Subgroups — C₅×#82333 #14327118

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 408 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×D₄×Dic₃	C₂	1	2	yes	maximal
3	C₅×#5212	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×C₃⋊#95	C₂	1	2	yes	maximal, complemented
5	C₅×#4984	C₂	1	2	yes	maximal, complemented
6	C₅×#4950	C₂	1	4	yes	maximal, complemented
7	C₅×#4936	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2349	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
12	C₂³×C₅×Dic₃	C₂²	1	4	yes	—
13	C₃×C₄×C₅×D₄	C₄	1	8	yes	complemented
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₅×#217	C₂²	1	4	yes	—
18	C₅×D₄×Dic₃	—	2	8	no	—
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
20	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
21	C₂×C₅×C₄⋊Dic₃	C₂²	1	4	yes	—
22	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
23	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
24	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
25	C₅×C₃⋊#95	C₂²	1	2	yes	—
26	C₅×C₃⋊#95	C₂²	1	2	yes	—
27	C₅×C₃⋊#95	C₂²	1	4	yes	—
28	#82333	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₄×C₅×D₄	—	3	2	no	—
30	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic
31	C₅×#389	—	3	2	no	—
32	C₅×#385	—	3	4	no	—
33	C₅×#382	—	3	1	no	—
34	C₅×#380	—	3	2	no	—
35	C₄×C₅×C₄⋊C₄	—	3	1	no	—
36	C₂×C₅×#95	—	3	2	no	—
37	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
38	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
39	C₂×C₃×C₅×D₄	D₄	1	4	yes	—
40	C₂×C₃×C₅×D₄	Q₈	1	4	yes	—
41	C₂²×C₃×C₄×C₅	—	4	4	no	—
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	8	yes	complemented
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₅×Dic₃	—	2	8	no	—
48	C₂²×C₅×Dic₃	—	2	8	no	—
49	C₂²×C₅×Dic₃	—	4	4	no	—
50	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
51	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
52	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
53	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
54	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
55	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
56	C₅×#217	—	2	8	no	—
57	C₅×C₄⋊Dic₃	—	2	4	no	—
58	C₅×C₄⋊Dic₃	—	2	4	no	—
59	C₅×C₄⋊Dic₃	—	4	4	no	—
60	C₄×C₅×Dic₃	—	2	4	no	—
61	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
62	C₂×D₄×Dic₃	C₂×C₅	1	2	yes	—
63	#5212	C₂×C₅	1	2	yes	complemented
64	C₂×C₃⋊#95	C₂×C₅	1	2	yes	complemented
65	#4984	C₂×C₅	1	2	yes	complemented
66	#4950	C₂×C₅	1	4	yes	complemented
67	#4936	C₂×C₅	1	1	yes	characteristic, complemented
68	C₄×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
70	C₂³×C₄×C₅	—	3	4	no	—
71	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
72	C₄×C₅×D₄	—	6	8	no	—
73	C₄×C₅×D₄	Dic₃	1	8	yes	complemented
74	C₂×C₅×C₄⋊C₄	—	3	2	no	—
75	C₂×C₅×C₄⋊C₄	—	3	2	no	—
76	C₂×C₅×C₄⋊C₄	—	3	4	no	—
77	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
78	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
79	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
80	C₂×C₄²×C₅	—	3	2	no	—
81	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
82	C₅×#95	—	3	1	no	—
83	C₅×#95	—	3	2	no	—
84	C₅×#95	—	3	4	no	—
85	C₅×#95	—	3	1	no	—
86	C₅×#95	—	3	2	no	—
87	#2349	—	3	1	no	Sylow
88	C₂³×C₃×C₅	—	2	4	no	—
89	C₂³×C₃×C₅	—	2	4	no	—
90	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
91	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
92	C₂³×C₃×C₅	C₂×Q₈	1	4	yes	—
93	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
94	C₃×C₅×D₄	C₄⋊C₄	1	16	yes	complemented
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	4	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	4	8	no	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
105	C₂×C₅×Dic₃	—	2	2	no	—
106	C₂×C₅×Dic₃	—	2	2	no	—
107	C₂×C₅×Dic₃	—	2	2	no	—
108	C₂×C₅×Dic₃	—	2	4	no	—
109	C₂×C₅×Dic₃	—	2	2	no	—
110	C₂×C₅×Dic₃	—	2	4	no	—
111	C₂×C₅×Dic₃	—	2	2	no	—
112	C₂×C₅×Dic₃	—	2	4	no	—
113	C₂×C₅×Dic₃	—	4	16	no	—
114	C₂×C₅×Dic₃	#41	1	4	yes	—
115	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
116	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
117	C₂³×Dic₃	C₂²×C₅	1	4	yes	—
118	C₃×C₄×D₄	C₄×C₅	1	8	yes	complemented
119	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
120	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
121	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
122	C₂×#217	C₂²×C₅	1	4	yes	—
123	D₄×Dic₃	—	2	8	no	—
124	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
125	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
126	C₂×C₄⋊Dic₃	C₂²×C₅	1	4	yes	—
127	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
128	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
129	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
130	C₃⋊#95	C₂²×C₅	1	2	yes	—
131	C₃⋊#95	C₂²×C₅	1	2	yes	—
132	C₃⋊#95	C₂²×C₅	1	4	yes	—
133	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
134	C₂×C₅×D₄	Dic₆	1	4	yes	—
135	C₂×C₅×D₄	D₁₂	1	4	yes	—
136	C₂×C₅×D₄	C₂×Dic₃	1	4	yes	—
137	C₂²×C₄×C₅	—	3	2	no	—
138	C₂²×C₄×C₅	—	3	2	no	—
139	C₂²×C₄×C₅	—	3	4	no	—
140	C₂²×C₄×C₅	—	4	4	no	—
141	C₂²×C₄×C₅	—	6	8	no	—
142	C₂²×C₄×C₅	—	6	8	no	—
143	C₂²×C₄×C₅	—	12	4	no	—
144	C₂²×C₄×C₅	C₂×Dic₃	1	8	yes	complemented
145	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
148	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
149	C₅×C₄⋊C₄	—	6	4	no	—
150	C₅×C₄⋊C₄	—	6	4	no	—
151	C₅×C₄⋊C₄	—	12	4	no	—
152	C₅×C₄⋊C₄	C₂×Dic₃	1	4	yes	complemented
153	C₅×C₂²⋊C₄	—	6	8	no	—
154	C₅×C₂²⋊C₄	C₂×Dic₃	1	8	yes	complemented
155	C₄²×C₅	—	6	4	no	—
156	C₄²×C₅	C₂×Dic₃	1	4	yes	complemented
157	C₂×C₄×D₄	—	3	2	no	—
158	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic
159	#389	—	3	2	no	—
160	#385	—	3	4	no	—
161	#382	—	3	1	no	—
162	#380	—	3	2	no	—
163	C₄×C₄⋊C₄	—	3	1	no	—
164	C₂×#95	—	3	2	no	—
165	C₂²×C₃×C₅	—	2	4	no	—
166	C₂²×C₃×C₅	—	2	4	no	—
167	C₂²×C₃×C₅	—	2	8	no	—
168	C₂²×C₃×C₅	—	2	8	no	—
169	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	8	yes	—
170	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
171	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
172	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
173	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
174	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
175	C₃×C₄×C₅	—	2	2	no	—
176	C₃×C₄×C₅	—	2	2	no	—
177	C₃×C₄×C₅	—	2	4	no	—
178	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
179	C₅×Dic₃	—	2	4	no	—
180	C₅×Dic₃	—	4	2	no	—
181	C₅×Dic₃	—	4	4	no	—
182	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
183	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
184	C₂×C₃×D₄	C₅×D₄	1	4	yes	—
185	C₂×C₃×D₄	C₅×Q₈	1	4	yes	—
186	C₂²×C₃×C₄	—	4	4	no	—
187	C₂²×C₃×C₄	C₂×C₄×C₅	1	8	yes	complemented
188	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
190	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
191	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
192	C₂²×Dic₃	—	2	8	no	—
193	C₂²×Dic₃	—	2	8	no	—
194	C₂²×Dic₃	—	4	4	no	—
195	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
196	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
197	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
198	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
199	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
200	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
201	#217	—	2	8	no	—
202	C₄⋊Dic₃	—	2	4	no	—
203	C₄⋊Dic₃	—	2	4	no	—
204	C₄⋊Dic₃	—	4	4	no	—
205	C₄×Dic₃	—	2	4	no	—
206	C₂³×C₅	—	2	4	no	—
207	C₂³×C₅	—	2	4	no	—
208	C₂³×C₅	C₂×Dic₆	1	4	yes	—
209	C₂³×C₅	C₂×D₁₂	1	4	yes	—
210	C₂³×C₅	C₂²×Dic₃	1	4	yes	—
211	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
212	C₅×D₄	C₄⋊Dic₃	1	16	yes	complemented
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	3	4	no	—
217	C₂×C₄×C₅	—	4	8	no	—
218	C₂×C₄×C₅	—	6	2	no	—
219	C₂×C₄×C₅	—	6	2	no	—
220	C₂×C₄×C₅	—	6	2	no	—
221	C₂×C₄×C₅	—	6	4	no	—
222	C₂×C₄×C₅	—	6	2	no	—
223	C₂×C₄×C₅	—	6	4	no	—
224	C₂×C₄×C₅	—	6	2	no	—
225	C₂×C₄×C₅	—	6	4	no	—
226	C₂×C₄×C₅	—	12	16	no	—
227	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
228	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
229	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
230	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
231	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
232	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
233	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
234	C₂³×C₄	—	3	4	no	—
235	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
236	C₄×D₄	—	6	8	no	—
237	C₄×D₄	C₅×Dic₃	1	8	yes	complemented
238	C₂×C₄⋊C₄	—	3	2	no	—
239	C₂×C₄⋊C₄	—	3	2	no	—
240	C₂×C₄⋊C₄	—	3	4	no	—
241	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
242	C₂×C₂²⋊C₄	—	3	4	no	—
243	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
244	C₂×C₄²	—	3	2	no	—
245	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
246	#95	—	3	1	no	—
247	#95	—	3	2	no	—
248	#95	—	3	4	no	—
249	#95	—	3	1	no	—
250	#95	—	3	2	no	—
251	C₂×C₃×C₅	—	2	8	no	—
252	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
253	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
254	C₂×C₃×C₅	#518	1	1	yes	characteristic
255	C₂×C₃×C₅	#546	1	2	yes	—
256	C₂×C₃×C₅	#554	1	2	yes	—
257	C₂³×C₃	—	2	4	no	—
258	C₂³×C₃	—	2	4	no	—
259	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
260	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
261	C₂³×C₃	C₂×C₅×Q₈	1	4	yes	—
262	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
263	C₃×D₄	C₅×C₄⋊C₄	1	16	yes	complemented
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	4	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	4	8	no	—
268	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
269	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
270	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
271	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
272	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
273	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
274	C₂×Dic₃	—	2	2	no	—
275	C₂×Dic₃	—	2	2	no	—
276	C₂×Dic₃	—	2	2	no	—
277	C₂×Dic₃	—	2	4	no	—
278	C₂×Dic₃	—	2	2	no	—
279	C₂×Dic₃	—	2	4	no	—
280	C₂×Dic₃	—	2	2	no	—
281	C₂×Dic₃	—	2	4	no	—
282	C₂×Dic₃	—	4	16	no	—
283	C₂×Dic₃	C₅×#41	1	4	yes	—
284	C₂²×C₅	—	2	8	no	—
285	C₂²×C₅	—	2	4	no	—
286	C₂²×C₅	—	2	8	no	—
287	C₂²×C₅	—	2	4	no	—
288	C₂²×C₅	C₂×C₄⋊Dic₃	1	8	yes	—
289	C₂²×C₅	C₂²×Dic₆	1	1	yes	characteristic
290	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
291	C₂²×C₅	#1004	1	2	yes	—
292	C₂²×C₅	D₃×#41	1	2	yes	—
293	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
294	C₄×C₅	—	2	2	no	—
295	C₄×C₅	—	2	4	no	—
296	C₄×C₅	—	2	2	no	—
297	C₄×C₅	—	6	4	no	—
298	C₄×C₅	—	12	2	no	—
299	C₄×C₅	—	12	4	no	—
300	C₄×C₅	C₂×C₄⋊Dic₃	1	4	yes	—
301	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
302	C₂×D₄	C₅×Dic₆	1	4	yes	—
303	C₂×D₄	C₅×D₁₂	1	4	yes	—
304	C₂×D₄	C₂×C₅×Dic₃	1	4	yes	—
305	C₂²×C₄	—	3	2	no	—
306	C₂²×C₄	—	3	4	no	—
307	C₂²×C₄	—	3	2	no	—
308	C₂²×C₄	—	4	4	no	—
309	C₂²×C₄	—	6	8	no	—
310	C₂²×C₄	—	6	8	no	—
311	C₂²×C₄	—	12	4	no	—
312	C₂²×C₄	C₂×C₅×Dic₃	1	8	yes	complemented
313	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
314	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
315	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
316	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
317	C₄⋊C₄	—	6	4	no	—
318	C₄⋊C₄	—	6	4	no	—
319	C₄⋊C₄	—	12	4	no	—
320	C₄⋊C₄	C₂×C₅×Dic₃	1	4	yes	complemented
321	C₂²⋊C₄	—	6	8	no	—
322	C₂²⋊C₄	C₂×C₅×Dic₃	1	8	yes	complemented
323	C₄²	—	6	4	no	—
324	C₄²	C₂×C₅×Dic₃	1	4	yes	complemented
325	C₃×C₅	#2349	1	1	yes	characteristic, complemented, Hall
326	C₂²×C₃	—	2	4	no	—
327	C₂²×C₃	—	2	4	no	—
328	C₂²×C₃	—	2	8	no	—
329	C₂²×C₃	—	2	8	no	—
330	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	8	yes	—
331	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
332	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
333	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
334	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
335	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
336	C₃×C₄	—	2	2	no	—
337	C₃×C₄	—	2	2	no	—
338	C₃×C₄	—	2	4	no	—
339	C₃×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
340	Dic₃	—	2	4	no	—
341	Dic₃	—	4	2	no	—
342	Dic₃	—	4	4	no	—
343	C₂×C₅	—	2	8	no	—
344	C₂×C₅	#5539	1	2	yes	—
345	C₂×C₅	#5554	1	2	yes	—
346	C₂×C₅	C₂²×C₄⋊Dic₃	1	1	yes	characteristic
347	C₂×C₅	#5798	1	1	yes	characteristic
348	C₂×C₅	Dic₃×#41	1	1	yes	characteristic
349	C₂³	—	2	4	no	—
350	C₂³	—	2	4	no	—
351	C₂³	C₂×C₅×Dic₆	1	4	yes	—
352	C₂³	C₂×C₅×D₁₂	1	4	yes	—
353	C₂³	C₂²×C₅×Dic₃	1	4	yes	—
354	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
355	D₄	C₅×C₄⋊Dic₃	1	16	yes	complemented
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	3	4	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	—	6	2	no	—
362	C₂×C₄	—	6	2	no	—
363	C₂×C₄	—	6	2	no	—
364	C₂×C₄	—	6	4	no	—
365	C₂×C₄	—	6	2	no	—
366	C₂×C₄	—	6	4	no	—
367	C₂×C₄	—	6	2	no	—
368	C₂×C₄	—	6	4	no	—
369	C₂×C₄	—	12	16	no	—
370	C₂×C₄	C₂×C₅×Dic₆	1	2	yes	—
371	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
372	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
373	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
374	C₂×C₄	C₂²×C₅×Dic₃	1	4	yes	—
375	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
376	C₂×C₃	—	2	8	no	—
377	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
378	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
379	C₂×C₃	C₅×#518	1	1	yes	characteristic
380	C₂×C₃	C₅×#546	1	2	yes	—
381	C₂×C₃	C₅×#554	1	2	yes	—
382	C₅	#82333	1	1	yes	characteristic, direct product factor, Sylow
383	C₂²	—	2	8	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	8	no	—
386	C₂²	—	2	4	no	—
387	C₂²	C₂×C₅×C₄⋊Dic₃	1	8	yes	—
388	C₂²	C₂²×C₅×Dic₆	1	1	yes	characteristic
389	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
390	C₂²	C₅×#1004	1	2	yes	—
391	C₂²	C₅×D₃×#41	1	2	yes	—
392	C₂²	C₂³×C₅×Dic₃	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	4	no	—
395	C₄	—	2	2	no	—
396	C₄	—	6	4	no	—
397	C₄	—	12	4	no	—
398	C₄	—	12	2	no	—
399	C₄	C₂×C₅×C₄⋊Dic₃	1	4	yes	—
400	C₃	C₅×#2349	1	1	yes	characteristic, complemented, Sylow
401	C₂	—	2	8	no	—
402	C₂	C₅×#5539	1	2	yes	—
403	C₂	C₅×#5554	1	2	yes	—
404	C₂	C₂²×C₅×C₄⋊Dic₃	1	1	yes	characteristic
405	C₂	C₅×#5798	1	1	yes	characteristic
406	C₂	C₅×Dic₃×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₃×C₅×D₄	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₅×#2349
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
3. C₅×#5212	C₂	semidirect
4. C₂×C₅×C₃⋊#95	C₂	semidirect
5. C₅×#4984	C₂	semidirect
6. C₅×#4950	C₂	semidirect
7. C₅×#4936	C₂	semidirect
8. C₄×C₅×C₄⋊Dic₃	C₂	semidirect
13. C₃×C₄×C₅×D₄	C₄	semidirect
28. #82333	C₅	direct (N × H)
42. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
53. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
54. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
55. C₃×C₄²×C₅	C₂×C₄	semidirect
63. #5212	C₂×C₅	semidirect
64. C₂×C₃⋊#95	C₂×C₅	semidirect
65. #4984	C₂×C₅	semidirect
66. #4950	C₂×C₅	semidirect
67. #4936	C₂×C₅	semidirect
68. C₄×C₄⋊Dic₃	C₂×C₅	semidirect
73. C₄×C₅×D₄	Dic₃	semidirect
94. C₃×C₅×D₄	C₄⋊C₄	semidirect
118. C₃×C₄×D₄	C₄×C₅	semidirect
144. C₂²×C₄×C₅	C₂×Dic₃	semidirect
152. C₅×C₄⋊C₄	C₂×Dic₃	semidirect
154. C₅×C₂²⋊C₄	C₂×Dic₃	semidirect
156. C₄²×C₅	C₂×Dic₃	semidirect
187. C₂²×C₃×C₄	C₂×C₄×C₅	semidirect
198. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
199. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
200. C₃×C₄²	C₂×C₄×C₅	semidirect
212. C₅×D₄	C₄⋊Dic₃	semidirect
237. C₄×D₄	C₅×Dic₃	semidirect
263. C₃×D₄	C₅×C₄⋊C₄	semidirect
312. C₂²×C₄	C₂×C₅×Dic₃	semidirect
320. C₄⋊C₄	C₂×C₅×Dic₃	semidirect
322. C₂²⋊C₄	C₂×C₅×Dic₃	semidirect
324. C₄²	C₂×C₅×Dic₃	semidirect
325. C₃×C₅	#2349	semidirect
355. D₄	C₅×C₄⋊Dic₃	semidirect
382. C₅	#82333	direct (N × H)
400. C₃	C₅×#2349	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×D₄×Dic₃	2
C₅×#5212	2
C₂×C₅×C₃⋊#95	2
C₅×#4984	2
C₅×#4950	2
C₅×#4936	2
C₄×C₅×C₄⋊Dic₃	2
C₅×#2349	3
#82333	5

Subgroups — C5×#82333 #14327118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#82333 #14327118