Subgroups — C₃×#10602707 #14289221

Order 1920.

500 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	C₃×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#65377	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65316	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65304	C₂	1	1	yes	maximal, characteristic
5	C₃×#64767	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×Q₈⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×D₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
8	#10602707	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	—	2	1	no	—
10	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
11	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
13	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
14	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	—	2	1	no	—
16	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×#688	—	2	1	no	—
18	C₂×C₃×#686	—	2	1	no	—
19	C₃×#4020	C₂²	1	1	yes	characteristic
20	C₃×#3941	—	2	1	no	—
21	C₃×#3941	—	2	1	no	—
22	C₃×#3941	—	2	2	no	—
23	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
24	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
25	C₃×C₄×#168	C₂²	1	1	yes	characteristic
26	C₃×#1627	—	5	1	no	maximal, Hall
27	C₅×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
28	#65377	C₂×C₃	1	1	yes	characteristic, complemented
29	#65316	C₂×C₃	1	1	yes	characteristic, complemented
30	#65304	C₂×C₃	1	1	yes	characteristic
31	#64767	C₂×C₃	1	1	yes	characteristic, complemented
32	Q₈⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
33	D₄⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×C₃×C₅×Q₈	—	2	2	no	—
35	C₂×C₃×C₅×Q₈	—	2	1	no	—
36	C₂×C₃×C₅×Q₈	—	4	2	no	—
37	C₂×C₃×C₅×Q₈	—	4	2	no	—
38	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
39	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	—	2	2	no	—
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂×C₃×D₂₀	—	2	1	no	—
43	C₂×C₃×D₂₀	—	2	1	no	—
44	C₂×C₃×D₂₀	—	2	1	no	—
45	C₃×C₅×C₄⋊C₄	—	2	2	no	—
46	C₃×C₅×C₄⋊C₄	—	2	1	no	—
47	C₃×C₅×C₄⋊C₄	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
49	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
50	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
51	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
52	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
53	C₃×C₄²×C₅	—	2	1	no	—
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₃×#688	—	4	2	no	—
56	C₃×#686	—	4	2	no	—
57	C₂×C₃×#168	—	2	1	no	—
58	C₂×C₃×#168	—	2	1	no	—
59	C₂×C₃×#168	—	2	1	no	—
60	C₃×D₄×Q₈	D₅	1	1	yes	characteristic, complemented
61	C₃×#486	—	5	1	no	—
62	C₃×#460	—	5	1	no	—
63	C₃×#459	—	5	1	no	—
64	C₃×#332	—	5	1	no	—
65	C₃×Q₈⋊C₈	—	5	1	no	—
66	C₃×D₄⋊C₈	—	5	1	no	—
67	C₂²×C₅×Q₈	—	2	1	no	—
68	C₅×C₄⋊Q₈	—	2	1	no	—
69	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
70	C₅×C₂²⋊Q₈	—	2	1	no	—
71	C₅×C₂²⋊Q₈	—	2	2	no	—
72	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
73	C₄×C₅×D₄	—	2	1	no	—
74	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
75	C₂×#688	—	2	1	no	—
76	C₂×#686	—	2	1	no	—
77	#4020	C₂²×C₃	1	1	yes	characteristic
78	#3941	—	2	1	no	—
79	#3941	—	2	1	no	—
80	#3941	—	2	2	no	—
81	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
82	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
83	C₄×#168	C₂²×C₃	1	1	yes	characteristic
84	#1627	—	5	1	no	Sylow
85	C₂³×C₃×C₅	—	2	1	no	—
86	C₂²×C₃×D₅	—	4	1	no	—
87	C₃×C₅×Q₈	—	2	1	no	—
88	C₃×C₅×Q₈	—	4	4	no	—
89	C₃×C₅×Q₈	—	4	1	no	—
90	C₃×C₅×Q₈	—	4	1	no	—
91	C₃×C₅×Q₈	D₈	1	2	yes	complemented
92	C₃×C₅×D₄	—	2	1	no	—
93	C₃×C₅×D₄	SD₁₆	1	2	yes	complemented
94	C₂×C₃×C₄×C₅	—	2	1	no	—
95	C₂×C₃×C₄×C₅	—	2	1	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	—	4	4	no	—
99	C₂×C₃×C₄×C₅	—	4	1	no	—
100	C₂×C₃×C₄×C₅	—	4	1	no	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₃×D₂₀	—	4	2	no	—
105	C₃×D₂₀	—	4	1	no	—
106	C₃×D₂₀	—	4	1	no	—
107	C₃×D₂₀	—	4	1	no	—
108	C₃×D₂₀	—	4	1	no	—
109	C₃×#168	—	4	1	no	—
110	C₃×#168	—	4	1	no	—
111	C₃×#168	—	4	1	no	—
112	C₂²×C₃×Q₈	—	2	1	no	—
113	C₂×C₃×SD₁₆	—	10	1	no	—
114	C₂×C₃×D₈	—	10	1	no	—
115	C₃×C₄⋊Q₈	—	2	1	no	—
116	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
117	C₃×#127	—	5	1	no	—
118	C₃×C₂²⋊Q₈	—	2	1	no	—
119	C₃×C₂²⋊Q₈	—	2	2	no	—
120	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
121	C₃×C₄×D₄	—	2	1	no	—
122	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
123	C₃×C₄⋊C₈	—	5	1	no	—
124	C₃×C₄⋊C₈	—	5	1	no	—
125	C₃×#102	—	10	1	no	—
126	C₃×#102	—	10	1	no	—
127	C₃×#102	—	10	2	no	—
128	C₃×C₄×C₈	—	5	1	no	—
129	C₂×C₅×Q₈	—	2	2	no	—
130	C₂×C₅×Q₈	—	2	1	no	—
131	C₂×C₅×Q₈	—	4	2	no	—
132	C₂×C₅×Q₈	—	4	2	no	—
133	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
134	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	—	2	2	no	—
136	C₂²×C₄×C₅	—	2	1	no	—
137	C₂×D₂₀	—	2	1	no	—
138	C₂×D₂₀	—	2	1	no	—
139	C₂×D₂₀	—	2	1	no	—
140	C₅×C₄⋊C₄	—	2	2	no	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₄⋊C₄	—	2	1	no	—
143	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
144	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
145	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
146	C₅×C₂²⋊C₄	—	2	2	no	—
147	C₅×C₂²⋊C₄	—	2	1	no	—
148	C₄²×C₅	—	2	1	no	—
149	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
150	#688	—	4	2	no	—
151	#686	—	4	2	no	—
152	C₂×#168	—	2	1	no	—
153	C₂×#168	—	2	1	no	—
154	C₂×#168	—	2	1	no	—
155	D₄×Q₈	C₃×D₅	1	1	yes	characteristic, complemented
156	#486	—	5	1	no	—
157	#460	—	5	1	no	—
158	#459	—	5	1	no	—
159	#332	—	5	1	no	—
160	Q₈⋊C₈	—	5	1	no	—
161	D₄⋊C₈	—	5	1	no	—
162	C₂²×C₃×C₅	—	2	2	no	—
163	C₂²×C₃×C₅	—	4	1	no	—
164	C₂²×C₃×C₅	—	4	1	no	—
165	C₂²×C₃×C₅	#120	1	1	yes	characteristic
166	C₂×C₃×D₅	—	8	1	no	—
167	C₂×C₃×D₅	—	8	1	no	—
168	C₂×C₃×D₅	—	8	1	no	—
169	C₃×C₄×C₅	—	2	2	no	—
170	C₃×C₄×C₅	—	2	1	no	—
171	C₃×C₄×C₅	—	4	2	no	—
172	C₃×C₄×C₅	—	4	1	no	—
173	C₃×C₄×C₅	—	4	1	no	—
174	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
175	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
176	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₃×C₄×C₅	#137	1	1	yes	characteristic
178	C₂×C₃×Q₈	—	2	2	no	—
179	C₂×C₃×Q₈	—	2	1	no	—
180	C₂×C₃×Q₈	—	4	2	no	—
181	C₂×C₃×Q₈	—	4	2	no	—
182	C₂×C₃×Q₈	C₂²⋊D₅	1	1	yes	characteristic
183	C₂×C₃×D₄	—	10	1	no	—
184	C₂×C₃×D₄	—	10	1	no	—
185	C₂×C₃×D₄	—	10	1	no	—
186	C₂×C₃×D₄	C₂²⋊D₅	1	1	yes	characteristic
187	C₂²×C₃×C₄	—	2	2	no	—
188	C₂²×C₃×C₄	—	2	1	no	—
189	C₃×SD₁₆	—	20	2	no	—
190	C₃×D₈	—	20	2	no	—
191	C₂×C₃×C₈	—	10	1	no	—
192	C₂×C₃×C₈	—	10	1	no	—
193	C₂×C₃×C₈	—	10	1	no	—
194	C₃×C₄⋊C₄	—	2	2	no	—
195	C₃×C₄⋊C₄	—	2	1	no	—
196	C₃×C₄⋊C₄	—	2	1	no	—
197	C₃×C₄⋊C₄	C₂²⋊D₅	1	1	yes	characteristic
198	C₃×C₄⋊C₄	C₂²⋊D₅	1	1	yes	characteristic
199	C₃×C₄⋊C₄	C₂²⋊D₅	1	2	yes	—
200	C₃×C₂²⋊C₄	—	2	2	no	—
201	C₃×C₂²⋊C₄	—	2	1	no	—
202	C₃×C₄²	—	2	1	no	—
203	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
204	C₂³×C₅	—	2	1	no	—
205	C₂²×D₅	—	4	1	no	—
206	C₅×Q₈	—	2	1	no	—
207	C₅×Q₈	—	4	4	no	—
208	C₅×Q₈	—	4	1	no	—
209	C₅×Q₈	—	4	1	no	—
210	C₅×Q₈	C₃×D₈	1	2	yes	complemented
211	C₅×D₄	—	2	1	no	—
212	C₅×D₄	C₃×SD₁₆	1	2	yes	complemented
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	4	4	no	—
218	C₂×C₄×C₅	—	4	1	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
223	D₂₀	—	4	2	no	—
224	D₂₀	—	4	1	no	—
225	D₂₀	—	4	1	no	—
226	D₂₀	—	4	1	no	—
227	D₂₀	—	4	1	no	—
228	#168	—	4	1	no	—
229	#168	—	4	1	no	—
230	#168	—	4	1	no	—
231	C₂²×Q₈	—	2	1	no	—
232	C₂×SD₁₆	—	10	1	no	—
233	C₂×D₈	—	10	1	no	—
234	C₄⋊Q₈	—	2	1	no	—
235	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
236	#127	—	5	1	no	—
237	C₂²⋊Q₈	—	2	1	no	—
238	C₂²⋊Q₈	—	2	2	no	—
239	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
242	C₄⋊C₈	—	5	1	no	—
243	C₄⋊C₈	—	5	1	no	—
244	#102	—	10	1	no	—
245	#102	—	10	1	no	—
246	#102	—	10	2	no	—
247	C₄×C₈	—	5	1	no	—
248	C₂×C₃×C₅	—	4	2	no	—
249	C₂×C₃×C₅	#447	1	1	yes	characteristic
250	C₂×C₃×C₅	#448	1	1	yes	characteristic
251	C₂×C₃×C₅	#454	1	1	yes	characteristic
252	C₃×D₅	—	16	1	no	—
253	C₂³×C₃	—	2	1	no	—
254	C₂³×C₃	—	20	1	no	—
255	C₃×Q₈	—	2	1	no	—
256	C₃×Q₈	—	4	4	no	—
257	C₃×Q₈	—	4	1	no	—
258	C₃×Q₈	—	4	1	no	—
259	C₃×Q₈	#686	1	2	yes	complemented
260	C₃×D₄	—	2	1	no	—
261	C₃×D₄	—	20	2	no	—
262	C₃×D₄	—	20	1	no	—
263	C₃×D₄	—	20	1	no	—
264	C₃×D₄	—	20	1	no	—
265	C₃×D₄	—	20	1	no	—
266	C₃×D₄	#688	1	2	yes	complemented
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	4	4	no	—
272	C₂×C₃×C₄	—	4	1	no	—
273	C₂×C₃×C₄	—	4	1	no	—
274	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
277	C₃×C₈	—	20	1	no	—
278	C₃×C₈	—	20	1	no	—
279	C₃×C₈	—	20	1	no	—
280	C₂²×C₅	—	2	2	no	—
281	C₂²×C₅	—	4	1	no	—
282	C₂²×C₅	—	4	1	no	—
283	C₂²×C₅	C₃×#120	1	1	yes	characteristic
284	C₂×D₅	—	8	1	no	—
285	C₂×D₅	—	8	1	no	—
286	C₂×D₅	—	8	1	no	—
287	C₄×C₅	—	2	2	no	—
288	C₄×C₅	—	2	1	no	—
289	C₄×C₅	—	4	2	no	—
290	C₄×C₅	—	4	1	no	—
291	C₄×C₅	—	4	1	no	—
292	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
293	C₄×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
294	C₄×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
295	C₄×C₅	C₃×#137	1	1	yes	characteristic
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×Q₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
301	C₂×D₄	—	10	1	no	—
302	C₂×D₄	—	10	1	no	—
303	C₂×D₄	—	10	1	no	—
304	C₂×D₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	1	no	—
307	SD₁₆	—	20	2	no	—
308	D₈	—	20	2	no	—
309	C₂×C₈	—	10	1	no	—
310	C₂×C₈	—	10	1	no	—
311	C₂×C₈	—	10	1	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
316	C₄⋊C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
317	C₄⋊C₄	C₃×C₂²⋊D₅	1	2	yes	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	2	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
322	C₃×C₅	#1627	1	1	yes	characteristic, complemented, Hall
323	C₂²×C₃	—	2	2	no	—
324	C₂²×C₃	—	4	1	no	—
325	C₂²×C₃	—	4	1	no	—
326	C₂²×C₃	—	40	1	no	—
327	C₂²×C₃	—	40	1	no	—
328	C₂²×C₃	—	40	1	no	—
329	C₂²×C₃	#4099	1	1	yes	characteristic
330	C₃×C₄	—	2	2	no	—
331	C₃×C₄	—	2	1	no	—
332	C₃×C₄	—	4	2	no	—
333	C₃×C₄	—	4	1	no	—
334	C₃×C₄	—	4	1	no	—
335	C₃×C₄	C₂×#686	1	1	yes	characteristic
336	C₃×C₄	#4078	1	1	yes	characteristic
337	C₃×C₄	C₂×#688	1	1	yes	characteristic
338	C₃×C₄	#4088	1	1	yes	characteristic
339	C₂×C₅	—	4	2	no	—
340	C₂×C₅	C₃×#447	1	1	yes	characteristic
341	C₂×C₅	C₃×#448	1	1	yes	characteristic
342	C₂×C₅	C₃×#454	1	1	yes	characteristic
343	D₅	—	16	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	20	1	no	—
346	Q₈	—	2	1	no	—
347	Q₈	—	4	4	no	—
348	Q₈	—	4	1	no	—
349	Q₈	—	4	1	no	—
350	Q₈	C₃×#686	1	2	yes	complemented
351	D₄	—	2	1	no	—
352	D₄	—	20	2	no	—
353	D₄	—	20	1	no	—
354	D₄	—	20	1	no	—
355	D₄	—	20	1	no	—
356	D₄	—	20	1	no	—
357	D₄	C₃×#688	1	2	yes	complemented
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
366	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
367	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
368	C₈	—	20	1	no	—
369	C₈	—	20	1	no	—
370	C₈	—	20	1	no	—
371	C₂×C₃	—	4	2	no	—
372	C₂×C₃	—	80	1	no	—
373	C₂×C₃	#65506	1	1	yes	characteristic
374	C₂×C₃	#65516	1	1	yes	characteristic
375	C₂×C₃	#65534	1	1	yes	characteristic
376	C₅	C₃×#1627	1	1	yes	characteristic, complemented, Sylow
377	C₂²	—	2	2	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	40	1	no	—
381	C₂²	—	40	1	no	—
382	C₂²	—	40	1	no	—
383	C₂²	C₃×#4099	1	1	yes	characteristic
384	C₄	—	2	2	no	—
385	C₄	—	2	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	1	no	—
389	C₄	C₂×C₃×#686	1	1	yes	characteristic
390	C₄	C₃×#4078	1	1	yes	characteristic
391	C₄	C₂×C₃×#688	1	1	yes	characteristic
392	C₄	C₃×#4088	1	1	yes	characteristic
393	C₃	#10602707	1	1	yes	characteristic, direct product factor, Sylow
394	C₂	—	4	2	no	—
395	C₂	—	80	1	no	—
396	C₂	C₃×#65506	1	1	yes	characteristic
397	C₂	C₃×#65516	1	1	yes	characteristic
398	C₂	C₃×#65534	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#4099
commutator, cosocle	C₄²×C₅	C₂³×C₃
Frattini	C₄²	C₂²×C₃×D₅
Fitting	C₃×C₅×D₄×Q₈	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₃×#65304	C₂
hypercenter	C₃×D₄×Q₈	D₅
hypocenter	C₅	C₃×#1627
LCS	G ▷ C₄²×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₄×Q₈	C₂	semidirect
2. C₃×#65377	C₂	semidirect
3. C₃×#65316	C₂	semidirect
5. C₃×#64767	C₂	semidirect
6. C₃×Q₈⋊#168	C₂	semidirect
7. C₃×D₄⋊#168	C₂	semidirect
8. #10602707	C₃	direct (N × H)
27. C₅×D₄×Q₈	C₂×C₃	semidirect
28. #65377	C₂×C₃	semidirect
29. #65316	C₂×C₃	semidirect
31. #64767	C₂×C₃	semidirect
32. Q₈⋊#168	C₂×C₃	semidirect
33. D₄⋊#168	C₂×C₃	semidirect
60. C₃×D₄×Q₈	D₅	semidirect
91. C₃×C₅×Q₈	D₈	semidirect
93. C₃×C₅×D₄	SD₁₆	semidirect
155. D₄×Q₈	C₃×D₅	semidirect
210. C₅×Q₈	C₃×D₈	semidirect
212. C₅×D₄	C₃×SD₁₆	semidirect
259. C₃×Q₈	#686	semidirect
266. C₃×D₄	#688	semidirect
322. C₃×C₅	#1627	semidirect
350. Q₈	C₃×#686	semidirect
357. D₄	C₃×#688	semidirect
376. C₅	C₃×#1627	semidirect
393. C₃	#10602707	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×D₄×Q₈	2
C₃×#65377	2
C₃×#65316	2
C₃×#65304	2
C₃×#64767	2
C₃×Q₈⋊#168	2
C₃×D₄⋊#168	2
#10602707	3
C₃×#1627	5

Subgroups — C3×#10602707 #14289221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10602707 #14289221