Subgroups — C₅×#73669 #14332542

Order 1920.

1008 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×Dic₆	C₂	1	2	yes	maximal
2	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₅×#4982	C₂	1	2	yes	maximal
4	C₅×#4979	C₂	1	2	yes	maximal
5	C₄×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
6	C₅×#4932	C₂	1	1	yes	maximal, characteristic
7	C₄×C₅×Dic₃⋊C₄	C₂	1	2	yes	maximal
8	C₅×#4657	C₂	1	2	yes	maximal
9	C₅×#4656	C₂	1	2	yes	maximal
10	C₅×#2399	—	3	1	no	maximal, Hall
11	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
17	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
18	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
19	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
20	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
21	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
22	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
24	C₄×C₅×Dic₆	—	2	8	no	—
25	C₃×C₅×#95	C₂²	1	1	yes	characteristic
26	C₃×C₅×#95	C₂²	1	1	yes	characteristic
27	C₅×C₃⋊#95	C₂²	1	2	yes	—
28	C₅×C₃⋊#95	C₂²	1	2	yes	—
29	C₅×C₃⋊#95	C₂²	1	2	yes	—
30	C₅×C₃⋊#95	C₂²	1	2	yes	—
31	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
32	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
33	#73669	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₄×C₅×Q₈	—	3	2	no	—
35	C₅×#398	—	3	2	no	—
36	C₅×#398	—	3	2	no	—
37	C₅×#395	—	3	2	no	—
38	C₅×#395	—	3	2	no	—
39	C₄×C₅×C₄⋊C₄	—	3	2	no	—
40	C₄×C₅×C₄⋊C₄	—	3	1	no	—
41	C₄×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic
42	C₅×#376	—	3	1	no	—
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
49	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
50	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
51	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
52	C₂×C₅×Dic₆	—	2	4	no	—
53	C₂×C₅×Dic₆	—	2	4	no	—
54	C₂×C₅×Dic₆	—	2	4	no	—
55	C₃×C₅×C₄⋊C₄	—	2	4	no	—
56	C₃×C₄²×C₅	—	2	4	no	—
57	C₃×C₄²×C₅	Q₈	1	4	yes	complemented
58	C₅×C₄⋊Dic₃	—	2	4	no	—
59	C₅×C₄⋊Dic₃	—	2	4	no	—
60	C₅×Dic₃⋊C₄	—	2	4	no	—
61	C₅×Dic₃⋊C₄	—	2	4	no	—
62	C₅×Dic₃⋊C₄	—	2	4	no	—
63	C₅×Dic₃⋊C₄	—	2	4	no	—
64	C₄×C₅×Dic₃	—	2	4	no	—
65	C₄×C₅×Dic₃	D₄	1	4	yes	—
66	C₄×C₅×Dic₃	Q₈	1	4	yes	complemented
67	C₂×C₄×Dic₆	C₂×C₅	1	2	yes	—
68	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
69	#4982	C₂×C₅	1	2	yes	—
70	#4979	C₂×C₅	1	2	yes	—
71	C₄×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic
72	#4932	C₂×C₅	1	1	yes	characteristic
73	C₄×Dic₃⋊C₄	C₂×C₅	1	2	yes	—
74	#4657	C₂×C₅	1	2	yes	—
75	#4656	C₂×C₅	1	2	yes	—
76	C₂²×C₅×Q₈	—	3	2	no	—
77	C₄×C₅×Q₈	—	6	8	no	—
78	C₂×C₅×C₄⋊C₄	—	3	2	no	—
79	C₂×C₅×C₄⋊C₄	—	3	2	no	—
80	C₂×C₅×C₄⋊C₄	—	3	2	no	—
81	C₂×C₅×C₄⋊C₄	—	3	2	no	—
82	C₂×C₅×C₄⋊C₄	—	3	2	no	—
83	C₂×C₅×C₄⋊C₄	—	3	2	no	—
84	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
85	C₂×C₄²×C₅	—	3	1	no	—
86	C₂×C₄²×C₅	—	3	1	no	—
87	C₂×C₄²×C₅	—	3	2	no	—
88	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
89	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
90	C₅×#95	—	3	2	no	—
91	C₅×#95	—	3	2	no	—
92	C₅×#95	—	3	1	no	—
93	C₅×#95	—	3	2	no	—
94	C₅×#95	—	3	2	no	—
95	C₅×#95	—	3	1	no	—
96	C₅×#95	C₂×D₃	1	1	yes	characteristic
97	C₅×#95	C₂×D₃	1	1	yes	characteristic
98	#2399	—	3	1	no	Sylow
99	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
112	C₂×C₃×C₄×C₅	#41	1	4	yes	—
113	C₂×C₅×Dic₃	—	2	2	no	—
114	C₂×C₅×Dic₃	—	2	2	no	—
115	C₂×C₅×Dic₃	—	2	2	no	—
116	C₂×C₅×Dic₃	—	2	2	no	—
117	C₂×C₅×Dic₃	—	2	2	no	—
118	C₂×C₅×Dic₃	—	2	2	no	—
119	C₂×C₅×Dic₃	—	2	2	no	—
120	C₂×C₅×Dic₃	—	2	2	no	—
121	C₂×C₅×Dic₃	—	2	2	no	—
122	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
123	C₂×C₅×Dic₃	C₂×Q₈	1	4	yes	—
124	C₂×C₅×Dic₃	#41	1	4	yes	—
125	C₅×Dic₆	—	2	16	no	—
126	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
127	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
128	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
129	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
131	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
132	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
133	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
134	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
135	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
136	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
137	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
138	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
139	C₄×Dic₆	—	2	8	no	—
140	C₃×#95	C₂²×C₅	1	1	yes	characteristic
141	C₃×#95	C₂²×C₅	1	1	yes	characteristic
142	C₃⋊#95	C₂²×C₅	1	2	yes	—
143	C₃⋊#95	C₂²×C₅	1	2	yes	—
144	C₃⋊#95	C₂²×C₅	1	2	yes	—
145	C₃⋊#95	C₂²×C₅	1	2	yes	—
146	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
147	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
148	C₂×C₅×Q₈	—	6	4	no	—
149	C₂×C₅×Q₈	—	6	4	no	—
150	C₂×C₅×Q₈	—	6	4	no	—
151	C₂²×C₄×C₅	—	3	2	no	—
152	C₂²×C₄×C₅	—	3	2	no	—
153	C₂²×C₄×C₅	—	3	2	no	—
154	C₂²×C₄×C₅	—	3	2	no	—
155	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
156	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
159	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
160	C₅×C₄⋊C₄	—	2	4	no	—
161	C₅×C₄⋊C₄	—	6	4	no	—
162	C₅×C₄⋊C₄	—	6	4	no	—
163	C₅×C₄⋊C₄	—	6	4	no	—
164	C₅×C₄⋊C₄	—	6	4	no	—
165	C₅×C₄⋊C₄	—	6	4	no	—
166	C₅×C₄⋊C₄	—	6	4	no	—
167	C₄²×C₅	—	2	4	no	—
168	C₄²×C₅	—	3	4	no	—
169	C₄²×C₅	—	3	4	no	—
170	C₄²×C₅	—	6	4	no	—
171	C₄²×C₅	Dic₆	1	4	yes	complemented
172	C₂×C₄×Q₈	—	3	2	no	—
173	#398	—	3	2	no	—
174	#398	—	3	2	no	—
175	#395	—	3	2	no	—
176	#395	—	3	2	no	—
177	C₄×C₄⋊C₄	—	3	2	no	—
178	C₄×C₄⋊C₄	—	3	1	no	—
179	C₄×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic
180	#376	—	3	1	no	—
181	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
182	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
183	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
185	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
186	C₃×C₄×C₅	—	2	4	no	—
187	C₃×C₄×C₅	—	2	2	no	—
188	C₃×C₄×C₅	—	2	2	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	C₄⋊Q₈	1	4	yes	—
191	C₅×Dic₃	—	2	4	no	—
192	C₅×Dic₃	—	2	4	no	—
193	C₅×Dic₃	—	2	4	no	—
194	C₅×Dic₃	—	4	2	no	—
195	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
196	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
197	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
198	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
199	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
200	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
201	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
202	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
203	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
204	C₂×Dic₆	—	2	4	no	—
205	C₂×Dic₆	—	2	4	no	—
206	C₂×Dic₆	—	2	4	no	—
207	C₃×C₄⋊C₄	—	2	4	no	—
208	C₃×C₄²	—	2	4	no	—
209	C₃×C₄²	C₅×Q₈	1	4	yes	complemented
210	C₄⋊Dic₃	—	2	4	no	—
211	C₄⋊Dic₃	—	2	4	no	—
212	Dic₃⋊C₄	—	2	4	no	—
213	Dic₃⋊C₄	—	2	4	no	—
214	Dic₃⋊C₄	—	2	4	no	—
215	Dic₃⋊C₄	—	2	4	no	—
216	C₄×Dic₃	—	2	4	no	—
217	C₄×Dic₃	C₅×D₄	1	4	yes	—
218	C₄×Dic₃	C₅×Q₈	1	4	yes	complemented
219	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
220	C₅×Q₈	—	6	16	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	3	4	no	—
229	C₂×C₄×C₅	—	3	4	no	—
230	C₂×C₄×C₅	—	3	4	no	—
231	C₂×C₄×C₅	—	6	2	no	—
232	C₂×C₄×C₅	—	6	2	no	—
233	C₂×C₄×C₅	—	6	2	no	—
234	C₂×C₄×C₅	—	6	2	no	—
235	C₂×C₄×C₅	—	6	2	no	—
236	C₂×C₄×C₅	—	6	2	no	—
237	C₂×C₄×C₅	—	6	2	no	—
238	C₂×C₄×C₅	—	6	2	no	—
239	C₂×C₄×C₅	—	6	2	no	—
240	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
241	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
242	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
243	C₂×C₄×C₅	#235	1	4	yes	—
244	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
245	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
246	C₂²×Q₈	—	3	2	no	—
247	C₄×Q₈	—	6	8	no	—
248	C₂×C₄⋊C₄	—	3	2	no	—
249	C₂×C₄⋊C₄	—	3	2	no	—
250	C₂×C₄⋊C₄	—	3	2	no	—
251	C₂×C₄⋊C₄	—	3	2	no	—
252	C₂×C₄⋊C₄	—	3	2	no	—
253	C₂×C₄⋊C₄	—	3	2	no	—
254	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
255	C₂×C₄²	—	3	1	no	—
256	C₂×C₄²	—	3	1	no	—
257	C₂×C₄²	—	3	2	no	—
258	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
259	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
260	#95	—	3	2	no	—
261	#95	—	3	2	no	—
262	#95	—	3	2	no	—
263	#95	—	3	1	no	—
264	#95	—	3	2	no	—
265	#95	—	3	1	no	—
266	#95	C₂×C₅×D₃	1	1	yes	characteristic
267	#95	C₂×C₅×D₃	1	1	yes	characteristic
268	C₂×C₃×C₅	#525	1	2	yes	—
269	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
270	C₂×C₃×C₅	#533	1	1	yes	characteristic
271	C₂×C₃×C₅	#533	1	1	yes	characteristic
272	C₂×C₃×C₅	#533	1	2	yes	—
273	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
282	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
283	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
284	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
285	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
286	C₂×C₃×C₄	C₅×#41	1	4	yes	—
287	C₂×Dic₃	—	2	2	no	—
288	C₂×Dic₃	—	2	2	no	—
289	C₂×Dic₃	—	2	2	no	—
290	C₂×Dic₃	—	2	2	no	—
291	C₂×Dic₃	—	2	2	no	—
292	C₂×Dic₃	—	2	2	no	—
293	C₂×Dic₃	—	2	2	no	—
294	C₂×Dic₃	—	2	2	no	—
295	C₂×Dic₃	—	2	2	no	—
296	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
297	C₂×Dic₃	C₂×C₅×Q₈	1	4	yes	—
298	C₂×Dic₃	C₅×#41	1	4	yes	—
299	Dic₆	—	2	16	no	—
300	C₂²×C₅	C₂²×Dic₆	1	1	yes	characteristic
301	C₂²×C₅	C₂×#235	1	2	yes	—
302	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
303	C₂²×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
304	C₂²×C₅	D₃×#41	1	2	yes	—
305	C₄×C₅	—	2	2	no	—
306	C₄×C₅	—	2	2	no	—
307	C₄×C₅	—	2	4	no	—
308	C₄×C₅	—	4	2	no	—
309	C₄×C₅	—	6	4	no	—
310	C₄×C₅	—	6	4	no	—
311	C₄×C₅	—	6	4	no	—
312	C₄×C₅	—	12	2	no	—
313	C₄×C₅	#888	1	4	yes	—
314	C₂×Q₈	—	6	4	no	—
315	C₂×Q₈	—	6	4	no	—
316	C₂×Q₈	—	6	4	no	—
317	C₂²×C₄	—	3	2	no	—
318	C₂²×C₄	—	3	2	no	—
319	C₂²×C₄	—	3	2	no	—
320	C₂²×C₄	—	3	2	no	—
321	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
322	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
323	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
324	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
325	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	6	4	no	—
328	C₄⋊C₄	—	6	4	no	—
329	C₄⋊C₄	—	6	4	no	—
330	C₄⋊C₄	—	6	4	no	—
331	C₄⋊C₄	—	6	4	no	—
332	C₄⋊C₄	—	6	4	no	—
333	C₄²	—	2	4	no	—
334	C₄²	—	3	4	no	—
335	C₄²	—	3	4	no	—
336	C₄²	—	6	4	no	—
337	C₄²	C₅×Dic₆	1	4	yes	complemented
338	C₃×C₅	#2399	1	1	yes	characteristic, complemented, Hall
339	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
340	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
341	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
342	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
343	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
344	C₃×C₄	—	2	4	no	—
345	C₃×C₄	—	2	2	no	—
346	C₃×C₄	—	2	2	no	—
347	C₃×C₄	—	4	2	no	—
348	C₃×C₄	C₅×C₄⋊Q₈	1	4	yes	—
349	Dic₃	—	2	4	no	—
350	Dic₃	—	2	4	no	—
351	Dic₃	—	2	4	no	—
352	Dic₃	—	4	2	no	—
353	C₂×C₅	#5470	1	1	yes	characteristic
354	C₂×C₅	C₂×#888	1	1	yes	characteristic
355	C₂×C₅	#5517	1	1	yes	characteristic
356	C₂×C₅	#5547	1	2	yes	—
357	C₂×C₅	#5578	1	2	yes	—
358	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
359	Q₈	—	6	16	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	3	4	no	—
368	C₂×C₄	—	3	4	no	—
369	C₂×C₄	—	3	4	no	—
370	C₂×C₄	—	6	2	no	—
371	C₂×C₄	—	6	2	no	—
372	C₂×C₄	—	6	2	no	—
373	C₂×C₄	—	6	2	no	—
374	C₂×C₄	—	6	2	no	—
375	C₂×C₄	—	6	2	no	—
376	C₂×C₄	—	6	2	no	—
377	C₂×C₄	—	6	2	no	—
378	C₂×C₄	—	6	2	no	—
379	C₂×C₄	C₂×C₅×Dic₆	1	2	yes	—
380	C₂×C₄	C₂×C₅×Dic₆	1	2	yes	—
381	C₂×C₄	C₂×C₅×Dic₆	1	2	yes	—
382	C₂×C₄	C₅×#235	1	4	yes	—
383	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
384	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
385	C₂×C₃	C₅×#525	1	2	yes	—
386	C₂×C₃	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
387	C₂×C₃	C₅×#533	1	1	yes	characteristic
388	C₂×C₃	C₅×#533	1	1	yes	characteristic
389	C₂×C₃	C₅×#533	1	2	yes	—
390	C₅	#73669	1	1	yes	characteristic, direct product factor, Sylow
391	C₂²	C₂²×C₅×Dic₆	1	1	yes	characteristic
392	C₂²	C₂×C₅×#235	1	2	yes	—
393	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
394	C₂²	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
395	C₂²	C₅×D₃×#41	1	2	yes	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	4	no	—
399	C₄	—	4	2	no	—
400	C₄	—	6	4	no	—
401	C₄	—	6	4	no	—
402	C₄	—	6	4	no	—
403	C₄	—	12	2	no	—
404	C₄	C₅×#888	1	4	yes	—
405	C₃	C₅×#2399	1	1	yes	characteristic, complemented, Sylow
406	C₂	C₅×#5470	1	1	yes	characteristic
407	C₂	C₂×C₅×#888	1	1	yes	characteristic
408	C₂	C₅×#5517	1	1	yes	characteristic
409	C₂	C₅×#5547	1	2	yes	—
410	C₂	C₅×#5578	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator, cosocle	C₂³×C₃	C₂⁴×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×C₄⋊C₄	C₂
socle, prime radical	C₂³×C₃×C₅	C₂⁴
hypercenter	C₄×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₅×#2399
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₄×C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
33. #73669	C₅	direct (N × H)
57. C₃×C₄²×C₅	Q₈	semidirect
66. C₄×C₅×Dic₃	Q₈	semidirect
171. C₄²×C₅	Dic₆	semidirect
209. C₃×C₄²	C₅×Q₈	semidirect
218. C₄×Dic₃	C₅×Q₈	semidirect
337. C₄²	C₅×Dic₆	semidirect
338. C₃×C₅	#2399	semidirect
390. C₅	#73669	direct (N × H)
405. C₃	C₅×#2399	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×Dic₆	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#4982	2
C₅×#4979	2
C₄×C₅×C₄⋊Dic₃	2
C₅×#4932	2
C₄×C₅×Dic₃⋊C₄	2
C₅×#4657	2
C₅×#4656	2
C₅×#2399	3
#73669	5

Subgroups — C5×#73669 #14332542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73669 #14332542