372	C₂×C₃	C₅×#535	1	2	yes	—
373	D₃	—	4	8	no	—
374	C₅	#82269	1	1	yes	characteristic, direct product factor, Sylow
375	C₂²	—	2	4	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	2	4	no	—
378	C₂²	—	6	16	no	—
379	C₂²	—	6	8	no	—
380	C₂²	—	12	32	no	—
381	C₂²	—	12	8	no	—
382	C₂²	—	12	8	no	—
383	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	4	yes	—
384	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
385	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
386	C₂²	C₅×#1009	1	4	yes	—
387	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
388	C₄	—	4	4	no	—
389	C₄	—	12	4	no	—
390	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	4	yes	—
391	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	4	yes	—
392	C₃	C₅×#2309	1	1	yes	characteristic, complemented, Sylow
393	C₂	—	2	4	no	—
394	C₂	—	12	8	no	—
395	C₂	C₅×#5521	1	2	yes	—
396	C₂	C₅×#5525	1	2	yes	—
397	C₂	C₂²×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
398	C₂	C₅×#5830	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₅×D₁₂	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₂×C₅×#117	D₃
hypocenter	C₃	C₅×#2309
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#117	C₂	semidirect
3. C₂×C₅×#926	C₂	semidirect
4. C₅×#4988	C₂	semidirect
5. C₅×#4955	C₂	semidirect
6. C₅×#4939	C₂	semidirect
12. C₂²×C₅×D₁₂	C₄	semidirect
16. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
18. C₂×C₃×C₄²×C₅	C₂²	semidirect
20. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
22. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
23. C₂×C₄×C₅×Dic₃	C₂²	semidirect
24. #82269	C₅	direct (N × H)
27. C₂×C₅×#117	D₃	semidirect
59. C₂×C₃×#117	C₂×C₅	semidirect
60. C₂×#926	C₂×C₅	semidirect
61. #4988	C₂×C₅	semidirect
62. #4955	C₂×C₅	semidirect
63. #4939	C₂×C₅	semidirect
74. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
79. C₂×C₄²×C₅	C₂×D₃	semidirect
96. C₂×C₃×C₄×C₅	C₂²⋊C₄	semidirect
111. C₂²×D₁₂	C₄×C₅	semidirect
115. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
117. C₂×C₃×C₄²	C₂²×C₅	semidirect
119. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
121. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
122. C₂×C₄×Dic₃	C₂²×C₅	semidirect
152. C₂×#117	C₅×D₃	semidirect
219. C₂×C₄×C₅	(C₂×D₃)⋊C₄	semidirect
236. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
241. C₂×C₄²	C₂×C₅×D₃	semidirect
263. C₂×C₃×C₄	C₅×C₂²⋊C₄	semidirect
318. C₃×C₅	#2309	semidirect
361. C₂×C₄	C₅×(C₂×D₃)⋊C₄	semidirect
374. C₅	#82269	direct (N × H)
392. C₃	C₅×#2309	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₅×D₁₂	2
C₂×C₃×C₅×#117	2
C₂×C₅×#926	2
C₅×#4988	2
C₅×#4955	2
C₅×#4939	2
C₅×#2309	3
#82269	5

Subgroups — C5×#82269 #14322428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#82269 #14322428