Subgroups — C₄×C₅×#834 #14295363

Order 1920.

824 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	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#834	C₂	1	2	yes	maximal
3	C₄×C₅×#217	C₂	1	2	yes	maximal, complemented
4	C₅×#4526	C₂	1	2	yes	maximal, complemented
5	C₄×C₅×#99	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
7	C₂³×C₃×C₄×C₅	C₄	1	1	yes	characteristic, complemented
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₃×C₄×C₅×D₄	—	2	2	no	—
10	C₃×C₄×C₅×D₄	—	2	2	no	—
11	C₂×C₃×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic, complemented
12	C₂×C₃×C₅×C₂²⋊C₄	C₄	1	1	yes	characteristic, complemented
13	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₄	1	1	yes	characteristic, complemented
15	C₂×C₅×#217	C₂²	1	4	yes	—
16	C₂×C₄×C₅×Dic₃	—	2	2	no	—
17	C₅×#834	C₄	1	8	yes	direct product factor
18	C₅×C₃⋊#95	—	2	2	no	—
19	C₄×#834	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic
21	C₂×C₅×#99	—	3	2	no	—
22	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
23	C₅×#342	—	3	2	no	—
24	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
25	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
26	C₂×C₃×C₅×D₄	—	2	2	no	—
27	C₂×C₃×C₅×D₄	—	2	2	no	—
28	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
29	C₂²×C₃×C₄×C₅	—	2	1	no	—
30	C₂²×C₃×C₄×C₅	—	2	1	no	—
31	C₂²×C₃×C₄×C₅	—	4	2	no	—
32	C₂²×C₃×C₄×C₅	—	4	2	no	—
33	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
40	C₂²×C₅×Dic₃	—	2	4	no	—
41	C₃×C₅×C₄⋊C₄	—	2	2	no	—
42	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
43	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
44	C₃×C₄²×C₅	—	2	1	no	—
45	C₃×C₄²×C₅	—	2	1	no	—
46	C₅×#217	—	2	4	no	—
47	C₅×#217	C₂×C₄	1	8	yes	complemented
48	C₄×C₅×Dic₃	—	4	4	no	—
49	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
50	C₂×#834	C₂×C₅	1	2	yes	—
51	C₄×#217	C₂×C₅	1	2	yes	complemented
52	#4526	C₂×C₅	1	2	yes	complemented
53	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
54	C₂³×C₄×C₅	Dic₃	1	1	yes	characteristic, complemented
55	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
56	C₄×C₅×D₄	—	2	2	no	—
57	C₄×C₅×D₄	—	2	2	no	—
58	C₂×C₅×C₄⋊C₄	Dic₃	1	1	yes	characteristic, complemented
59	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
60	C₂×C₅×C₂²⋊C₄	Dic₃	1	1	yes	characteristic, complemented
61	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
62	C₂×C₄²×C₅	—	6	2	no	—
63	C₂×C₄²×C₅	Dic₃	1	1	yes	characteristic, complemented
64	C₅×#99	—	3	8	no	—
65	C₅×#95	—	6	2	no	—
66	C₄×#99	—	3	1	no	Sylow
67	C₂³×C₃×C₅	—	2	1	no	—
68	C₂³×C₃×C₅	—	2	1	no	—
69	C₂³×C₃×C₅	—	4	1	no	—
70	C₂³×C₃×C₅	—	4	1	no	—
71	C₂³×C₃×C₅	—	4	1	no	—
72	C₂³×C₃×C₅	—	4	1	no	—
73	C₂³×C₃×C₅	C₄²	1	2	yes	complemented
74	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
75	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
76	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
77	C₂³×C₃×C₅	#41	1	2	yes	—
78	C₃×C₅×D₄	—	2	8	no	—
79	C₂×C₃×C₄×C₅	—	2	1	no	—
80	C₂×C₃×C₄×C₅	—	2	1	no	—
81	C₂×C₃×C₄×C₅	—	2	4	no	—
82	C₂×C₃×C₄×C₅	—	2	2	no	—
83	C₂×C₃×C₄×C₅	—	2	1	no	—
84	C₂×C₃×C₄×C₅	—	2	1	no	—
85	C₂×C₃×C₄×C₅	—	4	1	no	—
86	C₂×C₃×C₄×C₅	—	4	2	no	—
87	C₂×C₃×C₄×C₅	—	4	2	no	—
88	C₂×C₃×C₄×C₅	—	4	2	no	—
89	C₂×C₃×C₄×C₅	—	4	1	no	—
90	C₂×C₃×C₄×C₅	—	4	1	no	—
91	C₂×C₃×C₄×C₅	C₄²	1	2	yes	complemented
92	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₅×Dic₃	—	2	8	no	—
96	C₂×C₅×Dic₃	—	4	4	no	—
97	C₂×C₅×Dic₃	—	4	4	no	—
98	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
99	C₂³×C₃×C₄	C₄×C₅	1	1	yes	characteristic, complemented
100	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
101	C₃×C₄×D₄	—	2	2	no	—
102	C₃×C₄×D₄	—	2	2	no	—
103	C₂×C₃×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic, complemented
104	C₂×C₃×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic, complemented
105	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
106	C₂×C₃×C₄²	C₄×C₅	1	1	yes	characteristic, complemented
107	C₂×#217	C₂²×C₅	1	4	yes	—
108	C₂×C₄×Dic₃	—	2	2	no	—
109	#834	C₄×C₅	1	8	yes	direct product factor
110	C₃⋊#95	—	2	2	no	—
111	C₂⁴×C₅	C₂×Dic₃	1	1	yes	characteristic
112	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
113	C₂×C₅×D₄	—	2	2	no	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	C₄×D₃	1	4	yes	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	1	no	—
118	C₂²×C₄×C₅	—	4	2	no	—
119	C₂²×C₄×C₅	—	4	2	no	—
120	C₂²×C₄×C₅	—	6	4	no	—
121	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
126	C₂²×C₄×C₅	#67	1	2	yes	—
127	C₂²×C₄×C₅	#67	1	2	yes	—
128	C₅×C₄⋊C₄	—	2	2	no	—
129	C₅×C₂²⋊C₄	—	2	2	no	—
130	C₅×C₂²⋊C₄	—	2	2	no	—
131	C₅×C₂²⋊C₄	—	3	8	no	—
132	C₅×C₂²⋊C₄	—	6	4	no	—
133	C₄²×C₅	—	2	1	no	—
134	C₄²×C₅	—	2	1	no	—
135	C₄²×C₅	—	12	4	no	—
136	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic
137	C₂×#99	—	3	2	no	—
138	C₄×C₂²⋊C₄	—	3	2	no	—
139	#342	—	3	2	no	—
140	C₂²×C₃×C₅	—	2	2	no	—
141	C₂²×C₃×C₅	—	2	1	no	—
142	C₂²×C₃×C₅	—	2	2	no	—
143	C₂²×C₃×C₅	—	2	1	no	—
144	C₂²×C₃×C₅	—	2	2	no	—
145	C₂²×C₃×C₅	—	4	2	no	—
146	C₂²×C₃×C₅	—	4	2	no	—
147	C₂²×C₃×C₅	—	4	2	no	—
148	C₂²×C₃×C₅	—	4	2	no	—
149	C₂²×C₃×C₅	—	4	1	no	—
150	C₂²×C₃×C₅	—	4	1	no	—
151	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
152	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₃×C₅	#117	1	1	yes	characteristic
154	C₂²×C₃×C₅	C₄×D₄	1	4	yes	—
155	C₃×C₄×C₅	—	2	2	no	—
156	C₃×C₄×C₅	—	2	1	no	—
157	C₃×C₄×C₅	—	2	2	no	—
158	C₃×C₄×C₅	—	4	1	no	—
159	C₃×C₄×C₅	—	4	1	no	—
160	C₃×C₄×C₅	#99	1	2	yes	complemented
161	C₅×Dic₃	—	4	8	no	—
162	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
163	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
164	C₂×C₃×D₄	—	2	2	no	—
165	C₂×C₃×D₄	—	2	2	no	—
166	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
167	C₂²×C₃×C₄	—	2	1	no	—
168	C₂²×C₃×C₄	—	2	1	no	—
169	C₂²×C₃×C₄	—	4	2	no	—
170	C₂²×C₃×C₄	—	4	2	no	—
171	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
177	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
178	C₂²×Dic₃	—	2	4	no	—
179	C₃×C₄⋊C₄	—	2	2	no	—
180	C₃×C₂²⋊C₄	—	2	2	no	—
181	C₃×C₂²⋊C₄	—	2	2	no	—
182	C₃×C₄²	—	2	1	no	—
183	C₃×C₄²	—	2	1	no	—
184	#217	—	2	4	no	—
185	#217	C₂×C₄×C₅	1	8	yes	complemented
186	C₄×Dic₃	—	4	4	no	—
187	C₂³×C₅	—	2	1	no	—
188	C₂³×C₅	—	2	1	no	—
189	C₂³×C₅	—	4	1	no	—
190	C₂³×C₅	—	4	1	no	—
191	C₂³×C₅	—	4	1	no	—
192	C₂³×C₅	—	4	1	no	—
193	C₂³×C₅	C₄×Dic₃	1	2	yes	complemented
194	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
195	C₂³×C₅	#235	1	2	yes	—
196	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
197	C₂³×C₅	C₂×#67	1	2	yes	—
198	C₅×D₄	—	2	8	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	4	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	1	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	4	1	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	4	2	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	—	4	1	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	6	8	no	—
212	C₂×C₄×C₅	—	12	4	no	—
213	C₂×C₄×C₅	—	12	4	no	—
214	C₂×C₄×C₅	C₄×Dic₃	1	2	yes	complemented
215	C₂×C₄×C₅	#217	1	1	yes	characteristic
216	C₂×C₄×C₅	#217	1	2	yes	—
217	C₂×C₄×C₅	#217	1	1	yes	characteristic
218	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
219	C₂³×C₄	C₅×Dic₃	1	1	yes	characteristic, complemented
220	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
221	C₄×D₄	—	2	2	no	—
222	C₄×D₄	—	2	2	no	—
223	C₂×C₄⋊C₄	C₅×Dic₃	1	1	yes	characteristic, complemented
224	C₂×C₂²⋊C₄	—	3	4	no	—
225	C₂×C₂²⋊C₄	C₅×Dic₃	1	1	yes	characteristic, complemented
226	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
227	C₂×C₄²	—	6	2	no	—
228	C₂×C₄²	C₅×Dic₃	1	1	yes	characteristic, complemented
229	#99	—	3	8	no	—
230	#95	—	6	2	no	—
231	C₂×C₃×C₅	—	2	4	no	—
232	C₂×C₃×C₅	—	2	1	no	—
233	C₂×C₃×C₅	—	2	1	no	—
234	C₂×C₃×C₅	—	4	2	no	—
235	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₃×C₅	C₂×#99	1	1	yes	characteristic
237	C₂×C₃×C₅	#410	1	1	yes	characteristic
238	C₂³×C₃	—	2	1	no	—
239	C₂³×C₃	—	2	1	no	—
240	C₂³×C₃	—	4	1	no	—
241	C₂³×C₃	—	4	1	no	—
242	C₂³×C₃	—	4	1	no	—
243	C₂³×C₃	—	4	1	no	—
244	C₂³×C₃	C₄²×C₅	1	2	yes	complemented
245	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
246	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
247	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
248	C₂³×C₃	C₅×#41	1	2	yes	—
249	C₃×D₄	—	2	8	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	4	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	4	1	no	—
257	C₂×C₃×C₄	—	4	2	no	—
258	C₂×C₃×C₄	—	4	2	no	—
259	C₂×C₃×C₄	—	4	2	no	—
260	C₂×C₃×C₄	—	4	1	no	—
261	C₂×C₃×C₄	—	4	1	no	—
262	C₂×C₃×C₄	C₄²×C₅	1	2	yes	complemented
263	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
265	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×Dic₃	—	2	8	no	—
267	C₂×Dic₃	—	4	4	no	—
268	C₂×Dic₃	—	4	4	no	—
269	C₂²×C₅	—	2	1	no	—
270	C₂²×C₅	—	2	2	no	—
271	C₂²×C₅	—	2	1	no	—
272	C₂²×C₅	—	2	2	no	—
273	C₂²×C₅	—	2	2	no	—
274	C₂²×C₅	—	4	2	no	—
275	C₂²×C₅	—	4	2	no	—
276	C₂²×C₅	—	4	2	no	—
277	C₂²×C₅	—	4	2	no	—
278	C₂²×C₅	—	4	1	no	—
279	C₂²×C₅	—	4	1	no	—
280	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
281	C₂²×C₅	#926	1	1	yes	characteristic
282	C₂²×C₅	C₄×#67	1	4	yes	—
283	C₂²×C₅	C₂×#217	1	1	yes	characteristic
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	—	2	1	no	—
286	C₄×C₅	—	2	2	no	—
287	C₄×C₅	—	4	1	no	—
288	C₄×C₅	—	4	1	no	—
289	C₄×C₅	—	12	8	no	—
290	C₄×C₅	#834	1	2	yes	direct product factor
291	C₂⁴	C₂×C₅×Dic₃	1	1	yes	characteristic
292	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	C₄×C₅×D₃	1	4	yes	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	6	4	no	—
301	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
306	C₂²×C₄	C₅×#67	1	2	yes	—
307	C₂²×C₄	C₅×#67	1	2	yes	—
308	C₄⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	—	3	8	no	—
312	C₂²⋊C₄	—	6	4	no	—
313	C₄²	—	2	1	no	—
314	C₄²	—	2	1	no	—
315	C₄²	—	12	4	no	—
316	C₃×C₅	C₄×#99	1	1	yes	characteristic, complemented, Hall
317	C₂²×C₃	—	2	2	no	—
318	C₂²×C₃	—	2	1	no	—
319	C₂²×C₃	—	2	2	no	—
320	C₂²×C₃	—	2	1	no	—
321	C₂²×C₃	—	2	2	no	—
322	C₂²×C₃	—	4	2	no	—
323	C₂²×C₃	—	4	2	no	—
324	C₂²×C₃	—	4	2	no	—
325	C₂²×C₃	—	4	2	no	—
326	C₂²×C₃	—	4	1	no	—
327	C₂²×C₃	—	4	1	no	—
328	C₂²×C₃	C₂×C₄²×C₅	1	1	yes	characteristic
329	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
330	C₂²×C₃	C₅×#117	1	1	yes	characteristic
331	C₂²×C₃	C₄×C₅×D₄	1	4	yes	—
332	C₃×C₄	—	2	2	no	—
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	2	2	no	—
335	C₃×C₄	—	4	1	no	—
336	C₃×C₄	—	4	1	no	—
337	C₃×C₄	C₅×#99	1	2	yes	complemented
338	Dic₃	—	4	8	no	—
339	C₂×C₅	—	2	4	no	—
340	C₂×C₅	—	2	1	no	—
341	C₂×C₅	—	2	1	no	—
342	C₂×C₅	—	4	2	no	—
343	C₂×C₅	C₄×#217	1	1	yes	characteristic
344	C₂×C₅	C₂×#834	1	1	yes	characteristic
345	C₂×C₅	#5240	1	1	yes	characteristic
346	C₂³	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	4	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	1	no	—
352	C₂³	C₄×C₅×Dic₃	1	2	yes	complemented
353	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
354	C₂³	C₅×#235	1	2	yes	—
355	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
356	C₂³	C₂×C₅×#67	1	2	yes	—
357	D₄	—	2	8	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	6	8	no	—
371	C₂×C₄	—	12	4	no	—
372	C₂×C₄	—	12	4	no	—
373	C₂×C₄	C₄×C₅×Dic₃	1	2	yes	complemented
374	C₂×C₄	C₅×#217	1	1	yes	characteristic
375	C₂×C₄	C₅×#217	1	2	yes	—
376	C₂×C₄	C₅×#217	1	1	yes	characteristic
377	C₂×C₃	—	2	4	no	—
378	C₂×C₃	—	2	1	no	—
379	C₂×C₃	—	2	1	no	—
380	C₂×C₃	—	4	2	no	—
381	C₂×C₃	C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
382	C₂×C₃	C₂×C₅×#99	1	1	yes	characteristic
383	C₂×C₃	C₅×#410	1	1	yes	characteristic
384	C₅	C₄×#834	1	1	yes	characteristic, direct product factor, Sylow
385	C₂²	—	2	1	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	C₂×C₄×C₅×Dic₃	1	1	yes	characteristic
397	C₂²	C₅×#926	1	1	yes	characteristic
398	C₂²	C₄×C₅×#67	1	4	yes	—
399	C₂²	C₂×C₅×#217	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	2	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	12	8	no	—
406	C₄	C₅×#834	1	2	yes	direct product factor
407	C₃	C₄×C₅×#99	1	1	yes	characteristic, complemented, Sylow
408	C₂	—	2	4	no	—
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	4	2	no	—
412	C₂	C₄×C₅×#217	1	1	yes	characteristic
413	C₂	C₂×C₅×#834	1	1	yes	characteristic
414	C₂	C₅×#5240	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#217
commutator	C₂²×C₃	C₂×C₄²×C₅
Frattini	C₂⁴	C₂²×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
cosocle	C₂⁴×C₃	C₂³×C₅
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₄×C₅×#99
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ C₂×C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
3. C₄×C₅×#217	C₂	semidirect
4. C₅×#4526	C₂	semidirect
7. C₂³×C₃×C₄×C₅	C₄	semidirect
11. C₂×C₃×C₅×C₄⋊C₄	C₄	semidirect
12. C₂×C₃×C₅×C₂²⋊C₄	C₄	semidirect
14. C₂×C₃×C₄²×C₅	C₄	semidirect
17. C₅×#834	C₄	direct (N × H)
19. C₄×#834	C₅	direct (N × H)
47. C₅×#217	C₂×C₄	semidirect
51. C₄×#217	C₂×C₅	semidirect
52. #4526	C₂×C₅	semidirect
54. C₂³×C₄×C₅	Dic₃	semidirect
58. C₂×C₅×C₄⋊C₄	Dic₃	semidirect
60. C₂×C₅×C₂²⋊C₄	Dic₃	semidirect
63. C₂×C₄²×C₅	Dic₃	semidirect
73. C₂³×C₃×C₅	C₄²	semidirect
91. C₂×C₃×C₄×C₅	C₄²	semidirect
99. C₂³×C₃×C₄	C₄×C₅	semidirect
103. C₂×C₃×C₄⋊C₄	C₄×C₅	semidirect
104. C₂×C₃×C₂²⋊C₄	C₄×C₅	semidirect
106. C₂×C₃×C₄²	C₄×C₅	semidirect
109. #834	C₄×C₅	direct (N × H)
160. C₃×C₄×C₅	#99	semidirect
185. #217	C₂×C₄×C₅	semidirect
193. C₂³×C₅	C₄×Dic₃	semidirect
214. C₂×C₄×C₅	C₄×Dic₃	semidirect
219. C₂³×C₄	C₅×Dic₃	semidirect
223. C₂×C₄⋊C₄	C₅×Dic₃	semidirect
225. C₂×C₂²⋊C₄	C₅×Dic₃	semidirect
228. C₂×C₄²	C₅×Dic₃	semidirect
244. C₂³×C₃	C₄²×C₅	semidirect
262. C₂×C₃×C₄	C₄²×C₅	semidirect
290. C₄×C₅	#834	direct (N × H)
316. C₃×C₅	C₄×#99	semidirect
337. C₃×C₄	C₅×#99	semidirect
352. C₂³	C₄×C₅×Dic₃	semidirect
373. C₂×C₄	C₄×C₅×Dic₃	semidirect
384. C₅	C₄×#834	direct (N × H)
406. C₄	C₅×#834	direct (N × H)
407. C₃	C₄×C₅×#99	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₅×D₄	2
C₂×C₅×#834	2
C₄×C₅×#217	2
C₅×#4526	2
C₄×C₅×#99	3
C₄×#834	5

Subgroups — C4×C5×#834 #14295363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#834 #14295363