Subgroups — C₃×#10613493 #14439199

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4061	C₂	1	4	yes	maximal, complemented
2	C₃×D₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66050	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65456	C₂	1	4	yes	maximal, complemented
6	C₃×#65381	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65365	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64988	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×#676	C₂	1	1	yes	maximal, characteristic, complemented
10	#10613493	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
12	C₂×C₃×#711	C₂²	1	2	yes	—
13	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×#127	C₂²	1	1	yes	characteristic
16	C₃×#4090	C₂²	1	2	yes	—
17	C₂×C₃×#689	C₂²	1	4	yes	—
18	C₃×#4084	—	2	2	no	—
19	C₃×#4082	C₂²	1	2	yes	—
20	C₃×D₄×Dic₅	—	2	2	no	—
21	C₂×C₃×#687	C₂²	1	4	yes	—
22	C₃×#4061	—	2	16	no	—
23	C₂×C₃×Dic₂₀	C₂²	1	4	yes	—
24	C₂×C₃×#676	C₂²	1	2	yes	—
25	C₃×D₅×C₄⋊C₄	—	2	2	no	—
26	C₃×#4034	—	2	2	no	—
27	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
28	C₃×#4015	C₂²	1	1	yes	characteristic
29	C₃×#4015	C₂²	1	1	yes	characteristic
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₃×#3947	C₂²	1	2	yes	—
32	C₃×C₄×#168	C₂²	1	1	yes	characteristic
33	C₃×#3152	—	5	1	no	maximal, Hall
34	C₂×#4061	C₂×C₃	1	4	yes	complemented
35	D₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
36	#66050	C₂×C₃	1	1	yes	characteristic
37	C₅×#492	C₂×C₃	1	1	yes	characteristic, complemented
38	#65456	C₂×C₃	1	4	yes	complemented
39	#65381	C₂×C₃	1	1	yes	characteristic, complemented
40	#65365	C₂×C₃	1	1	yes	characteristic, complemented
41	#64988	C₂×C₃	1	1	yes	characteristic, complemented
42	C₄×#676	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
46	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
47	C₂²×C₃×Dic₅	—	2	2	no	—
48	C₃×Q₈×D₅	—	2	8	no	—
49	C₃×#711	—	2	8	no	—
50	C₂×C₃×C₄×D₅	—	2	2	no	—
51	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
52	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
53	C₂×C₃×Dic₁₀	—	2	2	no	—
54	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
55	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
56	C₃×C₅×SD₁₆	—	2	8	no	—
57	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	—	2	2	no	—
59	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₃×C₂²⋊Dic₅	—	2	4	no	—
61	C₃×#689	—	2	8	no	—
62	C₃×#687	—	2	8	no	—
63	C₃×C₄⋊Dic₅	—	2	2	no	—
64	C₃×C₄⋊Dic₅	—	2	2	no	—
65	C₃×#683	—	2	4	no	—
66	C₃×C₄×Dic₅	D₄	1	2	yes	—
67	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
68	C₂×C₃×#168	C₂³	1	2	yes	—
69	C₃×Dic₂₀	—	2	8	no	—
70	C₃×#676	D₄	1	8	yes	complemented
71	C₂×C₃×#137	—	5	4	no	—
72	C₃×#532	—	5	1	no	—
73	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
74	C₃×#497	—	5	4	no	—
75	C₃×#494	—	5	1	no	—
76	C₃×#494	—	5	1	no	—
77	C₃×#492	—	5	1	no	—
78	C₃×#492	D₅	1	1	yes	characteristic, complemented
79	C₃×C₄×M₁₆	—	5	1	no	—
80	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
81	C₂×#711	C₂²×C₃	1	2	yes	—
82	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	—
83	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
84	C₅×#127	C₂²×C₃	1	1	yes	characteristic
85	#4090	C₂²×C₃	1	2	yes	—
86	C₂×#689	C₂²×C₃	1	4	yes	—
87	#4084	—	2	2	no	—
88	#4082	C₂²×C₃	1	2	yes	—
89	D₄×Dic₅	—	2	2	no	—
90	C₂×#687	C₂²×C₃	1	4	yes	—
91	#4061	—	2	16	no	—
92	C₂×Dic₂₀	C₂²×C₃	1	4	yes	—
93	C₂×#676	C₂²×C₃	1	2	yes	—
94	D₅×C₄⋊C₄	—	2	2	no	—
95	#4034	—	2	2	no	—
96	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
97	#4015	C₂²×C₃	1	1	yes	characteristic
98	#4015	C₂²×C₃	1	1	yes	characteristic
99	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
100	#3947	C₂²×C₃	1	2	yes	—
101	C₄×#168	C₂²×C₃	1	1	yes	characteristic
102	#3152	—	5	1	no	Sylow
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
105	C₃×C₅×Q₈	—	2	4	no	—
106	C₃×C₅×D₄	—	2	4	no	—
107	C₃×C₅×D₄	—	4	4	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
111	C₃×C₂²⋊D₅	—	4	4	no	—
112	C₂×C₃×Dic₅	—	2	2	no	—
113	C₂×C₃×Dic₅	—	2	2	no	—
114	C₂×C₃×Dic₅	—	4	4	no	—
115	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
117	C₃×C₄×D₅	—	2	4	no	—
118	C₃×C₄×D₅	—	4	4	no	—
119	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
120	C₃×Dic₁₀	—	2	4	no	—
121	C₃×Dic₁₀	—	2	4	no	—
122	C₃×Dic₁₀	—	4	4	no	—
123	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
124	C₃×#168	C₂×D₄	1	4	yes	—
125	C₂×C₃×#41	—	5	2	no	—
126	C₂²×C₃×Q₈	—	5	2	no	—
127	C₃×#137	—	10	16	no	—
128	C₂×C₃×Q₁₆	—	5	4	no	—
129	C₂×C₃×Q₁₆	—	5	4	no	—
130	C₂×C₃×SD₁₆	—	5	4	no	—
131	C₂×C₃×SD₁₆	C₂×D₅	1	4	yes	—
132	C₂×C₃×M₁₆	—	5	2	no	—
133	C₃×C₄⋊Q₈	—	5	2	no	—
134	C₃×C₄⋊Q₈	—	5	1	no	—
135	C₃×C₄⋊Q₈	—	5	1	no	—
136	C₃×C₄⋊Q₈	—	10	2	no	—
137	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
138	C₃×#127	C₂×D₅	1	1	yes	characteristic
139	C₃×#124	—	5	2	no	—
140	C₃×#121	—	10	2	no	—
141	C₃×C₄×D₄	—	10	2	no	—
142	C₂×C₃×C₄⋊C₄	—	10	2	no	—
143	C₂×C₃×C₄²	—	5	1	no	—
144	C₃×#97	—	5	2	no	—
145	C₃×C₄×C₈	—	5	1	no	—
146	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
147	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
148	C₂×C₅×D₄	—	2	2	no	—
149	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
150	C₂×C₂²⋊D₅	—	2	2	no	—
151	C₂²×Dic₅	—	2	2	no	—
152	Q₈×D₅	—	2	8	no	—
153	#711	—	2	8	no	—
154	C₂×C₄×D₅	—	2	2	no	—
155	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
156	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
157	C₂×Dic₁₀	—	2	2	no	—
158	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
159	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
160	C₅×SD₁₆	—	2	8	no	—
161	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
162	C₅×C₄⋊C₄	—	2	2	no	—
163	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
164	C₂²⋊Dic₅	—	2	4	no	—
165	#689	—	2	8	no	—
166	#687	—	2	8	no	—
167	C₄⋊Dic₅	—	2	2	no	—
168	C₄⋊Dic₅	—	2	2	no	—
169	#683	—	2	4	no	—
170	C₄×Dic₅	C₃×D₄	1	2	yes	—
171	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
172	C₂×#168	C₂³×C₃	1	2	yes	—
173	Dic₂₀	—	2	8	no	—
174	#676	C₃×D₄	1	8	yes	complemented
175	C₂×#137	—	5	4	no	—
176	#532	—	5	1	no	—
177	C₂×C₄⋊Q₈	—	5	1	no	—
178	#497	—	5	4	no	—
179	#494	—	5	1	no	—
180	#494	—	5	1	no	—
181	#492	—	5	1	no	—
182	#492	C₃×D₅	1	1	yes	characteristic, complemented
183	C₄×M₁₆	—	5	1	no	—
184	C₂²×C₃×C₅	—	4	2	no	—
185	C₂²×C₃×C₅	—	4	4	no	—
186	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₃×D₅	—	2	2	no	—
188	C₂×C₃×D₅	#127	1	2	yes	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	#137	1	4	yes	complemented
191	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
192	C₃×Dic₅	—	2	2	no	—
193	C₃×Dic₅	—	4	2	no	—
194	C₃×Dic₅	—	4	2	no	—
195	C₃×Dic₅	#127	1	2	yes	—
196	C₃×#41	—	10	8	no	—
197	C₂×C₃×Q₈	—	5	2	no	—
198	C₂×C₃×Q₈	—	5	2	no	—
199	C₂×C₃×Q₈	—	10	2	no	—
200	C₂×C₃×Q₈	—	10	8	no	—
201	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
202	C₂×C₃×D₄	—	2	2	no	—
203	C₂×C₃×D₄	—	10	2	no	—
204	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
205	C₂²×C₃×C₄	—	5	1	no	—
206	C₂²×C₃×C₄	—	5	2	no	—
207	C₂²×C₃×C₄	—	10	2	no	—
208	C₂²×C₃×C₄	—	10	2	no	—
209	C₃×Q₁₆	—	10	8	no	—
210	C₃×Q₁₆	—	10	8	no	—
211	C₃×SD₁₆	—	2	8	no	—
212	C₃×SD₁₆	—	10	8	no	—
213	C₃×M₁₆	—	5	8	no	—
214	C₂×C₃×C₈	—	5	2	no	—
215	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
216	C₃×C₄⋊C₄	—	2	2	no	—
217	C₃×C₄⋊C₄	—	10	4	no	—
218	C₃×C₄⋊C₄	—	10	2	no	—
219	C₃×C₄⋊C₄	—	10	2	no	—
220	C₃×C₂²⋊C₄	—	10	4	no	—
221	C₃×C₄²	—	5	2	no	—
222	C₃×C₄²	—	5	1	no	—
223	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
224	C₂³×C₅	—	2	2	no	—
225	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
226	C₅×Q₈	—	2	4	no	—
227	C₅×D₄	—	2	4	no	—
228	C₅×D₄	—	4	4	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
231	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
232	C₂²⋊D₅	—	4	4	no	—
233	C₂×Dic₅	—	2	2	no	—
234	C₂×Dic₅	—	2	2	no	—
235	C₂×Dic₅	—	4	4	no	—
236	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
237	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
238	C₄×D₅	—	2	4	no	—
239	C₄×D₅	—	4	4	no	—
240	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
241	Dic₁₀	—	2	4	no	—
242	Dic₁₀	—	2	4	no	—
243	Dic₁₀	—	4	4	no	—
244	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
245	#168	C₂×C₃×D₄	1	4	yes	—
246	C₂×#41	—	5	2	no	—
247	C₂²×Q₈	—	5	2	no	—
248	#137	—	10	16	no	—
249	C₂×Q₁₆	—	5	4	no	—
250	C₂×Q₁₆	—	5	4	no	—
251	C₂×SD₁₆	—	5	4	no	—
252	C₂×SD₁₆	C₂×C₃×D₅	1	4	yes	—
253	C₂×M₁₆	—	5	2	no	—
254	C₄⋊Q₈	—	5	2	no	—
255	C₄⋊Q₈	—	5	1	no	—
256	C₄⋊Q₈	—	5	1	no	—
257	C₄⋊Q₈	—	10	2	no	—
258	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
259	#127	C₂×C₃×D₅	1	1	yes	characteristic
260	#124	—	5	2	no	—
261	#121	—	10	2	no	—
262	C₄×D₄	—	10	2	no	—
263	C₂×C₄⋊C₄	—	10	2	no	—
264	C₂×C₄²	—	5	1	no	—
265	#97	—	5	2	no	—
266	C₄×C₈	—	5	1	no	—
267	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
268	C₂×C₃×C₅	—	8	2	no	—
269	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
270	C₂×C₃×C₅	C₂×#137	1	2	yes	—
271	C₃×D₅	—	2	2	no	—
272	C₂³×C₃	—	2	2	no	—
273	C₂³×C₃	—	5	1	no	—
274	C₃×Q₈	—	2	4	no	—
275	C₃×Q₈	—	10	4	no	—
276	C₃×Q₈	—	10	4	no	—
277	C₃×Q₈	—	20	4	no	—
278	C₃×D₄	—	2	4	no	—
279	C₃×D₄	—	4	4	no	—
280	C₃×D₄	—	20	4	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	—	5	1	no	—
283	C₂×C₃×C₄	—	5	4	no	—
284	C₂×C₃×C₄	—	5	2	no	—
285	C₂×C₃×C₄	—	10	4	no	—
286	C₂×C₃×C₄	—	10	2	no	—
287	C₂×C₃×C₄	—	10	2	no	—
288	C₂×C₃×C₄	—	20	4	no	—
289	C₂×C₃×C₄	—	20	4	no	—
290	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
291	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
292	C₃×C₈	—	5	4	no	—
293	C₃×C₈	D₄×D₅	1	4	yes	—
294	C₂²×C₅	—	4	4	no	—
295	C₂²×C₅	—	4	2	no	—
296	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
297	C₂×D₅	—	2	2	no	—
298	C₂×D₅	C₃×#127	1	2	yes	—
299	C₄×C₅	—	4	2	no	—
300	C₄×C₅	C₃×#137	1	4	yes	complemented
301	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
302	Dic₅	—	2	2	no	—
303	Dic₅	—	4	2	no	—
304	Dic₅	—	4	2	no	—
305	Dic₅	C₃×#127	1	2	yes	—
306	#41	—	10	8	no	—
307	C₂×Q₈	—	5	2	no	—
308	C₂×Q₈	—	5	2	no	—
309	C₂×Q₈	—	10	2	no	—
310	C₂×Q₈	—	10	8	no	—
311	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	10	2	no	—
314	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
315	C₂²×C₄	—	5	1	no	—
316	C₂²×C₄	—	5	2	no	—
317	C₂²×C₄	—	10	2	no	—
318	C₂²×C₄	—	10	2	no	—
319	Q₁₆	—	10	8	no	—
320	Q₁₆	—	10	8	no	—
321	SD₁₆	—	2	8	no	—
322	SD₁₆	—	10	8	no	—
323	M₁₆	—	5	8	no	—
324	C₂×C₈	—	5	2	no	—
325	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	10	4	no	—
328	C₄⋊C₄	—	10	2	no	—
329	C₄⋊C₄	—	10	2	no	—
330	C₂²⋊C₄	—	10	4	no	—
331	C₄²	—	5	2	no	—
332	C₄²	—	5	1	no	—
333	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
334	C₃×C₅	#3152	1	1	yes	characteristic, complemented, Hall
335	C₂²×C₃	—	4	2	no	—
336	C₂²×C₃	—	4	4	no	—
337	C₂²×C₃	—	5	2	no	—
338	C₂²×C₃	—	10	2	no	—
339	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
340	C₃×C₄	—	4	2	no	—
341	C₃×C₄	—	5	2	no	—
342	C₃×C₄	—	10	2	no	—
343	C₃×C₄	—	20	2	no	—
344	C₃×C₄	—	20	2	no	—
345	C₃×C₄	#4061	1	4	yes	complemented
346	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
347	C₂×C₅	—	8	2	no	—
348	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
349	C₂×C₅	C₂×C₃×#137	1	2	yes	—
350	D₅	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	5	1	no	—
353	Q₈	—	2	4	no	—
354	Q₈	—	10	4	no	—
355	Q₈	—	10	4	no	—
356	Q₈	—	20	4	no	—
357	D₄	—	2	4	no	—
358	D₄	—	4	4	no	—
359	D₄	—	20	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	5	1	no	—
362	C₂×C₄	—	5	4	no	—
363	C₂×C₄	—	5	2	no	—
364	C₂×C₄	—	10	4	no	—
365	C₂×C₄	—	10	2	no	—
366	C₂×C₄	—	10	2	no	—
367	C₂×C₄	—	20	4	no	—
368	C₂×C₄	—	20	4	no	—
369	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
370	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
371	C₈	—	5	4	no	—
372	C₈	C₃×D₄×D₅	1	4	yes	—
373	C₂×C₃	—	8	2	no	—
374	C₂×C₃	—	10	2	no	—
375	C₂×C₃	D₅×#127	1	1	yes	characteristic
376	C₂×C₃	C₂×#4061	1	2	yes	—
377	C₅	C₃×#3152	1	1	yes	characteristic, complemented, Sylow
378	C₂²	—	4	2	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	5	2	no	—
381	C₂²	—	10	2	no	—
382	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
383	C₄	—	4	2	no	—
384	C₄	—	5	2	no	—
385	C₄	—	10	2	no	—
386	C₄	—	20	2	no	—
387	C₄	—	20	2	no	—
388	C₄	C₃×#4061	1	4	yes	complemented
389	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
390	C₃	#10613493	1	1	yes	characteristic, direct product factor, Sylow
391	C₂	—	8	2	no	—
392	C₂	—	10	2	no	—
393	C₂	C₃×D₅×#127	1	1	yes	characteristic
394	C₂	C₂×C₃×#4061	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#492	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×#66050	C₂
hypercenter	C₃×#492	D₅
hypocenter	C₅	C₃×#3152
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#492

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4061	C₂	semidirect
2. C₃×D₅×C₄⋊Q₈	C₂	semidirect
4. C₃×C₅×#492	C₂	semidirect
5. C₃×#65456	C₂	semidirect
6. C₃×#65381	C₂	semidirect
7. C₃×#65365	C₂	semidirect
8. C₃×#64988	C₂	semidirect
9. C₃×C₄×#676	C₂	semidirect
10. #10613493	C₃	direct (N × H)
34. C₂×#4061	C₂×C₃	semidirect
35. D₅×C₄⋊Q₈	C₂×C₃	semidirect
37. C₅×#492	C₂×C₃	semidirect
38. #65456	C₂×C₃	semidirect
39. #65381	C₂×C₃	semidirect
40. #65365	C₂×C₃	semidirect
41. #64988	C₂×C₃	semidirect
42. C₄×#676	C₂×C₃	semidirect
70. C₃×#676	D₄	semidirect
78. C₃×#492	D₅	semidirect
174. #676	C₃×D₄	semidirect
182. #492	C₃×D₅	semidirect
190. C₃×C₄×C₅	#137	semidirect
300. C₄×C₅	C₃×#137	semidirect
334. C₃×C₅	#3152	semidirect
345. C₃×C₄	#4061	semidirect
377. C₅	C₃×#3152	semidirect
388. C₄	C₃×#4061	semidirect
390. C₃	#10613493	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×#4061	2
C₃×D₅×C₄⋊Q₈	2
C₃×#66050	2
C₃×C₅×#492	2
C₃×#65456	2
C₃×#65381	2
C₃×#65365	2
C₃×#64988	2
C₃×C₄×#676	2
#10613493	3
C₃×#3152	5

Subgroups — C3×#10613493 #14439199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613493 #14439199