Subgroups — C₂×C₃×#65205 #14478270

Order 1920.

736 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4065	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4058	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3961	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3958	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65205	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#3932	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×D₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65205	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×#713	—	2	1	no	—
11	C₂×C₃×#711	—	2	1	no	—
12	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×#688	—	2	1	no	—
15	C₂×C₃×#687	—	2	1	no	—
16	C₃×#4065	—	2	2	no	—
17	C₃×#4065	C₂²	1	4	yes	complemented
18	C₃×#4058	—	2	2	no	—
19	C₃×#4058	C₂²	1	4	yes	complemented
20	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic
21	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
23	C₃×C₅×SD₃₂	C₂²	1	4	yes	complemented
24	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic
25	C₃×#3961	C₂²	1	4	yes	complemented
26	C₃×#3958	C₂²	1	4	yes	complemented
27	C₂×C₃×#672	C₂²	1	1	yes	characteristic
28	C₃×#3932	C₂²	1	4	yes	complemented
29	C₃×D₅×C₁₆	C₂²	1	4	yes	complemented
30	C₂×C₃×#508	—	5	1	no	maximal, Hall
31	C₂×#4065	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×#4058	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×C₅×SD₃₂	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#3961	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#3958	C₂×C₃	1	1	yes	characteristic, complemented
36	#65205	C₂×C₃	1	8	yes	direct product factor
37	C₂×#3932	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×D₅×C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×C₃×C₅×Q₈	—	2	1	no	—
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₃×C₂²⋊D₅	—	4	1	no	—
42	C₂²×C₃×Dic₅	—	4	1	no	—
43	C₃×#713	—	2	4	no	—
44	C₃×#713	—	4	2	no	—
45	C₃×#711	—	2	4	no	—
46	C₃×#711	—	4	2	no	—
47	C₂×C₃×D₂₀	—	2	1	no	—
48	C₂×C₃×D₂₀	—	4	1	no	—
49	C₂×C₃×C₄×D₅	—	4	1	no	—
50	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
51	C₂×C₃×Dic₁₀	—	2	1	no	—
52	C₃×C₅×Q₁₆	—	2	1	no	—
53	C₃×C₅×Q₁₆	C₂³	1	2	yes	—
54	C₃×C₅×D₈	—	2	1	no	—
55	C₃×C₅×D₈	C₂³	1	2	yes	—
56	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₃×#688	—	2	4	no	—
58	C₃×#687	—	2	4	no	—
59	C₂×C₃×#168	D₄	1	1	yes	characteristic
60	C₃×Dic₂₀	—	2	1	no	—
61	C₃×Dic₂₀	C₂³	1	2	yes	—
62	C₃×D₄₀	—	2	1	no	—
63	C₃×D₄₀	C₂³	1	2	yes	—
64	C₃×C₈×D₅	D₄	1	2	yes	—
65	C₃×C₈×D₅	C₂³	1	2	yes	—
66	C₃×C₅×C₁₆	C₂³	1	2	yes	—
67	C₃×#672	C₂³	1	2	yes	—
68	C₂×C₃×#135	—	5	1	no	—
69	C₂×C₃×#135	—	5	1	no	—
70	C₃×#508	—	5	8	no	—
71	C₂×C₃×Q₃₂	—	5	1	no	—
72	C₂×C₃×SD₃₂	—	5	1	no	—
73	C₂×C₃×SD₃₂	D₅	1	1	yes	characteristic, complemented
74	C₂×C₃×D₁₆	—	5	1	no	—
75	C₂²×C₃×C₁₆	—	5	1	no	—
76	C₂×#713	—	2	1	no	—
77	C₂×#711	—	2	1	no	—
78	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
80	C₂×#688	—	2	1	no	—
81	C₂×#687	—	2	1	no	—
82	#4065	—	2	2	no	—
83	#4065	C₂²×C₃	1	4	yes	complemented
84	#4058	—	2	2	no	—
85	#4058	C₂²×C₃	1	4	yes	complemented
86	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic
87	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
89	C₅×SD₃₂	C₂²×C₃	1	4	yes	complemented
90	C₂×C₅×C₁₆	C₂²×C₃	1	1	yes	characteristic
91	#3961	C₂²×C₃	1	4	yes	complemented
92	#3958	C₂²×C₃	1	4	yes	complemented
93	C₂×#672	C₂²×C₃	1	1	yes	characteristic
94	#3932	C₂²×C₃	1	4	yes	complemented
95	D₅×C₁₆	C₂²×C₃	1	4	yes	complemented
96	C₂×#508	—	5	1	no	Sylow
97	C₂³×C₃×C₅	—	4	1	no	—
98	C₂²×C₃×D₅	—	4	1	no	—
99	C₂²×C₃×D₅	D₈	1	1	yes	characteristic
100	C₃×C₅×Q₈	—	2	2	no	—
101	C₃×C₅×Q₈	—	4	1	no	—
102	C₃×C₅×D₄	—	2	2	no	—
103	C₃×C₅×D₄	—	4	1	no	—
104	C₂×C₃×C₄×C₅	—	4	1	no	—
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₃×C₂²⋊D₅	—	4	4	no	—
107	C₂×C₃×Dic₅	—	4	1	no	—
108	C₂×C₃×Dic₅	—	4	4	no	—
109	C₂×C₃×Dic₅	D₈	1	1	yes	characteristic
110	C₃×D₂₀	—	2	2	no	—
111	C₃×D₂₀	—	4	4	no	—
112	C₃×D₂₀	—	4	1	no	—
113	C₃×C₄×D₅	—	4	4	no	—
114	C₃×C₄×D₅	D₈	1	2	yes	—
115	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
116	C₃×Dic₁₀	—	2	2	no	—
117	C₃×Dic₁₀	—	4	1	no	—
118	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
119	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
120	C₃×#168	C₂×D₄	1	2	yes	—
121	C₂×C₃×#41	—	10	1	no	—
122	C₂×C₃×#41	—	10	1	no	—
123	C₃×#135	—	5	4	no	—
124	C₃×#135	—	5	4	no	—
125	C₃×#135	—	10	2	no	—
126	C₃×#135	—	10	2	no	—
127	C₂×C₃×Q₁₆	—	5	1	no	—
128	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
129	C₂×C₃×SD₁₆	—	10	1	no	—
130	C₂×C₃×SD₁₆	—	10	1	no	—
131	C₂×C₃×D₈	—	5	1	no	—
132	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
133	C₂²×C₃×C₈	—	5	1	no	—
134	C₃×Q₃₂	—	5	4	no	—
135	C₃×SD₃₂	—	5	4	no	—
136	C₃×SD₃₂	C₂×D₅	1	4	yes	complemented
137	C₃×D₁₆	—	5	4	no	—
138	C₂×C₃×C₁₆	—	5	1	no	—
139	C₂×C₃×C₁₆	—	5	4	no	—
140	C₂×C₃×C₁₆	C₂×D₅	1	1	yes	characteristic
141	C₂×C₅×Q₈	—	2	1	no	—
142	C₂×C₅×D₄	—	2	1	no	—
143	C₂×C₂²⋊D₅	—	4	1	no	—
144	C₂²×Dic₅	—	4	1	no	—
145	#713	—	2	4	no	—
146	#713	—	4	2	no	—
147	#711	—	2	4	no	—
148	#711	—	4	2	no	—
149	C₂×D₂₀	—	2	1	no	—
150	C₂×D₂₀	—	4	1	no	—
151	C₂×C₄×D₅	—	4	1	no	—
152	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
153	C₂×Dic₁₀	—	2	1	no	—
154	C₅×Q₁₆	—	2	1	no	—
155	C₅×Q₁₆	C₂³×C₃	1	2	yes	—
156	C₅×D₈	—	2	1	no	—
157	C₅×D₈	C₂³×C₃	1	2	yes	—
158	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
159	#688	—	2	4	no	—
160	#687	—	2	4	no	—
161	C₂×#168	C₃×D₄	1	1	yes	characteristic
162	Dic₂₀	—	2	1	no	—
163	Dic₂₀	C₂³×C₃	1	2	yes	—
164	D₄₀	—	2	1	no	—
165	D₄₀	C₂³×C₃	1	2	yes	—
166	C₈×D₅	C₃×D₄	1	2	yes	—
167	C₈×D₅	C₂³×C₃	1	2	yes	—
168	C₅×C₁₆	C₂³×C₃	1	2	yes	—
169	#672	C₂³×C₃	1	2	yes	—
170	C₂×#135	—	5	1	no	—
171	C₂×#135	—	5	1	no	—
172	#508	—	5	8	no	—
173	C₂×Q₃₂	—	5	1	no	—
174	C₂×SD₃₂	—	5	1	no	—
175	C₂×SD₃₂	C₃×D₅	1	1	yes	characteristic, complemented
176	C₂×D₁₆	—	5	1	no	—
177	C₂²×C₁₆	—	5	1	no	—
178	C₂²×C₃×C₅	—	4	2	no	—
179	C₂²×C₃×C₅	—	8	2	no	—
180	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
181	C₂×C₃×D₅	—	2	2	no	—
182	C₂×C₃×D₅	—	4	2	no	—
183	C₂×C₃×D₅	—	8	2	no	—
184	C₂×C₃×D₅	C₂×D₈	1	2	yes	—
185	C₃×C₄×C₅	—	4	2	no	—
186	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
187	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₃×Dic₅	—	4	2	no	—
189	C₃×Dic₅	C₂×D₈	1	2	yes	—
190	C₃×#41	—	10	4	no	—
191	C₃×#41	—	10	4	no	—
192	C₃×#41	—	20	2	no	—
193	C₃×#41	—	20	2	no	—
194	C₂×C₃×Q₈	—	2	1	no	—
195	C₂×C₃×Q₈	—	10	1	no	—
196	C₂×C₃×D₄	—	2	1	no	—
197	C₂×C₃×D₄	—	10	1	no	—
198	C₂×C₃×D₄	—	20	1	no	—
199	C₂×C₃×D₄	—	20	1	no	—
200	C₂²×C₃×C₄	—	5	1	no	—
201	C₂²×C₃×C₄	—	20	1	no	—
202	C₂²×C₃×C₄	—	20	1	no	—
203	C₃×Q₁₆	—	2	1	no	—
204	C₃×Q₁₆	—	5	2	no	—
205	C₃×Q₁₆	—	10	1	no	—
206	C₃×Q₁₆	C₂²×D₅	1	2	yes	—
207	C₃×SD₁₆	—	10	4	no	—
208	C₃×SD₁₆	—	10	4	no	—
209	C₃×D₈	—	2	1	no	—
210	C₃×D₈	—	5	2	no	—
211	C₃×D₈	—	10	1	no	—
212	C₃×D₈	C₂²×D₅	1	2	yes	—
213	C₂×C₃×C₈	—	5	1	no	—
214	C₂×C₃×C₈	—	5	2	no	—
215	C₂×C₃×C₈	—	5	2	no	—
216	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
217	C₃×C₁₆	—	5	2	no	—
218	C₃×C₁₆	C₂²×D₅	1	2	yes	—
219	C₂³×C₅	—	4	1	no	—
220	C₂²×D₅	—	4	1	no	—
221	C₂²×D₅	C₃×D₈	1	1	yes	characteristic
222	C₅×Q₈	—	2	2	no	—
223	C₅×Q₈	—	4	1	no	—
224	C₅×D₄	—	2	2	no	—
225	C₅×D₄	—	4	1	no	—
226	C₂×C₄×C₅	—	4	1	no	—
227	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
228	C₂²⋊D₅	—	4	4	no	—
229	C₂×Dic₅	—	4	1	no	—
230	C₂×Dic₅	—	4	4	no	—
231	C₂×Dic₅	C₃×D₈	1	1	yes	characteristic
232	D₂₀	—	2	2	no	—
233	D₂₀	—	4	4	no	—
234	D₂₀	—	4	1	no	—
235	C₄×D₅	—	4	4	no	—
236	C₄×D₅	C₃×D₈	1	2	yes	—
237	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
238	Dic₁₀	—	2	2	no	—
239	Dic₁₀	—	4	1	no	—
240	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
241	C₅×C₈	C₂⁴×C₃	1	1	yes	characteristic
242	#168	C₂×C₃×D₄	1	2	yes	—
243	C₂×#41	—	10	1	no	—
244	C₂×#41	—	10	1	no	—
245	#135	—	5	4	no	—
246	#135	—	5	4	no	—
247	#135	—	10	2	no	—
248	#135	—	10	2	no	—
249	C₂×Q₁₆	—	5	1	no	—
250	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
251	C₂×SD₁₆	—	10	1	no	—
252	C₂×SD₁₆	—	10	1	no	—
253	C₂×D₈	—	5	1	no	—
254	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
255	C₂²×C₈	—	5	1	no	—
256	Q₃₂	—	5	4	no	—
257	SD₃₂	—	5	4	no	—
258	SD₃₂	C₂×C₃×D₅	1	4	yes	complemented
259	D₁₆	—	5	4	no	—
260	C₂×C₁₆	—	5	1	no	—
261	C₂×C₁₆	—	5	4	no	—
262	C₂×C₁₆	C₂×C₃×D₅	1	1	yes	characteristic
263	C₂×C₃×C₅	—	8	2	no	—
264	C₂×C₃×C₅	#508	1	2	yes	complemented
265	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
266	C₃×D₅	—	2	2	no	—
267	C₃×D₅	—	8	2	no	—
268	C₂³×C₃	—	4	1	no	—
269	C₂³×C₃	—	5	1	no	—
270	C₂³×C₃	—	20	1	no	—
271	C₃×Q₈	—	2	2	no	—
272	C₃×Q₈	—	4	1	no	—
273	C₃×Q₈	—	10	2	no	—
274	C₃×Q₈	—	20	1	no	—
275	C₃×D₄	—	2	2	no	—
276	C₃×D₄	—	4	1	no	—
277	C₃×D₄	—	10	2	no	—
278	C₃×D₄	—	20	4	no	—
279	C₃×D₄	—	20	4	no	—
280	C₃×D₄	—	20	1	no	—
281	C₂×C₃×C₄	—	4	1	no	—
282	C₂×C₃×C₄	—	5	1	no	—
283	C₂×C₃×C₄	—	5	2	no	—
284	C₂×C₃×C₄	—	5	2	no	—
285	C₂×C₃×C₄	—	20	4	no	—
286	C₂×C₃×C₄	—	20	4	no	—
287	C₂×C₃×C₄	—	20	1	no	—
288	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
289	C₃×C₈	—	5	2	no	—
290	C₃×C₈	D₄×D₅	1	1	yes	characteristic
291	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
292	C₂²×C₅	—	4	2	no	—
293	C₂²×C₅	—	8	2	no	—
294	C₂²×C₅	C₂×C₃×D₈	1	1	yes	characteristic
295	C₂×D₅	—	2	2	no	—
296	C₂×D₅	—	4	2	no	—
297	C₂×D₅	—	8	2	no	—
298	C₂×D₅	C₂×C₃×D₈	1	2	yes	—
299	C₄×C₅	—	4	2	no	—
300	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
301	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
302	Dic₅	—	4	2	no	—
303	Dic₅	C₂×C₃×D₈	1	2	yes	—
304	#41	—	10	4	no	—
305	#41	—	10	4	no	—
306	#41	—	20	2	no	—
307	#41	—	20	2	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	10	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	10	1	no	—
312	C₂×D₄	—	20	1	no	—
313	C₂×D₄	—	20	1	no	—
314	C₂²×C₄	—	5	1	no	—
315	C₂²×C₄	—	20	1	no	—
316	C₂²×C₄	—	20	1	no	—
317	Q₁₆	—	2	1	no	—
318	Q₁₆	—	5	2	no	—
319	Q₁₆	—	10	1	no	—
320	Q₁₆	C₂²×C₃×D₅	1	2	yes	—
321	SD₁₆	—	10	4	no	—
322	SD₁₆	—	10	4	no	—
323	D₈	—	2	1	no	—
324	D₈	—	5	2	no	—
325	D₈	—	10	1	no	—
326	D₈	C₂²×C₃×D₅	1	2	yes	—
327	C₂×C₈	—	5	1	no	—
328	C₂×C₈	—	5	2	no	—
329	C₂×C₈	—	5	2	no	—
330	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
331	C₁₆	—	5	2	no	—
332	C₁₆	C₂²×C₃×D₅	1	2	yes	—
333	C₃×C₅	C₂×#508	1	1	yes	characteristic, complemented, Hall
334	C₂²×C₃	—	4	2	no	—
335	C₂²×C₃	—	5	2	no	—
336	C₂²×C₃	—	8	2	no	—
337	C₂²×C₃	—	10	2	no	—
338	C₂²×C₃	—	20	2	no	—
339	C₂²×C₃	—	40	2	no	—
340	C₂²×C₃	D₅×D₈	1	1	yes	characteristic
341	C₃×C₄	—	4	2	no	—
342	C₃×C₄	—	5	2	no	—
343	C₃×C₄	—	20	2	no	—
344	C₃×C₄	D₅×D₈	1	1	yes	characteristic
345	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
346	C₂×C₅	—	8	2	no	—
347	C₂×C₅	C₃×#508	1	2	yes	complemented
348	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
349	D₅	—	2	2	no	—
350	D₅	—	8	2	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	5	1	no	—
353	C₂³	—	20	1	no	—
354	Q₈	—	2	2	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	10	2	no	—
357	Q₈	—	20	1	no	—
358	D₄	—	2	2	no	—
359	D₄	—	4	1	no	—
360	D₄	—	10	2	no	—
361	D₄	—	20	4	no	—
362	D₄	—	20	4	no	—
363	D₄	—	20	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	5	1	no	—
366	C₂×C₄	—	5	2	no	—
367	C₂×C₄	—	5	2	no	—
368	C₂×C₄	—	20	4	no	—
369	C₂×C₄	—	20	4	no	—
370	C₂×C₄	—	20	1	no	—
371	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
372	C₈	—	5	2	no	—
373	C₈	C₃×D₄×D₅	1	1	yes	characteristic
374	C₈	C₂³×C₃×D₅	1	1	yes	characteristic
375	C₂×C₃	—	8	2	no	—
376	C₂×C₃	—	10	2	no	—
377	C₂×C₃	—	40	2	no	—
378	C₂×C₃	#65205	1	2	yes	direct product factor
379	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
380	C₅	C₂×C₃×#508	1	1	yes	characteristic, complemented, Sylow
381	C₂²	—	4	2	no	—
382	C₂²	—	5	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	10	2	no	—
385	C₂²	—	20	2	no	—
386	C₂²	—	40	2	no	—
387	C₂²	C₃×D₅×D₈	1	1	yes	characteristic
388	C₄	—	4	2	no	—
389	C₄	—	5	2	no	—
390	C₄	—	20	2	no	—
391	C₄	C₃×D₅×D₈	1	1	yes	characteristic
392	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
393	C₃	C₂×#65205	1	1	yes	characteristic, direct product factor, Sylow
394	C₂	—	8	2	no	—
395	C₂	—	10	2	no	—
396	C₂	—	40	2	no	—
397	C₂	C₃×#65205	1	2	yes	direct product factor
398	C₂	C₂×C₃×D₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₅×D₈
commutator, cosocle	C₅×C₈	C₂⁴×C₃
Frattini	C₈	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×SD₃₂	C₂
socle	C₂²×C₃×C₅	C₂×D₈
hypercenter	C₂×C₃×SD₃₂	D₅
hypocenter	C₅	C₂×C₃×#508
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₂×C₃×SD₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4065	C₂	semidirect
2. C₂×C₃×#4058	C₂	semidirect
3. C₂×C₃×C₅×SD₃₂	C₂	semidirect
4. C₂×C₃×#3961	C₂	semidirect
5. C₂×C₃×#3958	C₂	semidirect
6. C₃×#65205	C₂	direct (N × H)
7. C₂×C₃×#3932	C₂	semidirect
8. C₂×C₃×D₅×C₁₆	C₂	semidirect
9. C₂×#65205	C₃	direct (N × H)
17. C₃×#4065	C₂²	semidirect
19. C₃×#4058	C₂²	semidirect
23. C₃×C₅×SD₃₂	C₂²	semidirect
25. C₃×#3961	C₂²	semidirect
26. C₃×#3958	C₂²	semidirect
28. C₃×#3932	C₂²	semidirect
29. C₃×D₅×C₁₆	C₂²	semidirect
31. C₂×#4065	C₂×C₃	semidirect
32. C₂×#4058	C₂×C₃	semidirect
33. C₂×C₅×SD₃₂	C₂×C₃	semidirect
34. C₂×#3961	C₂×C₃	semidirect
35. C₂×#3958	C₂×C₃	semidirect
36. #65205	C₂×C₃	direct (N × H)
37. C₂×#3932	C₂×C₃	semidirect
38. C₂×D₅×C₁₆	C₂×C₃	semidirect
73. C₂×C₃×SD₃₂	D₅	semidirect
83. #4065	C₂²×C₃	semidirect
85. #4058	C₂²×C₃	semidirect
89. C₅×SD₃₂	C₂²×C₃	semidirect
91. #3961	C₂²×C₃	semidirect
92. #3958	C₂²×C₃	semidirect
94. #3932	C₂²×C₃	semidirect
95. D₅×C₁₆	C₂²×C₃	semidirect
136. C₃×SD₃₂	C₂×D₅	semidirect
175. C₂×SD₃₂	C₃×D₅	semidirect
258. SD₃₂	C₂×C₃×D₅	semidirect
264. C₂×C₃×C₅	#508	semidirect
333. C₃×C₅	C₂×#508	semidirect
347. C₂×C₅	C₃×#508	semidirect
378. C₂×C₃	#65205	direct (N × H)
380. C₅	C₂×C₃×#508	semidirect
393. C₃	C₂×#65205	direct (N × H)
397. C₂	C₃×#65205	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×#4065	2
C₂×C₃×#4058	2
C₂×C₃×C₅×SD₃₂	2
C₂×C₃×#3961	2
C₂×C₃×#3958	2
C₃×#65205	2
C₂×C₃×#3932	2
C₂×C₃×D₅×C₁₆	2
C₂×#65205	3
C₂×C₃×#508	5

Subgroups — C2×C3×#65205 #14478270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65205 #14478270