Subgroups — C₂×#11746871 #14413788

Order 1920.

976 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊(C₃⋊#168)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#90955	C₂	1	2	yes	maximal
5	C₂×#90952	C₂	1	2	yes	maximal, complemented
6	#11746871	C₂	1	8	yes	maximal, direct product factor
7	C₂×#65124	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₄×D₅	C₄	1	1	yes	characteristic
9	C₂²×C₃×C₄×D₅	C₄	1	1	yes	characteristic
10	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃⋊#168	C₂²	1	2	yes	—
13	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
14	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
15	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
16	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
17	C₃×C₄²×D₅	C₄	1	4	yes	—
18	C₃×C₄²×D₅	C₂²	1	4	yes	—
19	C₄⋊(C₃⋊#168)	C₂²	1	4	yes	complemented
20	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
21	#90955	C₂²	1	8	yes	—
22	#90952	C₂²	1	8	yes	complemented
23	C₂×#4926	—	5	1	no	maximal, Hall
24	C₂×C₄²×D₅	D₃	1	1	yes	characteristic
25	C₂×C₅×C₄⋊C₈	—	3	1	no	—
26	C₂×#3952	—	3	2	no	—
27	C₂×#3947	—	3	2	no	—
28	C₂×C₄⋊#168	—	3	1	no	—
29	#65124	—	3	8	no	—
30	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₄×D₅	—	2	4	no	—
38	C₂×C₃×C₄×D₅	—	2	4	no	—
39	C₂×C₃×C₄×D₅	—	2	2	no	—
40	C₂×C₃×C₄×D₅	—	2	2	no	—
41	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
42	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
43	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
45	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
46	C₃×C₄²×C₅	C₂³	1	2	yes	—
47	C₂×C₃⋊#168	—	2	4	no	—
48	C₂×C₃⋊#168	C₂³	1	4	yes	—
49	C₂×C₅×C₃⋊C₈	—	2	4	no	—
50	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
51	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
52	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
53	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
54	C₃×C₄×Dic₅	C₂³	1	2	yes	—
55	C₂²×C₃×C₄²	—	5	1	no	—
56	C₂×#830	—	5	2	no	—
57	#4926	—	5	8	no	—
58	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
59	C₂×C₄⋊(C₃⋊C₈)	D₅	1	1	yes	characteristic, complemented
60	C₂×#803	—	5	2	no	—
61	C₂²×C₄×D₅	Dic₃	1	1	yes	characteristic
62	C₂²×C₄×D₅	Dic₃	1	1	yes	characteristic
63	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
64	C₂²×C₅×C₈	—	3	2	no	—
65	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
66	C₂×C₄×Dic₅	Dic₃	1	1	yes	characteristic
67	C₂×C₄×Dic₅	Dic₃	1	1	yes	characteristic
68	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
69	C₂²×#168	—	3	2	no	—
70	C₄²×D₅	Dic₃	1	4	yes	—
71	C₄²×D₅	C₂×D₃	1	4	yes	—
72	C₅×C₄⋊C₈	—	3	4	no	—
73	#3952	—	3	8	no	—
74	#3947	—	3	8	no	—
75	C₄⋊#168	—	3	4	no	—
76	C₂×#432	—	15	1	no	Sylow
77	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₃×D₅	—	2	2	no	—
79	C₂²×C₃×D₅	—	2	2	no	—
80	C₂²×C₃×D₅	M₁₆	1	4	yes	—
81	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
82	C₂×C₃×C₄×C₅	—	2	2	no	—
83	C₂×C₃×C₄×C₅	M₁₆	1	4	yes	—
84	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
85	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
87	C₂×C₃×C₄×C₅	#41	1	2	yes	—
88	C₂×C₃×C₄×C₅	#41	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
90	C₂×C₃×Dic₅	—	2	2	no	—
91	C₂×C₃×Dic₅	—	2	2	no	—
92	C₂×C₃×Dic₅	—	2	2	no	—
93	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
94	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
95	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
96	C₃×C₄×D₅	—	2	8	no	—
97	C₃×C₄×D₅	—	2	4	no	—
98	C₃×C₄×D₅	—	2	8	no	—
99	C₃×C₄×D₅	—	2	2	no	—
100	C₃×C₄×D₅	—	2	2	no	—
101	C₃⋊#168	—	2	4	no	—
102	C₅×C₃⋊C₈	—	2	4	no	—
103	C₂³×C₃×C₄	—	5	1	no	—
104	C₂³×C₃×C₄	—	5	1	no	—
105	C₂³×C₃×C₄	—	5	1	no	—
106	C₂×C₃×C₄²	—	5	1	no	—
107	C₂×C₃×C₄²	—	5	1	no	—
108	C₂×C₃×C₄²	—	5	1	no	—
109	C₂×C₃×C₄²	—	5	4	no	—
110	C₂×C₃×C₄²	—	5	4	no	—
111	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
112	C₂²×C₃⋊C₈	—	5	2	no	—
113	C₂²×C₃⋊C₈	C₂×D₅	1	2	yes	—
114	#830	—	5	8	no	—
115	C₄⋊(C₃⋊C₈)	—	5	4	no	—
116	C₄⋊(C₃⋊C₈)	C₂×D₅	1	4	yes	complemented
117	#803	—	5	8	no	—
118	C₂³×D₅	C₂×Dic₃	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
122	C₂²×Dic₅	C₂×Dic₃	1	1	yes	characteristic
123	C₂²×Dic₅	C₂×Dic₃	1	1	yes	characteristic
124	C₂²×Dic₅	C₂×Dic₃	1	1	yes	characteristic
125	C₂×C₄×D₅	—	2	4	no	—
126	C₂×C₄×D₅	—	2	4	no	—
127	C₂×C₄×D₅	—	2	2	no	—
128	C₂×C₄×D₅	—	2	2	no	—
129	C₂×C₄×D₅	C₂×Dic₃	1	4	yes	—
130	C₂×C₄×D₅	C₂×Dic₃	1	4	yes	—
131	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
132	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
133	C₂×C₅×C₈	—	3	4	no	—
134	C₂×C₅×C₈	—	6	4	no	—
135	C₄²×C₅	C₂×Dic₃	1	2	yes	—
136	C₄²×C₅	C₂²×D₃	1	2	yes	—
137	C₄×Dic₅	C₂×Dic₃	1	2	yes	—
138	C₄×Dic₅	C₂×Dic₃	1	4	yes	—
139	C₄×Dic₅	C₂×Dic₃	1	4	yes	—
140	C₄×Dic₅	C₂²×D₃	1	2	yes	—
141	C₂×#168	—	3	4	no	—
142	C₂×#168	—	6	4	no	—
143	C₂²×C₄²	—	5	1	no	—
144	#432	—	15	8	no	—
145	C₂×C₄⋊C₈	—	3	1	no	—
146	C₂×C₄⋊C₈	—	15	1	no	—
147	C₂×C₂²⋊C₈	—	15	2	no	—
148	C₂×#97	—	15	2	no	—
149	C₂²×C₃×C₅	#117	1	2	yes	—
150	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
151	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
152	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₃×D₅	—	2	2	no	—
154	C₂×C₃×D₅	—	2	2	no	—
155	C₂×C₃×D₅	—	2	8	no	—
156	C₂×C₃×D₅	C₂×M₁₆	1	4	yes	—
157	C₃×C₄×C₅	—	2	2	no	—
158	C₃×C₄×C₅	#117	1	2	yes	—
159	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	—
160	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
161	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
162	C₃×Dic₅	—	2	2	no	—
163	C₃×Dic₅	—	2	2	no	—
164	C₃×Dic₅	—	2	2	no	—
165	C₂⁴×C₃	—	5	1	no	—
166	C₂²×C₃×C₄	—	5	1	no	—
167	C₂²×C₃×C₄	—	5	1	no	—
168	C₂²×C₃×C₄	—	5	1	no	—
169	C₂²×C₃×C₄	—	5	4	no	—
170	C₂²×C₃×C₄	—	5	2	no	—
171	C₂²×C₃×C₄	—	5	4	no	—
172	C₂²×C₃×C₄	—	5	2	no	—
173	C₂²×C₃×C₄	—	10	4	no	—
174	C₂²×C₃×C₄	—	10	4	no	—
175	C₂²×C₃×C₄	—	10	2	no	—
176	C₂²×C₃×C₄	—	10	2	no	—
177	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
180	C₃×C₄²	—	5	4	no	—
181	C₃×C₄²	—	5	2	no	—
182	C₃×C₄²	—	5	4	no	—
183	C₃×C₄²	—	5	2	no	—
184	C₃×C₄²	C₄×D₅	1	2	yes	—
185	C₃×C₄²	C₂²×D₅	1	2	yes	—
186	C₂×C₃⋊C₈	—	2	4	no	—
187	C₂×C₃⋊C₈	—	5	4	no	—
188	C₂×C₃⋊C₈	—	10	4	no	—
189	C₂×C₃⋊C₈	C₂²×D₅	1	4	yes	—
190	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
191	C₂²×D₅	—	2	2	no	—
192	C₂²×D₅	—	2	2	no	—
193	C₂²×D₅	#208	1	4	yes	—
194	C₂²×D₅	C₂²×Dic₃	1	2	yes	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	#208	1	4	yes	—
197	C₂×C₄×C₅	#235	1	2	yes	—
198	C₂×C₄×C₅	#235	1	2	yes	—
199	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
200	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
201	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
203	C₂×Dic₅	—	2	2	no	—
204	C₂×Dic₅	—	2	2	no	—
205	C₂×Dic₅	—	2	2	no	—
206	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
207	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
208	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
209	C₄×D₅	—	2	8	no	—
210	C₄×D₅	—	2	8	no	—
211	C₄×D₅	—	2	4	no	—
212	C₄×D₅	—	2	2	no	—
213	C₄×D₅	—	2	2	no	—
214	C₅×C₈	—	6	4	no	—
215	#168	—	6	4	no	—
216	C₂³×C₄	—	5	1	no	—
217	C₂³×C₄	—	5	1	no	—
218	C₂³×C₄	—	5	1	no	—
219	C₂²×C₈	—	3	2	no	—
220	C₂²×C₈	—	15	2	no	—
221	C₂×C₄²	—	5	1	no	—
222	C₂×C₄²	—	5	1	no	—
223	C₂×C₄²	—	5	1	no	—
224	C₂×C₄²	—	5	4	no	—
225	C₂×C₄²	—	5	4	no	—
226	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
227	C₄⋊C₈	—	3	4	no	—
228	C₄⋊C₈	—	15	4	no	—
229	C₂²⋊C₈	—	15	8	no	—
230	#97	—	15	8	no	—
231	C₂×C₃×C₅	#432	1	4	yes	complemented
232	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
233	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
234	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
235	C₃×D₅	—	2	4	no	—
236	C₂³×C₃	—	5	2	no	—
237	C₂³×C₃	—	5	4	no	—
238	C₂³×C₃	—	10	2	no	—
239	C₂³×C₃	—	10	2	no	—
240	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	5	2	no	—
243	C₂×C₃×C₄	—	5	2	no	—
244	C₂×C₃×C₄	—	5	2	no	—
245	C₂×C₃×C₄	—	10	8	no	—
246	C₂×C₃×C₄	—	10	2	no	—
247	C₂×C₃×C₄	—	10	2	no	—
248	C₂×C₃×C₄	—	10	2	no	—
249	C₂×C₃×C₄	—	10	2	no	—
250	C₂×C₃×C₄	—	10	2	no	—
251	C₂×C₃×C₄	—	10	4	no	—
252	C₂×C₃×C₄	—	10	8	no	—
253	C₂×C₃×C₄	#676	1	4	yes	—
254	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
255	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
257	C₂×C₃×C₄	#711	1	2	yes	—
258	C₂×C₃×C₄	#713	1	2	yes	—
259	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
260	C₃⋊C₈	—	2	4	no	—
261	C₃⋊C₈	—	10	4	no	—
262	C₂²×C₅	C₂×#208	1	2	yes	—
263	C₂²×C₅	C₂×#208	1	2	yes	—
264	C₂²×C₅	#926	1	2	yes	—
265	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
266	C₂×D₅	—	2	8	no	—
267	C₂×D₅	—	2	2	no	—
268	C₂×D₅	—	2	2	no	—
269	C₂×D₅	C₂×#208	1	4	yes	—
270	C₄×C₅	—	2	2	no	—
271	C₄×C₅	C₂×#208	1	4	yes	—
272	C₄×C₅	#926	1	2	yes	—
273	C₄×C₅	C₂×#235	1	1	yes	characteristic
274	C₄×C₅	C₂×#235	1	1	yes	characteristic
275	Dic₅	—	2	2	no	—
276	Dic₅	—	2	2	no	—
277	Dic₅	—	2	2	no	—
278	C₂⁴	—	5	1	no	—
279	C₂²×C₄	—	5	1	no	—
280	C₂²×C₄	—	5	1	no	—
281	C₂²×C₄	—	5	1	no	—
282	C₂²×C₄	—	5	4	no	—
283	C₂²×C₄	—	5	4	no	—
284	C₂²×C₄	—	5	2	no	—
285	C₂²×C₄	—	5	2	no	—
286	C₂²×C₄	—	10	4	no	—
287	C₂²×C₄	—	10	2	no	—
288	C₂²×C₄	—	10	2	no	—
289	C₂²×C₄	—	10	4	no	—
290	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
291	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
293	C₂×C₈	—	3	4	no	—
294	C₂×C₈	—	6	4	no	—
295	C₂×C₈	—	15	4	no	—
296	C₂×C₈	—	30	4	no	—
297	C₄²	—	5	4	no	—
298	C₄²	—	5	4	no	—
299	C₄²	—	5	2	no	—
300	C₄²	—	5	2	no	—
301	C₄²	D₅×Dic₃	1	2	yes	—
302	C₄²	C₂×D₃×D₅	1	2	yes	—
303	C₃×C₅	C₂×#432	1	1	yes	characteristic, complemented, Hall
304	C₂²×C₃	—	5	4	no	—
305	C₂²×C₃	—	10	2	no	—
306	C₂²×C₃	—	10	2	no	—
307	C₂²×C₃	—	10	8	no	—
308	C₂²×C₃	#4038	1	2	yes	—
309	C₂²×C₃	C₂×#676	1	2	yes	—
310	C₂²×C₃	D₅×M₁₆	1	2	yes	—
311	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
312	C₃×C₄	—	2	2	no	—
313	C₃×C₄	—	10	2	no	—
314	C₃×C₄	—	10	2	no	—
315	C₃×C₄	—	10	2	no	—
316	C₃×C₄	#4038	1	2	yes	—
317	C₃×C₄	C₂×#676	1	4	yes	—
318	C₃×C₄	C₂×#711	1	1	yes	characteristic
319	C₃×C₄	C₂×#713	1	1	yes	characteristic
320	C₂×C₅	#4926	1	4	yes	complemented
321	C₂×C₅	C₂²×#208	1	1	yes	characteristic
322	C₂×C₅	C₂²×#208	1	1	yes	characteristic
323	C₂×C₅	C₂×#926	1	1	yes	characteristic
324	D₅	—	2	4	no	—
325	C₂³	—	5	2	no	—
326	C₂³	—	5	4	no	—
327	C₂³	—	10	2	no	—
328	C₂³	—	10	2	no	—
329	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	5	2	no	—
332	C₂×C₄	—	5	2	no	—
333	C₂×C₄	—	5	2	no	—
334	C₂×C₄	—	10	8	no	—
335	C₂×C₄	—	10	2	no	—
336	C₂×C₄	—	10	2	no	—
337	C₂×C₄	—	10	2	no	—
338	C₂×C₄	—	10	2	no	—
339	C₂×C₄	—	10	2	no	—
340	C₂×C₄	—	10	8	no	—
341	C₂×C₄	—	10	4	no	—
342	C₂×C₄	#6649	1	4	yes	—
343	C₂×C₄	#6772	1	2	yes	—
344	C₂×C₄	#6773	1	2	yes	—
345	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
346	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
347	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
349	C₈	—	6	4	no	—
350	C₈	—	30	4	no	—
351	C₂×C₃	—	10	4	no	—
352	C₂×C₃	#65124	1	4	yes	complemented
353	C₂×C₃	C₂×#4038	1	1	yes	characteristic
354	C₂×C₃	C₂²×#676	1	1	yes	characteristic
355	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
356	C₅	C₂×#4926	1	1	yes	characteristic, complemented, Sylow
357	C₂²	—	5	4	no	—
358	C₂²	—	10	8	no	—
359	C₂²	—	10	2	no	—
360	C₂²	—	10	2	no	—
361	C₂²	D₅×#208	1	2	yes	—
362	C₂²	C₂×#6649	1	2	yes	—
363	C₂²	#91358	1	2	yes	—
364	C₂²	C₂²×D₅×Dic₃	1	1	yes	characteristic
365	C₄	—	2	2	no	—
366	C₄	—	10	2	no	—
367	C₄	—	10	2	no	—
368	C₄	—	10	2	no	—
369	C₄	C₂×#6649	1	4	yes	—
370	C₄	#91358	1	2	yes	—
371	C₄	C₂×#6772	1	1	yes	characteristic
372	C₄	C₂×#6773	1	1	yes	characteristic
373	C₃	C₂×#65124	1	1	yes	characteristic, complemented, Sylow
374	C₂	—	10	4	no	—
375	C₂	#11746871	1	4	yes	direct product factor
376	C₂	C₂×D₅×#208	1	1	yes	characteristic
377	C₂	C₂²×#6649	1	1	yes	characteristic
378	C₂	C₂×#91358	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃×D₅
commutator	C₂²×C₃×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	C₂×#432
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₄⋊(C₃⋊#168)	C₂	semidirect
3. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
5. C₂×#90952	C₂	semidirect
6. #11746871	C₂	direct (N × H)
19. C₄⋊(C₃⋊#168)	C₂²	semidirect
20. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
22. #90952	C₂²	semidirect
59. C₂×C₄⋊(C₃⋊C₈)	D₅	semidirect
116. C₄⋊(C₃⋊C₈)	C₂×D₅	semidirect
231. C₂×C₃×C₅	#432	semidirect
303. C₃×C₅	C₂×#432	semidirect
320. C₂×C₅	#4926	semidirect
352. C₂×C₃	#65124	semidirect
356. C₅	C₂×#4926	semidirect
373. C₃	C₂×#65124	semidirect
375. C₂	#11746871	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²×D₅	2
C₂×C₄⋊(C₃⋊#168)	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₂×#90955	2
C₂×#90952	2
#11746871	2
C₂×#65124	3
C₂×#4926	5

Subgroups — C2×#11746871 #14413788

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11746871 #14413788