Subgroups — C₅×D₄×#217 #14325910

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#217	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×D₄×Dic₃	C₂	1	2	yes	maximal, complemented
4	C₅×#5247	C₂	1	2	yes	maximal, complemented
5	C₅×#5221	C₂	1	2	yes	maximal, complemented
6	C₅×#5220	C₂	1	4	yes	maximal, complemented
7	C₅×#5212	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₅×#217	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₄×C₂²⋊C₄	—	3	1	no	maximal, Hall
10	C₂⁵×C₃×C₅	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×D₄	—	2	8	no	—
12	C₂²×C₃×C₅×D₄	C₄	1	8	yes	complemented
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₂³×C₅×Dic₃	C₂²	1	4	yes	complemented
18	C₂×C₅×#217	—	2	8	no	—
19	C₂×C₅×#217	C₂²	1	1	yes	characteristic
20	C₂×C₅×#217	C₂²	1	2	yes	—
21	C₂×C₅×#217	C₂²	1	1	yes	characteristic
22	C₂×C₅×#217	C₂²	1	4	yes	complemented
23	C₂×C₅×#217	C₂²	1	4	yes	complemented
24	C₂×C₅×#217	C₂²	1	4	yes	complemented
25	C₅×D₄×Dic₃	—	2	8	no	—
26	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
27	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
28	C₅×C₃⋊#95	C₂²	1	2	yes	complemented
29	C₅×C₃⋊#95	C₂²	1	2	yes	complemented
30	D₄×#217	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂³×C₅×D₄	D₃	1	1	yes	characteristic
32	C₂×C₄×C₅×D₄	—	3	2	no	—
33	C₂²×C₅×C₂²⋊C₄	—	3	2	no	—
34	C₅×#390	—	3	2	no	—
35	C₅×#386	—	3	4	no	—
36	C₅×#380	—	3	1	no	—
37	C₅×#379	—	3	2	no	—
38	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
39	C₂⁴×C₃×C₅	—	2	4	no	—
40	C₂⁴×C₃×C₅	—	2	8	no	—
41	C₂⁴×C₃×C₅	—	2	4	no	—
42	C₂⁴×C₃×C₅	—	4	4	no	—
43	C₂⁴×C₃×C₅	C₂×C₄	1	8	yes	complemented
44	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
45	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
46	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
47	C₂×C₃×C₅×D₄	—	2	8	no	—
48	C₂×C₃×C₅×D₄	—	2	32	no	—
49	C₂×C₃×C₅×D₄	—	2	4	no	—
50	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
51	C₂×C₃×C₅×D₄	C₂×C₄	1	8	yes	complemented
52	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
53	C₂×C₃×C₅×D₄	D₄	1	8	yes	—
54	C₂²×C₃×C₄×C₅	—	2	4	no	—
55	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	complemented
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₅×Dic₃	—	2	8	no	—
59	C₂²×C₅×Dic₃	—	2	8	no	—
60	C₂²×C₅×Dic₃	—	4	4	no	—
61	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
62	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
63	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
64	C₅×#217	—	2	8	no	—
65	C₅×#217	—	2	4	no	—
66	C₅×#217	—	2	2	no	—
67	C₅×#217	—	2	8	no	—
68	C₅×#217	—	4	4	no	—
69	C₅×#217	D₄	1	4	yes	direct product factor
70	C₅×C₄⋊Dic₃	—	2	4	no	—
71	C₄×C₅×Dic₃	—	2	4	no	—
72	C₂³×C₃×D₄	C₂×C₅	1	1	yes	characteristic
73	C₂²×#217	C₂×C₅	1	2	yes	complemented
74	C₂×D₄×Dic₃	C₂×C₅	1	2	yes	complemented
75	#5247	C₂×C₅	1	2	yes	complemented
76	#5221	C₂×C₅	1	2	yes	complemented
77	#5220	C₂×C₅	1	4	yes	complemented
78	#5212	C₂×C₅	1	1	yes	characteristic, complemented
79	C₄×#217	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂⁵×C₅	C₂×D₃	1	2	yes	—
81	C₂²×C₅×D₄	—	2	8	no	—
82	C₂²×C₅×D₄	Dic₃	1	8	yes	complemented
83	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
84	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
85	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
86	C₂³×C₄×C₅	—	3	4	no	—
87	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
88	C₄×C₅×D₄	—	6	8	no	—
89	C₂×C₅×C₄⋊C₄	—	3	2	no	—
90	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
91	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
92	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
93	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
94	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
95	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
96	C₂×C₅×C₂²⋊C₄	—	6	8	no	—
97	C₂×C₄²×C₅	—	3	2	no	—
98	C₅×#95	—	3	2	no	—
99	C₅×#95	—	3	2	no	—
100	D₄×C₂²⋊C₄	—	3	1	no	Sylow
101	C₂³×C₃×C₅	—	2	2	no	—
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂³×C₃×C₅	—	2	4	no	—
105	C₂³×C₃×C₅	—	2	2	no	—
106	C₂³×C₃×C₅	—	2	16	no	—
107	C₂³×C₃×C₅	—	2	16	no	—
108	C₂³×C₃×C₅	—	2	2	no	—
109	C₂³×C₃×C₅	—	2	4	no	—
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	—	2	4	no	—
112	C₂³×C₃×C₅	—	4	8	no	—
113	C₂³×C₃×C₅	—	4	16	no	—
114	C₂³×C₃×C₅	—	4	16	no	—
115	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
116	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
117	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
118	C₂³×C₃×C₅	C₂×D₄	1	8	yes	—
119	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
120	C₂³×C₃×C₅	#41	1	2	yes	—
121	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
122	C₃×C₅×D₄	—	2	16	no	—
123	C₃×C₅×D₄	—	2	8	no	—
124	C₃×C₅×D₄	C₂²⋊C₄	1	16	yes	complemented
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	8	no	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
130	C₂×C₅×Dic₃	—	2	2	no	—
131	C₂×C₅×Dic₃	—	2	2	no	—
132	C₂×C₅×Dic₃	—	2	2	no	—
133	C₂×C₅×Dic₃	—	2	4	no	—
134	C₂×C₅×Dic₃	—	2	4	no	—
135	C₂×C₅×Dic₃	—	2	2	no	—
136	C₂×C₅×Dic₃	—	2	2	no	—
137	C₂×C₅×Dic₃	—	2	4	no	—
138	C₂×C₅×Dic₃	—	4	16	no	—
139	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	complemented
140	C₂⁵×C₃	C₂²×C₅	1	2	yes	—
141	C₂²×C₃×D₄	—	2	8	no	—
142	C₂²×C₃×D₄	C₄×C₅	1	8	yes	complemented
143	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
144	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
145	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
146	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
147	C₂³×Dic₃	C₂²×C₅	1	4	yes	complemented
148	C₂×#217	—	2	8	no	—
149	C₂×#217	C₂²×C₅	1	1	yes	characteristic
150	C₂×#217	C₂²×C₅	1	2	yes	—
151	C₂×#217	C₂²×C₅	1	1	yes	characteristic
152	C₂×#217	C₂²×C₅	1	4	yes	complemented
153	C₂×#217	C₂²×C₅	1	4	yes	complemented
154	C₂×#217	C₂²×C₅	1	4	yes	complemented
155	D₄×Dic₃	—	2	8	no	—
156	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
157	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
158	C₃⋊#95	C₂²×C₅	1	2	yes	complemented
159	C₃⋊#95	C₂²×C₅	1	2	yes	complemented
160	C₂⁴×C₅	—	2	4	no	—
161	C₂⁴×C₅	—	2	4	no	—
162	C₂⁴×C₅	—	2	8	no	—
163	C₂⁴×C₅	—	4	4	no	—
164	C₂⁴×C₅	C₂×Dic₃	1	8	yes	complemented
165	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
166	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
167	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
168	C₂×C₅×D₄	—	2	8	no	—
169	C₂×C₅×D₄	—	2	32	no	—
170	C₂×C₅×D₄	—	2	4	no	—
171	C₂×C₅×D₄	C₂×Dic₃	1	4	yes	—
172	C₂×C₅×D₄	C₂×Dic₃	1	8	yes	complemented
173	C₂×C₅×D₄	C₂×Dic₃	1	4	yes	complemented
174	C₂×C₅×D₄	#67	1	8	yes	—
175	C₂²×C₄×C₅	—	2	4	no	—
176	C₂²×C₄×C₅	—	3	2	no	—
177	C₂²×C₄×C₅	—	3	2	no	—
178	C₂²×C₄×C₅	—	3	4	no	—
179	C₂²×C₄×C₅	—	6	8	no	—
180	C₂²×C₄×C₅	—	6	8	no	—
181	C₂²×C₄×C₅	—	12	4	no	—
182	C₂²×C₄×C₅	C₂×Dic₃	1	4	yes	complemented
183	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
185	C₅×C₄⋊C₄	—	6	4	no	—
186	C₅×C₂²⋊C₄	—	3	4	no	—
187	C₅×C₂²⋊C₄	—	6	8	no	—
188	C₅×C₂²⋊C₄	—	6	4	no	—
189	C₅×C₂²⋊C₄	—	6	2	no	—
190	C₅×C₂²⋊C₄	—	6	8	no	—
191	C₅×C₂²⋊C₄	—	12	4	no	—
192	C₄²×C₅	—	6	4	no	—
193	C₂³×D₄	C₅×D₃	1	1	yes	characteristic
194	C₂×C₄×D₄	—	3	2	no	—
195	C₂²×C₂²⋊C₄	—	3	2	no	—
196	#390	—	3	2	no	—
197	#386	—	3	4	no	—
198	#380	—	3	1	no	—
199	#379	—	3	2	no	—
200	C₄×C₂²⋊C₄	—	3	1	no	—
201	C₂²×C₃×C₅	—	2	2	no	—
202	C₂²×C₃×C₅	—	2	4	no	—
203	C₂²×C₃×C₅	—	2	2	no	—
204	C₂²×C₃×C₅	—	2	4	no	—
205	C₂²×C₃×C₅	—	2	8	no	—
206	C₂²×C₃×C₅	—	2	4	no	—
207	C₂²×C₃×C₅	—	2	4	no	—
208	C₂²×C₃×C₅	—	2	8	no	—
209	C₂²×C₃×C₅	—	2	4	no	—
210	C₂²×C₃×C₅	—	2	4	no	—
211	C₂²×C₃×C₅	—	2	4	no	—
212	C₂²×C₃×C₅	—	4	32	no	—
213	C₂²×C₃×C₅	—	4	4	no	—
214	C₂²×C₃×C₅	—	4	4	no	—
215	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	8	yes	complemented
216	C₂²×C₃×C₅	C₄×D₄	1	4	yes	complemented
217	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
218	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
219	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
220	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
221	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
222	C₃×C₄×C₅	—	2	2	no	—
223	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	complemented
224	C₅×Dic₃	—	2	4	no	—
225	C₅×Dic₃	—	4	4	no	—
226	C₅×Dic₃	—	4	2	no	—
227	C₂⁴×C₃	—	2	4	no	—
228	C₂⁴×C₃	—	2	8	no	—
229	C₂⁴×C₃	—	2	4	no	—
230	C₂⁴×C₃	—	4	4	no	—
231	C₂⁴×C₃	C₂×C₄×C₅	1	8	yes	complemented
232	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
233	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
234	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
235	C₂×C₃×D₄	—	2	8	no	—
236	C₂×C₃×D₄	—	2	32	no	—
237	C₂×C₃×D₄	—	2	4	no	—
238	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
239	C₂×C₃×D₄	C₂×C₄×C₅	1	8	yes	complemented
240	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
241	C₂×C₃×D₄	C₅×D₄	1	8	yes	—
242	C₂²×C₃×C₄	—	2	4	no	—
243	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	complemented
244	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
245	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
246	C₂²×Dic₃	—	2	8	no	—
247	C₂²×Dic₃	—	2	8	no	—
248	C₂²×Dic₃	—	4	4	no	—
249	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
250	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
251	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
252	#217	—	2	8	no	—
253	#217	—	2	4	no	—
254	#217	—	2	2	no	—
255	#217	—	2	8	no	—
256	#217	—	4	4	no	—
257	#217	C₅×D₄	1	4	yes	direct product factor
258	C₄⋊Dic₃	—	2	4	no	—
259	C₄×Dic₃	—	2	4	no	—
260	C₂³×C₅	—	2	2	no	—
261	C₂³×C₅	—	2	2	no	—
262	C₂³×C₅	—	2	4	no	—
263	C₂³×C₅	—	2	2	no	—
264	C₂³×C₅	—	2	2	no	—
265	C₂³×C₅	—	2	16	no	—
266	C₂³×C₅	—	2	16	no	—
267	C₂³×C₅	—	2	2	no	—
268	C₂³×C₅	—	2	2	no	—
269	C₂³×C₅	—	2	4	no	—
270	C₂³×C₅	—	2	4	no	—
271	C₂³×C₅	—	4	8	no	—
272	C₂³×C₅	—	4	16	no	—
273	C₂³×C₅	—	4	16	no	—
274	C₂³×C₅	D₃×D₄	1	2	yes	—
275	C₂³×C₅	#237	1	2	yes	—
276	C₂³×C₅	C₂²×Dic₃	1	4	yes	—
277	C₂³×C₅	C₂²×Dic₃	1	2	yes	—
278	C₂³×C₅	C₂²×Dic₃	1	4	yes	—
279	C₂³×C₅	C₂×#67	1	8	yes	—
280	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
281	C₅×D₄	—	2	16	no	—
282	C₅×D₄	—	2	8	no	—
283	C₅×D₄	#217	1	16	yes	direct product factor
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	8	no	—
286	C₂×C₄×C₅	—	3	4	no	—
287	C₂×C₄×C₅	—	6	2	no	—
288	C₂×C₄×C₅	—	6	2	no	—
289	C₂×C₄×C₅	—	6	4	no	—
290	C₂×C₄×C₅	—	6	2	no	—
291	C₂×C₄×C₅	—	6	2	no	—
292	C₂×C₄×C₅	—	6	4	no	—
293	C₂×C₄×C₅	—	6	2	no	—
294	C₂×C₄×C₅	—	6	4	no	—
295	C₂×C₄×C₅	—	12	16	no	—
296	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
297	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
298	C₂×C₄×C₅	C₂×#67	1	4	yes	—
299	C₂⁵	C₂×C₅×D₃	1	2	yes	—
300	C₂²×D₄	—	2	8	no	—
301	C₂²×D₄	C₅×Dic₃	1	8	yes	complemented
302	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
303	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
304	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
305	C₂³×C₄	—	3	4	no	—
306	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
307	C₄×D₄	—	6	8	no	—
308	C₂×C₄⋊C₄	—	3	2	no	—
309	C₂×C₂²⋊C₄	—	3	1	no	—
310	C₂×C₂²⋊C₄	—	3	2	no	—
311	C₂×C₂²⋊C₄	—	3	4	no	—
312	C₂×C₂²⋊C₄	—	3	4	no	—
313	C₂×C₂²⋊C₄	—	3	1	no	—
314	C₂×C₂²⋊C₄	—	3	4	no	—
315	C₂×C₂²⋊C₄	—	6	8	no	—
316	C₂×C₄²	—	3	2	no	—
317	#95	—	3	2	no	—
318	#95	—	3	2	no	—
319	C₂×C₃×C₅	—	2	4	no	—
320	C₂×C₃×C₅	—	2	8	no	—
321	C₂×C₃×C₅	—	4	4	no	—
322	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
323	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
324	C₂×C₃×C₅	#518	1	1	yes	characteristic
325	C₂×C₃×C₅	D₄²	1	2	yes	—
326	C₂×C₃×C₅	#546	1	2	yes	—
327	C₂³×C₃	—	2	2	no	—
328	C₂³×C₃	—	2	2	no	—
329	C₂³×C₃	—	2	2	no	—
330	C₂³×C₃	—	2	4	no	—
331	C₂³×C₃	—	2	2	no	—
332	C₂³×C₃	—	2	16	no	—
333	C₂³×C₃	—	2	16	no	—
334	C₂³×C₃	—	2	2	no	—
335	C₂³×C₃	—	2	4	no	—
336	C₂³×C₃	—	2	2	no	—
337	C₂³×C₃	—	2	4	no	—
338	C₂³×C₃	—	4	8	no	—
339	C₂³×C₃	—	4	16	no	—
340	C₂³×C₃	—	4	16	no	—
341	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
342	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
343	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
344	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
345	C₂³×C₃	C₂×C₅×D₄	1	8	yes	—
346	C₂³×C₃	C₅×#41	1	2	yes	—
347	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
348	C₃×D₄	—	2	16	no	—
349	C₃×D₄	—	2	8	no	—
350	C₃×D₄	C₅×C₂²⋊C₄	1	16	yes	complemented
351	C₂×C₃×C₄	—	2	2	no	—
352	C₂×C₃×C₄	—	2	8	no	—
353	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
354	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
355	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
356	C₂×Dic₃	—	2	2	no	—
357	C₂×Dic₃	—	2	2	no	—
358	C₂×Dic₃	—	2	2	no	—
359	C₂×Dic₃	—	2	4	no	—
360	C₂×Dic₃	—	2	4	no	—
361	C₂×Dic₃	—	2	2	no	—
362	C₂×Dic₃	—	2	2	no	—
363	C₂×Dic₃	—	2	4	no	—
364	C₂×Dic₃	—	4	16	no	—
365	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	complemented
366	C₂²×C₅	—	2	4	no	—
367	C₂²×C₅	—	2	2	no	—
368	C₂²×C₅	—	2	4	no	—
369	C₂²×C₅	—	2	8	no	—
370	C₂²×C₅	—	2	4	no	—
371	C₂²×C₅	—	2	4	no	—
372	C₂²×C₅	—	2	8	no	—
373	C₂²×C₅	—	2	2	no	—
374	C₂²×C₅	—	2	4	no	—
375	C₂²×C₅	—	2	4	no	—
376	C₂²×C₅	—	2	4	no	—
377	C₂²×C₅	—	4	32	no	—
378	C₂²×C₅	—	4	4	no	—
379	C₂²×C₅	—	4	4	no	—
380	C₂²×C₅	D₄×Dic₃	1	4	yes	complemented
381	C₂²×C₅	C₂×#217	1	8	yes	complemented
382	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
383	C₂²×C₅	C₂×#237	1	1	yes	characteristic
384	C₂²×C₅	#1004	1	2	yes	—
385	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
386	C₂²×C₅	C₂²×#67	1	2	yes	—
387	C₄×C₅	—	2	2	no	—
388	C₄×C₅	—	6	4	no	—
389	C₄×C₅	—	12	4	no	—
390	C₄×C₅	—	12	2	no	—
391	C₄×C₅	C₂×#217	1	4	yes	complemented
392	C₂⁴	—	2	4	no	—
393	C₂⁴	—	2	4	no	—
394	C₂⁴	—	2	8	no	—
395	C₂⁴	—	4	4	no	—
396	C₂⁴	C₂×C₅×Dic₃	1	8	yes	complemented
397	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
398	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
399	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
400	C₂×D₄	—	2	8	no	—
401	C₂×D₄	—	2	32	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	C₂×C₅×Dic₃	1	4	yes	—
404	C₂×D₄	C₂×C₅×Dic₃	1	8	yes	complemented
405	C₂×D₄	C₂×C₅×Dic₃	1	4	yes	complemented
406	C₂×D₄	C₅×#67	1	8	yes	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	3	2	no	—
409	C₂²×C₄	—	3	2	no	—
410	C₂²×C₄	—	3	4	no	—
411	C₂²×C₄	—	6	8	no	—
412	C₂²×C₄	—	6	8	no	—
413	C₂²×C₄	—	12	4	no	—
414	C₂²×C₄	C₂×C₅×Dic₃	1	4	yes	complemented
415	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
416	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
417	C₄⋊C₄	—	6	4	no	—
418	C₂²⋊C₄	—	3	4	no	—
419	C₂²⋊C₄	—	6	8	no	—
420	C₂²⋊C₄	—	6	4	no	—
421	C₂²⋊C₄	—	6	2	no	—
422	C₂²⋊C₄	—	6	8	no	—
423	C₂²⋊C₄	—	12	4	no	—
424	C₄²	—	6	4	no	—
425	C₃×C₅	D₄×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
426	C₂²×C₃	—	2	2	no	—
427	C₂²×C₃	—	2	4	no	—
428	C₂²×C₃	—	2	2	no	—
429	C₂²×C₃	—	2	4	no	—
430	C₂²×C₃	—	2	8	no	—
431	C₂²×C₃	—	2	4	no	—
432	C₂²×C₃	—	2	4	no	—
433	C₂²×C₃	—	2	8	no	—
434	C₂²×C₃	—	2	4	no	—
435	C₂²×C₃	—	2	4	no	—
436	C₂²×C₃	—	2	4	no	—
437	C₂²×C₃	—	4	32	no	—
438	C₂²×C₃	—	4	4	no	—
439	C₂²×C₃	—	4	4	no	—
440	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	8	yes	complemented
441	C₂²×C₃	C₄×C₅×D₄	1	4	yes	complemented
442	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
443	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
444	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
445	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
446	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
447	C₃×C₄	—	2	2	no	—
448	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	complemented
449	Dic₃	—	2	4	no	—
450	Dic₃	—	4	4	no	—
451	Dic₃	—	4	2	no	—
452	C₂×C₅	—	2	4	no	—
453	C₂×C₅	—	2	8	no	—
454	C₂×C₅	—	4	4	no	—
455	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
456	C₂×C₅	#5798	1	1	yes	characteristic
457	C₂×C₅	D₄×#67	1	2	yes	—
458	C₂×C₅	#5806	1	2	yes	—
459	C₂×C₅	C₂²×#217	1	1	yes	characteristic
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	4	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	16	no	—
466	C₂³	—	2	16	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	4	no	—
470	C₂³	—	2	4	no	—
471	C₂³	—	4	8	no	—
472	C₂³	—	4	16	no	—
473	C₂³	—	4	16	no	—
474	C₂³	C₅×D₃×D₄	1	2	yes	—
475	C₂³	C₅×#237	1	2	yes	—
476	C₂³	C₂²×C₅×Dic₃	1	4	yes	—
477	C₂³	C₂²×C₅×Dic₃	1	2	yes	—
478	C₂³	C₂²×C₅×Dic₃	1	4	yes	—
479	C₂³	C₂×C₅×#67	1	8	yes	—
480	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
481	D₄	—	2	16	no	—
482	D₄	—	2	8	no	—
483	D₄	C₅×#217	1	16	yes	direct product factor
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	8	no	—
486	C₂×C₄	—	3	4	no	—
487	C₂×C₄	—	6	2	no	—
488	C₂×C₄	—	6	2	no	—
489	C₂×C₄	—	6	4	no	—
490	C₂×C₄	—	6	2	no	—
491	C₂×C₄	—	6	2	no	—
492	C₂×C₄	—	6	4	no	—
493	C₂×C₄	—	6	2	no	—
494	C₂×C₄	—	6	4	no	—
495	C₂×C₄	—	12	16	no	—
496	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
497	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
498	C₂×C₄	C₂×C₅×#67	1	4	yes	—
499	C₂×C₃	—	2	4	no	—
500	C₂×C₃	—	2	8	no	—
501	C₂×C₃	—	4	4	no	—
502	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
503	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
504	C₂×C₃	C₅×#518	1	1	yes	characteristic
505	C₂×C₃	C₅×D₄²	1	2	yes	—
506	C₂×C₃	C₅×#546	1	2	yes	—
507	C₅	D₄×#217	1	1	yes	characteristic, direct product factor, Sylow
508	C₂²	—	2	4	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	4	no	—
511	C₂²	—	2	8	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	2	4	no	—
514	C₂²	—	2	8	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	4	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	2	4	no	—
519	C₂²	—	4	32	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	4	no	—
522	C₂²	C₅×D₄×Dic₃	1	4	yes	complemented
523	C₂²	C₂×C₅×#217	1	8	yes	complemented
524	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
525	C₂²	C₂×C₅×#237	1	1	yes	characteristic
526	C₂²	C₅×#1004	1	2	yes	—
527	C₂²	C₂³×C₅×Dic₃	1	1	yes	characteristic
528	C₂²	C₂²×C₅×#67	1	2	yes	—
529	C₄	—	2	2	no	—
530	C₄	—	6	4	no	—
531	C₄	—	12	4	no	—
532	C₄	—	12	2	no	—
533	C₄	C₂×C₅×#217	1	4	yes	complemented
534	C₃	C₅×D₄×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
535	C₂	—	2	4	no	—
536	C₂	—	2	8	no	—
537	C₂	—	4	4	no	—
538	C₂	C₂×C₅×D₄×Dic₃	1	1	yes	characteristic
539	C₂	C₅×#5798	1	1	yes	characteristic
540	C₂	C₅×D₄×#67	1	2	yes	—
541	C₂	C₅×#5806	1	2	yes	—
542	C₂	C₂²×C₅×#217	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×#217	C₂	semidirect
3. C₂×C₅×D₄×Dic₃	C₂	semidirect
4. C₅×#5247	C₂	semidirect
5. C₅×#5221	C₂	semidirect
6. C₅×#5220	C₂	semidirect
7. C₅×#5212	C₂	semidirect
8. C₄×C₅×#217	C₂	semidirect
12. C₂²×C₃×C₅×D₄	C₄	semidirect
17. C₂³×C₅×Dic₃	C₂²	semidirect
22. C₂×C₅×#217	C₂²	semidirect
23. C₂×C₅×#217	C₂²	semidirect
24. C₂×C₅×#217	C₂²	semidirect
26. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
27. C₂×C₄×C₅×Dic₃	C₂²	semidirect
28. C₅×C₃⋊#95	C₂²	semidirect
29. C₅×C₃⋊#95	C₂²	semidirect
30. D₄×#217	C₅	direct (N × H)
43. C₂⁴×C₃×C₅	C₂×C₄	semidirect
51. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
52. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
55. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
69. C₅×#217	D₄	direct (N × H)
73. C₂²×#217	C₂×C₅	semidirect
74. C₂×D₄×Dic₃	C₂×C₅	semidirect
75. #5247	C₂×C₅	semidirect
76. #5221	C₂×C₅	semidirect
77. #5220	C₂×C₅	semidirect
78. #5212	C₂×C₅	semidirect
79. C₄×#217	C₂×C₅	semidirect
82. C₂²×C₅×D₄	Dic₃	semidirect
124. C₃×C₅×D₄	C₂²⋊C₄	semidirect
139. C₂×C₅×Dic₃	C₂×D₄	semidirect
142. C₂²×C₃×D₄	C₄×C₅	semidirect
147. C₂³×Dic₃	C₂²×C₅	semidirect
152. C₂×#217	C₂²×C₅	semidirect
153. C₂×#217	C₂²×C₅	semidirect
154. C₂×#217	C₂²×C₅	semidirect
156. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
157. C₂×C₄×Dic₃	C₂²×C₅	semidirect
158. C₃⋊#95	C₂²×C₅	semidirect
159. C₃⋊#95	C₂²×C₅	semidirect
164. C₂⁴×C₅	C₂×Dic₃	semidirect
172. C₂×C₅×D₄	C₂×Dic₃	semidirect
173. C₂×C₅×D₄	C₂×Dic₃	semidirect
182. C₂²×C₄×C₅	C₂×Dic₃	semidirect
215. C₂²×C₃×C₅	C₂×C₂²⋊C₄	semidirect
216. C₂²×C₃×C₅	C₄×D₄	semidirect
223. C₃×C₄×C₅	C₂×C₂²⋊C₄	semidirect
231. C₂⁴×C₃	C₂×C₄×C₅	semidirect
239. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
240. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
243. C₂²×C₃×C₄	C₂×C₄×C₅	semidirect
257. #217	C₅×D₄	direct (N × H)
283. C₅×D₄	#217	direct (N × H)
301. C₂²×D₄	C₅×Dic₃	semidirect
350. C₃×D₄	C₅×C₂²⋊C₄	semidirect
365. C₂×Dic₃	C₂×C₅×D₄	semidirect
380. C₂²×C₅	D₄×Dic₃	semidirect
381. C₂²×C₅	C₂×#217	semidirect
391. C₄×C₅	C₂×#217	semidirect
396. C₂⁴	C₂×C₅×Dic₃	semidirect
404. C₂×D₄	C₂×C₅×Dic₃	semidirect
405. C₂×D₄	C₂×C₅×Dic₃	semidirect
414. C₂²×C₄	C₂×C₅×Dic₃	semidirect
425. C₃×C₅	D₄×C₂²⋊C₄	semidirect
440. C₂²×C₃	C₂×C₅×C₂²⋊C₄	semidirect
441. C₂²×C₃	C₄×C₅×D₄	semidirect
448. C₃×C₄	C₂×C₅×C₂²⋊C₄	semidirect
483. D₄	C₅×#217	direct (N × H)
507. C₅	D₄×#217	direct (N × H)
522. C₂²	C₅×D₄×Dic₃	semidirect
523. C₂²	C₂×C₅×#217	semidirect
533. C₄	C₂×C₅×#217	semidirect
534. C₃	C₅×D₄×C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅×D₄	2
C₂²×C₅×#217	2
C₂×C₅×D₄×Dic₃	2
C₅×#5247	2
C₅×#5221	2
C₅×#5220	2
C₅×#5212	2
C₄×C₅×#217	2
C₅×D₄×C₂²⋊C₄	3
D₄×#217	5

Subgroups — C5×D4×#217 #14325910

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₄×#217 #14325910