Subgroups — C₅×Dic₃×#135 #14416218

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₃×#41	C₂	1	2	yes	maximal, complemented
3	C₅×#5233	C₂	1	2	yes	maximal, complemented
4	C₅×Dic₃×Q₁₆	C₂	1	2	yes	maximal, complemented
5	C₅×Dic₃×SD₁₆	C₂	1	4	yes	maximal, complemented
6	C₅×Dic₃×D₈	C₂	1	2	yes	maximal, complemented
7	C₅×#5106	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×#135	—	3	1	no	maximal, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₃×C₅×#135	C₄	1	8	yes	complemented
12	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₅×Q₈×Dic₃	C₂²	1	4	yes	—
17	C₅×D₄×Dic₃	—	2	4	no	—
18	C₅×D₄×Dic₃	C₂²	1	4	yes	—
19	C₅×#926	—	2	2	no	—
20	C₅×#926	C₂²	1	2	yes	—
21	C₂×C₄×C₅×Dic₃	—	2	2	no	—
22	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
23	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₅×#835	C₂²	1	4	yes	—
25	C₅×#832	C₂²	1	4	yes	—
26	C₅×#818	C₂²	1	2	yes	—
27	C₅×#817	C₂²	1	2	yes	—
28	C₅×C₈×Dic₃	C₂²	1	2	yes	—
29	C₅×C₈×Dic₃	C₂²	1	2	yes	—
30	Dic₃×#135	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#135	D₃	1	1	yes	characteristic
32	C₄×C₅×#41	—	3	2	no	—
33	C₄×C₅×Q₁₆	—	3	2	no	—
34	C₄×C₅×SD₁₆	—	3	4	no	—
35	C₄×C₅×D₈	—	3	2	no	—
36	C₅×#427	—	3	1	no	—
37	C₅×#416	—	3	2	no	—
38	C₂×C₄×C₅×C₈	—	3	1	no	—
39	C₃×C₅×#41	—	2	4	no	—
40	C₃×C₅×#41	C₂×C₄	1	8	yes	complemented
41	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
42	C₂×C₃×C₅×D₄	—	2	2	no	—
43	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	—	2	2	no	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₅×Dic₃	—	2	4	no	—
47	C₂²×C₅×Dic₃	D₄	1	2	yes	—
48	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
49	C₃×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
50	C₃×C₅×D₈	C₂×C₄	1	4	yes	complemented
51	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
52	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
54	C₅×#217	—	2	2	no	—
55	C₅×#217	—	2	4	no	—
56	C₅×C₄⋊Dic₃	—	2	4	no	—
57	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
58	C₄×C₅×Dic₃	—	2	2	no	—
59	C₄×C₅×Dic₃	—	2	4	no	—
60	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
61	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
62	C₄×C₅×Dic₃	C₂³	1	2	yes	—
63	C₂×C₅×C₃⋊C₈	—	2	2	no	—
64	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
65	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic
66	Dic₃×#41	C₂×C₅	1	2	yes	complemented
67	#5233	C₂×C₅	1	2	yes	complemented
68	Dic₃×Q₁₆	C₂×C₅	1	2	yes	complemented
69	Dic₃×SD₁₆	C₂×C₅	1	4	yes	complemented
70	Dic₃×D₈	C₂×C₅	1	2	yes	complemented
71	#5106	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×C₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×C₅×#41	C₂×D₃	1	2	yes	—
74	C₅×#135	Dic₃	1	8	yes	direct product factor
75	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
76	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
77	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
78	C₂²×C₅×C₈	—	3	1	no	—
79	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
80	C₄×C₅×Q₈	—	3	4	no	—
81	C₄×C₅×D₄	—	3	4	no	—
82	C₄×C₅×D₄	—	6	4	no	—
83	C₅×#117	—	3	2	no	—
84	C₅×#117	—	6	2	no	—
85	C₂×C₄²×C₅	—	3	1	no	—
86	C₂×C₄²×C₅	—	6	2	no	—
87	C₅×#107	—	3	2	no	—
88	C₅×#106	—	3	2	no	—
89	C₅×#103	—	3	4	no	—
90	C₅×#102	—	3	4	no	—
91	C₄×C₅×C₈	—	3	2	no	—
92	C₄×C₅×C₈	—	3	2	no	—
93	C₄×#135	—	3	1	no	Sylow
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
96	C₃×C₅×Q₈	—	2	2	no	—
97	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
98	C₃×C₅×D₄	—	2	8	no	—
99	C₃×C₅×D₄	—	2	2	no	—
100	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	8	no	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	#41	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
107	C₂×C₅×Dic₃	—	2	4	no	—
108	C₂×C₅×Dic₃	—	2	4	no	—
109	C₂×C₅×Dic₃	—	4	8	no	—
110	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
111	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
112	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
113	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
114	C₅×C₃⋊C₈	—	2	2	no	—
115	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
116	C₃×#135	C₄×C₅	1	8	yes	complemented
117	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
118	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
119	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
120	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
121	Q₈×Dic₃	C₂²×C₅	1	4	yes	—
122	D₄×Dic₃	—	2	4	no	—
123	D₄×Dic₃	C₂²×C₅	1	4	yes	—
124	#926	—	2	2	no	—
125	#926	C₂²×C₅	1	2	yes	—
126	C₂×C₄×Dic₃	—	2	2	no	—
127	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
128	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
129	#835	C₂²×C₅	1	4	yes	—
130	#832	C₂²×C₅	1	4	yes	—
131	#818	C₂²×C₅	1	2	yes	—
132	#817	C₂²×C₅	1	2	yes	—
133	C₈×Dic₃	C₂²×C₅	1	2	yes	—
134	C₈×Dic₃	C₂²×C₅	1	2	yes	—
135	C₅×#41	—	2	4	no	—
136	C₅×#41	C₂×Dic₃	1	8	yes	complemented
137	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
138	C₂×C₅×D₄	—	2	2	no	—
139	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
140	C₂²×C₄×C₅	—	2	2	no	—
141	C₂²×C₄×C₅	—	3	2	no	—
142	C₂²×C₄×C₅	—	6	4	no	—
143	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
144	C₅×Q₁₆	C₂×Dic₃	1	4	yes	complemented
145	C₅×SD₁₆	C₂×Dic₃	1	8	yes	complemented
146	C₅×D₈	C₂×Dic₃	1	4	yes	complemented
147	C₂×C₅×C₈	—	3	2	no	—
148	C₂×C₅×C₈	—	6	2	no	—
149	C₂×C₅×C₈	C₂×Dic₃	1	4	yes	complemented
150	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
151	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
152	C₅×C₄⋊C₄	—	3	4	no	—
153	C₅×C₄⋊C₄	—	6	4	no	—
154	C₅×C₂²⋊C₄	—	6	4	no	—
155	C₅×C₂²⋊C₄	—	6	2	no	—
156	C₄²×C₅	—	3	1	no	—
157	C₄²×C₅	—	3	1	no	—
158	C₄²×C₅	—	3	2	no	—
159	C₄²×C₅	—	6	4	no	—
160	C₄²×C₅	—	6	2	no	—
161	C₂×#135	C₅×D₃	1	1	yes	characteristic
162	C₄×#41	—	3	2	no	—
163	C₄×Q₁₆	—	3	2	no	—
164	C₄×SD₁₆	—	3	4	no	—
165	C₄×D₈	—	3	2	no	—
166	#427	—	3	1	no	—
167	#416	—	3	2	no	—
168	C₂×C₄×C₈	—	3	1	no	—
169	C₂²×C₃×C₅	—	2	2	no	—
170	C₂²×C₃×C₅	—	2	4	no	—
171	C₂²×C₃×C₅	—	4	4	no	—
172	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
173	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
174	C₃×C₄×C₅	—	2	4	no	—
175	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
176	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
177	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
178	C₅×Dic₃	—	2	2	no	—
179	C₅×Dic₃	—	4	4	no	—
180	C₅×Dic₃	#135	1	4	yes	direct product factor
181	C₃×#41	—	2	4	no	—
182	C₃×#41	C₂×C₄×C₅	1	8	yes	complemented
183	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
184	C₂×C₃×D₄	—	2	2	no	—
185	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
186	C₂²×C₃×C₄	—	2	2	no	—
187	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
188	C₂²×Dic₃	—	2	4	no	—
189	C₂²×Dic₃	C₅×D₄	1	2	yes	—
190	C₃×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
191	C₃×SD₁₆	C₂×C₄×C₅	1	8	yes	complemented
192	C₃×D₈	C₂×C₄×C₅	1	4	yes	complemented
193	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
194	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
195	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
196	#217	—	2	2	no	—
197	#217	—	2	4	no	—
198	C₄⋊Dic₃	—	2	4	no	—
199	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
200	C₄×Dic₃	—	2	2	no	—
201	C₄×Dic₃	—	2	4	no	—
202	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
203	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
204	C₄×Dic₃	C₂³×C₅	1	2	yes	—
205	C₂×C₃⋊C₈	—	2	2	no	—
206	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
207	C₂³×C₅	—	2	2	no	—
208	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
209	C₅×Q₈	—	2	2	no	—
210	C₅×Q₈	C₂²×Dic₃	1	4	yes	—
211	C₅×D₄	—	2	8	no	—
212	C₅×D₄	—	2	2	no	—
213	C₅×D₄	C₂²×Dic₃	1	4	yes	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	8	no	—
216	C₂×C₄×C₅	—	3	2	no	—
217	C₂×C₄×C₅	—	3	2	no	—
218	C₂×C₄×C₅	—	6	4	no	—
219	C₂×C₄×C₅	—	6	4	no	—
220	C₂×C₄×C₅	—	12	8	no	—
221	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	#237	1	2	yes	—
223	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
224	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
225	C₅×C₈	—	6	2	no	—
226	C₅×C₈	C₂²×Dic₃	1	2	yes	—
227	C₅×C₈	C₂²×Dic₃	1	2	yes	—
228	C₂×#41	C₂×C₅×D₃	1	2	yes	—
229	#135	C₅×Dic₃	1	8	yes	direct product factor
230	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
231	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
232	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
233	C₂²×C₈	—	3	1	no	—
234	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
235	C₄×Q₈	—	3	4	no	—
236	C₄×D₄	—	3	4	no	—
237	C₄×D₄	—	6	4	no	—
238	#117	—	3	2	no	—
239	#117	—	6	2	no	—
240	C₂×C₄²	—	3	1	no	—
241	C₂×C₄²	—	6	2	no	—
242	#107	—	3	2	no	—
243	#106	—	3	2	no	—
244	#103	—	3	4	no	—
245	#102	—	3	4	no	—
246	C₄×C₈	—	3	2	no	—
247	C₄×C₈	—	3	2	no	—
248	C₂×C₃×C₅	—	2	2	no	—
249	C₂×C₃×C₅	—	4	4	no	—
250	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
251	C₂×C₃×C₅	C₂×#135	1	2	yes	—
252	C₂³×C₃	—	2	2	no	—
253	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
254	C₃×Q₈	—	2	2	no	—
255	C₃×Q₈	C₂²×C₄×C₅	1	4	yes	—
256	C₃×D₄	—	2	8	no	—
257	C₃×D₄	—	2	2	no	—
258	C₃×D₄	C₂²×C₄×C₅	1	4	yes	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	8	no	—
261	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
262	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
263	C₂×C₃×C₄	C₅×#41	1	2	yes	—
264	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
265	C₂×Dic₃	—	2	4	no	—
266	C₂×Dic₃	—	2	4	no	—
267	C₂×Dic₃	—	4	8	no	—
268	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
269	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
270	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
271	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
272	C₃⋊C₈	—	2	2	no	—
273	C₂²×C₅	—	2	2	no	—
274	C₂²×C₅	—	2	4	no	—
275	C₂²×C₅	—	4	4	no	—
276	C₂²×C₅	D₄×Dic₃	1	2	yes	—
277	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
278	C₄×C₅	—	2	4	no	—
279	C₄×C₅	—	3	4	no	—
280	C₄×C₅	—	6	2	no	—
281	C₄×C₅	—	12	4	no	—
282	C₄×C₅	D₄×Dic₃	1	2	yes	—
283	C₄×C₅	C₂×#237	1	1	yes	characteristic
284	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
285	#41	—	2	4	no	—
286	#41	C₂×C₅×Dic₃	1	8	yes	complemented
287	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	3	2	no	—
292	C₂²×C₄	—	6	4	no	—
293	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
294	Q₁₆	C₂×C₅×Dic₃	1	4	yes	complemented
295	SD₁₆	C₂×C₅×Dic₃	1	8	yes	complemented
296	D₈	C₂×C₅×Dic₃	1	4	yes	complemented
297	C₂×C₈	—	3	2	no	—
298	C₂×C₈	—	6	2	no	—
299	C₂×C₈	C₂×C₅×Dic₃	1	4	yes	complemented
300	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
301	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
302	C₄⋊C₄	—	3	4	no	—
303	C₄⋊C₄	—	6	4	no	—
304	C₂²⋊C₄	—	6	4	no	—
305	C₂²⋊C₄	—	6	2	no	—
306	C₄²	—	3	1	no	—
307	C₄²	—	3	1	no	—
308	C₄²	—	3	2	no	—
309	C₄²	—	6	4	no	—
310	C₄²	—	6	2	no	—
311	C₃×C₅	C₄×#135	1	1	yes	characteristic, complemented, Hall
312	C₂²×C₃	—	2	2	no	—
313	C₂²×C₃	—	2	4	no	—
314	C₂²×C₃	—	4	4	no	—
315	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
316	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
317	C₃×C₄	—	2	4	no	—
318	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
319	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
320	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
321	Dic₃	—	2	2	no	—
322	Dic₃	—	4	4	no	—
323	Dic₃	C₅×#135	1	4	yes	direct product factor
324	C₂×C₅	—	2	2	no	—
325	C₂×C₅	—	4	4	no	—
326	C₂×C₅	D₃×#135	1	2	yes	—
327	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
328	C₂³	—	2	2	no	—
329	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
330	Q₈	—	2	2	no	—
331	Q₈	C₂²×C₅×Dic₃	1	4	yes	—
332	D₄	—	2	8	no	—
333	D₄	—	2	2	no	—
334	D₄	C₂²×C₅×Dic₃	1	4	yes	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	3	2	no	—
338	C₂×C₄	—	3	2	no	—
339	C₂×C₄	—	6	4	no	—
340	C₂×C₄	—	6	4	no	—
341	C₂×C₄	—	12	8	no	—
342	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
343	C₂×C₄	C₅×#237	1	2	yes	—
344	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
345	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
346	C₈	—	6	2	no	—
347	C₈	C₂²×C₅×Dic₃	1	2	yes	—
348	C₈	C₂²×C₅×Dic₃	1	2	yes	—
349	C₂×C₃	—	2	2	no	—
350	C₂×C₃	—	4	4	no	—
351	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
352	C₂×C₃	C₂×C₅×#135	1	2	yes	—
353	C₅	Dic₃×#135	1	1	yes	characteristic, direct product factor, Sylow
354	C₂²	—	2	2	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	4	4	no	—
357	C₂²	C₅×D₄×Dic₃	1	2	yes	—
358	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
359	C₄	—	2	4	no	—
360	C₄	—	3	4	no	—
361	C₄	—	6	2	no	—
362	C₄	—	12	4	no	—
363	C₄	C₅×D₄×Dic₃	1	2	yes	—
364	C₄	C₂×C₅×#237	1	1	yes	characteristic
365	C₄	C₂³×C₅×Dic₃	1	1	yes	characteristic
366	C₃	C₄×C₅×#135	1	1	yes	characteristic, complemented, Sylow
367	C₂	—	2	2	no	—
368	C₂	—	4	4	no	—
369	C₂	C₅×D₃×#135	1	2	yes	—
370	C₂	C₂×C₅×D₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting, prime radical	C₂×C₃×C₅×#135	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×#135	D₃
hypocenter	C₃	C₄×C₅×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#135

Complements

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

N	H ≅ G/N	type
2. C₅×Dic₃×#41	C₂	semidirect
3. C₅×#5233	C₂	semidirect
4. C₅×Dic₃×Q₁₆	C₂	semidirect
5. C₅×Dic₃×SD₁₆	C₂	semidirect
6. C₅×Dic₃×D₈	C₂	semidirect
7. C₅×#5106	C₂	semidirect
8. C₂×C₅×C₈×Dic₃	C₂	semidirect
11. C₃×C₅×#135	C₄	semidirect
30. Dic₃×#135	C₅	direct (N × H)
40. C₃×C₅×#41	C₂×C₄	semidirect
48. C₃×C₅×Q₁₆	C₂×C₄	semidirect
49. C₃×C₅×SD₁₆	C₂×C₄	semidirect
50. C₃×C₅×D₈	C₂×C₄	semidirect
51. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
66. Dic₃×#41	C₂×C₅	semidirect
67. #5233	C₂×C₅	semidirect
68. Dic₃×Q₁₆	C₂×C₅	semidirect
69. Dic₃×SD₁₆	C₂×C₅	semidirect
70. Dic₃×D₈	C₂×C₅	semidirect
71. #5106	C₂×C₅	semidirect
72. C₂×C₈×Dic₃	C₂×C₅	semidirect
74. C₅×#135	Dic₃	direct (N × H)
116. C₃×#135	C₄×C₅	semidirect
136. C₅×#41	C₂×Dic₃	semidirect
144. C₅×Q₁₆	C₂×Dic₃	semidirect
145. C₅×SD₁₆	C₂×Dic₃	semidirect
146. C₅×D₈	C₂×Dic₃	semidirect
149. C₂×C₅×C₈	C₂×Dic₃	semidirect
180. C₅×Dic₃	#135	direct (N × H)
182. C₃×#41	C₂×C₄×C₅	semidirect
190. C₃×Q₁₆	C₂×C₄×C₅	semidirect
191. C₃×SD₁₆	C₂×C₄×C₅	semidirect
192. C₃×D₈	C₂×C₄×C₅	semidirect
193. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
229. #135	C₅×Dic₃	direct (N × H)
286. #41	C₂×C₅×Dic₃	semidirect
294. Q₁₆	C₂×C₅×Dic₃	semidirect
295. SD₁₆	C₂×C₅×Dic₃	semidirect
296. D₈	C₂×C₅×Dic₃	semidirect
299. C₂×C₈	C₂×C₅×Dic₃	semidirect
311. C₃×C₅	C₄×#135	semidirect
323. Dic₃	C₅×#135	direct (N × H)
353. C₅	Dic₃×#135	direct (N × H)
366. C₃	C₄×C₅×#135	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#135	2
C₅×Dic₃×#41	2
C₅×#5233	2
C₅×Dic₃×Q₁₆	2
C₅×Dic₃×SD₁₆	2
C₅×Dic₃×D₈	2
C₅×#5106	2
C₂×C₅×C₈×Dic₃	2
C₄×C₅×#135	3
Dic₃×#135	5

Subgroups — C5×Dic3×#135 #14416218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Dic₃×#135 #14416218