Subgroups — C₃×C₅×#3026 #14276060

Order 1920.

1600 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#534	C₂	1	3	yes	maximal, complemented
3	C₃×C₅×#458	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×B(4,𝔽₂)	C₂	1	4	yes	maximal, complemented
5	C₂×C₃×C₅×#99	C₂	1	3	yes	maximal, complemented
6	C₅×#3026	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₅×H(5,𝔽₂)	—	2	6	no	—
8	C₃×C₅×H(5,𝔽₂)	C₂²	1	4	yes	—
9	C₂×C₃×C₅×#41	—	2	3	no	—
10	C₂²×C₃×C₅×D₄	—	2	3	no	—
11	C₂²×C₃×C₅×D₄	C₂²	1	3	yes	—
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
13	C₃×C₅×#123	—	2	3	no	—
14	C₃×C₅×#123	C₂²	1	6	yes	complemented
15	C₃×C₅×#121	—	2	6	no	—
16	C₃×C₅×#120	—	2	3	no	—
17	C₃×C₅×#120	C₂²	1	6	yes	complemented
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	complemented
19	C₃×C₅×#99	C₂²	1	12	yes	complemented
20	C₃×#3026	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₅×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
22	C₅×#534	C₂×C₃	1	3	yes	complemented
23	C₅×#458	C₂×C₃	1	4	yes	complemented
24	C₅×B(4,𝔽₂)	C₂×C₃	1	4	yes	complemented
25	C₂×C₅×#99	C₂×C₃	1	3	yes	complemented
26	C₂⁴×C₃×C₅	—	2	1	no	—
27	C₂⁴×C₃×C₅	D₄	1	3	yes	complemented
28	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
29	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic, complemented
30	C₃×C₅×#41	—	2	12	no	—
31	C₃×C₅×#41	—	2	12	no	—
32	C₂×C₃×C₅×Q₈	—	2	1	no	—
33	C₂×C₃×C₅×D₄	—	2	3	no	—
34	C₂×C₃×C₅×D₄	—	2	12	no	—
35	C₂×C₃×C₅×D₄	—	2	6	no	—
36	C₂×C₃×C₅×D₄	—	2	12	no	—
37	C₂×C₃×C₅×D₄	—	2	6	no	—
38	C₂×C₃×C₅×D₄	—	2	3	no	—
39	C₂×C₃×C₅×D₄	—	2	3	no	—
40	C₂×C₃×C₅×D₄	—	2	6	no	—
41	C₂×C₃×C₅×D₄	D₄	1	6	yes	complemented
42	C₂×C₃×C₅×D₄	C₂³	1	6	yes	—
43	C₂²×C₃×C₄×C₅	—	2	3	no	—
44	C₂²×C₃×C₄×C₅	—	2	3	no	—
45	C₂²×C₃×C₄×C₅	D₄	1	3	yes	complemented
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic, complemented
47	C₃×C₅×C₄⋊C₄	—	2	6	no	—
48	C₃×C₅×C₂²⋊C₄	—	2	3	no	—
49	C₃×C₅×C₂²⋊C₄	—	2	6	no	—
50	C₃×C₅×C₂²⋊C₄	—	2	6	no	—
51	C₃×C₅×C₂²⋊C₄	C₂³	1	6	yes	complemented
52	C₂×C₃×H(5,𝔽₂)	C₂×C₅	1	1	yes	characteristic, complemented
53	C₃×#534	C₂×C₅	1	3	yes	complemented
54	C₃×#458	C₂×C₅	1	4	yes	complemented
55	C₃×B(4,𝔽₂)	C₂×C₅	1	4	yes	complemented
56	C₂×C₃×#99	C₂×C₅	1	3	yes	complemented
57	C₅×H(5,𝔽₂)	—	2	6	no	—
58	C₅×H(5,𝔽₂)	C₂²×C₃	1	4	yes	—
59	C₂×C₅×#41	—	2	3	no	—
60	C₂²×C₅×D₄	—	2	3	no	—
61	C₂²×C₅×D₄	C₂²×C₃	1	3	yes	—
62	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
63	C₅×#123	—	2	3	no	—
64	C₅×#123	C₂²×C₃	1	6	yes	complemented
65	C₅×#121	—	2	6	no	—
66	C₅×#120	—	2	3	no	—
67	C₅×#120	C₂²×C₃	1	6	yes	complemented
68	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	complemented
69	C₅×#99	C₂²×C₃	1	12	yes	complemented
70	#3026	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
71	C₂³×C₃×C₅	—	2	4	no	—
72	C₂³×C₃×C₅	—	2	3	no	—
73	C₂³×C₃×C₅	—	2	3	no	—
74	C₂³×C₃×C₅	—	2	3	no	—
75	C₂³×C₃×C₅	—	8	1	no	—
76	C₂³×C₃×C₅	—	8	1	no	—
77	C₂³×C₃×C₅	—	8	3	no	—
78	C₂³×C₃×C₅	—	8	2	no	—
79	C₂³×C₃×C₅	C₂×D₄	1	6	yes	—
80	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
81	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
82	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
83	C₃×C₅×Q₈	—	2	4	no	—
84	C₃×C₅×D₄	—	2	12	no	—
85	C₃×C₅×D₄	—	2	12	no	—
86	C₃×C₅×D₄	—	2	12	no	—
87	C₃×C₅×D₄	—	4	1	no	—
88	C₃×C₅×D₄	—	4	3	no	—
89	C₃×C₅×D₄	—	8	6	no	—
90	C₂×C₃×C₄×C₅	—	2	12	no	—
91	C₂×C₃×C₄×C₅	—	2	3	no	—
92	C₂×C₃×C₄×C₅	—	2	3	no	—
93	C₂×C₃×C₄×C₅	—	2	6	no	—
94	C₂×C₃×C₄×C₅	—	2	3	no	—
95	C₂×C₃×C₄×C₅	—	8	3	no	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
97	C₃×H(5,𝔽₂)	—	2	6	no	—
98	C₃×H(5,𝔽₂)	C₂²×C₅	1	4	yes	—
99	C₂×C₃×#41	—	2	3	no	—
100	C₂²×C₃×D₄	—	2	3	no	—
101	C₂²×C₃×D₄	C₂²×C₅	1	3	yes	—
102	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
103	C₃×#123	—	2	3	no	—
104	C₃×#123	C₂²×C₅	1	6	yes	complemented
105	C₃×#121	—	2	6	no	—
106	C₃×#120	—	2	3	no	—
107	C₃×#120	C₂²×C₅	1	6	yes	complemented
108	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	complemented
109	C₃×#99	C₂²×C₅	1	12	yes	complemented
110	C₂⁴×C₅	—	2	1	no	—
111	C₂⁴×C₅	C₃×D₄	1	3	yes	complemented
112	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
113	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic, complemented
114	C₅×#41	—	2	12	no	—
115	C₅×#41	—	2	12	no	—
116	C₂×C₅×Q₈	—	2	1	no	—
117	C₂×C₅×D₄	—	2	3	no	—
118	C₂×C₅×D₄	—	2	12	no	—
119	C₂×C₅×D₄	—	2	6	no	—
120	C₂×C₅×D₄	—	2	12	no	—
121	C₂×C₅×D₄	—	2	6	no	—
122	C₂×C₅×D₄	—	2	3	no	—
123	C₂×C₅×D₄	—	2	3	no	—
124	C₂×C₅×D₄	—	2	6	no	—
125	C₂×C₅×D₄	C₃×D₄	1	6	yes	complemented
126	C₂×C₅×D₄	C₂³×C₃	1	6	yes	—
127	C₂²×C₄×C₅	—	2	3	no	—
128	C₂²×C₄×C₅	—	2	3	no	—
129	C₂²×C₄×C₅	C₃×D₄	1	3	yes	complemented
130	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic, complemented
131	C₅×C₄⋊C₄	—	2	6	no	—
132	C₅×C₂²⋊C₄	—	2	3	no	—
133	C₅×C₂²⋊C₄	—	2	6	no	—
134	C₅×C₂²⋊C₄	—	2	6	no	—
135	C₅×C₂²⋊C₄	C₂³×C₃	1	6	yes	complemented
136	C₂×H(5,𝔽₂)	C₂×C₃×C₅	1	1	yes	characteristic, complemented
137	#534	C₂×C₃×C₅	1	3	yes	complemented
138	#458	C₂×C₃×C₅	1	4	yes	complemented
139	B(4,𝔽₂)	C₂×C₃×C₅	1	4	yes	complemented
140	C₂×#99	C₂×C₃×C₅	1	3	yes	complemented
141	C₂²×C₃×C₅	—	2	6	no	—
142	C₂²×C₃×C₅	—	4	3	no	—
143	C₂²×C₃×C₅	—	4	3	no	—
144	C₂²×C₃×C₅	—	4	1	no	—
145	C₂²×C₃×C₅	—	4	6	no	—
146	C₂²×C₃×C₅	—	4	6	no	—
147	C₂²×C₃×C₅	—	4	6	no	—
148	C₂²×C₃×C₅	—	4	1	no	—
149	C₂²×C₃×C₅	—	8	3	no	—
150	C₂²×C₃×C₅	—	8	4	no	—
151	C₂²×C₃×C₅	#120	1	1	yes	characteristic
152	C₂²×C₃×C₅	#120	1	3	yes	—
153	C₂²×C₃×C₅	C₂²×D₄	1	3	yes	—
154	C₃×C₄×C₅	—	2	6	no	—
155	C₃×C₄×C₅	—	4	6	no	—
156	C₃×C₄×C₅	—	4	1	no	—
157	C₂⁴×C₃	—	2	1	no	—
158	C₂⁴×C₃	C₅×D₄	1	3	yes	complemented
159	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
160	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic, complemented
161	C₃×#41	—	2	12	no	—
162	C₃×#41	—	2	12	no	—
163	C₂×C₃×Q₈	—	2	1	no	—
164	C₂×C₃×D₄	—	2	3	no	—
165	C₂×C₃×D₄	—	2	12	no	—
166	C₂×C₃×D₄	—	2	6	no	—
167	C₂×C₃×D₄	—	2	12	no	—
168	C₂×C₃×D₄	—	2	6	no	—
169	C₂×C₃×D₄	—	2	3	no	—
170	C₂×C₃×D₄	—	2	3	no	—
171	C₂×C₃×D₄	—	2	6	no	—
172	C₂×C₃×D₄	C₅×D₄	1	6	yes	complemented
173	C₂×C₃×D₄	C₂³×C₅	1	6	yes	—
174	C₂²×C₃×C₄	—	2	3	no	—
175	C₂²×C₃×C₄	—	2	3	no	—
176	C₂²×C₃×C₄	C₅×D₄	1	3	yes	complemented
177	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic, complemented
178	C₃×C₄⋊C₄	—	2	6	no	—
179	C₃×C₂²⋊C₄	—	2	3	no	—
180	C₃×C₂²⋊C₄	—	2	6	no	—
181	C₃×C₂²⋊C₄	—	2	6	no	—
182	C₃×C₂²⋊C₄	C₂³×C₅	1	6	yes	complemented
183	C₂³×C₅	—	2	4	no	—
184	C₂³×C₅	—	2	3	no	—
185	C₂³×C₅	—	2	3	no	—
186	C₂³×C₅	—	2	3	no	—
187	C₂³×C₅	—	8	1	no	—
188	C₂³×C₅	—	8	1	no	—
189	C₂³×C₅	—	8	3	no	—
190	C₂³×C₅	—	8	2	no	—
191	C₂³×C₅	C₂×C₃×D₄	1	6	yes	—
192	C₂³×C₅	C₂×C₃×D₄	1	3	yes	—
193	C₂³×C₅	C₂×C₃×D₄	1	3	yes	—
194	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
195	C₅×Q₈	—	2	4	no	—
196	C₅×D₄	—	2	12	no	—
197	C₅×D₄	—	2	12	no	—
198	C₅×D₄	—	2	12	no	—
199	C₅×D₄	—	4	1	no	—
200	C₅×D₄	—	4	3	no	—
201	C₅×D₄	—	8	6	no	—
202	C₂×C₄×C₅	—	2	12	no	—
203	C₂×C₄×C₅	—	2	3	no	—
204	C₂×C₄×C₅	—	2	3	no	—
205	C₂×C₄×C₅	—	2	6	no	—
206	C₂×C₄×C₅	—	2	3	no	—
207	C₂×C₄×C₅	—	8	3	no	—
208	C₂×C₄×C₅	C₂×C₃×D₄	1	6	yes	—
209	H(5,𝔽₂)	—	2	6	no	—
210	H(5,𝔽₂)	C₂²×C₃×C₅	1	4	yes	—
211	C₂×#41	—	2	3	no	—
212	C₂²×D₄	—	2	3	no	—
213	C₂²×D₄	C₂²×C₃×C₅	1	3	yes	—
214	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
215	#123	—	2	3	no	—
216	#123	C₂²×C₃×C₅	1	6	yes	complemented
217	#121	—	2	6	no	—
218	#120	—	2	3	no	—
219	#120	C₂²×C₃×C₅	1	6	yes	complemented
220	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	3	yes	complemented
221	#99	C₂²×C₃×C₅	1	12	yes	complemented
222	C₂×C₃×C₅	—	2	3	no	—
223	C₂×C₃×C₅	—	2	1	no	—
224	C₂×C₃×C₅	—	2	3	no	—
225	C₂×C₃×C₅	—	4	6	no	—
226	C₂×C₃×C₅	—	8	1	no	—
227	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
228	C₂³×C₃	—	2	4	no	—
229	C₂³×C₃	—	2	3	no	—
230	C₂³×C₃	—	2	3	no	—
231	C₂³×C₃	—	2	3	no	—
232	C₂³×C₃	—	8	1	no	—
233	C₂³×C₃	—	8	1	no	—
234	C₂³×C₃	—	8	3	no	—
235	C₂³×C₃	—	8	2	no	—
236	C₂³×C₃	C₂×C₅×D₄	1	6	yes	—
237	C₂³×C₃	C₂×C₅×D₄	1	3	yes	—
238	C₂³×C₃	C₂×C₅×D₄	1	3	yes	—
239	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
240	C₃×Q₈	—	2	4	no	—
241	C₃×D₄	—	2	12	no	—
242	C₃×D₄	—	2	12	no	—
243	C₃×D₄	—	2	12	no	—
244	C₃×D₄	—	4	1	no	—
245	C₃×D₄	—	4	3	no	—
246	C₃×D₄	—	8	6	no	—
247	C₂×C₃×C₄	—	2	12	no	—
248	C₂×C₃×C₄	—	2	3	no	—
249	C₂×C₃×C₄	—	2	3	no	—
250	C₂×C₃×C₄	—	2	6	no	—
251	C₂×C₃×C₄	—	2	3	no	—
252	C₂×C₃×C₄	—	8	3	no	—
253	C₂×C₃×C₄	C₂×C₅×D₄	1	6	yes	—
254	C₂²×C₅	—	2	6	no	—
255	C₂²×C₅	—	4	3	no	—
256	C₂²×C₅	—	4	3	no	—
257	C₂²×C₅	—	4	1	no	—
258	C₂²×C₅	—	4	6	no	—
259	C₂²×C₅	—	4	6	no	—
260	C₂²×C₅	—	4	6	no	—
261	C₂²×C₅	—	4	1	no	—
262	C₂²×C₅	—	8	3	no	—
263	C₂²×C₅	—	8	4	no	—
264	C₂²×C₅	C₃×#120	1	1	yes	characteristic
265	C₂²×C₅	C₃×#120	1	3	yes	—
266	C₂²×C₅	C₂²×C₃×D₄	1	3	yes	—
267	C₄×C₅	—	2	6	no	—
268	C₄×C₅	—	4	6	no	—
269	C₄×C₅	—	4	1	no	—
270	C₂⁴	—	2	1	no	—
271	C₂⁴	C₃×C₅×D₄	1	3	yes	complemented
272	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
273	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic, complemented
274	#41	—	2	12	no	—
275	#41	—	2	12	no	—
276	C₂×Q₈	—	2	1	no	—
277	C₂×D₄	—	2	3	no	—
278	C₂×D₄	—	2	12	no	—
279	C₂×D₄	—	2	6	no	—
280	C₂×D₄	—	2	12	no	—
281	C₂×D₄	—	2	6	no	—
282	C₂×D₄	—	2	3	no	—
283	C₂×D₄	—	2	3	no	—
284	C₂×D₄	—	2	6	no	—
285	C₂×D₄	C₃×C₅×D₄	1	6	yes	complemented
286	C₂×D₄	C₂³×C₃×C₅	1	6	yes	—
287	C₂²×C₄	—	2	3	no	—
288	C₂²×C₄	—	2	3	no	—
289	C₂²×C₄	C₃×C₅×D₄	1	3	yes	complemented
290	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic, complemented
291	C₄⋊C₄	—	2	6	no	—
292	C₂²⋊C₄	—	2	3	no	—
293	C₂²⋊C₄	—	2	6	no	—
294	C₂²⋊C₄	—	2	6	no	—
295	C₂²⋊C₄	C₂³×C₃×C₅	1	6	yes	complemented
296	C₃×C₅	#3026	1	1	yes	characteristic, direct product factor, Hall
297	C₂²×C₃	—	2	6	no	—
298	C₂²×C₃	—	4	3	no	—
299	C₂²×C₃	—	4	3	no	—
300	C₂²×C₃	—	4	1	no	—
301	C₂²×C₃	—	4	6	no	—
302	C₂²×C₃	—	4	6	no	—
303	C₂²×C₃	—	4	6	no	—
304	C₂²×C₃	—	4	1	no	—
305	C₂²×C₃	—	8	3	no	—
306	C₂²×C₃	—	8	4	no	—
307	C₂²×C₃	C₅×#120	1	1	yes	characteristic
308	C₂²×C₃	C₅×#120	1	3	yes	—
309	C₂²×C₃	C₂²×C₅×D₄	1	3	yes	—
310	C₃×C₄	—	2	6	no	—
311	C₃×C₄	—	4	6	no	—
312	C₃×C₄	—	4	1	no	—
313	C₂×C₅	—	2	3	no	—
314	C₂×C₅	—	2	1	no	—
315	C₂×C₅	—	2	3	no	—
316	C₂×C₅	—	4	6	no	—
317	C₂×C₅	—	8	1	no	—
318	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
319	C₂³	—	2	4	no	—
320	C₂³	—	2	3	no	—
321	C₂³	—	2	3	no	—
322	C₂³	—	2	3	no	—
323	C₂³	—	8	1	no	—
324	C₂³	—	8	1	no	—
325	C₂³	—	8	3	no	—
326	C₂³	—	8	2	no	—
327	C₂³	C₂×C₃×C₅×D₄	1	6	yes	—
328	C₂³	C₂×C₃×C₅×D₄	1	3	yes	—
329	C₂³	C₂×C₃×C₅×D₄	1	3	yes	—
330	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
331	Q₈	—	2	4	no	—
332	D₄	—	2	12	no	—
333	D₄	—	2	12	no	—
334	D₄	—	2	12	no	—
335	D₄	—	4	1	no	—
336	D₄	—	4	3	no	—
337	D₄	—	8	6	no	—
338	C₂×C₄	—	2	12	no	—
339	C₂×C₄	—	2	3	no	—
340	C₂×C₄	—	2	3	no	—
341	C₂×C₄	—	2	6	no	—
342	C₂×C₄	—	2	3	no	—
343	C₂×C₄	—	8	3	no	—
344	C₂×C₄	C₂×C₃×C₅×D₄	1	6	yes	—
345	C₂×C₃	—	2	3	no	—
346	C₂×C₃	—	2	1	no	—
347	C₂×C₃	—	2	3	no	—
348	C₂×C₃	—	4	6	no	—
349	C₂×C₃	—	8	1	no	—
350	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
351	C₅	C₃×#3026	1	1	yes	characteristic, direct product factor, Sylow
352	C₂²	—	2	6	no	—
353	C₂²	—	4	3	no	—
354	C₂²	—	4	3	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	6	no	—
357	C₂²	—	4	6	no	—
358	C₂²	—	4	6	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	8	3	no	—
361	C₂²	—	8	4	no	—
362	C₂²	C₃×C₅×#120	1	1	yes	characteristic
363	C₂²	C₃×C₅×#120	1	3	yes	—
364	C₂²	C₂²×C₃×C₅×D₄	1	3	yes	—
365	C₄	—	2	6	no	—
366	C₄	—	4	6	no	—
367	C₄	—	4	1	no	—
368	C₃	C₅×#3026	1	1	yes	characteristic, direct product factor, Sylow
369	C₂	—	2	3	no	—
370	C₂	—	2	1	no	—
371	C₂	—	2	3	no	—
372	C₂	—	4	6	no	—
373	C₂	—	8	1	no	—
374	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃×C₅	C₂×#120
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂⁴×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×H(5,𝔽₂)	C₂	semidirect
2. C₃×C₅×#534	C₂	semidirect
3. C₃×C₅×#458	C₂	semidirect
4. C₃×C₅×B(4,𝔽₂)	C₂	semidirect
5. C₂×C₃×C₅×#99	C₂	semidirect
6. C₅×#3026	C₃	direct (N × H)
12. C₂²×C₃×C₅×D₄	C₂²	semidirect
14. C₃×C₅×#123	C₂²	semidirect
17. C₃×C₅×#120	C₂²	semidirect
18. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
19. C₃×C₅×#99	C₂²	semidirect
20. C₃×#3026	C₅	direct (N × H)
21. C₂×C₅×H(5,𝔽₂)	C₂×C₃	semidirect
22. C₅×#534	C₂×C₃	semidirect
23. C₅×#458	C₂×C₃	semidirect
24. C₅×B(4,𝔽₂)	C₂×C₃	semidirect
25. C₂×C₅×#99	C₂×C₃	semidirect
27. C₂⁴×C₃×C₅	D₄	semidirect
29. C₂⁴×C₃×C₅	C₂³	semidirect
41. C₂×C₃×C₅×D₄	D₄	semidirect
45. C₂²×C₃×C₄×C₅	D₄	semidirect
46. C₂²×C₃×C₄×C₅	C₂³	semidirect
51. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
52. C₂×C₃×H(5,𝔽₂)	C₂×C₅	semidirect
53. C₃×#534	C₂×C₅	semidirect
54. C₃×#458	C₂×C₅	semidirect
55. C₃×B(4,𝔽₂)	C₂×C₅	semidirect
56. C₂×C₃×#99	C₂×C₅	semidirect
62. C₂²×C₅×D₄	C₂²×C₃	semidirect
64. C₅×#123	C₂²×C₃	semidirect
67. C₅×#120	C₂²×C₃	semidirect
68. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
69. C₅×#99	C₂²×C₃	semidirect
70. #3026	C₃×C₅	direct (N × H)
102. C₂²×C₃×D₄	C₂²×C₅	semidirect
104. C₃×#123	C₂²×C₅	semidirect
107. C₃×#120	C₂²×C₅	semidirect
108. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
109. C₃×#99	C₂²×C₅	semidirect
111. C₂⁴×C₅	C₃×D₄	semidirect
113. C₂⁴×C₅	C₂³×C₃	semidirect
125. C₂×C₅×D₄	C₃×D₄	semidirect
129. C₂²×C₄×C₅	C₃×D₄	semidirect
130. C₂²×C₄×C₅	C₂³×C₃	semidirect
135. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
136. C₂×H(5,𝔽₂)	C₂×C₃×C₅	semidirect
137. #534	C₂×C₃×C₅	semidirect
138. #458	C₂×C₃×C₅	semidirect
139. B(4,𝔽₂)	C₂×C₃×C₅	semidirect
140. C₂×#99	C₂×C₃×C₅	semidirect
158. C₂⁴×C₃	C₅×D₄	semidirect
160. C₂⁴×C₃	C₂³×C₅	semidirect
172. C₂×C₃×D₄	C₅×D₄	semidirect
176. C₂²×C₃×C₄	C₅×D₄	semidirect
177. C₂²×C₃×C₄	C₂³×C₅	semidirect
182. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
214. C₂²×D₄	C₂²×C₃×C₅	semidirect
216. #123	C₂²×C₃×C₅	semidirect
219. #120	C₂²×C₃×C₅	semidirect
220. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
221. #99	C₂²×C₃×C₅	semidirect
271. C₂⁴	C₃×C₅×D₄	semidirect
273. C₂⁴	C₂³×C₃×C₅	semidirect
285. C₂×D₄	C₃×C₅×D₄	semidirect
289. C₂²×C₄	C₃×C₅×D₄	semidirect
290. C₂²×C₄	C₂³×C₃×C₅	semidirect
295. C₂²⋊C₄	C₂³×C₃×C₅	semidirect
296. C₃×C₅	#3026	direct (N × H)
351. C₅	C₃×#3026	direct (N × H)
368. C₃	C₅×#3026	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×H(5,𝔽₂)	2
C₃×C₅×#534	2
C₃×C₅×#458	2
C₃×C₅×B(4,𝔽₂)	2
C₂×C₃×C₅×#99	2
C₅×#3026	3
C₃×#3026	5

Subgroups — C3×C5×#3026 #14276060

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3026 #14276060