Subgroups — C₂×C₅×#5493 #14480302

Order 1920.

3968 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×#67	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#930	C₂	1	4	yes	maximal, complemented
4	C₅×#5493	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₅×#886	C₂	1	4	yes	maximal, complemented
6	C₂×C₅×#882	C₂	1	4	yes	maximal, complemented
7	C₂×C₅×#534	—	3	1	no	maximal, Hall
8	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
9	C₂⁴×C₅×D₃	C₂²	1	2	yes	complemented
10	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	complemented
11	C₂²×C₅×#67	—	2	16	no	—
12	C₂²×C₅×#67	C₂²	1	4	yes	—
13	C₂²×C₅×#67	C₂²	1	4	yes	complemented
14	C₂²×C₅×#67	C₂²	1	16	yes	complemented
15	C₂³×C₅×Dic₃	C₂²	1	2	yes	complemented
16	C₂²×C₅×D₁₂	C₂²	1	4	yes	complemented
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
19	C₅×#930	C₂²	1	32	yes	complemented
20	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
21	C₂×C₅×C₄⋊Dic₃	C₂²	1	4	yes	complemented
22	C₅×#886	C₂²	1	32	yes	complemented
23	C₅×#882	C₂²	1	32	yes	complemented
24	C₂×#5493	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂³×C₅×D₄	—	3	2	no	—
26	C₅×#534	—	3	16	no	—
27	C₂×C₅×#123	—	3	4	no	—
28	C₂×C₅×#121	—	3	4	no	—
29	C₂×C₅×#120	—	3	4	no	—
30	C₂²×C₅×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
31	C₂⁴×C₃×C₅	—	4	4	no	—
32	C₂⁴×C₃×C₅	D₄	1	8	yes	complemented
33	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
34	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
35	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
36	C₂³×C₅×D₃	—	2	8	no	—
37	C₂³×C₅×D₃	—	4	8	no	—
38	C₂³×C₅×D₃	C₂³	1	4	yes	—
39	C₂³×C₅×D₃	C₂³	1	8	yes	complemented
40	C₂²×C₃×C₄×C₅	—	4	4	no	—
41	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	complemented
43	C₂×C₅×#67	—	2	16	no	—
44	C₂×C₅×#67	—	2	16	no	—
45	C₂×C₅×#67	—	2	64	no	—
46	C₂×C₅×#67	C₂³	1	16	yes	—
47	C₂×C₅×#67	C₂³	1	16	yes	complemented
48	C₂²×C₅×Dic₃	—	2	8	no	—
49	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
50	C₂²×C₅×Dic₃	C₂³	1	8	yes	complemented
51	C₂×C₅×D₁₂	—	4	8	no	—
52	C₂×C₅×D₁₂	C₂³	1	16	yes	complemented
53	C₃×C₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
54	C₅×(C₂×D₃)⋊C₄	C₂³	1	32	yes	complemented
55	C₅×C₄⋊Dic₃	C₂³	1	16	yes	complemented
56	C₂³×#67	C₂×C₅	1	2	yes	complemented
57	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
58	C₂×#930	C₂×C₅	1	4	yes	complemented
59	#5493	C₂×C₅	1	16	yes	direct product factor
60	C₂×#886	C₂×C₅	1	4	yes	complemented
61	C₂×#882	C₂×C₅	1	4	yes	complemented
62	C₂⁵×C₅	—	3	2	no	—
63	C₂⁵×C₅	C₂×D₃	1	1	yes	characteristic
64	C₂²×C₅×D₄	—	3	4	no	—
65	C₂²×C₅×D₄	—	3	4	no	—
66	C₂²×C₅×D₄	—	3	16	no	—
67	C₂²×C₅×D₄	—	3	4	no	—
68	C₂²×C₅×D₄	—	6	16	no	—
69	C₂³×C₄×C₅	—	3	2	no	—
70	C₂³×C₄×C₅	C₂×D₃	1	2	yes	complemented
71	C₅×#123	—	3	32	no	—
72	C₅×#121	—	3	32	no	—
73	C₅×#120	—	3	32	no	—
74	C₂×C₅×C₄⋊C₄	—	3	4	no	—
75	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
76	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
77	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	8	yes	complemented
78	C₂×#534	—	3	1	no	Sylow
79	C₂³×C₃×C₅	—	2	4	no	—
80	C₂³×C₃×C₅	—	2	8	no	—
81	C₂³×C₃×C₅	—	4	16	no	—
82	C₂³×C₃×C₅	—	4	8	no	—
83	C₂³×C₃×C₅	C₂×D₄	1	8	yes	—
84	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
85	C₂³×C₃×C₅	C₂×D₄	1	16	yes	complemented
86	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
87	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
88	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
89	C₂²×C₅×D₃	—	2	8	no	—
90	C₂²×C₅×D₃	—	2	16	no	—
91	C₂²×C₅×D₃	—	2	16	no	—
92	C₂²×C₅×D₃	—	4	16	no	—
93	C₂²×C₅×D₃	—	4	32	no	—
94	C₂²×C₅×D₃	C₂⁴	1	8	yes	—
95	C₂×C₃×C₄×C₅	—	2	8	no	—
96	C₂×C₃×C₄×C₅	—	4	8	no	—
97	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
98	C₅×#67	—	2	32	no	—
99	C₅×#67	—	2	32	no	—
100	C₂×C₅×Dic₃	—	2	8	no	—
101	C₂×C₅×Dic₃	—	2	16	no	—
102	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
103	C₅×D₁₂	—	4	16	no	—
104	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
105	C₂⁴×D₃	C₂²×C₅	1	2	yes	complemented
106	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	complemented
107	C₂²×#67	—	2	16	no	—
108	C₂²×#67	C₂²×C₅	1	4	yes	—
109	C₂²×#67	C₂²×C₅	1	4	yes	complemented
110	C₂²×#67	C₂²×C₅	1	16	yes	complemented
111	C₂³×Dic₃	C₂²×C₅	1	2	yes	complemented
112	C₂²×D₁₂	C₂²×C₅	1	4	yes	complemented
113	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
114	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
115	#930	C₂²×C₅	1	32	yes	complemented
116	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	8	yes	complemented
117	C₂×C₄⋊Dic₃	C₂²×C₅	1	4	yes	complemented
118	#886	C₂²×C₅	1	32	yes	complemented
119	#882	C₂²×C₅	1	32	yes	complemented
120	C₂⁴×C₅	—	3	4	no	—
121	C₂⁴×C₅	—	3	8	no	—
122	C₂⁴×C₅	—	4	4	no	—
123	C₂⁴×C₅	—	6	8	no	—
124	C₂⁴×C₅	—	12	8	no	—
125	C₂⁴×C₅	D₁₂	1	8	yes	complemented
126	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
127	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
128	C₂⁴×C₅	C₂²×D₃	1	4	yes	—
129	C₂×C₅×D₄	—	3	16	no	—
130	C₂×C₅×D₄	—	3	16	no	—
131	C₂×C₅×D₄	—	3	16	no	—
132	C₂×C₅×D₄	—	6	16	no	—
133	C₂×C₅×D₄	—	6	16	no	—
134	C₂×C₅×D₄	—	6	64	no	—
135	C₂×C₅×D₄	—	12	8	no	—
136	C₂²×C₄×C₅	—	3	8	no	—
137	C₂²×C₄×C₅	—	3	4	no	—
138	C₂²×C₄×C₅	—	4	4	no	—
139	C₂²×C₄×C₅	—	6	8	no	—
140	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
141	C₂²×C₄×C₅	C₂²×D₃	1	8	yes	complemented
142	C₅×C₄⋊C₄	—	3	16	no	—
143	C₅×C₂²⋊C₄	—	3	32	no	—
144	C₅×C₂²⋊C₄	C₂²×D₃	1	16	yes	complemented
145	C₂³×D₄	—	3	2	no	—
146	#534	—	3	16	no	—
147	C₂×#123	—	3	4	no	—
148	C₂×#121	—	3	4	no	—
149	C₂×#120	—	3	4	no	—
150	C₂²×C₂²⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
151	C₂²×C₃×C₅	—	2	16	no	—
152	C₂²×C₃×C₅	—	2	8	no	—
153	C₂²×C₃×C₅	—	2	4	no	—
154	C₂²×C₃×C₅	—	2	8	no	—
155	C₂²×C₃×C₅	—	4	16	no	—
156	C₂²×C₃×C₅	C₂²×D₄	1	8	yes	—
157	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
158	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
159	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
160	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
161	C₂×C₅×D₃	—	2	8	no	—
162	C₂×C₅×D₃	—	2	16	no	—
163	C₂×C₅×D₃	—	4	32	no	—
164	C₂×C₅×D₃	—	4	16	no	—
165	C₃×C₄×C₅	—	2	8	no	—
166	C₅×Dic₃	—	2	8	no	—
167	C₂⁴×C₃	—	4	4	no	—
168	C₂⁴×C₃	C₅×D₄	1	8	yes	complemented
169	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
170	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
171	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
172	C₂³×D₃	—	2	8	no	—
173	C₂³×D₃	—	4	8	no	—
174	C₂³×D₃	C₂³×C₅	1	4	yes	—
175	C₂³×D₃	C₂³×C₅	1	8	yes	complemented
176	C₂²×C₃×C₄	—	4	4	no	—
177	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
178	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	complemented
179	C₂×#67	—	2	16	no	—
180	C₂×#67	—	2	16	no	—
181	C₂×#67	—	2	64	no	—
182	C₂×#67	C₂³×C₅	1	16	yes	—
183	C₂×#67	C₂³×C₅	1	16	yes	complemented
184	C₂²×Dic₃	—	2	8	no	—
185	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
186	C₂²×Dic₃	C₂³×C₅	1	8	yes	complemented
187	C₂×D₁₂	—	4	8	no	—
188	C₂×D₁₂	C₂³×C₅	1	16	yes	complemented
189	C₃×C₂²⋊C₄	C₂³×C₅	1	16	yes	complemented
190	(C₂×D₃)⋊C₄	C₂³×C₅	1	32	yes	complemented
191	C₄⋊Dic₃	C₂³×C₅	1	16	yes	complemented
192	C₂³×C₅	—	2	4	no	—
193	C₂³×C₅	—	2	8	no	—
194	C₂³×C₅	—	3	8	no	—
195	C₂³×C₅	—	4	16	no	—
196	C₂³×C₅	—	4	8	no	—
197	C₂³×C₅	—	6	16	no	—
198	C₂³×C₅	—	6	8	no	—
199	C₂³×C₅	—	6	16	no	—
200	C₂³×C₅	—	12	16	no	—
201	C₂³×C₅	—	12	32	no	—
202	C₂³×C₅	C₂×D₁₂	1	8	yes	—
203	C₂³×C₅	C₂×D₁₂	1	4	yes	—
204	C₂³×C₅	C₂×D₁₂	1	16	yes	complemented
205	C₂³×C₅	C₂³×D₃	1	4	yes	—
206	C₂³×C₅	C₂³×D₃	1	2	yes	—
207	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
208	C₅×D₄	—	6	32	no	—
209	C₅×D₄	—	6	32	no	—
210	C₅×D₄	—	12	16	no	—
211	C₂×C₄×C₅	—	2	8	no	—
212	C₂×C₄×C₅	—	3	8	no	—
213	C₂×C₄×C₅	—	4	8	no	—
214	C₂×C₄×C₅	—	6	16	no	—
215	C₂×C₄×C₅	—	6	8	no	—
216	C₂×C₄×C₅	C₂³×D₃	1	8	yes	—
217	C₂⁵	—	3	2	no	—
218	C₂⁵	C₂×C₅×D₃	1	1	yes	characteristic
219	C₂²×D₄	—	3	4	no	—
220	C₂²×D₄	—	3	4	no	—
221	C₂²×D₄	—	3	16	no	—
222	C₂²×D₄	—	3	4	no	—
223	C₂²×D₄	—	6	16	no	—
224	C₂³×C₄	—	3	2	no	—
225	C₂³×C₄	C₂×C₅×D₃	1	2	yes	complemented
226	#123	—	3	32	no	—
227	#121	—	3	32	no	—
228	#120	—	3	32	no	—
229	C₂×C₄⋊C₄	—	3	4	no	—
230	C₂×C₂²⋊C₄	—	3	8	no	—
231	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	4	yes	complemented
232	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	8	yes	complemented
233	C₂×C₃×C₅	—	2	8	no	—
234	C₂×C₃×C₅	—	2	4	no	—
235	C₂×C₃×C₅	#534	1	4	yes	complemented
236	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
237	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
238	C₅×D₃	—	4	8	no	—
239	C₂³×C₃	—	2	4	no	—
240	C₂³×C₃	—	2	8	no	—
241	C₂³×C₃	—	4	16	no	—
242	C₂³×C₃	—	4	8	no	—
243	C₂³×C₃	C₂×C₅×D₄	1	8	yes	—
244	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
245	C₂³×C₃	C₂×C₅×D₄	1	16	yes	complemented
246	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
247	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
248	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
249	C₂²×D₃	—	2	8	no	—
250	C₂²×D₃	—	2	16	no	—
251	C₂²×D₃	—	2	16	no	—
252	C₂²×D₃	—	4	16	no	—
253	C₂²×D₃	—	4	32	no	—
254	C₂²×D₃	C₂⁴×C₅	1	8	yes	—
255	C₂×C₃×C₄	—	2	8	no	—
256	C₂×C₃×C₄	—	4	8	no	—
257	C₂×C₃×C₄	C₂⁴×C₅	1	8	yes	—
258	#67	—	2	32	no	—
259	#67	—	2	32	no	—
260	C₂×Dic₃	—	2	8	no	—
261	C₂×Dic₃	—	2	16	no	—
262	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
263	D₁₂	—	4	16	no	—
264	C₂²×C₅	—	2	4	no	—
265	C₂²×C₅	—	2	8	no	—
266	C₂²×C₅	—	2	16	no	—
267	C₂²×C₅	—	2	8	no	—
268	C₂²×C₅	—	4	16	no	—
269	C₂²×C₅	—	6	8	no	—
270	C₂²×C₅	—	6	16	no	—
271	C₂²×C₅	—	12	32	no	—
272	C₂²×C₅	—	12	16	no	—
273	C₂²×C₅	C₂²×D₁₂	1	8	yes	—
274	C₂²×C₅	C₂²×D₁₂	1	4	yes	—
275	C₂²×C₅	C₂²×D₁₂	1	2	yes	—
276	C₂²×C₅	#1004	1	4	yes	—
277	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
278	C₄×C₅	—	2	8	no	—
279	C₄×C₅	—	6	8	no	—
280	C₂⁴	—	3	4	no	—
281	C₂⁴	—	3	8	no	—
282	C₂⁴	—	4	4	no	—
283	C₂⁴	—	6	8	no	—
284	C₂⁴	—	12	8	no	—
285	C₂⁴	C₅×D₁₂	1	8	yes	complemented
286	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
287	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
288	C₂⁴	C₂²×C₅×D₃	1	4	yes	—
289	C₂×D₄	—	3	16	no	—
290	C₂×D₄	—	3	16	no	—
291	C₂×D₄	—	3	16	no	—
292	C₂×D₄	—	6	16	no	—
293	C₂×D₄	—	6	16	no	—
294	C₂×D₄	—	6	64	no	—
295	C₂×D₄	—	12	8	no	—
296	C₂²×C₄	—	3	4	no	—
297	C₂²×C₄	—	3	8	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	—	6	8	no	—
300	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
301	C₂²×C₄	C₂²×C₅×D₃	1	8	yes	complemented
302	C₄⋊C₄	—	3	16	no	—
303	C₂²⋊C₄	—	3	32	no	—
304	C₂²⋊C₄	C₂²×C₅×D₃	1	16	yes	complemented
305	C₃×C₅	C₂×#534	1	1	yes	characteristic, complemented, Hall
306	C₂²×C₃	—	2	16	no	—
307	C₂²×C₃	—	2	8	no	—
308	C₂²×C₃	—	2	4	no	—
309	C₂²×C₃	—	2	8	no	—
310	C₂²×C₃	—	4	16	no	—
311	C₂²×C₃	C₂²×C₅×D₄	1	8	yes	—
312	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
313	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
314	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
315	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
316	C₂×D₃	—	2	8	no	—
317	C₂×D₃	—	2	16	no	—
318	C₂×D₃	—	4	32	no	—
319	C₂×D₃	—	4	16	no	—
320	C₃×C₄	—	2	8	no	—
321	Dic₃	—	2	8	no	—
322	C₂×C₅	—	2	8	no	—
323	C₂×C₅	—	2	4	no	—
324	C₂×C₅	—	12	8	no	—
325	C₂×C₅	#5493	1	4	yes	direct product factor
326	C₂×C₅	C₂³×D₁₂	1	1	yes	characteristic
327	C₂×C₅	C₂×#1004	1	2	yes	—
328	C₂³	—	2	4	no	—
329	C₂³	—	2	8	no	—
330	C₂³	—	3	8	no	—
331	C₂³	—	4	16	no	—
332	C₂³	—	4	8	no	—
333	C₂³	—	6	16	no	—
334	C₂³	—	6	8	no	—
335	C₂³	—	6	16	no	—
336	C₂³	—	12	16	no	—
337	C₂³	—	12	32	no	—
338	C₂³	C₂×C₅×D₁₂	1	8	yes	—
339	C₂³	C₂×C₅×D₁₂	1	4	yes	—
340	C₂³	C₂×C₅×D₁₂	1	16	yes	complemented
341	C₂³	C₂³×C₅×D₃	1	4	yes	—
342	C₂³	C₂³×C₅×D₃	1	2	yes	—
343	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
344	D₄	—	6	32	no	—
345	D₄	—	6	32	no	—
346	D₄	—	12	16	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	3	8	no	—
349	C₂×C₄	—	4	8	no	—
350	C₂×C₄	—	6	16	no	—
351	C₂×C₄	—	6	8	no	—
352	C₂×C₄	C₂³×C₅×D₃	1	8	yes	—
353	C₂×C₃	—	2	8	no	—
354	C₂×C₃	—	2	4	no	—
355	C₂×C₃	C₅×#534	1	4	yes	complemented
356	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
357	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
358	D₃	—	4	8	no	—
359	C₅	C₂×#5493	1	1	yes	characteristic, direct product factor, Sylow
360	C₂²	—	2	4	no	—
361	C₂²	—	2	8	no	—
362	C₂²	—	2	16	no	—
363	C₂²	—	2	8	no	—
364	C₂²	—	4	16	no	—
365	C₂²	—	6	8	no	—
366	C₂²	—	6	16	no	—
367	C₂²	—	12	32	no	—
368	C₂²	—	12	16	no	—
369	C₂²	C₂²×C₅×D₁₂	1	8	yes	—
370	C₂²	C₂²×C₅×D₁₂	1	4	yes	—
371	C₂²	C₂²×C₅×D₁₂	1	2	yes	—
372	C₂²	C₅×#1004	1	4	yes	—
373	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
374	C₄	—	2	8	no	—
375	C₄	—	6	8	no	—
376	C₃	C₂×C₅×#534	1	1	yes	characteristic, complemented, Sylow
377	C₂	—	2	8	no	—
378	C₂	—	2	4	no	—
379	C₂	—	12	8	no	—
380	C₂	C₅×#5493	1	4	yes	direct product factor
381	C₂	C₂³×C₅×D₁₂	1	1	yes	characteristic
382	C₂	C₂×C₅×#1004	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂²×C₃×C₅×C₂²⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂²×C₅×C₂²⋊C₄	D₃
hypocenter	C₃	C₂×C₅×#534
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₅×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₅×#67	C₂	semidirect
2. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
3. C₂×C₅×#930	C₂	semidirect
4. C₅×#5493	C₂	direct (N × H)
5. C₂×C₅×#886	C₂	semidirect
6. C₂×C₅×#882	C₂	semidirect
9. C₂⁴×C₅×D₃	C₂²	semidirect
10. C₂³×C₃×C₄×C₅	C₂²	semidirect
13. C₂²×C₅×#67	C₂²	semidirect
14. C₂²×C₅×#67	C₂²	semidirect
15. C₂³×C₅×Dic₃	C₂²	semidirect
16. C₂²×C₅×D₁₂	C₂²	semidirect
17. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
18. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
19. C₅×#930	C₂²	semidirect
20. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
21. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
22. C₅×#886	C₂²	semidirect
23. C₅×#882	C₂²	semidirect
24. C₂×#5493	C₅	direct (N × H)
30. C₂²×C₅×C₂²⋊C₄	D₃	semidirect
32. C₂⁴×C₃×C₅	D₄	semidirect
39. C₂³×C₅×D₃	C₂³	semidirect
42. C₂²×C₃×C₄×C₅	C₂³	semidirect
47. C₂×C₅×#67	C₂³	semidirect
50. C₂²×C₅×Dic₃	C₂³	semidirect
52. C₂×C₅×D₁₂	C₂³	semidirect
53. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
54. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
55. C₅×C₄⋊Dic₃	C₂³	semidirect
56. C₂³×#67	C₂×C₅	semidirect
57. C₂²×C₃×C₂²⋊C₄	C₂×C₅	semidirect
58. C₂×#930	C₂×C₅	semidirect
59. #5493	C₂×C₅	direct (N × H)
60. C₂×#886	C₂×C₅	semidirect
61. C₂×#882	C₂×C₅	semidirect
70. C₂³×C₄×C₅	C₂×D₃	semidirect
76. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
77. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
85. C₂³×C₃×C₅	C₂×D₄	semidirect
105. C₂⁴×D₃	C₂²×C₅	semidirect
106. C₂³×C₃×C₄	C₂²×C₅	semidirect
109. C₂²×#67	C₂²×C₅	semidirect
110. C₂²×#67	C₂²×C₅	semidirect
111. C₂³×Dic₃	C₂²×C₅	semidirect
112. C₂²×D₁₂	C₂²×C₅	semidirect
113. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
114. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
115. #930	C₂²×C₅	semidirect
116. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
117. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
118. #886	C₂²×C₅	semidirect
119. #882	C₂²×C₅	semidirect
125. C₂⁴×C₅	D₁₂	semidirect
141. C₂²×C₄×C₅	C₂²×D₃	semidirect
144. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
150. C₂²×C₂²⋊C₄	C₅×D₃	semidirect
168. C₂⁴×C₃	C₅×D₄	semidirect
175. C₂³×D₃	C₂³×C₅	semidirect
178. C₂²×C₃×C₄	C₂³×C₅	semidirect
183. C₂×#67	C₂³×C₅	semidirect
186. C₂²×Dic₃	C₂³×C₅	semidirect
188. C₂×D₁₂	C₂³×C₅	semidirect
189. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
190. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
191. C₄⋊Dic₃	C₂³×C₅	semidirect
204. C₂³×C₅	C₂×D₁₂	semidirect
225. C₂³×C₄	C₂×C₅×D₃	semidirect
231. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
232. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
235. C₂×C₃×C₅	#534	semidirect
245. C₂³×C₃	C₂×C₅×D₄	semidirect
285. C₂⁴	C₅×D₁₂	semidirect
301. C₂²×C₄	C₂²×C₅×D₃	semidirect
304. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
305. C₃×C₅	C₂×#534	semidirect
325. C₂×C₅	#5493	direct (N × H)
340. C₂³	C₂×C₅×D₁₂	semidirect
355. C₂×C₃	C₅×#534	semidirect
359. C₅	C₂×#5493	direct (N × H)
376. C₃	C₂×C₅×#534	semidirect
380. C₂	C₅×#5493	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₅×#67	2
C₂²×C₃×C₅×C₂²⋊C₄	2
C₂×C₅×#930	2
C₅×#5493	2
C₂×C₅×#886	2
C₂×C₅×#882	2
C₂×C₅×#534	3
C₂×#5493	5

Subgroups — C2×C5×#5493 #14480302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5493 #14480302