Subgroups — C₃×#65924 #11755601

Order 960.

856 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×D₄×D₅	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4086	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4085	C₂	1	2	yes	maximal, complemented
6	C₃×#4083	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4030	C₂	1	2	yes	maximal, complemented
8	C₃×#4028	C₂	1	2	yes	maximal, complemented
9	C₃×#4027	C₂	1	2	yes	maximal, complemented
10	#65924	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂⁴×C₃×C₅	C₂²	1	1	yes	characteristic, complemented
12	C₂³×C₃×D₅	C₂²	1	1	yes	characteristic, complemented
13	C₂³×C₃×D₅	C₂²	1	2	yes	complemented
14	C₂×C₃×C₅×D₄	C₂²	1	2	yes	complemented
15	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
17	C₂×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
18	C₂×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
19	C₂×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
20	C₂×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
21	C₂×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
22	C₂²×C₃×Dic₅	C₂²	1	2	yes	complemented
23	C₃×D₄×D₅	—	2	8	no	—
24	C₂×C₃×D₂₀	C₂²	1	2	yes	complemented
25	C₂×C₃×D₂₀	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×C₄×D₅	C₂²	1	2	yes	complemented
27	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
28	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
30	C₃×#685	C₂²	1	2	yes	complemented
31	C₃×#685	C₂²	1	2	yes	complemented
32	C₃×#683	C₂²	1	2	yes	complemented
33	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
34	C₃×D₄²	—	5	1	no	maximal, Hall
35	C₂²×C₂²⋊D₅	C₂×C₃	1	2	yes	complemented
36	C₂×D₄×D₅	C₂×C₃	1	2	yes	complemented
37	C₅×#120	C₂×C₃	1	1	yes	characteristic, complemented
38	#4086	C₂×C₃	1	1	yes	characteristic, complemented
39	#4085	C₂×C₃	1	2	yes	complemented
40	#4083	C₂×C₃	1	1	yes	characteristic, complemented
41	#4030	C₂×C₃	1	2	yes	complemented
42	#4028	C₂×C₃	1	2	yes	complemented
43	#4027	C₂×C₃	1	2	yes	complemented
44	C₂³×C₃×C₅	—	2	4	no	—
45	C₂³×C₃×C₅	—	4	1	no	—
46	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
47	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
48	C₂³×C₃×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×D₅	—	2	4	no	—
50	C₂²×C₃×D₅	—	2	4	no	—
51	C₂²×C₃×D₅	—	2	4	no	—
52	C₂²×C₃×D₅	—	4	1	no	—
53	C₂²×C₃×D₅	—	4	2	no	—
54	C₂²×C₃×D₅	C₂³	1	2	yes	—
55	C₂²×C₃×D₅	C₂³	1	2	yes	—
56	C₃×C₅×D₄	—	2	4	no	—
57	C₃×C₅×D₄	—	4	1	no	—
58	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₃×C₂²⋊D₅	—	2	4	no	—
61	C₃×C₂²⋊D₅	—	2	4	no	—
62	C₃×C₂²⋊D₅	—	2	4	no	—
63	C₃×C₂²⋊D₅	—	2	4	no	—
64	C₃×C₂²⋊D₅	D₄	1	8	yes	complemented
65	C₂×C₃×Dic₅	—	2	4	no	—
66	C₂×C₃×Dic₅	C₂³	1	2	yes	—
67	C₂×C₃×Dic₅	C₂³	1	2	yes	—
68	C₃×D₂₀	—	2	4	no	—
69	C₃×D₂₀	—	4	1	no	—
70	C₃×C₄×D₅	—	2	4	no	—
71	C₂²×C₃×D₄	—	5	2	no	—
72	C₂²×C₃×D₄	—	5	2	no	—
73	C₃×#127	—	5	1	no	—
74	C₃×#121	—	5	2	no	—
75	C₃×#121	—	5	2	no	—
76	C₃×#120	—	5	1	no	—
77	C₃×#120	—	5	2	no	—
78	C₃×#120	D₅	1	1	yes	characteristic, complemented
79	C₃×C₄×D₄	—	5	2	no	—
80	C₂⁴×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
81	C₂³×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
82	C₂³×D₅	C₂²×C₃	1	2	yes	complemented
83	C₂×C₅×D₄	C₂²×C₃	1	2	yes	complemented
84	C₂×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
85	C₂×C₂²⋊D₅	—	2	8	no	—
86	C₂×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
87	C₂×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
88	C₂×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
89	C₂×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
90	C₂×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
91	C₂²×Dic₅	C₂²×C₃	1	2	yes	complemented
92	D₄×D₅	—	2	8	no	—
93	C₂×D₂₀	C₂²×C₃	1	2	yes	complemented
94	C₂×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
95	C₂×C₄×D₅	C₂²×C₃	1	2	yes	complemented
96	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
97	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
98	C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
99	#685	C₂²×C₃	1	2	yes	complemented
100	#685	C₂²×C₃	1	2	yes	complemented
101	#683	C₂²×C₃	1	2	yes	complemented
102	C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
103	D₄²	—	5	1	no	Sylow
104	C₂²×C₃×C₅	—	2	2	no	—
105	C₂²×C₃×C₅	—	2	2	no	—
106	C₂²×C₃×C₅	—	2	2	no	—
107	C₂²×C₃×C₅	—	2	2	no	—
108	C₂²×C₃×C₅	—	2	1	no	—
109	C₂²×C₃×C₅	—	2	1	no	—
110	C₂²×C₃×C₅	—	4	4	no	—
111	C₂²×C₃×C₅	C₂×D₄	1	4	yes	complemented
112	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
113	C₂×C₃×D₅	—	2	2	no	—
114	C₂×C₃×D₅	—	2	2	no	—
115	C₂×C₃×D₅	—	2	2	no	—
116	C₂×C₃×D₅	—	2	2	no	—
117	C₂×C₃×D₅	—	2	2	no	—
118	C₂×C₃×D₅	—	4	4	no	—
119	C₂×C₃×D₅	—	4	8	no	—
120	C₂×C₃×D₅	C₂×D₄	1	4	yes	complemented
121	C₃×C₄×C₅	—	2	2	no	—
122	C₃×C₄×C₅	—	2	1	no	—
123	C₃×Dic₅	—	2	2	no	—
124	C₃×Dic₅	C₂×D₄	1	4	yes	complemented
125	C₂⁴×C₃	—	5	1	no	—
126	C₂⁴×C₃	—	5	2	no	—
127	C₂⁴×C₃	C₂×D₅	1	1	yes	characteristic, complemented
128	C₂×C₃×D₄	—	5	2	no	—
129	C₂×C₃×D₄	—	5	2	no	—
130	C₂×C₃×D₄	—	5	2	no	—
131	C₂×C₃×D₄	—	5	2	no	—
132	C₂×C₃×D₄	—	5	2	no	—
133	C₂×C₃×D₄	—	5	2	no	—
134	C₂×C₃×D₄	—	5	1	no	—
135	C₂×C₃×D₄	—	10	8	no	—
136	C₂×C₃×D₄	—	10	8	no	—
137	C₂×C₃×D₄	C₂×D₅	1	2	yes	complemented
138	C₂×C₃×D₄	C₂×D₅	1	1	yes	characteristic, complemented
139	C₂²×C₃×C₄	—	5	2	no	—
140	C₂²×C₃×C₄	—	5	2	no	—
141	C₃×C₄⋊C₄	—	5	2	no	—
142	C₃×C₂²⋊C₄	—	5	1	no	—
143	C₃×C₂²⋊C₄	—	5	2	no	—
144	C₃×C₂²⋊C₄	—	5	2	no	—
145	C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
146	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
147	C₃×C₄²	—	5	1	no	—
148	C₂³×C₅	—	2	4	no	—
149	C₂³×C₅	—	4	1	no	—
150	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
151	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
152	C₂³×C₅	C₂³×C₃	1	2	yes	—
153	C₂²×D₅	—	2	4	no	—
154	C₂²×D₅	—	2	4	no	—
155	C₂²×D₅	—	2	4	no	—
156	C₂²×D₅	—	4	1	no	—
157	C₂²×D₅	—	4	2	no	—
158	C₂²×D₅	C₂³×C₃	1	2	yes	—
159	C₂²×D₅	C₂³×C₃	1	2	yes	—
160	C₅×D₄	—	2	4	no	—
161	C₅×D₄	—	4	1	no	—
162	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
163	C₂×C₄×C₅	C₂³×C₃	1	2	yes	—
164	C₂²⋊D₅	—	2	4	no	—
165	C₂²⋊D₅	—	2	4	no	—
166	C₂²⋊D₅	—	2	4	no	—
167	C₂²⋊D₅	—	2	4	no	—
168	C₂²⋊D₅	C₃×D₄	1	8	yes	complemented
169	C₂×Dic₅	—	2	4	no	—
170	C₂×Dic₅	C₂³×C₃	1	2	yes	—
171	C₂×Dic₅	C₂³×C₃	1	2	yes	—
172	D₂₀	—	2	4	no	—
173	D₂₀	—	4	1	no	—
174	C₄×D₅	—	2	4	no	—
175	C₂²×D₄	—	5	2	no	—
176	C₂²×D₄	—	5	2	no	—
177	#127	—	5	1	no	—
178	#121	—	5	2	no	—
179	#121	—	5	2	no	—
180	#120	—	5	1	no	—
181	#120	—	5	2	no	—
182	#120	C₃×D₅	1	1	yes	characteristic, complemented
183	C₄×D₄	—	5	2	no	—
184	C₂×C₃×C₅	—	2	4	no	—
185	C₂×C₃×C₅	—	4	1	no	—
186	C₂×C₃×C₅	—	4	1	no	—
187	C₂×C₃×C₅	C₂²×D₄	1	2	yes	—
188	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
189	C₃×D₅	—	2	4	no	—
190	C₃×D₅	—	4	2	no	—
191	C₂³×C₃	—	2	4	no	—
192	C₂³×C₃	—	4	1	no	—
193	C₂³×C₃	—	5	2	no	—
194	C₂³×C₃	—	5	2	no	—
195	C₂³×C₃	—	10	4	no	—
196	C₂³×C₃	—	10	4	no	—
197	C₂³×C₃	—	10	4	no	—
198	C₂³×C₃	—	20	2	no	—
199	C₂³×C₃	—	20	1	no	—
200	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
201	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
202	C₂³×C₃	C₂²×D₅	1	2	yes	—
203	C₃×D₄	—	2	4	no	—
204	C₃×D₄	—	4	1	no	—
205	C₃×D₄	—	5	8	no	—
206	C₃×D₄	—	10	4	no	—
207	C₃×D₄	—	10	4	no	—
208	C₃×D₄	—	10	4	no	—
209	C₃×D₄	—	10	4	no	—
210	C₃×D₄	—	10	4	no	—
211	C₃×D₄	—	20	1	no	—
212	C₂×C₃×C₄	—	5	2	no	—
213	C₂×C₃×C₄	—	5	2	no	—
214	C₂×C₃×C₄	—	10	4	no	—
215	C₂×C₃×C₄	—	10	4	no	—
216	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
217	C₂×C₃×C₄	C₂²×D₅	1	2	yes	—
218	C₂²×C₅	—	2	2	no	—
219	C₂²×C₅	—	2	2	no	—
220	C₂²×C₅	—	2	2	no	—
221	C₂²×C₅	—	2	2	no	—
222	C₂²×C₅	—	2	1	no	—
223	C₂²×C₅	—	2	1	no	—
224	C₂²×C₅	—	4	4	no	—
225	C₂²×C₅	C₂×C₃×D₄	1	4	yes	complemented
226	C₂²×C₅	C₂⁴×C₃	1	1	yes	characteristic
227	C₂×D₅	—	2	2	no	—
228	C₂×D₅	—	2	2	no	—
229	C₂×D₅	—	2	2	no	—
230	C₂×D₅	—	2	2	no	—
231	C₂×D₅	—	2	2	no	—
232	C₂×D₅	—	4	4	no	—
233	C₂×D₅	—	4	8	no	—
234	C₂×D₅	C₂×C₃×D₄	1	4	yes	complemented
235	C₄×C₅	—	2	2	no	—
236	C₄×C₅	—	2	1	no	—
237	Dic₅	—	2	2	no	—
238	Dic₅	C₂×C₃×D₄	1	4	yes	complemented
239	C₂⁴	—	5	1	no	—
240	C₂⁴	—	5	2	no	—
241	C₂⁴	C₂×C₃×D₅	1	1	yes	characteristic, complemented
242	C₂×D₄	—	5	2	no	—
243	C₂×D₄	—	5	2	no	—
244	C₂×D₄	—	5	2	no	—
245	C₂×D₄	—	5	2	no	—
246	C₂×D₄	—	5	2	no	—
247	C₂×D₄	—	5	2	no	—
248	C₂×D₄	—	5	1	no	—
249	C₂×D₄	—	10	8	no	—
250	C₂×D₄	—	10	8	no	—
251	C₂×D₄	C₂×C₃×D₅	1	2	yes	complemented
252	C₂×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
253	C₂²×C₄	—	5	2	no	—
254	C₂²×C₄	—	5	2	no	—
255	C₄⋊C₄	—	5	2	no	—
256	C₂²⋊C₄	—	5	1	no	—
257	C₂²⋊C₄	—	5	2	no	—
258	C₂²⋊C₄	—	5	2	no	—
259	C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	complemented
260	C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
261	C₄²	—	5	1	no	—
262	C₃×C₅	D₄²	1	1	yes	characteristic, complemented, Hall
263	C₂²×C₃	—	2	2	no	—
264	C₂²×C₃	—	2	2	no	—
265	C₂²×C₃	—	2	2	no	—
266	C₂²×C₃	—	2	2	no	—
267	C₂²×C₃	—	2	1	no	—
268	C₂²×C₃	—	2	1	no	—
269	C₂²×C₃	—	4	4	no	—
270	C₂²×C₃	—	5	4	no	—
271	C₂²×C₃	—	10	2	no	—
272	C₂²×C₃	—	10	2	no	—
273	C₂²×C₃	—	10	2	no	—
274	C₂²×C₃	—	10	2	no	—
275	C₂²×C₃	—	10	2	no	—
276	C₂²×C₃	—	20	8	no	—
277	C₂²×C₃	—	20	4	no	—
278	C₂²×C₃	D₄×D₅	1	4	yes	complemented
279	C₂²×C₃	C₂³×D₅	1	1	yes	characteristic
280	C₃×C₄	—	2	2	no	—
281	C₃×C₄	—	2	1	no	—
282	C₃×C₄	—	5	4	no	—
283	C₃×C₄	—	10	2	no	—
284	C₂×C₅	—	2	4	no	—
285	C₂×C₅	—	4	1	no	—
286	C₂×C₅	—	4	1	no	—
287	C₂×C₅	C₂²×C₃×D₄	1	2	yes	—
288	C₂×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
289	D₅	—	2	4	no	—
290	D₅	—	4	2	no	—
291	C₂³	—	2	4	no	—
292	C₂³	—	4	1	no	—
293	C₂³	—	5	2	no	—
294	C₂³	—	5	2	no	—
295	C₂³	—	10	4	no	—
296	C₂³	—	10	4	no	—
297	C₂³	—	10	4	no	—
298	C₂³	—	20	2	no	—
299	C₂³	—	20	1	no	—
300	C₂³	C₂²×C₃×D₅	1	1	yes	characteristic
301	C₂³	C₂²×C₃×D₅	1	1	yes	characteristic
302	C₂³	C₂²×C₃×D₅	1	2	yes	—
303	D₄	—	2	4	no	—
304	D₄	—	4	1	no	—
305	D₄	—	5	8	no	—
306	D₄	—	10	4	no	—
307	D₄	—	10	4	no	—
308	D₄	—	10	4	no	—
309	D₄	—	10	4	no	—
310	D₄	—	10	4	no	—
311	D₄	—	20	1	no	—
312	C₂×C₄	—	5	2	no	—
313	C₂×C₄	—	5	2	no	—
314	C₂×C₄	—	10	4	no	—
315	C₂×C₄	—	10	4	no	—
316	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
317	C₂×C₄	C₂²×C₃×D₅	1	2	yes	—
318	C₂×C₃	—	2	4	no	—
319	C₂×C₃	—	4	1	no	—
320	C₂×C₃	—	4	1	no	—
321	C₂×C₃	—	10	4	no	—
322	C₂×C₃	—	20	2	no	—
323	C₂×C₃	C₂×D₄×D₅	1	2	yes	—
324	C₂×C₃	#4144	1	1	yes	characteristic
325	C₅	C₃×D₄²	1	1	yes	characteristic, complemented, Sylow
326	C₂²	—	2	2	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	4	4	no	—
333	C₂²	—	5	4	no	—
334	C₂²	—	10	2	no	—
335	C₂²	—	10	2	no	—
336	C₂²	—	10	2	no	—
337	C₂²	—	10	2	no	—
338	C₂²	—	10	2	no	—
339	C₂²	—	20	8	no	—
340	C₂²	—	20	4	no	—
341	C₂²	C₃×D₄×D₅	1	4	yes	complemented
342	C₂²	C₂³×C₃×D₅	1	1	yes	characteristic
343	C₄	—	2	2	no	—
344	C₄	—	2	1	no	—
345	C₄	—	5	4	no	—
346	C₄	—	10	2	no	—
347	C₃	#65924	1	1	yes	characteristic, direct product factor, Sylow
348	C₂	—	2	4	no	—
349	C₂	—	4	1	no	—
350	C₂	—	4	1	no	—
351	C₂	—	10	4	no	—
352	C₂	—	20	2	no	—
353	C₂	C₂×C₃×D₄×D₅	1	2	yes	—
354	C₂	C₃×#4144	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₅
Fitting	C₃×C₅×#120	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₃×#120	D₅
hypocenter	C₅	C₃×D₄²
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#120

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₂²⋊D₅	C₂	semidirect
2. C₂×C₃×D₄×D₅	C₂	semidirect
3. C₃×C₅×#120	C₂	semidirect
4. C₃×#4086	C₂	semidirect
5. C₃×#4085	C₂	semidirect
6. C₃×#4083	C₂	semidirect
7. C₃×#4030	C₂	semidirect
8. C₃×#4028	C₂	semidirect
9. C₃×#4027	C₂	semidirect
10. #65924	C₃	direct (N × H)
11. C₂⁴×C₃×C₅	C₂²	semidirect
12. C₂³×C₃×D₅	C₂²	semidirect
13. C₂³×C₃×D₅	C₂²	semidirect
14. C₂×C₃×C₅×D₄	C₂²	semidirect
15. C₂×C₃×C₅×D₄	C₂²	semidirect
18. C₂×C₃×C₂²⋊D₅	C₂²	semidirect
19. C₂×C₃×C₂²⋊D₅	C₂²	semidirect
20. C₂×C₃×C₂²⋊D₅	C₂²	semidirect
21. C₂×C₃×C₂²⋊D₅	C₂²	semidirect
22. C₂²×C₃×Dic₅	C₂²	semidirect
24. C₂×C₃×D₂₀	C₂²	semidirect
25. C₂×C₃×D₂₀	C₂²	semidirect
26. C₂×C₃×C₄×D₅	C₂²	semidirect
27. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
28. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
29. C₃×C₂²⋊Dic₅	C₂²	semidirect
30. C₃×#685	C₂²	semidirect
31. C₃×#685	C₂²	semidirect
32. C₃×#683	C₂²	semidirect
33. C₃×C₄×Dic₅	C₂²	semidirect
35. C₂²×C₂²⋊D₅	C₂×C₃	semidirect
36. C₂×D₄×D₅	C₂×C₃	semidirect
37. C₅×#120	C₂×C₃	semidirect
38. #4086	C₂×C₃	semidirect
39. #4085	C₂×C₃	semidirect
40. #4083	C₂×C₃	semidirect
41. #4030	C₂×C₃	semidirect
42. #4028	C₂×C₃	semidirect
43. #4027	C₂×C₃	semidirect
64. C₃×C₂²⋊D₅	D₄	semidirect
78. C₃×#120	D₅	semidirect
80. C₂⁴×C₅	C₂²×C₃	semidirect
81. C₂³×D₅	C₂²×C₃	semidirect
82. C₂³×D₅	C₂²×C₃	semidirect
83. C₂×C₅×D₄	C₂²×C₃	semidirect
84. C₂×C₅×D₄	C₂²×C₃	semidirect
87. C₂×C₂²⋊D₅	C₂²×C₃	semidirect
88. C₂×C₂²⋊D₅	C₂²×C₃	semidirect
89. C₂×C₂²⋊D₅	C₂²×C₃	semidirect
90. C₂×C₂²⋊D₅	C₂²×C₃	semidirect
91. C₂²×Dic₅	C₂²×C₃	semidirect
93. C₂×D₂₀	C₂²×C₃	semidirect
94. C₂×D₂₀	C₂²×C₃	semidirect
95. C₂×C₄×D₅	C₂²×C₃	semidirect
96. C₅×C₂²⋊C₄	C₂²×C₃	semidirect
97. C₅×C₂²⋊C₄	C₂²×C₃	semidirect
98. C₂²⋊Dic₅	C₂²×C₃	semidirect
99. #685	C₂²×C₃	semidirect
100. #685	C₂²×C₃	semidirect
101. #683	C₂²×C₃	semidirect
102. C₄×Dic₅	C₂²×C₃	semidirect
111. C₂²×C₃×C₅	C₂×D₄	semidirect
120. C₂×C₃×D₅	C₂×D₄	semidirect
124. C₃×Dic₅	C₂×D₄	semidirect
127. C₂⁴×C₃	C₂×D₅	semidirect
137. C₂×C₃×D₄	C₂×D₅	semidirect
138. C₂×C₃×D₄	C₂×D₅	semidirect
145. C₃×C₂²⋊C₄	C₂×D₅	semidirect
146. C₃×C₂²⋊C₄	C₂×D₅	semidirect
168. C₂²⋊D₅	C₃×D₄	semidirect
182. #120	C₃×D₅	semidirect
225. C₂²×C₅	C₂×C₃×D₄	semidirect
234. C₂×D₅	C₂×C₃×D₄	semidirect
238. Dic₅	C₂×C₃×D₄	semidirect
241. C₂⁴	C₂×C₃×D₅	semidirect
251. C₂×D₄	C₂×C₃×D₅	semidirect
252. C₂×D₄	C₂×C₃×D₅	semidirect
259. C₂²⋊C₄	C₂×C₃×D₅	semidirect
260. C₂²⋊C₄	C₂×C₃×D₅	semidirect
262. C₃×C₅	D₄²	semidirect
278. C₂²×C₃	D₄×D₅	semidirect
325. C₅	C₃×D₄²	semidirect
341. C₂²	C₃×D₄×D₅	semidirect
347. C₃	#65924	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₂²⋊D₅	2
C₂×C₃×D₄×D₅	2
C₃×C₅×#120	2
C₃×#4086	2
C₃×#4085	2
C₃×#4083	2
C₃×#4030	2
C₃×#4028	2
C₃×#4027	2
#65924	3
C₃×D₄²	5

Subgroups — C3×#65924 #11755601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#65924 #11755601