Subgroups — C₂×C₃×C₅×B(4,𝔽₂) #14276057

Order 1920.

2036 conjugacy classes of subgroups.

The subgroup lattice has 380 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	C₂×C₃×C₅×#120	C₂	1	3	yes	maximal, complemented
3	C₃×C₅×B(4,𝔽₂)	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×C₅×#99	C₂	1	3	yes	maximal, complemented
5	C₂×C₅×B(4,𝔽₂)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic, complemented
7	C₃×C₅×H(5,𝔽₂)	—	2	6	no	—
8	C₃×C₅×H(5,𝔽₂)	C₂²	1	4	yes	complemented
9	C₂×C₃×C₅×#41	—	2	3	no	—
10	C₂²×C₃×C₅×D₄	—	2	3	no	—
11	C₂²×C₃×C₅×D₄	—	2	3	no	—
12	C₂²×C₃×C₅×D₄	C₂²	1	3	yes	—
13	C₃×C₅×#120	—	2	6	no	—
14	C₃×C₅×#120	C₂²	1	12	yes	complemented
15	C₂×C₃×C₅×C₂²⋊C₄	—	2	3	no	—
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	complemented
17	C₃×C₅×#99	C₂²	1	12	yes	complemented
18	C₂×C₃×B(4,𝔽₂)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₅×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
20	C₂×C₅×#120	C₂×C₃	1	3	yes	complemented
21	C₅×B(4,𝔽₂)	C₂×C₃	1	8	yes	direct product factor
22	C₂×C₅×#99	C₂×C₃	1	3	yes	complemented
23	C₂⁴×C₃×C₅	—	2	1	no	—
24	C₂⁴×C₃×C₅	—	2	3	no	—
25	C₂⁴×C₃×C₅	—	2	3	no	—
26	C₂⁴×C₃×C₅	—	4	4	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	2	yes	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	6	no	—
37	C₂×C₃×C₅×D₄	—	2	12	no	—
38	C₂×C₃×C₅×D₄	—	2	12	no	—
39	C₂×C₃×C₅×D₄	—	4	12	no	—
40	C₂×C₃×C₅×D₄	D₄	1	6	yes	complemented
41	C₂×C₃×C₅×D₄	C₂³	1	6	yes	—
42	C₂²×C₃×C₄×C₅	—	2	3	no	—
43	C₂²×C₃×C₄×C₅	—	2	3	no	—
44	C₂²×C₃×C₄×C₅	D₄	1	3	yes	complemented
45	C₃×C₅×C₂²⋊C₄	—	2	3	no	—
46	C₃×C₅×C₂²⋊C₄	—	2	12	no	—
47	C₃×C₅×C₂²⋊C₄	C₂³	1	6	yes	complemented
48	C₂×C₃×H(5,𝔽₂)	C₂×C₅	1	1	yes	characteristic, complemented
49	C₂×C₃×#120	C₂×C₅	1	3	yes	complemented
50	C₃×B(4,𝔽₂)	C₂×C₅	1	8	yes	direct product factor
51	C₂×C₃×#99	C₂×C₅	1	3	yes	complemented
52	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
53	C₅×H(5,𝔽₂)	—	2	6	no	—
54	C₅×H(5,𝔽₂)	C₂²×C₃	1	4	yes	complemented
55	C₂×C₅×#41	—	2	3	no	—
56	C₂²×C₅×D₄	—	2	3	no	—
57	C₂²×C₅×D₄	—	2	3	no	—
58	C₂²×C₅×D₄	C₂²×C₃	1	3	yes	—
59	C₅×#120	—	2	6	no	—
60	C₅×#120	C₂²×C₃	1	12	yes	complemented
61	C₂×C₅×C₂²⋊C₄	—	2	3	no	—
62	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	complemented
63	C₅×#99	C₂²×C₃	1	12	yes	complemented
64	C₂×B(4,𝔽₂)	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
65	C₂³×C₃×C₅	—	2	12	no	—
66	C₂³×C₃×C₅	—	2	4	no	—
67	C₂³×C₃×C₅	—	2	3	no	—
68	C₂³×C₃×C₅	—	2	6	no	—
69	C₂³×C₃×C₅	—	2	3	no	—
70	C₂³×C₃×C₅	—	4	2	no	—
71	C₂³×C₃×C₅	—	4	4	no	—
72	C₂³×C₃×C₅	—	4	6	no	—
73	C₂³×C₃×C₅	—	4	12	no	—
74	C₂³×C₃×C₅	—	4	6	no	—
75	C₂³×C₃×C₅	—	4	3	no	—
76	C₂³×C₃×C₅	—	4	1	no	—
77	C₂³×C₃×C₅	—	8	2	no	—
78	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
79	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
80	C₂³×C₃×C₅	C₂×D₄	1	6	yes	complemented
81	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
82	C₃×C₅×Q₈	—	2	4	no	—
83	C₃×C₅×D₄	—	2	12	no	—
84	C₃×C₅×D₄	—	2	12	no	—
85	C₃×C₅×D₄	—	2	12	no	—
86	C₃×C₅×D₄	—	4	24	no	—
87	C₂×C₃×C₄×C₅	—	2	12	no	—
88	C₂×C₃×C₄×C₅	—	2	3	no	—
89	C₂×C₃×C₄×C₅	—	2	3	no	—
90	C₂×C₃×C₄×C₅	—	2	6	no	—
91	C₂×C₃×C₄×C₅	—	4	6	no	—
92	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	complemented
93	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic, complemented
94	C₃×H(5,𝔽₂)	—	2	6	no	—
95	C₃×H(5,𝔽₂)	C₂²×C₅	1	4	yes	complemented
96	C₂×C₃×#41	—	2	3	no	—
97	C₂²×C₃×D₄	—	2	3	no	—
98	C₂²×C₃×D₄	—	2	3	no	—
99	C₂²×C₃×D₄	C₂²×C₅	1	3	yes	—
100	C₃×#120	—	2	6	no	—
101	C₃×#120	C₂²×C₅	1	12	yes	complemented
102	C₂×C₃×C₂²⋊C₄	—	2	3	no	—
103	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	complemented
104	C₃×#99	C₂²×C₅	1	12	yes	complemented
105	C₂⁴×C₅	—	2	1	no	—
106	C₂⁴×C₅	—	2	3	no	—
107	C₂⁴×C₅	—	2	3	no	—
108	C₂⁴×C₅	—	4	4	no	—
109	C₂⁴×C₅	C₃×D₄	1	3	yes	complemented
110	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
111	C₂⁴×C₅	C₂³×C₃	1	2	yes	complemented
112	C₅×#41	—	2	12	no	—
113	C₅×#41	—	2	12	no	—
114	C₂×C₅×Q₈	—	2	1	no	—
115	C₂×C₅×D₄	—	2	3	no	—
116	C₂×C₅×D₄	—	2	12	no	—
117	C₂×C₅×D₄	—	2	6	no	—
118	C₂×C₅×D₄	—	2	6	no	—
119	C₂×C₅×D₄	—	2	12	no	—
120	C₂×C₅×D₄	—	2	12	no	—
121	C₂×C₅×D₄	—	4	12	no	—
122	C₂×C₅×D₄	C₃×D₄	1	6	yes	complemented
123	C₂×C₅×D₄	C₂³×C₃	1	6	yes	—
124	C₂²×C₄×C₅	—	2	3	no	—
125	C₂²×C₄×C₅	—	2	3	no	—
126	C₂²×C₄×C₅	C₃×D₄	1	3	yes	complemented
127	C₅×C₂²⋊C₄	—	2	3	no	—
128	C₅×C₂²⋊C₄	—	2	12	no	—
129	C₅×C₂²⋊C₄	C₂³×C₃	1	6	yes	complemented
130	C₂×H(5,𝔽₂)	C₂×C₃×C₅	1	1	yes	characteristic, complemented
131	C₂×#120	C₂×C₃×C₅	1	3	yes	complemented
132	B(4,𝔽₂)	C₂×C₃×C₅	1	8	yes	direct product factor
133	C₂×#99	C₂×C₃×C₅	1	3	yes	complemented
134	C₂²×C₃×C₅	—	2	6	no	—
135	C₂²×C₃×C₅	—	2	12	no	—
136	C₂²×C₃×C₅	—	2	6	no	—
137	C₂²×C₃×C₅	—	4	3	no	—
138	C₂²×C₃×C₅	—	4	1	no	—
139	C₂²×C₃×C₅	—	4	6	no	—
140	C₂²×C₃×C₅	—	4	6	no	—
141	C₂²×C₃×C₅	—	4	12	no	—
142	C₂²×C₃×C₅	—	4	2	no	—
143	C₂²×C₃×C₅	—	4	4	no	—
144	C₂²×C₃×C₅	—	4	6	no	—
145	C₂²×C₃×C₅	—	8	3	no	—
146	C₂²×C₃×C₅	—	8	4	no	—
147	C₂²×C₃×C₅	#120	1	3	yes	—
148	C₂²×C₃×C₅	#120	1	1	yes	characteristic
149	C₂²×C₃×C₅	C₂²×D₄	1	3	yes	—
150	C₃×C₄×C₅	—	2	6	no	—
151	C₃×C₄×C₅	—	4	6	no	—
152	C₂⁴×C₃	—	2	1	no	—
153	C₂⁴×C₃	—	2	3	no	—
154	C₂⁴×C₃	—	2	3	no	—
155	C₂⁴×C₃	—	4	4	no	—
156	C₂⁴×C₃	C₅×D₄	1	3	yes	complemented
157	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
158	C₂⁴×C₃	C₂³×C₅	1	2	yes	complemented
159	C₃×#41	—	2	12	no	—
160	C₃×#41	—	2	12	no	—
161	C₂×C₃×Q₈	—	2	1	no	—
162	C₂×C₃×D₄	—	2	3	no	—
163	C₂×C₃×D₄	—	2	12	no	—
164	C₂×C₃×D₄	—	2	6	no	—
165	C₂×C₃×D₄	—	2	6	no	—
166	C₂×C₃×D₄	—	2	12	no	—
167	C₂×C₃×D₄	—	2	12	no	—
168	C₂×C₃×D₄	—	4	12	no	—
169	C₂×C₃×D₄	C₅×D₄	1	6	yes	complemented
170	C₂×C₃×D₄	C₂³×C₅	1	6	yes	—
171	C₂²×C₃×C₄	—	2	3	no	—
172	C₂²×C₃×C₄	—	2	3	no	—
173	C₂²×C₃×C₄	C₅×D₄	1	3	yes	complemented
174	C₃×C₂²⋊C₄	—	2	3	no	—
175	C₃×C₂²⋊C₄	—	2	12	no	—
176	C₃×C₂²⋊C₄	C₂³×C₅	1	6	yes	complemented
177	C₂³×C₅	—	2	12	no	—
178	C₂³×C₅	—	2	4	no	—
179	C₂³×C₅	—	2	3	no	—
180	C₂³×C₅	—	2	6	no	—
181	C₂³×C₅	—	2	3	no	—
182	C₂³×C₅	—	4	2	no	—
183	C₂³×C₅	—	4	4	no	—
184	C₂³×C₅	—	4	6	no	—
185	C₂³×C₅	—	4	12	no	—
186	C₂³×C₅	—	4	6	no	—
187	C₂³×C₅	—	4	3	no	—
188	C₂³×C₅	—	4	1	no	—
189	C₂³×C₅	—	8	2	no	—
190	C₂³×C₅	C₂×C₃×D₄	1	3	yes	—
191	C₂³×C₅	C₂×C₃×D₄	1	3	yes	—
192	C₂³×C₅	C₂×C₃×D₄	1	6	yes	complemented
193	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
194	C₅×Q₈	—	2	4	no	—
195	C₅×D₄	—	2	12	no	—
196	C₅×D₄	—	2	12	no	—
197	C₅×D₄	—	2	12	no	—
198	C₅×D₄	—	4	24	no	—
199	C₂×C₄×C₅	—	2	12	no	—
200	C₂×C₄×C₅	—	2	3	no	—
201	C₂×C₄×C₅	—	2	3	no	—
202	C₂×C₄×C₅	—	2	6	no	—
203	C₂×C₄×C₅	—	4	6	no	—
204	C₂×C₄×C₅	C₂×C₃×D₄	1	6	yes	complemented
205	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
206	H(5,𝔽₂)	—	2	6	no	—
207	H(5,𝔽₂)	C₂²×C₃×C₅	1	4	yes	complemented
208	C₂×#41	—	2	3	no	—
209	C₂²×D₄	—	2	3	no	—
210	C₂²×D₄	—	2	3	no	—
211	C₂²×D₄	C₂²×C₃×C₅	1	3	yes	—
212	#120	—	2	6	no	—
213	#120	C₂²×C₃×C₅	1	12	yes	complemented
214	C₂×C₂²⋊C₄	—	2	3	no	—
215	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	3	yes	complemented
216	#99	C₂²×C₃×C₅	1	12	yes	complemented
217	C₂×C₃×C₅	—	2	3	no	—
218	C₂×C₃×C₅	—	2	3	no	—
219	C₂×C₃×C₅	—	4	4	no	—
220	C₂×C₃×C₅	—	4	6	no	—
221	C₂×C₃×C₅	B(4,𝔽₂)	1	2	yes	direct product factor
222	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
223	C₂³×C₃	—	2	12	no	—
224	C₂³×C₃	—	2	4	no	—
225	C₂³×C₃	—	2	3	no	—
226	C₂³×C₃	—	2	6	no	—
227	C₂³×C₃	—	2	3	no	—
228	C₂³×C₃	—	4	2	no	—
229	C₂³×C₃	—	4	4	no	—
230	C₂³×C₃	—	4	6	no	—
231	C₂³×C₃	—	4	12	no	—
232	C₂³×C₃	—	4	6	no	—
233	C₂³×C₃	—	4	3	no	—
234	C₂³×C₃	—	4	1	no	—
235	C₂³×C₃	—	8	2	no	—
236	C₂³×C₃	C₂×C₅×D₄	1	3	yes	—
237	C₂³×C₃	C₂×C₅×D₄	1	3	yes	—
238	C₂³×C₃	C₂×C₅×D₄	1	6	yes	complemented
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	24	no	—
245	C₂×C₃×C₄	—	2	12	no	—
246	C₂×C₃×C₄	—	2	3	no	—
247	C₂×C₃×C₄	—	2	3	no	—
248	C₂×C₃×C₄	—	2	6	no	—
249	C₂×C₃×C₄	—	4	6	no	—
250	C₂×C₃×C₄	C₂×C₅×D₄	1	6	yes	complemented
251	C₂²×C₅	—	2	6	no	—
252	C₂²×C₅	—	2	12	no	—
253	C₂²×C₅	—	2	6	no	—
254	C₂²×C₅	—	4	3	no	—
255	C₂²×C₅	—	4	1	no	—
256	C₂²×C₅	—	4	6	no	—
257	C₂²×C₅	—	4	6	no	—
258	C₂²×C₅	—	4	12	no	—
259	C₂²×C₅	—	4	4	no	—
260	C₂²×C₅	—	4	6	no	—
261	C₂²×C₅	—	4	2	no	—
262	C₂²×C₅	—	8	3	no	—
263	C₂²×C₅	—	8	4	no	—
264	C₂²×C₅	C₃×#120	1	3	yes	—
265	C₂²×C₅	C₃×#120	1	1	yes	characteristic
266	C₂²×C₅	C₂²×C₃×D₄	1	3	yes	—
267	C₄×C₅	—	2	6	no	—
268	C₄×C₅	—	4	6	no	—
269	C₂⁴	—	2	1	no	—
270	C₂⁴	—	2	3	no	—
271	C₂⁴	—	2	3	no	—
272	C₂⁴	—	4	4	no	—
273	C₂⁴	C₃×C₅×D₄	1	3	yes	complemented
274	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
275	C₂⁴	C₂³×C₃×C₅	1	2	yes	complemented
276	#41	—	2	12	no	—
277	#41	—	2	12	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×D₄	—	2	3	no	—
280	C₂×D₄	—	2	12	no	—
281	C₂×D₄	—	2	6	no	—
282	C₂×D₄	—	2	6	no	—
283	C₂×D₄	—	2	12	no	—
284	C₂×D₄	—	2	12	no	—
285	C₂×D₄	—	4	12	no	—
286	C₂×D₄	C₃×C₅×D₄	1	6	yes	complemented
287	C₂×D₄	C₂³×C₃×C₅	1	6	yes	—
288	C₂²×C₄	—	2	3	no	—
289	C₂²×C₄	—	2	3	no	—
290	C₂²×C₄	C₃×C₅×D₄	1	3	yes	complemented
291	C₂²⋊C₄	—	2	3	no	—
292	C₂²⋊C₄	—	2	12	no	—
293	C₂²⋊C₄	C₂³×C₃×C₅	1	6	yes	complemented
294	C₃×C₅	C₂×B(4,𝔽₂)	1	1	yes	characteristic, direct product factor, Hall
295	C₂²×C₃	—	2	6	no	—
296	C₂²×C₃	—	2	12	no	—
297	C₂²×C₃	—	2	6	no	—
298	C₂²×C₃	—	4	3	no	—
299	C₂²×C₃	—	4	1	no	—
300	C₂²×C₃	—	4	6	no	—
301	C₂²×C₃	—	4	6	no	—
302	C₂²×C₃	—	4	12	no	—
303	C₂²×C₃	—	4	4	no	—
304	C₂²×C₃	—	4	6	no	—
305	C₂²×C₃	—	4	2	no	—
306	C₂²×C₃	—	8	3	no	—
307	C₂²×C₃	—	8	4	no	—
308	C₂²×C₃	C₅×#120	1	3	yes	—
309	C₂²×C₃	C₅×#120	1	1	yes	characteristic
310	C₂²×C₃	C₂²×C₅×D₄	1	3	yes	—
311	C₃×C₄	—	2	6	no	—
312	C₃×C₄	—	4	6	no	—
313	C₂×C₅	—	2	3	no	—
314	C₂×C₅	—	2	3	no	—
315	C₂×C₅	—	4	4	no	—
316	C₂×C₅	—	4	6	no	—
317	C₂×C₅	C₃×B(4,𝔽₂)	1	2	yes	direct product factor
318	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
319	C₂³	—	2	12	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	2	3	no	—
322	C₂³	—	2	6	no	—
323	C₂³	—	2	3	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	4	no	—
326	C₂³	—	4	6	no	—
327	C₂³	—	4	12	no	—
328	C₂³	—	4	6	no	—
329	C₂³	—	4	3	no	—
330	C₂³	—	4	1	no	—
331	C₂³	—	8	2	no	—
332	C₂³	C₂×C₃×C₅×D₄	1	3	yes	—
333	C₂³	C₂×C₃×C₅×D₄	1	3	yes	—
334	C₂³	C₂×C₃×C₅×D₄	1	6	yes	complemented
335	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
336	Q₈	—	2	4	no	—
337	D₄	—	2	12	no	—
338	D₄	—	2	12	no	—
339	D₄	—	2	12	no	—
340	D₄	—	4	24	no	—
341	C₂×C₄	—	2	12	no	—
342	C₂×C₄	—	2	3	no	—
343	C₂×C₄	—	2	3	no	—
344	C₂×C₄	—	2	6	no	—
345	C₂×C₄	—	4	6	no	—
346	C₂×C₄	C₂×C₃×C₅×D₄	1	6	yes	complemented
347	C₂×C₃	—	2	3	no	—
348	C₂×C₃	—	2	3	no	—
349	C₂×C₃	—	4	4	no	—
350	C₂×C₃	—	4	6	no	—
351	C₂×C₃	C₅×B(4,𝔽₂)	1	2	yes	direct product factor
352	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
353	C₅	C₂×C₃×B(4,𝔽₂)	1	1	yes	characteristic, direct product factor, Sylow
354	C₂²	—	2	6	no	—
355	C₂²	—	2	12	no	—
356	C₂²	—	2	6	no	—
357	C₂²	—	4	3	no	—
358	C₂²	—	4	1	no	—
359	C₂²	—	4	6	no	—
360	C₂²	—	4	6	no	—
361	C₂²	—	4	12	no	—
362	C₂²	—	4	4	no	—
363	C₂²	—	4	6	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	8	3	no	—
366	C₂²	—	8	4	no	—
367	C₂²	C₃×C₅×#120	1	3	yes	—
368	C₂²	C₃×C₅×#120	1	1	yes	characteristic
369	C₂²	C₂²×C₃×C₅×D₄	1	3	yes	—
370	C₄	—	2	6	no	—
371	C₄	—	4	6	no	—
372	C₃	C₂×C₅×B(4,𝔽₂)	1	1	yes	characteristic, direct product factor, Sylow
373	C₂	—	2	3	no	—
374	C₂	—	2	3	no	—
375	C₂	—	4	4	no	—
376	C₂	—	4	6	no	—
377	C₂	C₃×C₅×B(4,𝔽₂)	1	2	yes	direct product factor
378	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#120
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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. C₂×C₃×C₅×#120	C₂	semidirect
3. C₃×C₅×B(4,𝔽₂)	C₂	direct (N × H)
4. C₂×C₃×C₅×#99	C₂	semidirect
5. C₂×C₅×B(4,𝔽₂)	C₃	direct (N × H)
6. C₂⁵×C₃×C₅	C₂²	semidirect
8. C₃×C₅×H(5,𝔽₂)	C₂²	semidirect
14. C₃×C₅×#120	C₂²	semidirect
16. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
17. C₃×C₅×#99	C₂²	semidirect
18. C₂×C₃×B(4,𝔽₂)	C₅	direct (N × H)
19. C₂×C₅×H(5,𝔽₂)	C₂×C₃	semidirect
20. C₂×C₅×#120	C₂×C₃	semidirect
21. C₅×B(4,𝔽₂)	C₂×C₃	direct (N × H)
22. C₂×C₅×#99	C₂×C₃	semidirect
27. C₂⁴×C₃×C₅	D₄	semidirect
29. C₂⁴×C₃×C₅	C₂³	semidirect
40. C₂×C₃×C₅×D₄	D₄	semidirect
44. C₂²×C₃×C₄×C₅	D₄	semidirect
47. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
48. C₂×C₃×H(5,𝔽₂)	C₂×C₅	semidirect
49. C₂×C₃×#120	C₂×C₅	semidirect
50. C₃×B(4,𝔽₂)	C₂×C₅	direct (N × H)
51. C₂×C₃×#99	C₂×C₅	semidirect
52. C₂⁵×C₅	C₂²×C₃	semidirect
54. C₅×H(5,𝔽₂)	C₂²×C₃	semidirect
60. C₅×#120	C₂²×C₃	semidirect
62. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
63. C₅×#99	C₂²×C₃	semidirect
64. C₂×B(4,𝔽₂)	C₃×C₅	direct (N × H)
80. C₂³×C₃×C₅	C₂×D₄	semidirect
92. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
93. C₂⁵×C₃	C₂²×C₅	semidirect
95. C₃×H(5,𝔽₂)	C₂²×C₅	semidirect
101. C₃×#120	C₂²×C₅	semidirect
103. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
104. C₃×#99	C₂²×C₅	semidirect
109. C₂⁴×C₅	C₃×D₄	semidirect
111. C₂⁴×C₅	C₂³×C₃	semidirect
122. C₂×C₅×D₄	C₃×D₄	semidirect
126. C₂²×C₄×C₅	C₃×D₄	semidirect
129. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
130. C₂×H(5,𝔽₂)	C₂×C₃×C₅	semidirect
131. C₂×#120	C₂×C₃×C₅	semidirect
132. B(4,𝔽₂)	C₂×C₃×C₅	direct (N × H)
133. C₂×#99	C₂×C₃×C₅	semidirect
156. C₂⁴×C₃	C₅×D₄	semidirect
158. C₂⁴×C₃	C₂³×C₅	semidirect
169. C₂×C₃×D₄	C₅×D₄	semidirect
173. C₂²×C₃×C₄	C₅×D₄	semidirect
176. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
192. C₂³×C₅	C₂×C₃×D₄	semidirect
204. C₂×C₄×C₅	C₂×C₃×D₄	semidirect
205. C₂⁵	C₂²×C₃×C₅	semidirect
207. H(5,𝔽₂)	C₂²×C₃×C₅	semidirect
213. #120	C₂²×C₃×C₅	semidirect
215. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
216. #99	C₂²×C₃×C₅	semidirect
221. C₂×C₃×C₅	B(4,𝔽₂)	direct (N × H)
238. C₂³×C₃	C₂×C₅×D₄	semidirect
250. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
273. C₂⁴	C₃×C₅×D₄	semidirect
275. C₂⁴	C₂³×C₃×C₅	semidirect
286. C₂×D₄	C₃×C₅×D₄	semidirect
290. C₂²×C₄	C₃×C₅×D₄	semidirect
293. C₂²⋊C₄	C₂³×C₃×C₅	semidirect
294. C₃×C₅	C₂×B(4,𝔽₂)	direct (N × H)
317. C₂×C₅	C₃×B(4,𝔽₂)	direct (N × H)
334. C₂³	C₂×C₃×C₅×D₄	semidirect
346. C₂×C₄	C₂×C₃×C₅×D₄	semidirect
351. C₂×C₃	C₅×B(4,𝔽₂)	direct (N × H)
353. C₅	C₂×C₃×B(4,𝔽₂)	direct (N × H)
372. C₃	C₂×C₅×B(4,𝔽₂)	direct (N × H)
377. C₂	C₃×C₅×B(4,𝔽₂)	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
C₂×C₃×C₅×#120	2
C₃×C₅×B(4,𝔽₂)	2
C₂×C₃×C₅×#99	2
C₂×C₅×B(4,𝔽₂)	3
C₂×C₃×B(4,𝔽₂)	5

Subgroups — C2×C3×C5×B(4,𝔽2) #14276057

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×B(4,𝔽₂) #14276057