Subgroups — C₂×C₅×#5135 #14427984

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#930	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5135	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#821	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#817	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#469	—	3	1	no	maximal, Hall
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂²×C₅×#67	—	2	2	no	—
10	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
11	C₂×C₃×C₅×M₁₆	—	2	4	no	—
12	C₂×C₃×C₅×M₁₆	C₂²	1	4	yes	complemented
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₅×#930	—	2	4	no	—
16	C₅×#930	C₂²	1	8	yes	complemented
17	C₂×C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
19	C₂×C₅×D₂₄	—	2	4	no	—
20	C₂×C₅×D₂₄	C₂²	1	4	yes	complemented
21	C₅×#821	C₂²	1	8	yes	complemented
22	C₅×#817	C₂²	1	4	yes	complemented
23	C₂×#5135	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂²×C₅×D₈	—	3	1	no	—
25	C₂²×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
26	C₂×C₅×#121	—	3	2	no	—
27	C₅×#469	—	3	8	no	—
28	C₂×C₅×#106	—	3	1	no	—
29	C₂×C₅×#102	—	3	2	no	—
30	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
31	C₂³×C₅×D₃	—	2	2	no	—
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	—	2	2	no	—
34	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂×C₅×#67	—	2	8	no	—
39	C₂×C₅×#67	—	4	8	no	—
40	C₂²×C₅×Dic₃	—	2	2	no	—
41	C₂×C₅×D₁₂	—	2	4	no	—
42	C₂×C₅×D₁₂	—	2	4	no	—
43	C₂×C₅×D₁₂	—	2	2	no	—
44	C₂×C₅×D₁₂	C₂³	1	4	yes	—
45	C₃×C₅×M₁₆	—	2	8	no	—
46	C₂×C₃×C₅×C₈	—	2	2	no	—
47	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
48	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
49	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
50	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
51	C₅×C₄⋊Dic₃	—	2	2	no	—
52	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
53	C₅×D₂₄	—	2	8	no	—
54	C₂²×C₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
55	C₂×#930	C₂×C₅	1	2	yes	complemented
56	C₂²×D₂₄	C₂×C₅	1	1	yes	characteristic, complemented
57	#5135	C₂×C₅	1	8	yes	direct product factor
58	C₂×#821	C₂×C₅	1	2	yes	complemented
59	C₂×#817	C₂×C₅	1	1	yes	characteristic, complemented
60	C₂²×C₅×D₄	—	3	2	no	—
61	C₂²×C₅×D₄	—	6	2	no	—
62	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
63	C₂×C₅×D₈	—	3	4	no	—
64	C₂×C₅×D₈	—	6	4	no	—
65	C₂×C₅×M₁₆	—	2	4	no	—
66	C₂×C₅×M₁₆	C₂×D₃	1	4	yes	complemented
67	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
69	C₅×#121	—	3	8	no	—
70	C₅×#121	—	6	4	no	—
71	C₂×C₅×C₄⋊C₄	—	3	2	no	—
72	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
73	C₅×#106	—	3	4	no	—
74	C₅×#102	—	3	8	no	—
75	C₂×#469	—	3	1	no	Sylow
76	C₂³×C₃×C₅	—	2	2	no	—
77	C₂³×C₃×C₅	—	2	4	no	—
78	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
79	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₅×D₃	—	2	4	no	—
81	C₂²×C₅×D₃	—	4	4	no	—
82	C₂²×C₅×D₃	—	4	4	no	—
83	C₂²×C₅×D₃	—	4	4	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	4	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	#41	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
93	C₅×#67	—	4	16	no	—
94	C₂×C₅×Dic₃	—	2	4	no	—
95	C₂×C₅×Dic₃	—	4	4	no	—
96	C₅×D₁₂	—	2	4	no	—
97	C₅×D₁₂	—	2	4	no	—
98	C₅×D₁₂	—	4	4	no	—
99	C₃×C₅×C₈	—	2	2	no	—
100	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
101	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
102	C₂²×#67	—	2	2	no	—
103	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
104	C₂×C₃×M₁₆	—	2	4	no	—
105	C₂×C₃×M₁₆	C₂²×C₅	1	4	yes	complemented
106	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
107	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
108	#930	—	2	4	no	—
109	#930	C₂²×C₅	1	8	yes	complemented
110	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
111	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
112	C₂×D₂₄	—	2	4	no	—
113	C₂×D₂₄	C₂²×C₅	1	4	yes	complemented
114	#821	C₂²×C₅	1	8	yes	complemented
115	#817	C₂²×C₅	1	4	yes	complemented
116	C₂⁴×C₅	—	6	2	no	—
117	C₂⁴×C₅	D₁₂	1	1	yes	characteristic
118	C₂×C₅×D₄	—	3	4	no	—
119	C₂×C₅×D₄	—	6	8	no	—
120	C₂×C₅×D₄	—	6	2	no	—
121	C₂×C₅×D₄	—	6	4	no	—
122	C₂×C₅×D₄	—	6	4	no	—
123	C₂×C₅×D₄	—	12	8	no	—
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	6	2	no	—
127	C₂²×C₄×C₅	D₁₂	1	2	yes	—
128	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
130	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
131	C₅×D₈	—	6	8	no	—
132	C₅×M₁₆	—	2	8	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	#67	1	4	yes	complemented
135	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
136	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
137	C₅×C₄⋊C₄	—	3	4	no	—
138	C₅×C₄⋊C₄	—	6	2	no	—
139	C₅×C₂²⋊C₄	—	6	8	no	—
140	C₂²×D₈	—	3	1	no	—
141	C₂²×M₁₆	C₅×D₃	1	1	yes	characteristic, complemented
142	C₂×#121	—	3	2	no	—
143	#469	—	3	8	no	—
144	C₂×#106	—	3	1	no	—
145	C₂×#102	—	3	2	no	—
146	C₂²×C₃×C₅	—	2	2	no	—
147	C₂²×C₃×C₅	—	2	4	no	—
148	C₂²×C₃×C₅	—	4	4	no	—
149	C₂²×C₃×C₅	#121	1	2	yes	—
150	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	4	yes	—
151	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₅×D₃	—	4	4	no	—
153	C₂×C₅×D₃	—	4	4	no	—
154	C₂×C₅×D₃	—	4	4	no	—
155	C₂×C₅×D₃	—	8	8	no	—
156	C₃×C₄×C₅	—	2	2	no	—
157	C₃×C₄×C₅	#121	1	2	yes	—
158	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
159	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
160	C₅×Dic₃	—	4	4	no	—
161	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
162	C₂³×D₃	—	2	2	no	—
163	C₂²×C₃×C₄	—	2	2	no	—
164	C₂²×C₃×C₄	—	2	2	no	—
165	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
166	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
167	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
168	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
169	C₂×#67	—	2	8	no	—
170	C₂×#67	—	4	8	no	—
171	C₂²×Dic₃	—	2	2	no	—
172	C₂×D₁₂	—	2	4	no	—
173	C₂×D₁₂	—	2	4	no	—
174	C₂×D₁₂	—	2	2	no	—
175	C₂×D₁₂	C₂³×C₅	1	4	yes	—
176	C₃×M₁₆	—	2	8	no	—
177	C₂×C₃×C₈	—	2	2	no	—
178	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
179	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
180	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
181	(C₂×D₃)⋊C₄	—	2	8	no	—
182	C₄⋊Dic₃	—	2	2	no	—
183	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
184	D₂₄	—	2	8	no	—
185	C₂³×C₅	—	2	4	no	—
186	C₂³×C₅	—	2	2	no	—
187	C₂³×C₅	—	6	4	no	—
188	C₂³×C₅	—	12	4	no	—
189	C₂³×C₅	—	12	4	no	—
190	C₂³×C₅	—	12	4	no	—
191	C₂³×C₅	C₂×D₁₂	1	2	yes	—
192	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
193	C₅×D₄	—	6	4	no	—
194	C₅×D₄	—	6	4	no	—
195	C₅×D₄	—	12	16	no	—
196	C₅×D₄	—	12	4	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	4	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	6	4	no	—
202	C₂×C₄×C₅	—	12	4	no	—
203	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
204	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
205	C₂×C₄×C₅	#235	1	2	yes	—
206	C₂×C₄×C₅	C₂×#67	1	2	yes	—
207	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
208	C₅×C₈	—	2	2	no	—
209	C₅×C₈	C₂×#67	1	4	yes	complemented
210	C₂²×D₄	—	3	2	no	—
211	C₂²×D₄	—	6	2	no	—
212	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
213	C₂×D₈	—	3	4	no	—
214	C₂×D₈	—	6	4	no	—
215	C₂×M₁₆	—	2	4	no	—
216	C₂×M₁₆	C₂×C₅×D₃	1	4	yes	complemented
217	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
218	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
219	#121	—	3	8	no	—
220	#121	—	6	4	no	—
221	C₂×C₄⋊C₄	—	3	2	no	—
222	C₂×C₂²⋊C₄	—	6	2	no	—
223	#106	—	3	4	no	—
224	#102	—	3	8	no	—
225	C₂×C₃×C₅	—	4	2	no	—
226	C₂×C₃×C₅	#469	1	4	yes	complemented
227	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
228	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
229	C₅×D₃	—	8	4	no	—
230	C₂³×C₃	—	2	2	no	—
231	C₂³×C₃	—	2	4	no	—
232	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
233	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
234	C₂²×D₃	—	2	4	no	—
235	C₂²×D₃	—	4	4	no	—
236	C₂²×D₃	—	4	4	no	—
237	C₂²×D₃	—	4	4	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
243	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
245	C₂×C₃×C₄	C₅×#41	1	2	yes	—
246	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
247	#67	—	4	16	no	—
248	C₂×Dic₃	—	2	4	no	—
249	C₂×Dic₃	—	4	4	no	—
250	D₁₂	—	2	4	no	—
251	D₁₂	—	2	4	no	—
252	D₁₂	—	4	4	no	—
253	C₃×C₈	—	2	2	no	—
254	C₃×C₈	C₂×C₅×D₄	1	4	yes	complemented
255	C₂²×C₅	—	2	4	no	—
256	C₂²×C₅	—	2	2	no	—
257	C₂²×C₅	—	4	4	no	—
258	C₂²×C₅	—	12	4	no	—
259	C₂²×C₅	—	12	4	no	—
260	C₂²×C₅	—	12	4	no	—
261	C₂²×C₅	—	24	8	no	—
262	C₂²×C₅	#908	1	4	yes	—
263	C₂²×C₅	#930	1	2	yes	—
264	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
265	C₄×C₅	—	2	2	no	—
266	C₄×C₅	—	12	4	no	—
267	C₄×C₅	#930	1	2	yes	—
268	C₄×C₅	C₂×#235	1	1	yes	characteristic
269	C₄×C₅	C₂²×#67	1	1	yes	characteristic
270	C₂⁴	—	6	2	no	—
271	C₂⁴	C₅×D₁₂	1	1	yes	characteristic
272	C₂×D₄	—	3	4	no	—
273	C₂×D₄	—	6	8	no	—
274	C₂×D₄	—	6	2	no	—
275	C₂×D₄	—	6	4	no	—
276	C₂×D₄	—	6	4	no	—
277	C₂×D₄	—	12	8	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	6	2	no	—
281	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
282	C₂²×C₄	C₅×D₁₂	1	2	yes	—
283	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
284	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
285	D₈	—	6	8	no	—
286	M₁₆	—	2	8	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	C₅×#67	1	4	yes	complemented
289	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
290	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
291	C₄⋊C₄	—	3	4	no	—
292	C₄⋊C₄	—	6	2	no	—
293	C₂²⋊C₄	—	6	8	no	—
294	C₃×C₅	C₂×#469	1	1	yes	characteristic, complemented, Hall
295	C₂²×C₃	—	2	2	no	—
296	C₂²×C₃	—	2	4	no	—
297	C₂²×C₃	—	4	4	no	—
298	C₂²×C₃	C₅×#121	1	2	yes	—
299	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	4	yes	—
300	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
301	C₂×D₃	—	4	4	no	—
302	C₂×D₃	—	4	4	no	—
303	C₂×D₃	—	4	4	no	—
304	C₂×D₃	—	8	8	no	—
305	C₃×C₄	—	2	2	no	—
306	C₃×C₄	C₅×#121	1	2	yes	—
307	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
308	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
309	Dic₃	—	4	4	no	—
310	C₂×C₅	—	4	2	no	—
311	C₂×C₅	—	24	4	no	—
312	C₂×C₅	#5135	1	4	yes	direct product factor
313	C₂×C₅	C₂×#908	1	2	yes	—
314	C₂×C₅	C₂×#930	1	1	yes	characteristic
315	C₂³	—	2	4	no	—
316	C₂³	—	2	2	no	—
317	C₂³	—	6	4	no	—
318	C₂³	—	12	4	no	—
319	C₂³	—	12	4	no	—
320	C₂³	—	12	4	no	—
321	C₂³	C₂×C₅×D₁₂	1	2	yes	—
322	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
323	D₄	—	6	4	no	—
324	D₄	—	6	4	no	—
325	D₄	—	12	16	no	—
326	D₄	—	12	4	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	6	4	no	—
332	C₂×C₄	—	12	4	no	—
333	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
334	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
335	C₂×C₄	C₅×#235	1	2	yes	—
336	C₂×C₄	C₂×C₅×#67	1	2	yes	—
337	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
338	C₈	—	2	2	no	—
339	C₈	C₂×C₅×#67	1	4	yes	complemented
340	C₂×C₃	—	4	2	no	—
341	C₂×C₃	C₅×#469	1	4	yes	complemented
342	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
343	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
344	D₃	—	8	4	no	—
345	C₅	C₂×#5135	1	1	yes	characteristic, direct product factor, Sylow
346	C₂²	—	2	4	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	12	4	no	—
350	C₂²	—	12	4	no	—
351	C₂²	—	12	4	no	—
352	C₂²	—	24	8	no	—
353	C₂²	C₅×#908	1	4	yes	—
354	C₂²	C₅×#930	1	2	yes	—
355	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	12	4	no	—
358	C₄	C₅×#930	1	2	yes	—
359	C₄	C₂×C₅×#235	1	1	yes	characteristic
360	C₄	C₂²×C₅×#67	1	1	yes	characteristic
361	C₃	C₂×C₅×#469	1	1	yes	characteristic, complemented, Sylow
362	C₂	—	4	2	no	—
363	C₂	—	24	4	no	—
364	C₂	C₅×#5135	1	4	yes	direct product factor
365	C₂	C₂×C₅×#908	1	2	yes	—
366	C₂	C₂×C₅×#930	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×M₁₆	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂²×C₅×M₁₆	D₃
hypocenter	C₃	C₂×C₅×#469
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂²×C₅×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×M₁₆	C₂	semidirect
2. C₂×C₅×#930	C₂	semidirect
3. C₂²×C₅×D₂₄	C₂	semidirect
4. C₅×#5135	C₂	direct (N × H)
5. C₂×C₅×#821	C₂	semidirect
6. C₂×C₅×#817	C₂	semidirect
12. C₂×C₃×C₅×M₁₆	C₂²	semidirect
16. C₅×#930	C₂²	semidirect
20. C₂×C₅×D₂₄	C₂²	semidirect
21. C₅×#821	C₂²	semidirect
22. C₅×#817	C₂²	semidirect
23. C₂×#5135	C₅	direct (N × H)
25. C₂²×C₅×M₁₆	D₃	semidirect
47. C₂×C₃×C₅×C₈	D₄	semidirect
54. C₂²×C₃×M₁₆	C₂×C₅	semidirect
55. C₂×#930	C₂×C₅	semidirect
56. C₂²×D₂₄	C₂×C₅	semidirect
57. #5135	C₂×C₅	direct (N × H)
58. C₂×#821	C₂×C₅	semidirect
59. C₂×#817	C₂×C₅	semidirect
66. C₂×C₅×M₁₆	C₂×D₃	semidirect
100. C₃×C₅×C₈	C₂×D₄	semidirect
105. C₂×C₃×M₁₆	C₂²×C₅	semidirect
109. #930	C₂²×C₅	semidirect
113. C₂×D₂₄	C₂²×C₅	semidirect
114. #821	C₂²×C₅	semidirect
115. #817	C₂²×C₅	semidirect
134. C₂×C₅×C₈	#67	semidirect
141. C₂²×M₁₆	C₅×D₃	semidirect
178. C₂×C₃×C₈	C₅×D₄	semidirect
209. C₅×C₈	C₂×#67	semidirect
216. C₂×M₁₆	C₂×C₅×D₃	semidirect
226. C₂×C₃×C₅	#469	semidirect
254. C₃×C₈	C₂×C₅×D₄	semidirect
288. C₂×C₈	C₅×#67	semidirect
294. C₃×C₅	C₂×#469	semidirect
312. C₂×C₅	#5135	direct (N × H)
339. C₈	C₂×C₅×#67	semidirect
341. C₂×C₃	C₅×#469	semidirect
345. C₅	C₂×#5135	direct (N × H)
361. C₃	C₂×C₅×#469	semidirect
364. C₂	C₅×#5135	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×C₅×M₁₆	2
C₂×C₅×#930	2
C₂²×C₅×D₂₄	2
C₅×#5135	2
C₂×C₅×#821	2
C₂×C₅×#817	2
C₂×C₅×#469	3
C₂×#5135	5

Subgroups — C2×C5×#5135 #14427984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5135 #14427984