Subgroups — C₂×C₃×#65204 #14478378

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4058	C₂	1	1	yes	maximal, characteristic
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×#3959	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65204	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×Dic₄₀	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#3930	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65204	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×Q₈×D₅	—	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×#689	—	2	1	no	—
15	C₂×C₃×#687	—	2	1	no	—
16	C₃×D₅×Q₁₆	—	2	2	no	—
17	C₃×D₅×Q₁₆	C₂²	1	4	yes	complemented
18	C₃×#4058	—	2	2	no	—
19	C₃×#4058	C₂²	1	4	yes	—
20	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic
21	C₂×C₃×Dic₂₀	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×#3959	C₂²	1	4	yes	complemented
27	C₂×C₃×#672	C₂²	1	1	yes	characteristic
28	C₃×Dic₄₀	C₂²	1	4	yes	complemented
29	C₃×#3930	C₂²	1	4	yes	complemented
30	C₂×C₃×#510	—	5	1	no	maximal, Hall
31	C₂×D₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×#4058	C₂×C₃	1	1	yes	characteristic
33	C₂×C₅×SD₃₂	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#3961	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#3959	C₂×C₃	1	1	yes	characteristic, complemented
36	#65204	C₂×C₃	1	8	yes	direct product factor
37	C₂×Dic₄₀	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×#3930	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×Q₈×D₅	—	2	4	no	—
44	C₃×Q₈×D₅	—	4	2	no	—
45	C₃×#711	—	2	4	no	—
46	C₃×#711	—	4	2	no	—
47	C₂×C₃×C₄×D₅	—	4	1	no	—
48	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
49	C₂×C₃×Dic₁₀	—	2	1	no	—
50	C₂×C₃×Dic₁₀	—	2	1	no	—
51	C₂×C₃×Dic₁₀	—	4	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×#689	—	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	—	2	1	no	—
62	C₃×Dic₂₀	C₂³	1	2	yes	—
63	C₃×Dic₂₀	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	C₂²×C₃×Q₁₆	—	5	1	no	—
70	C₃×#510	—	5	8	no	—
71	C₂×C₃×Q₃₂	—	5	1	no	—
72	C₂×C₃×Q₃₂	—	5	1	no	—
73	C₂×C₃×SD₃₂	—	5	1	no	—
74	C₂×C₃×SD₃₂	D₅	1	1	yes	characteristic, complemented
75	C₂×C₃×M₃₂	—	5	1	no	—
76	C₂×Q₈×D₅	—	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×#689	—	2	1	no	—
81	C₂×#687	—	2	1	no	—
82	D₅×Q₁₆	—	2	2	no	—
83	D₅×Q₁₆	C₂²×C₃	1	4	yes	complemented
84	#4058	—	2	2	no	—
85	#4058	C₂²×C₃	1	4	yes	—
86	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic
87	C₂×Dic₂₀	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	#3959	C₂²×C₃	1	4	yes	complemented
93	C₂×#672	C₂²×C₃	1	1	yes	characteristic
94	Dic₄₀	C₂²×C₃	1	4	yes	complemented
95	#3930	C₂²×C₃	1	4	yes	complemented
96	C₂×#510	—	5	1	no	Sylow
97	C₂³×C₃×C₅	—	4	1	no	—
98	C₂²×C₃×D₅	D₈	1	1	yes	characteristic
99	C₃×C₅×Q₈	—	2	2	no	—
100	C₃×C₅×Q₈	—	4	1	no	—
101	C₃×C₅×D₄	—	2	2	no	—
102	C₃×C₅×D₄	—	4	1	no	—
103	C₂×C₃×C₄×C₅	—	4	1	no	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₃×C₂²⋊D₅	—	4	4	no	—
106	C₂×C₃×Dic₅	—	4	1	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×C₄×D₅	—	4	4	no	—
111	C₃×C₄×D₅	D₈	1	2	yes	—
112	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
113	C₃×Dic₁₀	—	2	2	no	—
114	C₃×Dic₁₀	—	2	2	no	—
115	C₃×Dic₁₀	—	4	1	no	—
116	C₃×Dic₁₀	—	4	1	no	—
117	C₃×Dic₁₀	—	4	4	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	C₂²×C₃×Q₈	—	10	1	no	—
123	C₃×#135	—	5	4	no	—
124	C₃×#135	—	10	2	no	—
125	C₂×C₃×Q₁₆	—	5	4	no	—
126	C₂×C₃×Q₁₆	—	5	1	no	—
127	C₂×C₃×Q₁₆	—	5	1	no	—
128	C₂×C₃×Q₁₆	—	10	2	no	—
129	C₂×C₃×Q₁₆	—	10	1	no	—
130	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
131	C₂×C₃×SD₁₆	—	10	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×Q₃₂	—	5	4	no	—
136	C₃×SD₃₂	—	5	4	no	—
137	C₃×SD₃₂	C₂×D₅	1	4	yes	complemented
138	C₃×M₃₂	—	5	4	no	—
139	C₂×C₃×C₁₆	—	5	1	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	Q₈×D₅	—	2	4	no	—
146	Q₈×D₅	—	4	2	no	—
147	#711	—	2	4	no	—
148	#711	—	4	2	no	—
149	C₂×C₄×D₅	—	4	1	no	—
150	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
151	C₂×Dic₁₀	—	2	1	no	—
152	C₂×Dic₁₀	—	2	1	no	—
153	C₂×Dic₁₀	—	4	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	#689	—	2	4	no	—
160	#687	—	2	4	no	—
161	C₂×#168	C₃×D₄	1	1	yes	characteristic
162	Dic₂₀	—	2	1	no	—
163	Dic₂₀	—	2	1	no	—
164	Dic₂₀	C₂³×C₃	1	2	yes	—
165	Dic₂₀	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	C₂²×Q₁₆	—	5	1	no	—
172	#510	—	5	8	no	—
173	C₂×Q₃₂	—	5	1	no	—
174	C₂×Q₃₂	—	5	1	no	—
175	C₂×SD₃₂	—	5	1	no	—
176	C₂×SD₃₂	C₃×D₅	1	1	yes	characteristic, complemented
177	C₂×M₃₂	—	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	C₂×D₈	1	2	yes	—
183	C₃×C₄×C₅	—	4	2	no	—
184	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
185	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
186	C₃×Dic₅	—	4	2	no	—
187	C₃×Dic₅	—	4	2	no	—
188	C₃×Dic₅	C₂×D₈	1	2	yes	—
189	C₃×#41	—	10	4	no	—
190	C₃×#41	—	20	2	no	—
191	C₂×C₃×Q₈	—	2	1	no	—
192	C₂×C₃×Q₈	—	10	4	no	—
193	C₂×C₃×Q₈	—	10	1	no	—
194	C₂×C₃×Q₈	—	10	1	no	—
195	C₂×C₃×Q₈	—	20	1	no	—
196	C₂×C₃×Q₈	—	20	2	no	—
197	C₂×C₃×D₄	—	2	1	no	—
198	C₂×C₃×D₄	—	20	1	no	—
199	C₂²×C₃×C₄	—	5	1	no	—
200	C₂²×C₃×C₄	—	20	1	no	—
201	C₂²×C₃×C₄	—	20	1	no	—
202	C₃×Q₁₆	—	2	1	no	—
203	C₃×Q₁₆	—	5	2	no	—
204	C₃×Q₁₆	—	5	2	no	—
205	C₃×Q₁₆	—	10	4	no	—
206	C₃×Q₁₆	—	10	1	no	—
207	C₃×Q₁₆	—	10	1	no	—
208	C₃×Q₁₆	C₂²×D₅	1	2	yes	—
209	C₃×SD₁₆	—	10	4	no	—
210	C₃×D₈	—	2	1	no	—
211	C₃×D₈	C₂²×D₅	1	2	yes	—
212	C₂×C₃×C₈	—	5	1	no	—
213	C₂×C₃×C₈	—	5	2	no	—
214	C₂×C₃×C₈	—	5	2	no	—
215	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
216	C₃×C₁₆	—	5	2	no	—
217	C₃×C₁₆	C₂²×D₅	1	2	yes	—
218	C₂³×C₅	—	4	1	no	—
219	C₂²×D₅	C₃×D₈	1	1	yes	characteristic
220	C₅×Q₈	—	2	2	no	—
221	C₅×Q₈	—	4	1	no	—
222	C₅×D₄	—	2	2	no	—
223	C₅×D₄	—	4	1	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
226	C₂²⋊D₅	—	4	4	no	—
227	C₂×Dic₅	—	4	1	no	—
228	C₂×Dic₅	—	4	1	no	—
229	C₂×Dic₅	—	4	4	no	—
230	C₂×Dic₅	C₃×D₈	1	1	yes	characteristic
231	C₄×D₅	—	4	4	no	—
232	C₄×D₅	C₃×D₈	1	2	yes	—
233	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
234	Dic₁₀	—	2	2	no	—
235	Dic₁₀	—	2	2	no	—
236	Dic₁₀	—	4	1	no	—
237	Dic₁₀	—	4	1	no	—
238	Dic₁₀	—	4	4	no	—
239	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
240	C₅×C₈	C₂⁴×C₃	1	1	yes	characteristic
241	#168	C₂×C₃×D₄	1	2	yes	—
242	C₂×#41	—	10	1	no	—
243	C₂²×Q₈	—	10	1	no	—
244	#135	—	5	4	no	—
245	#135	—	10	2	no	—
246	C₂×Q₁₆	—	5	4	no	—
247	C₂×Q₁₆	—	5	1	no	—
248	C₂×Q₁₆	—	5	1	no	—
249	C₂×Q₁₆	—	10	2	no	—
250	C₂×Q₁₆	—	10	1	no	—
251	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
252	C₂×SD₁₆	—	10	1	no	—
253	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
254	C₂²×C₈	—	5	1	no	—
255	Q₃₂	—	5	4	no	—
256	Q₃₂	—	5	4	no	—
257	SD₃₂	—	5	4	no	—
258	SD₃₂	C₂×C₃×D₅	1	4	yes	complemented
259	M₃₂	—	5	4	no	—
260	C₂×C₁₆	—	5	1	no	—
261	C₂×C₁₆	C₂×C₃×D₅	1	1	yes	characteristic
262	C₂×C₃×C₅	—	8	2	no	—
263	C₂×C₃×C₅	#510	1	2	yes	complemented
264	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
265	C₃×D₅	—	2	2	no	—
266	C₂³×C₃	—	4	1	no	—
267	C₂³×C₃	—	5	1	no	—
268	C₃×Q₈	—	2	2	no	—
269	C₃×Q₈	—	4	1	no	—
270	C₃×Q₈	—	10	2	no	—
271	C₃×Q₈	—	10	2	no	—
272	C₃×Q₈	—	20	4	no	—
273	C₃×Q₈	—	20	1	no	—
274	C₃×Q₈	—	20	1	no	—
275	C₃×D₄	—	2	2	no	—
276	C₃×D₄	—	4	1	no	—
277	C₃×D₄	—	20	4	no	—
278	C₂×C₃×C₄	—	4	1	no	—
279	C₂×C₃×C₄	—	5	1	no	—
280	C₂×C₃×C₄	—	5	2	no	—
281	C₂×C₃×C₄	—	5	2	no	—
282	C₂×C₃×C₄	—	20	4	no	—
283	C₂×C₃×C₄	—	20	4	no	—
284	C₂×C₃×C₄	—	20	1	no	—
285	C₂×C₃×C₄	—	20	1	no	—
286	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
287	C₃×C₈	—	5	2	no	—
288	C₃×C₈	D₄×D₅	1	1	yes	characteristic
289	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
290	C₂²×C₅	—	4	2	no	—
291	C₂²×C₅	—	8	2	no	—
292	C₂²×C₅	C₂×C₃×D₈	1	1	yes	characteristic
293	C₂×D₅	—	2	2	no	—
294	C₂×D₅	C₂×C₃×D₈	1	2	yes	—
295	C₄×C₅	—	4	2	no	—
296	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
297	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
298	Dic₅	—	4	2	no	—
299	Dic₅	—	4	2	no	—
300	Dic₅	C₂×C₃×D₈	1	2	yes	—
301	#41	—	10	4	no	—
302	#41	—	20	2	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	10	4	no	—
305	C₂×Q₈	—	10	1	no	—
306	C₂×Q₈	—	10	1	no	—
307	C₂×Q₈	—	20	1	no	—
308	C₂×Q₈	—	20	2	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	20	1	no	—
311	C₂²×C₄	—	5	1	no	—
312	C₂²×C₄	—	20	1	no	—
313	C₂²×C₄	—	20	1	no	—
314	Q₁₆	—	2	1	no	—
315	Q₁₆	—	5	2	no	—
316	Q₁₆	—	5	2	no	—
317	Q₁₆	—	10	4	no	—
318	Q₁₆	—	10	1	no	—
319	Q₁₆	—	10	1	no	—
320	Q₁₆	C₂²×C₃×D₅	1	2	yes	—
321	SD₁₆	—	10	4	no	—
322	D₈	—	2	1	no	—
323	D₈	C₂²×C₃×D₅	1	2	yes	—
324	C₂×C₈	—	5	1	no	—
325	C₂×C₈	—	5	2	no	—
326	C₂×C₈	—	5	2	no	—
327	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
328	C₁₆	—	5	2	no	—
329	C₁₆	C₂²×C₃×D₅	1	2	yes	—
330	C₃×C₅	C₂×#510	1	1	yes	characteristic, complemented, Hall
331	C₂²×C₃	—	4	2	no	—
332	C₂²×C₃	—	5	2	no	—
333	C₂²×C₃	—	8	2	no	—
334	C₂²×C₃	—	10	2	no	—
335	C₂²×C₃	D₅×D₈	1	1	yes	characteristic
336	C₃×C₄	—	4	2	no	—
337	C₃×C₄	—	5	2	no	—
338	C₃×C₄	—	20	2	no	—
339	C₃×C₄	—	20	2	no	—
340	C₃×C₄	D₅×D₈	1	1	yes	characteristic
341	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
342	C₂×C₅	—	8	2	no	—
343	C₂×C₅	C₃×#510	1	2	yes	complemented
344	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
345	D₅	—	2	2	no	—
346	C₂³	—	4	1	no	—
347	C₂³	—	5	1	no	—
348	Q₈	—	2	2	no	—
349	Q₈	—	4	1	no	—
350	Q₈	—	10	2	no	—
351	Q₈	—	10	2	no	—
352	Q₈	—	20	4	no	—
353	Q₈	—	20	1	no	—
354	Q₈	—	20	1	no	—
355	D₄	—	2	2	no	—
356	D₄	—	4	1	no	—
357	D₄	—	20	4	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	5	1	no	—
360	C₂×C₄	—	5	2	no	—
361	C₂×C₄	—	5	2	no	—
362	C₂×C₄	—	20	4	no	—
363	C₂×C₄	—	20	4	no	—
364	C₂×C₄	—	20	1	no	—
365	C₂×C₄	—	20	1	no	—
366	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
367	C₈	—	5	2	no	—
368	C₈	C₃×D₄×D₅	1	1	yes	characteristic
369	C₈	C₂³×C₃×D₅	1	1	yes	characteristic
370	C₂×C₃	—	8	2	no	—
371	C₂×C₃	—	10	2	no	—
372	C₂×C₃	#65204	1	2	yes	direct product factor
373	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
374	C₅	C₂×C₃×#510	1	1	yes	characteristic, complemented, Sylow
375	C₂²	—	4	2	no	—
376	C₂²	—	5	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	10	2	no	—
379	C₂²	C₃×D₅×D₈	1	1	yes	characteristic
380	C₄	—	4	2	no	—
381	C₄	—	5	2	no	—
382	C₄	—	20	2	no	—
383	C₄	—	20	2	no	—
384	C₄	C₃×D₅×D₈	1	1	yes	characteristic
385	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
386	C₃	C₂×#65204	1	1	yes	characteristic, direct product factor, Sylow
387	C₂	—	8	2	no	—
388	C₂	—	10	2	no	—
389	C₂	C₃×#65204	1	2	yes	direct product factor
390	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
prime radical	C₂×C₃×#4058	C₂
hypercenter	C₂×C₃×SD₃₂	D₅
hypocenter	C₅	C₂×C₃×#510
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×D₅×Q₁₆	C₂	semidirect
3. C₂×C₃×C₅×SD₃₂	C₂	semidirect
4. C₂×C₃×#3961	C₂	semidirect
5. C₂×C₃×#3959	C₂	semidirect
6. C₃×#65204	C₂	direct (N × H)
7. C₂×C₃×Dic₄₀	C₂	semidirect
8. C₂×C₃×#3930	C₂	semidirect
9. C₂×#65204	C₃	direct (N × H)
17. C₃×D₅×Q₁₆	C₂²	semidirect
23. C₃×C₅×SD₃₂	C₂²	semidirect
25. C₃×#3961	C₂²	semidirect
26. C₃×#3959	C₂²	semidirect
28. C₃×Dic₄₀	C₂²	semidirect
29. C₃×#3930	C₂²	semidirect
31. C₂×D₅×Q₁₆	C₂×C₃	semidirect
33. C₂×C₅×SD₃₂	C₂×C₃	semidirect
34. C₂×#3961	C₂×C₃	semidirect
35. C₂×#3959	C₂×C₃	semidirect
36. #65204	C₂×C₃	direct (N × H)
37. C₂×Dic₄₀	C₂×C₃	semidirect
38. C₂×#3930	C₂×C₃	semidirect
74. C₂×C₃×SD₃₂	D₅	semidirect
83. D₅×Q₁₆	C₂²×C₃	semidirect
89. C₅×SD₃₂	C₂²×C₃	semidirect
91. #3961	C₂²×C₃	semidirect
92. #3959	C₂²×C₃	semidirect
94. Dic₄₀	C₂²×C₃	semidirect
95. #3930	C₂²×C₃	semidirect
137. C₃×SD₃₂	C₂×D₅	semidirect
176. C₂×SD₃₂	C₃×D₅	semidirect
258. SD₃₂	C₂×C₃×D₅	semidirect
263. C₂×C₃×C₅	#510	semidirect
330. C₃×C₅	C₂×#510	semidirect
343. C₂×C₅	C₃×#510	semidirect
372. C₂×C₃	#65204	direct (N × H)
374. C₅	C₂×C₃×#510	semidirect
386. C₃	C₂×#65204	direct (N × H)
389. C₂	C₃×#65204	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×D₅×Q₁₆	2
C₂×C₃×#4058	2
C₂×C₃×C₅×SD₃₂	2
C₂×C₃×#3961	2
C₂×C₃×#3959	2
C₃×#65204	2
C₂×C₃×Dic₄₀	2
C₂×C₃×#3930	2
C₂×#65204	3
C₂×C₃×#510	5

Subgroups — C2×C3×#65204 #14478378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65204 #14478378