Subgroups — C₂×#11746875 #14413790

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×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊(C₃⋊#168)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×(C₂×D₃)⋊#168	C₂	1	2	yes	maximal
5	C₂×#90953	C₂	1	2	yes	maximal, complemented
6	#11746875	C₂	1	8	yes	maximal, direct product factor
7	C₂×#65215	—	3	1	no	maximal, Hall
8	C₂²×C₄×C₅×D₃	C₄	1	1	yes	characteristic
9	C₂²×C₄×C₅×D₃	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃⋊#168	C₂²	1	2	yes	—
13	C₂×C₄×C₅×Dic₃	C₄	1	1	yes	characteristic
14	C₂×C₄×C₅×Dic₃	C₄	1	1	yes	characteristic
15	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
16	C₄²×C₅×D₃	C₄	1	4	yes	—
17	C₄²×C₅×D₃	C₂²	1	4	yes	—
18	C₂²×C₃×#168	C₂²	1	2	yes	—
19	C₄⋊(C₃⋊#168)	C₂²	1	4	yes	complemented
20	C₃×C₄⋊#168	C₂²	1	4	yes	complemented
21	(C₂×D₃)⋊#168	C₂²	1	8	yes	—
22	#90953	C₂²	1	8	yes	complemented
23	C₂×#4835	—	5	1	no	maximal, Hall
24	C₂²×C₄²×C₅	—	3	1	no	—
25	C₂×C₂²⋊#168	—	3	2	no	—
26	#65215	—	3	8	no	—
27	C₂×C₄⋊#168	—	3	1	no	—
28	C₂×C₄⋊#168	D₃	1	1	yes	characteristic, complemented
29	C₂×#3935	—	3	2	no	—
30	C₂³×C₅×D₃	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×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×C₅×D₃	—	2	4	no	—
38	C₂×C₄×C₅×D₃	—	2	4	no	—
39	C₂×C₄×C₅×D₃	—	2	2	no	—
40	C₂×C₄×C₅×D₃	—	2	2	no	—
41	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
42	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
43	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
44	C₂×C₄×C₅×D₃	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	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
50	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
51	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
52	C₄×C₅×Dic₃	C₂³	1	2	yes	—
53	C₂×C₃×#168	—	2	4	no	—
54	C₂×C₃×#168	C₂³	1	4	yes	—
55	C₂×C₄²×D₃	D₅	1	1	yes	characteristic
56	C₂×C₃×C₄⋊C₈	—	5	1	no	—
57	C₂×(C₂×D₃)⋊C₈	—	5	2	no	—
58	C₂×#815	—	5	2	no	—
59	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
60	#4835	—	5	8	no	—
61	C₂³×C₄×C₅	—	3	1	no	—
62	C₂³×C₄×C₅	—	3	1	no	—
63	C₂³×C₄×C₅	—	3	1	no	—
64	C₂×C₄²×C₅	—	3	1	no	—
65	C₂×C₄²×C₅	—	3	1	no	—
66	C₂×C₄²×C₅	—	3	1	no	—
67	C₂×C₄²×C₅	—	3	4	no	—
68	C₂×C₄²×C₅	—	3	4	no	—
69	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
70	C₂²×#168	—	3	2	no	—
71	C₂²×#168	C₂×D₃	1	2	yes	—
72	C₂²⋊#168	—	3	8	no	—
73	C₄⋊#168	—	3	4	no	—
74	C₄⋊#168	C₂×D₃	1	4	yes	complemented
75	#3935	—	3	8	no	—
76	C₂×#432	—	15	1	no	Sylow
77	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₅×D₃	—	2	2	no	—
79	C₂²×C₅×D₃	—	2	2	no	—
80	C₂²×C₅×D₃	M₁₆	1	4	yes	—
81	C₂²×C₅×D₃	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×C₅×Dic₃	—	2	2	no	—
91	C₂×C₅×Dic₃	—	2	2	no	—
92	C₂×C₅×Dic₃	—	2	2	no	—
93	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
94	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
95	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
96	C₄×C₅×D₃	—	2	8	no	—
97	C₄×C₅×D₃	—	2	4	no	—
98	C₄×C₅×D₃	—	2	8	no	—
99	C₄×C₅×D₃	—	2	2	no	—
100	C₄×C₅×D₃	—	2	2	no	—
101	C₃⋊#168	—	2	4	no	—
102	C₃×#168	—	2	4	no	—
103	C₂²×C₄×D₃	Dic₅	1	1	yes	characteristic
104	C₂²×C₄×D₃	Dic₅	1	1	yes	characteristic
105	C₂²×C₄×D₃	C₂×D₅	1	1	yes	characteristic
106	C₂²×C₃×C₈	—	5	2	no	—
107	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
108	C₂×C₄×Dic₃	Dic₅	1	1	yes	characteristic
109	C₂×C₄×Dic₃	Dic₅	1	1	yes	characteristic
110	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
111	C₂²×C₃⋊C₈	—	5	2	no	—
112	C₄²×D₃	Dic₅	1	4	yes	—
113	C₄²×D₃	C₂×D₅	1	4	yes	—
114	C₃×C₄⋊C₈	—	5	4	no	—
115	(C₂×D₃)⋊C₈	—	5	8	no	—
116	#815	—	5	8	no	—
117	C₄⋊(C₃⋊C₈)	—	5	4	no	—
118	C₂⁴×C₅	—	3	1	no	—
119	C₂²×C₄×C₅	—	3	1	no	—
120	C₂²×C₄×C₅	—	3	1	no	—
121	C₂²×C₄×C₅	—	3	1	no	—
122	C₂²×C₄×C₅	—	3	4	no	—
123	C₂²×C₄×C₅	—	3	2	no	—
124	C₂²×C₄×C₅	—	3	4	no	—
125	C₂²×C₄×C₅	—	3	2	no	—
126	C₂²×C₄×C₅	—	6	4	no	—
127	C₂²×C₄×C₅	—	6	4	no	—
128	C₂²×C₄×C₅	—	6	2	no	—
129	C₂²×C₄×C₅	—	6	2	no	—
130	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
133	C₄²×C₅	—	3	4	no	—
134	C₄²×C₅	—	3	2	no	—
135	C₄²×C₅	—	3	4	no	—
136	C₄²×C₅	—	3	2	no	—
137	C₄²×C₅	C₄×D₃	1	2	yes	—
138	C₄²×C₅	C₂²×D₃	1	2	yes	—
139	C₂×#168	—	2	4	no	—
140	C₂×#168	—	3	4	no	—
141	C₂×#168	—	6	4	no	—
142	C₂×#168	C₂²×D₃	1	4	yes	—
143	C₂²×C₄²	—	3	1	no	—
144	#432	—	15	8	no	—
145	C₂×C₄⋊C₈	—	5	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×C₅×D₃	—	2	2	no	—
154	C₂×C₅×D₃	—	2	2	no	—
155	C₂×C₅×D₃	—	2	8	no	—
156	C₂×C₅×D₃	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	C₅×Dic₃	—	2	2	no	—
163	C₅×Dic₃	—	2	2	no	—
164	C₅×Dic₃	—	2	2	no	—
165	C₂³×D₃	C₂×Dic₅	1	1	yes	characteristic
166	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
169	C₂²×Dic₃	C₂×Dic₅	1	1	yes	characteristic
170	C₂²×Dic₃	C₂×Dic₅	1	1	yes	characteristic
171	C₂²×Dic₃	C₂×Dic₅	1	1	yes	characteristic
172	C₂×C₄×D₃	—	2	4	no	—
173	C₂×C₄×D₃	—	2	4	no	—
174	C₂×C₄×D₃	—	2	2	no	—
175	C₂×C₄×D₃	—	2	2	no	—
176	C₂×C₄×D₃	C₂×Dic₅	1	2	yes	—
177	C₂×C₄×D₃	C₂×Dic₅	1	4	yes	—
178	C₂×C₄×D₃	C₂×Dic₅	1	4	yes	—
179	C₂×C₄×D₃	C₂²×D₅	1	2	yes	—
180	C₂×C₃×C₈	—	5	4	no	—
181	C₂×C₃×C₈	—	10	4	no	—
182	C₃×C₄²	C₂×Dic₅	1	2	yes	—
183	C₃×C₄²	C₂²×D₅	1	2	yes	—
184	C₄×Dic₃	C₂×Dic₅	1	2	yes	—
185	C₄×Dic₃	C₂×Dic₅	1	4	yes	—
186	C₄×Dic₃	C₂×Dic₅	1	4	yes	—
187	C₄×Dic₃	C₂²×D₅	1	2	yes	—
188	C₂×C₃⋊C₈	—	5	4	no	—
189	C₂×C₃⋊C₈	—	10	4	no	—
190	C₂³×C₅	—	3	4	no	—
191	C₂³×C₅	—	3	2	no	—
192	C₂³×C₅	—	6	2	no	—
193	C₂³×C₅	—	6	2	no	—
194	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	3	2	no	—
197	C₂×C₄×C₅	—	3	2	no	—
198	C₂×C₄×C₅	—	3	2	no	—
199	C₂×C₄×C₅	—	6	8	no	—
200	C₂×C₄×C₅	—	6	2	no	—
201	C₂×C₄×C₅	—	6	2	no	—
202	C₂×C₄×C₅	—	6	2	no	—
203	C₂×C₄×C₅	—	6	4	no	—
204	C₂×C₄×C₅	—	6	8	no	—
205	C₂×C₄×C₅	—	6	2	no	—
206	C₂×C₄×C₅	—	6	2	no	—
207	C₂×C₄×C₅	ΓL(1,𝔽₂₅)	1	4	yes	—
208	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
209	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
211	C₂×C₄×C₅	#237	1	2	yes	—
212	C₂×C₄×C₅	#239	1	2	yes	—
213	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
214	#168	—	2	4	no	—
215	#168	—	6	4	no	—
216	C₂³×C₄	—	3	1	no	—
217	C₂³×C₄	—	3	1	no	—
218	C₂³×C₄	—	3	1	no	—
219	C₂²×C₈	—	5	2	no	—
220	C₂²×C₈	—	15	2	no	—
221	C₂×C₄²	—	3	1	no	—
222	C₂×C₄²	—	3	1	no	—
223	C₂×C₄²	—	3	1	no	—
224	C₂×C₄²	—	3	4	no	—
225	C₂×C₄²	—	3	4	no	—
226	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
227	C₄⋊C₈	—	5	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	C₅×D₃	—	2	4	no	—
236	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
237	C₂²×D₃	—	2	2	no	—
238	C₂²×D₃	—	2	2	no	—
239	C₂²×D₃	#681	1	4	yes	—
240	C₂²×D₃	C₂²×Dic₅	1	2	yes	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	#681	1	4	yes	—
243	C₂×C₃×C₄	#709	1	2	yes	—
244	C₂×C₃×C₄	#709	1	2	yes	—
245	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
246	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
247	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
249	C₂×Dic₃	—	2	2	no	—
250	C₂×Dic₃	—	2	2	no	—
251	C₂×Dic₃	—	2	2	no	—
252	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
253	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
254	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
255	C₄×D₃	—	2	8	no	—
256	C₄×D₃	—	2	2	no	—
257	C₄×D₃	—	2	2	no	—
258	C₄×D₃	—	2	8	no	—
259	C₄×D₃	—	2	4	no	—
260	C₃×C₈	—	10	4	no	—
261	C₃⋊C₈	—	10	4	no	—
262	C₂²×C₅	—	3	4	no	—
263	C₂²×C₅	—	6	2	no	—
264	C₂²×C₅	—	6	2	no	—
265	C₂²×C₅	—	6	8	no	—
266	C₂²×C₅	#892	1	2	yes	—
267	C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
268	C₂²×C₅	D₃×M₁₆	1	2	yes	—
269	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
270	C₄×C₅	—	2	2	no	—
271	C₄×C₅	—	6	2	no	—
272	C₄×C₅	—	6	2	no	—
273	C₄×C₅	—	6	2	no	—
274	C₄×C₅	#892	1	2	yes	—
275	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	4	yes	—
276	C₄×C₅	C₂×#237	1	1	yes	characteristic
277	C₄×C₅	C₂×#239	1	1	yes	characteristic
278	C₂⁴	—	3	1	no	—
279	C₂²×C₄	—	3	1	no	—
280	C₂²×C₄	—	3	1	no	—
281	C₂²×C₄	—	3	1	no	—
282	C₂²×C₄	—	3	4	no	—
283	C₂²×C₄	—	3	4	no	—
284	C₂²×C₄	—	3	2	no	—
285	C₂²×C₄	—	3	2	no	—
286	C₂²×C₄	—	6	4	no	—
287	C₂²×C₄	—	6	2	no	—
288	C₂²×C₄	—	6	2	no	—
289	C₂²×C₄	—	6	4	no	—
290	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
291	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
293	C₂×C₈	—	5	4	no	—
294	C₂×C₈	—	10	4	no	—
295	C₂×C₈	—	15	4	no	—
296	C₂×C₈	—	30	4	no	—
297	C₄²	—	3	4	no	—
298	C₄²	—	3	4	no	—
299	C₄²	—	3	2	no	—
300	C₄²	—	3	2	no	—
301	C₄²	D₃×Dic₅	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	C₂×#681	1	2	yes	—
305	C₂²×C₃	C₂×#681	1	2	yes	—
306	C₂²×C₃	#4072	1	2	yes	—
307	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
308	C₂×D₃	—	2	2	no	—
309	C₂×D₃	—	2	2	no	—
310	C₂×D₃	—	2	8	no	—
311	C₂×D₃	C₂×#681	1	4	yes	—
312	C₃×C₄	—	2	2	no	—
313	C₃×C₄	C₂×#681	1	4	yes	—
314	C₃×C₄	#4072	1	2	yes	—
315	C₃×C₄	C₂×#709	1	1	yes	characteristic
316	C₃×C₄	C₂×#709	1	1	yes	characteristic
317	Dic₃	—	2	2	no	—
318	Dic₃	—	2	2	no	—
319	Dic₃	—	2	2	no	—
320	C₂×C₅	—	6	4	no	—
321	C₂×C₅	#4835	1	4	yes	complemented
322	C₂×C₅	C₂×#892	1	1	yes	characteristic
323	C₂×C₅	C₂²×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
324	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
325	C₂³	—	3	2	no	—
326	C₂³	—	3	4	no	—
327	C₂³	—	6	2	no	—
328	C₂³	—	6	2	no	—
329	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	3	2	no	—
332	C₂×C₄	—	3	2	no	—
333	C₂×C₄	—	3	2	no	—
334	C₂×C₄	—	6	8	no	—
335	C₂×C₄	—	6	2	no	—
336	C₂×C₄	—	6	2	no	—
337	C₂×C₄	—	6	2	no	—
338	C₂×C₄	—	6	2	no	—
339	C₂×C₄	—	6	2	no	—
340	C₂×C₄	—	6	8	no	—
341	C₂×C₄	—	6	4	no	—
342	C₂×C₄	#6650	1	4	yes	—
343	C₂×C₄	#6765	1	2	yes	—
344	C₂×C₄	#6769	1	2	yes	—
345	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
346	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
347	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
349	C₈	—	10	4	no	—
350	C₈	—	30	4	no	—
351	C₂×C₃	#65215	1	4	yes	complemented
352	C₂×C₃	C₂²×#681	1	1	yes	characteristic
353	C₂×C₃	C₂²×#681	1	1	yes	characteristic
354	C₂×C₃	C₂×#4072	1	1	yes	characteristic
355	D₃	—	2	4	no	—
356	C₅	C₂×#4835	1	1	yes	characteristic, complemented, Sylow
357	C₂²	—	3	4	no	—
358	C₂²	—	6	8	no	—
359	C₂²	—	6	2	no	—
360	C₂²	—	6	2	no	—
361	C₂²	D₃×#681	1	2	yes	—
362	C₂²	C₂×#6650	1	2	yes	—
363	C₂²	#91338	1	2	yes	—
364	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
365	C₄	—	2	2	no	—
366	C₄	—	6	2	no	—
367	C₄	—	6	2	no	—
368	C₄	—	6	2	no	—
369	C₄	C₂×#6650	1	4	yes	—
370	C₄	#91338	1	2	yes	—
371	C₄	C₂×#6765	1	1	yes	characteristic
372	C₄	C₂×#6769	1	1	yes	characteristic
373	C₃	C₂×#65215	1	1	yes	characteristic, complemented, Sylow
374	C₂	—	6	4	no	—
375	C₂	#11746875	1	4	yes	direct product factor
376	C₂	C₂×D₃×#681	1	1	yes	characteristic
377	C₂	C₂²×#6650	1	1	yes	characteristic
378	C₂	C₂×#91338	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×C₅×D₃	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×C₃×C₄⋊#168	C₂	semidirect
5. C₂×#90953	C₂	semidirect
6. #11746875	C₂	direct (N × H)
19. C₄⋊(C₃⋊#168)	C₂²	semidirect
20. C₃×C₄⋊#168	C₂²	semidirect
22. #90953	C₂²	semidirect
28. C₂×C₄⋊#168	D₃	semidirect
74. C₄⋊#168	C₂×D₃	semidirect
231. C₂×C₃×C₅	#432	semidirect
303. C₃×C₅	C₂×#432	semidirect
321. C₂×C₅	#4835	semidirect
351. C₂×C₃	#65215	semidirect
356. C₅	C₂×#4835	semidirect
373. C₃	C₂×#65215	semidirect
375. C₂	#11746875	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×C₄²×C₅×D₃	2
C₂×C₄⋊(C₃⋊#168)	2
C₂×C₃×C₄⋊#168	2
C₂×(C₂×D₃)⋊#168	2
C₂×#90953	2
#11746875	2
C₂×#65215	3
C₂×#4835	5

Subgroups — C2×#11746875 #14413790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11746875 #14413790