Subgroups — C₃×#66163 #11755840

Order 960.

668 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#4093	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4092	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4085	C₂	1	2	yes	maximal, complemented
6	C₃×#4083	C₂	1	2	yes	maximal, complemented
7	C₃×D₄×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4076	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#4075	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#685	C₂	1	2	yes	maximal, complemented
12	#66163	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×D₅	C₂²	1	2	yes	—
14	C₃×C₅×#41	—	2	4	no	—
15	C₂×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×D₄	C₂²	1	2	yes	complemented
18	C₂²×C₃×C₄×C₅	C₂²	1	2	yes	complemented
19	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
22	C₂×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
23	C₂²×C₃×Dic₅	C₂²	1	2	yes	complemented
24	C₃×D₄×D₅	—	2	4	no	—
25	C₂×C₃×D₂₀	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
27	C₃×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
28	C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
29	C₃×#685	C₂²	1	2	yes	—
30	C₃×#685	C₂²	1	1	yes	characteristic
31	C₃×#685	C₂²	1	2	yes	complemented
32	C₃×#685	C₂²	1	2	yes	complemented
33	C₃×#685	C₂²	1	2	yes	complemented
34	C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
35	C₃×#683	C₂²	1	2	yes	complemented
36	C₃×#683	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
38	C₃×#546	—	5	1	no	maximal, Hall
39	C₂×C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
41	#4093	C₂×C₃	1	1	yes	characteristic, complemented
42	#4092	C₂×C₃	1	1	yes	characteristic, complemented
43	#4085	C₂×C₃	1	2	yes	complemented
44	#4083	C₂×C₃	1	2	yes	complemented
45	D₄×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
46	#4076	C₂×C₃	1	1	yes	characteristic, complemented
47	#4075	C₂×C₃	1	2	yes	complemented
48	C₄×C₂²⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×#685	C₂×C₃	1	2	yes	complemented
50	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
51	C₂³×C₃×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×D₅	—	2	4	no	—
53	C₂²×C₃×D₅	—	2	4	no	—
54	C₂²×C₃×D₅	—	4	2	no	—
55	C₂²×C₃×D₅	C₂³	1	2	yes	—
56	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
57	C₃×C₅×Q₈	—	2	2	no	—
58	C₃×C₅×D₄	—	2	4	no	—
59	C₃×C₅×D₄	D₄	1	4	yes	complemented
60	C₂×C₃×C₄×C₅	—	2	4	no	—
61	C₂×C₃×C₄×C₅	—	2	2	no	—
62	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
64	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₃×C₂²⋊D₅	—	2	4	no	—
66	C₃×C₂²⋊D₅	—	2	2	no	—
67	C₃×C₂²⋊D₅	—	4	2	no	—
68	C₂×C₃×Dic₅	—	4	2	no	—
69	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
70	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
71	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
72	C₂×C₃×Dic₅	C₂³	1	2	yes	—
73	C₃×D₂₀	—	2	2	no	—
74	C₃×C₄×D₅	—	2	2	no	—
75	C₂×C₃×#41	D₅	1	1	yes	characteristic, complemented
76	C₂²×C₃×D₄	—	5	1	no	—
77	C₃×#124	—	5	1	no	—
78	C₃×#123	—	5	2	no	—
79	C₃×C₂²⋊Q₈	—	5	1	no	—
80	C₃×#121	—	5	2	no	—
81	C₃×#121	—	5	1	no	—
82	C₃×#120	—	5	2	no	—
83	C₃×C₄×D₄	—	5	1	no	—
84	C₃×C₄×D₄	—	5	1	no	—
85	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
86	C₂³×D₅	C₂²×C₃	1	2	yes	—
87	C₅×#41	—	2	4	no	—
88	C₂×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
89	C₂×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₅×D₄	C₂²×C₃	1	2	yes	complemented
91	C₂²×C₄×C₅	C₂²×C₃	1	2	yes	complemented
92	C₂²×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
93	C₂×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
94	C₂×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
96	C₂²×Dic₅	C₂²×C₃	1	2	yes	complemented
97	D₄×D₅	—	2	4	no	—
98	C₂×D₂₀	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
100	C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
101	C₂²⋊Dic₅	C₂²×C₃	1	2	yes	complemented
102	#685	C₂²×C₃	1	1	yes	characteristic
103	#685	C₂²×C₃	1	2	yes	—
104	#685	C₂²×C₃	1	2	yes	complemented
105	#685	C₂²×C₃	1	2	yes	complemented
106	#685	C₂²×C₃	1	2	yes	complemented
107	C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
108	#683	C₂²×C₃	1	1	yes	characteristic, complemented
109	#683	C₂²×C₃	1	2	yes	complemented
110	C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
111	#546	—	5	1	no	Sylow
112	C₂²×C₃×C₅	—	2	2	no	—
113	C₂²×C₃×C₅	—	2	2	no	—
114	C₂²×C₃×C₅	—	2	1	no	—
115	C₂²×C₃×C₅	—	2	1	no	—
116	C₂²×C₃×C₅	—	2	1	no	—
117	C₂²×C₃×C₅	C₂×D₄	1	4	yes	—
118	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
119	C₂×C₃×D₅	—	2	1	no	—
120	C₂×C₃×D₅	—	2	1	no	—
121	C₂×C₃×D₅	—	2	2	no	—
122	C₂×C₃×D₅	—	2	2	no	—
123	C₂×C₃×D₅	—	2	2	no	—
124	C₂×C₃×D₅	—	4	8	no	—
125	C₂×C₃×D₅	#41	1	2	yes	complemented
126	C₃×C₄×C₅	—	2	1	no	—
127	C₃×C₄×C₅	—	2	2	no	—
128	C₃×C₄×C₅	C₂×D₄	1	2	yes	—
129	C₃×Dic₅	—	2	1	no	—
130	C₃×Dic₅	—	2	1	no	—
131	C₃×Dic₅	—	2	1	no	—
132	C₃×Dic₅	—	2	2	no	—
133	C₂⁴×C₃	—	5	2	no	—
134	C₃×#41	—	2	4	no	—
135	C₂×C₃×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
136	C₂×C₃×D₄	—	5	1	no	—
137	C₂×C₃×D₄	—	5	2	no	—
138	C₂×C₃×D₄	—	5	2	no	—
139	C₂×C₃×D₄	—	5	1	no	—
140	C₂×C₃×D₄	—	10	4	no	—
141	C₂×C₃×D₄	C₂×D₅	1	1	yes	characteristic
142	C₂×C₃×D₄	C₂×D₅	1	2	yes	complemented
143	C₂²×C₃×C₄	—	5	2	no	—
144	C₂²×C₃×C₄	—	5	1	no	—
145	C₂²×C₃×C₄	C₂×D₅	1	2	yes	complemented
146	C₂²×C₃×C₄	C₂×D₅	1	1	yes	characteristic, complemented
147	C₃×C₄⋊C₄	—	5	1	no	—
148	C₃×C₄⋊C₄	—	5	2	no	—
149	C₃×C₄⋊C₄	—	5	1	no	—
150	C₃×C₂²⋊C₄	—	5	2	no	—
151	C₃×C₂²⋊C₄	—	5	1	no	—
152	C₃×C₂²⋊C₄	—	5	1	no	—
153	C₃×C₂²⋊C₄	—	5	2	no	—
154	C₃×C₂²⋊C₄	—	5	2	no	—
155	C₃×C₂²⋊C₄	—	5	2	no	—
156	C₃×C₂²⋊C₄	—	5	2	no	—
157	C₃×C₄²	—	5	1	no	—
158	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
159	C₂³×C₅	C₂³×C₃	1	2	yes	—
160	C₂²×D₅	—	2	4	no	—
161	C₂²×D₅	—	2	4	no	—
162	C₂²×D₅	—	4	2	no	—
163	C₂²×D₅	C₂³×C₃	1	2	yes	—
164	C₂²×D₅	C₂³×C₃	1	1	yes	characteristic
165	C₅×Q₈	—	2	2	no	—
166	C₅×D₄	—	2	4	no	—
167	C₅×D₄	C₃×D₄	1	4	yes	complemented
168	C₂×C₄×C₅	—	2	4	no	—
169	C₂×C₄×C₅	—	2	2	no	—
170	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
171	C₂×C₄×C₅	C₂³×C₃	1	2	yes	—
172	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
173	C₂²⋊D₅	—	2	4	no	—
174	C₂²⋊D₅	—	2	2	no	—
175	C₂²⋊D₅	—	4	2	no	—
176	C₂×Dic₅	—	4	2	no	—
177	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
178	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
179	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
180	C₂×Dic₅	C₂³×C₃	1	2	yes	—
181	D₂₀	—	2	2	no	—
182	C₄×D₅	—	2	2	no	—
183	C₂×#41	C₃×D₅	1	1	yes	characteristic, complemented
184	C₂²×D₄	—	5	1	no	—
185	#124	—	5	1	no	—
186	#123	—	5	2	no	—
187	C₂²⋊Q₈	—	5	1	no	—
188	#121	—	5	2	no	—
189	#121	—	5	1	no	—
190	#120	—	5	2	no	—
191	C₄×D₄	—	5	1	no	—
192	C₄×D₄	—	5	1	no	—
193	C₂×C₂²⋊C₄	—	5	2	no	—
194	C₂×C₃×C₅	—	2	4	no	—
195	C₂×C₃×C₅	—	4	1	no	—
196	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
198	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
199	C₃×D₅	—	2	2	no	—
200	C₃×D₅	—	4	2	no	—
201	C₂³×C₃	—	5	1	no	—
202	C₂³×C₃	—	5	2	no	—
203	C₂³×C₃	—	10	4	no	—
204	C₂³×C₃	—	10	4	no	—
205	C₂³×C₃	—	20	2	no	—
206	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
207	C₂³×C₃	C₂²×D₅	1	2	yes	—
208	C₃×Q₈	—	2	2	no	—
209	C₃×D₄	—	2	4	no	—
210	C₃×D₄	—	10	2	no	—
211	C₃×D₄	—	10	4	no	—
212	C₃×D₄	—	10	2	no	—
213	C₃×D₄	—	20	2	no	—
214	C₃×D₄	C₂²⋊D₅	1	4	yes	complemented
215	C₂×C₃×C₄	—	2	4	no	—
216	C₂×C₃×C₄	—	2	2	no	—
217	C₂×C₃×C₄	—	5	1	no	—
218	C₂×C₃×C₄	—	5	1	no	—
219	C₂×C₃×C₄	—	5	2	no	—
220	C₂×C₃×C₄	—	5	1	no	—
221	C₂×C₃×C₄	—	10	2	no	—
222	C₂×C₃×C₄	—	20	2	no	—
223	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
224	C₂×C₃×C₄	C₂²×D₅	1	2	yes	—
225	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
226	C₂²×C₅	—	2	2	no	—
227	C₂²×C₅	—	2	2	no	—
228	C₂²×C₅	—	2	1	no	—
229	C₂²×C₅	—	2	1	no	—
230	C₂²×C₅	—	2	1	no	—
231	C₂²×C₅	C₂×C₃×D₄	1	4	yes	—
232	C₂²×C₅	C₂⁴×C₃	1	1	yes	characteristic
233	C₂×D₅	—	2	1	no	—
234	C₂×D₅	—	2	1	no	—
235	C₂×D₅	—	2	2	no	—
236	C₂×D₅	—	2	2	no	—
237	C₂×D₅	—	2	2	no	—
238	C₂×D₅	—	4	8	no	—
239	C₂×D₅	C₃×#41	1	2	yes	complemented
240	C₄×C₅	—	2	1	no	—
241	C₄×C₅	—	2	2	no	—
242	C₄×C₅	C₂×C₃×D₄	1	2	yes	—
243	Dic₅	—	2	1	no	—
244	Dic₅	—	2	1	no	—
245	Dic₅	—	2	1	no	—
246	Dic₅	—	2	2	no	—
247	C₂⁴	—	5	2	no	—
248	#41	—	2	4	no	—
249	C₂×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
250	C₂×D₄	—	5	1	no	—
251	C₂×D₄	—	5	2	no	—
252	C₂×D₄	—	5	2	no	—
253	C₂×D₄	—	5	1	no	—
254	C₂×D₄	—	10	4	no	—
255	C₂×D₄	C₂×C₃×D₅	1	1	yes	characteristic
256	C₂×D₄	C₂×C₃×D₅	1	2	yes	complemented
257	C₂²×C₄	—	5	2	no	—
258	C₂²×C₄	—	5	1	no	—
259	C₂²×C₄	C₂×C₃×D₅	1	2	yes	complemented
260	C₂²×C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
261	C₄⋊C₄	—	5	1	no	—
262	C₄⋊C₄	—	5	1	no	—
263	C₄⋊C₄	—	5	2	no	—
264	C₂²⋊C₄	—	5	2	no	—
265	C₂²⋊C₄	—	5	1	no	—
266	C₂²⋊C₄	—	5	1	no	—
267	C₂²⋊C₄	—	5	2	no	—
268	C₂²⋊C₄	—	5	2	no	—
269	C₂²⋊C₄	—	5	2	no	—
270	C₂²⋊C₄	—	5	2	no	—
271	C₄²	—	5	1	no	—
272	C₃×C₅	#546	1	1	yes	characteristic, complemented, Hall
273	C₂²×C₃	—	2	2	no	—
274	C₂²×C₃	—	2	2	no	—
275	C₂²×C₃	—	2	1	no	—
276	C₂²×C₃	—	2	1	no	—
277	C₂²×C₃	—	2	1	no	—
278	C₂²×C₃	—	5	2	no	—
279	C₂²×C₃	—	10	1	no	—
280	C₂²×C₃	—	10	1	no	—
281	C₂²×C₃	—	10	2	no	—
282	C₂²×C₃	—	10	2	no	—
283	C₂²×C₃	—	10	2	no	—
284	C₂²×C₃	—	20	8	no	—
285	C₂²×C₃	C₂×C₂²⋊D₅	1	4	yes	—
286	C₂²×C₃	C₂³×D₅	1	1	yes	characteristic
287	C₃×C₄	—	2	1	no	—
288	C₃×C₄	—	2	2	no	—
289	C₃×C₄	—	10	1	no	—
290	C₃×C₄	—	10	1	no	—
291	C₃×C₄	—	10	2	no	—
292	C₃×C₄	—	10	1	no	—
293	C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
294	C₂×C₅	—	2	4	no	—
295	C₂×C₅	—	4	1	no	—
296	C₂×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
297	C₂×C₅	C₂×C₃×#41	1	1	yes	characteristic
298	C₂×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
299	D₅	—	2	2	no	—
300	D₅	—	4	2	no	—
301	C₂³	—	5	1	no	—
302	C₂³	—	5	2	no	—
303	C₂³	—	10	4	no	—
304	C₂³	—	10	4	no	—
305	C₂³	—	20	2	no	—
306	C₂³	C₂²×C₃×D₅	1	1	yes	characteristic
307	C₂³	C₂²×C₃×D₅	1	2	yes	—
308	Q₈	—	2	2	no	—
309	D₄	—	2	4	no	—
310	D₄	—	10	2	no	—
311	D₄	—	10	4	no	—
312	D₄	—	10	2	no	—
313	D₄	—	20	2	no	—
314	D₄	C₃×C₂²⋊D₅	1	4	yes	complemented
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	5	1	no	—
318	C₂×C₄	—	5	1	no	—
319	C₂×C₄	—	5	2	no	—
320	C₂×C₄	—	5	1	no	—
321	C₂×C₄	—	10	2	no	—
322	C₂×C₄	—	20	2	no	—
323	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
324	C₂×C₄	C₂²×C₃×D₅	1	2	yes	—
325	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
326	C₂×C₃	—	2	4	no	—
327	C₂×C₃	—	4	1	no	—
328	C₂×C₃	—	10	2	no	—
329	C₂×C₃	—	20	2	no	—
330	C₂×C₃	D₅×#41	1	1	yes	characteristic
331	C₂×C₃	#4149	1	1	yes	characteristic
332	C₂×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
333	C₅	C₃×#546	1	1	yes	characteristic, complemented, Sylow
334	C₂²	—	2	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	5	2	no	—
340	C₂²	—	10	1	no	—
341	C₂²	—	10	1	no	—
342	C₂²	—	10	2	no	—
343	C₂²	—	10	2	no	—
344	C₂²	—	10	2	no	—
345	C₂²	—	20	8	no	—
346	C₂²	C₂×C₃×C₂²⋊D₅	1	4	yes	—
347	C₂²	C₂³×C₃×D₅	1	1	yes	characteristic
348	C₄	—	2	1	no	—
349	C₄	—	2	2	no	—
350	C₄	—	10	1	no	—
351	C₄	—	10	1	no	—
352	C₄	—	10	2	no	—
353	C₄	—	10	1	no	—
354	C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
355	C₃	#66163	1	1	yes	characteristic, direct product factor, Sylow
356	C₂	—	2	4	no	—
357	C₂	—	4	1	no	—
358	C₂	—	10	2	no	—
359	C₂	—	20	2	no	—
360	C₂	C₃×D₅×#41	1	1	yes	characteristic
361	C₂	C₃×#4149	1	1	yes	characteristic
362	C₂	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×#41	D₅
hypocenter	C₅	C₃×#546
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#41	C₂	semidirect
2. C₂×C₃×D₄×D₅	C₂	semidirect
3. C₃×#4093	C₂	semidirect
4. C₃×#4092	C₂	semidirect
5. C₃×#4085	C₂	semidirect
6. C₃×#4083	C₂	semidirect
7. C₃×D₄×Dic₅	C₂	semidirect
8. C₃×#4076	C₂	semidirect
9. C₃×#4075	C₂	semidirect
10. C₃×C₄×C₂²⋊D₅	C₂	semidirect
11. C₂×C₃×#685	C₂	semidirect
12. #66163	C₃	direct (N × H)
15. C₂×C₃×C₅×Q₈	C₂²	semidirect
17. C₂×C₃×C₅×D₄	C₂²	semidirect
18. C₂²×C₃×C₄×C₅	C₂²	semidirect
19. C₂²×C₃×C₄×C₅	C₂²	semidirect
22. C₂×C₃×C₂²⋊D₅	C₂²	semidirect
23. C₂²×C₃×Dic₅	C₂²	semidirect
27. C₃×C₂²⋊Dic₅	C₂²	semidirect
28. C₃×C₂²⋊Dic₅	C₂²	semidirect
31. C₃×#685	C₂²	semidirect
32. C₃×#685	C₂²	semidirect
33. C₃×#685	C₂²	semidirect
34. C₃×C₄⋊Dic₅	C₂²	semidirect
35. C₃×#683	C₂²	semidirect
36. C₃×#683	C₂²	semidirect
37. C₃×C₄×Dic₅	C₂²	semidirect
39. C₂×C₅×#41	C₂×C₃	semidirect
40. C₂×D₄×D₅	C₂×C₃	semidirect
41. #4093	C₂×C₃	semidirect
42. #4092	C₂×C₃	semidirect
43. #4085	C₂×C₃	semidirect
44. #4083	C₂×C₃	semidirect
45. D₄×Dic₅	C₂×C₃	semidirect
46. #4076	C₂×C₃	semidirect
47. #4075	C₂×C₃	semidirect
48. C₄×C₂²⋊D₅	C₂×C₃	semidirect
49. C₂×#685	C₂×C₃	semidirect
59. C₃×C₅×D₄	D₄	semidirect
75. C₂×C₃×#41	D₅	semidirect
88. C₂×C₅×Q₈	C₂²×C₃	semidirect
90. C₂×C₅×D₄	C₂²×C₃	semidirect
91. C₂²×C₄×C₅	C₂²×C₃	semidirect
92. C₂²×C₄×C₅	C₂²×C₃	semidirect
95. C₂×C₂²⋊D₅	C₂²×C₃	semidirect
96. C₂²×Dic₅	C₂²×C₃	semidirect
100. C₂²⋊Dic₅	C₂²×C₃	semidirect
101. C₂²⋊Dic₅	C₂²×C₃	semidirect
104. #685	C₂²×C₃	semidirect
105. #685	C₂²×C₃	semidirect
106. #685	C₂²×C₃	semidirect
107. C₄⋊Dic₅	C₂²×C₃	semidirect
108. #683	C₂²×C₃	semidirect
109. #683	C₂²×C₃	semidirect
110. C₄×Dic₅	C₂²×C₃	semidirect
125. C₂×C₃×D₅	#41	semidirect
135. C₂×C₃×Q₈	C₂×D₅	semidirect
142. C₂×C₃×D₄	C₂×D₅	semidirect
145. C₂²×C₃×C₄	C₂×D₅	semidirect
146. C₂²×C₃×C₄	C₂×D₅	semidirect
167. C₅×D₄	C₃×D₄	semidirect
183. C₂×#41	C₃×D₅	semidirect
214. C₃×D₄	C₂²⋊D₅	semidirect
239. C₂×D₅	C₃×#41	semidirect
249. C₂×Q₈	C₂×C₃×D₅	semidirect
256. C₂×D₄	C₂×C₃×D₅	semidirect
259. C₂²×C₄	C₂×C₃×D₅	semidirect
260. C₂²×C₄	C₂×C₃×D₅	semidirect
272. C₃×C₅	#546	semidirect
314. D₄	C₃×C₂²⋊D₅	semidirect
333. C₅	C₃×#546	semidirect
355. C₃	#66163	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×C₅×#41	2
C₂×C₃×D₄×D₅	2
C₃×#4093	2
C₃×#4092	2
C₃×#4085	2
C₃×#4083	2
C₃×D₄×Dic₅	2
C₃×#4076	2
C₃×#4075	2
C₃×C₄×C₂²⋊D₅	2
C₂×C₃×#685	2
#66163	3
C₃×#546	5

Subgroups — C3×#66163 #11755840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#66163 #11755840