Subgroups — C₂×C₅×#5157 #14427675

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#938	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#832	C₂	1	2	yes	maximal, complemented
5	C₅×#5157	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#818	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#466	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
9	C₂²×C₅×#67	—	2	2	no	—
10	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×D₈	—	2	4	no	—
12	C₂×C₃×C₅×D₈	C₂²	1	4	yes	complemented
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#217	—	2	2	no	—
15	C₅×#938	—	2	4	no	—
16	C₅×#938	C₂²	1	8	yes	complemented
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
18	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×D₃×C₈	—	2	4	no	—
20	C₂×C₅×D₃×C₈	C₂²	1	4	yes	complemented
21	C₅×#832	C₂²	1	8	yes	complemented
22	C₅×#818	C₂²	1	4	yes	complemented
23	C₂×#5157	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂²×C₅×D₈	D₃	1	1	yes	characteristic, complemented
25	C₂³×C₅×C₈	—	3	1	no	—
26	C₂×C₅×#121	—	3	2	no	—
27	C₅×#466	—	3	8	no	—
28	C₂×C₅×#107	—	3	1	no	—
29	C₂×C₅×#102	—	3	2	no	—
30	C₂⁴×C₃×C₅	—	2	2	no	—
31	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
32	C₂×C₃×C₅×D₄	—	2	4	no	—
33	C₂×C₃×C₅×D₄	—	2	2	no	—
34	C₂×C₃×C₅×D₄	—	2	4	no	—
35	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₅×#67	—	2	8	no	—
38	C₂×C₅×#67	—	4	8	no	—
39	C₂²×C₅×Dic₃	—	2	2	no	—
40	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
41	C₂×C₄×C₅×D₃	—	2	2	no	—
42	C₂×C₄×C₅×D₃	—	2	2	no	—
43	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
44	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
45	C₃×C₅×D₈	—	2	8	no	—
46	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
47	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
48	C₅×#217	—	2	8	no	—
49	C₅×C₄⋊Dic₃	—	2	2	no	—
50	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
51	C₂×C₅×C₃⋊C₈	—	2	2	no	—
52	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
53	C₅×D₃×C₈	—	2	8	no	—
54	C₂²×C₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
55	C₂×#938	C₂×C₅	1	2	yes	complemented
56	C₂²×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
57	C₂×#832	C₂×C₅	1	2	yes	complemented
58	#5157	C₂×C₅	1	8	yes	direct product factor
59	C₂×#818	C₂×C₅	1	1	yes	characteristic, complemented
60	C₂²×C₅×D₄	—	6	2	no	—
61	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
62	C₂³×C₄×C₅	—	3	1	no	—
63	C₂×C₅×D₈	—	2	4	no	—
64	C₂×C₅×D₈	C₂×D₃	1	4	yes	complemented
65	C₂²×C₅×C₈	—	3	1	no	—
66	C₂²×C₅×C₈	—	3	4	no	—
67	C₂²×C₅×C₈	—	6	4	no	—
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×#107	—	3	4	no	—
74	C₅×#102	—	3	8	no	—
75	C₂×#466	—	3	1	no	Sylow
76	C₂³×C₃×C₅	—	2	4	no	—
77	C₂³×C₃×C₅	—	4	4	no	—
78	C₂³×C₃×C₅	—	4	4	no	—
79	C₂³×C₃×C₅	—	4	4	no	—
80	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₅×D₃	—	2	2	no	—
82	C₂²×C₅×D₃	—	2	2	no	—
83	C₂²×C₅×D₃	D₈	1	4	yes	complemented
84	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
85	C₃×C₅×D₄	—	2	4	no	—
86	C₃×C₅×D₄	—	2	4	no	—
87	C₃×C₅×D₄	—	4	4	no	—
88	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	#41	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
92	C₅×#67	—	4	16	no	—
93	C₂×C₅×Dic₃	—	2	2	no	—
94	C₂×C₅×Dic₃	—	2	4	no	—
95	C₂×C₅×Dic₃	—	4	4	no	—
96	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
97	C₄×C₅×D₃	—	2	4	no	—
98	C₄×C₅×D₃	—	2	2	no	—
99	C₄×C₅×D₃	—	2	2	no	—
100	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
101	C₅×C₃⋊C₈	—	2	2	no	—
102	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
103	C₂²×#67	—	2	2	no	—
104	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
105	C₂×C₃×D₈	—	2	4	no	—
106	C₂×C₃×D₈	C₂²×C₅	1	4	yes	complemented
107	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
108	C₂×#217	—	2	2	no	—
109	#938	—	2	4	no	—
110	#938	C₂²×C₅	1	8	yes	complemented
111	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
112	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
113	C₂×D₃×C₈	—	2	4	no	—
114	C₂×D₃×C₈	C₂²×C₅	1	4	yes	complemented
115	#832	C₂²×C₅	1	8	yes	complemented
116	#818	C₂²×C₅	1	4	yes	complemented
117	C₂⁴×C₅	—	2	2	no	—
118	C₂⁴×C₅	—	3	1	no	—
119	C₂×C₅×D₄	—	2	2	no	—
120	C₂×C₅×D₄	—	2	4	no	—
121	C₂×C₅×D₄	—	2	4	no	—
122	C₂×C₅×D₄	—	6	8	no	—
123	C₂×C₅×D₄	—	12	8	no	—
124	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
125	C₂²×C₄×C₅	—	3	1	no	—
126	C₂²×C₄×C₅	—	3	2	no	—
127	C₂²×C₄×C₅	—	3	2	no	—
128	C₂²×C₄×C₅	—	6	2	no	—
129	C₂²×C₄×C₅	—	6	2	no	—
130	C₂²×C₄×C₅	—	6	2	no	—
131	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
132	C₅×D₈	—	2	8	no	—
133	C₂×C₅×C₈	—	3	2	no	—
134	C₂×C₅×C₈	—	6	2	no	—
135	C₂×C₅×C₈	—	6	8	no	—
136	C₂×C₅×C₈	#67	1	4	yes	complemented
137	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
138	C₅×C₄⋊C₄	—	3	4	no	—
139	C₅×C₄⋊C₄	—	6	2	no	—
140	C₅×C₂²⋊C₄	—	6	8	no	—
141	C₂²×D₈	C₅×D₃	1	1	yes	characteristic, complemented
142	C₂³×C₈	—	3	1	no	—
143	C₂×#121	—	3	2	no	—
144	#466	—	3	8	no	—
145	C₂×#107	—	3	1	no	—
146	C₂×#102	—	3	2	no	—
147	C₂²×C₃×C₅	—	4	4	no	—
148	C₂²×C₃×C₅	—	4	4	no	—
149	C₂²×C₃×C₅	—	4	4	no	—
150	C₂²×C₃×C₅	—	8	8	no	—
151	C₂²×C₃×C₅	#121	1	2	yes	—
152	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
153	C₂²×C₃×C₅	#135	1	2	yes	—
154	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₅×D₃	—	2	2	no	—
156	C₂×C₅×D₃	—	2	2	no	—
157	C₂×C₅×D₃	—	2	8	no	—
158	C₂×C₅×D₃	C₂×D₈	1	4	yes	complemented
159	C₃×C₄×C₅	#121	1	2	yes	—
160	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
161	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
162	C₅×Dic₃	—	2	2	no	—
163	C₅×Dic₃	—	4	4	no	—
164	C₂⁴×C₃	—	2	2	no	—
165	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
166	C₂×C₃×D₄	—	2	4	no	—
167	C₂×C₃×D₄	—	2	2	no	—
168	C₂×C₃×D₄	—	2	4	no	—
169	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
170	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
171	C₂×#67	—	2	8	no	—
172	C₂×#67	—	4	8	no	—
173	C₂²×Dic₃	—	2	2	no	—
174	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
175	C₂×C₄×D₃	—	2	2	no	—
176	C₂×C₄×D₃	—	2	2	no	—
177	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
178	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
179	C₃×D₈	—	2	8	no	—
180	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
181	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
182	#217	—	2	8	no	—
183	C₄⋊Dic₃	—	2	2	no	—
184	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
185	C₂×C₃⋊C₈	—	2	2	no	—
186	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
187	D₃×C₈	—	2	8	no	—
188	C₂³×C₅	—	2	4	no	—
189	C₂³×C₅	—	3	4	no	—
190	C₂³×C₅	—	3	2	no	—
191	C₂³×C₅	—	4	4	no	—
192	C₂³×C₅	—	4	4	no	—
193	C₂³×C₅	—	4	4	no	—
194	C₂³×C₅	—	6	2	no	—
195	C₂³×C₅	—	6	2	no	—
196	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
197	C₅×D₄	—	2	4	no	—
198	C₅×D₄	—	2	4	no	—
199	C₅×D₄	—	4	4	no	—
200	C₅×D₄	—	12	16	no	—
201	C₂×C₄×C₅	—	3	2	no	—
202	C₂×C₄×C₅	—	6	2	no	—
203	C₂×C₄×C₅	—	6	4	no	—
204	C₂×C₄×C₅	—	6	2	no	—
205	C₂×C₄×C₅	—	6	2	no	—
206	C₂×C₄×C₅	—	6	4	no	—
207	C₂×C₄×C₅	—	12	4	no	—
208	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
209	C₂×C₄×C₅	#237	1	2	yes	—
210	C₂×C₄×C₅	C₂×#67	1	2	yes	—
211	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
212	C₅×C₈	—	6	2	no	—
213	C₅×C₈	C₂×#67	1	4	yes	complemented
214	C₂²×D₄	—	6	2	no	—
215	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
216	C₂³×C₄	—	3	1	no	—
217	C₂×D₈	—	2	4	no	—
218	C₂×D₈	C₂×C₅×D₃	1	4	yes	complemented
219	C₂²×C₈	—	3	1	no	—
220	C₂²×C₈	—	3	4	no	—
221	C₂²×C₈	—	6	4	no	—
222	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
223	#121	—	3	8	no	—
224	#121	—	6	4	no	—
225	C₂×C₄⋊C₄	—	3	2	no	—
226	C₂×C₂²⋊C₄	—	6	2	no	—
227	#107	—	3	4	no	—
228	#102	—	3	8	no	—
229	C₂×C₃×C₅	—	8	4	no	—
230	C₂×C₃×C₅	#466	1	4	yes	complemented
231	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
232	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
233	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
234	C₅×D₃	—	2	4	no	—
235	C₂³×C₃	—	2	4	no	—
236	C₂³×C₃	—	4	4	no	—
237	C₂³×C₃	—	4	4	no	—
238	C₂³×C₃	—	4	4	no	—
239	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
240	C₂²×D₃	—	2	2	no	—
241	C₂²×D₃	—	2	2	no	—
242	C₂²×D₃	C₅×D₈	1	4	yes	complemented
243	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
244	C₃×D₄	—	2	4	no	—
245	C₃×D₄	—	2	4	no	—
246	C₃×D₄	—	4	4	no	—
247	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
249	C₂×C₃×C₄	C₅×#41	1	2	yes	—
250	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
251	#67	—	4	16	no	—
252	C₂×Dic₃	—	2	2	no	—
253	C₂×Dic₃	—	2	4	no	—
254	C₂×Dic₃	—	4	4	no	—
255	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
256	C₄×D₃	—	2	4	no	—
257	C₄×D₃	—	2	2	no	—
258	C₄×D₃	—	2	2	no	—
259	C₃×C₈	C₂×C₅×D₄	1	4	yes	complemented
260	C₃⋊C₈	—	2	2	no	—
261	C₂²×C₅	—	3	4	no	—
262	C₂²×C₅	—	4	4	no	—
263	C₂²×C₅	—	4	4	no	—
264	C₂²×C₅	—	4	4	no	—
265	C₂²×C₅	—	6	8	no	—
266	C₂²×C₅	—	6	2	no	—
267	C₂²×C₅	—	6	2	no	—
268	C₂²×C₅	—	8	8	no	—
269	C₂²×C₅	D₃×D₈	1	2	yes	—
270	C₂²×C₅	#912	1	2	yes	—
271	C₂²×C₅	#938	1	2	yes	—
272	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
273	C₄×C₅	—	6	2	no	—
274	C₄×C₅	—	12	4	no	—
275	C₄×C₅	#938	1	2	yes	—
276	C₄×C₅	C₂×#237	1	1	yes	characteristic
277	C₄×C₅	C₂²×#67	1	1	yes	characteristic
278	C₂⁴	—	2	2	no	—
279	C₂⁴	—	3	1	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	6	8	no	—
284	C₂×D₄	—	12	8	no	—
285	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
286	C₂²×C₄	—	3	1	no	—
287	C₂²×C₄	—	3	2	no	—
288	C₂²×C₄	—	3	2	no	—
289	C₂²×C₄	—	6	2	no	—
290	C₂²×C₄	—	6	2	no	—
291	C₂²×C₄	—	6	2	no	—
292	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
293	D₈	—	2	8	no	—
294	C₂×C₈	—	3	2	no	—
295	C₂×C₈	—	6	2	no	—
296	C₂×C₈	—	6	8	no	—
297	C₂×C₈	C₅×#67	1	4	yes	complemented
298	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
299	C₄⋊C₄	—	3	4	no	—
300	C₄⋊C₄	—	6	2	no	—
301	C₂²⋊C₄	—	6	8	no	—
302	C₃×C₅	C₂×#466	1	1	yes	characteristic, complemented, Hall
303	C₂²×C₃	—	4	4	no	—
304	C₂²×C₃	—	4	4	no	—
305	C₂²×C₃	—	4	4	no	—
306	C₂²×C₃	—	8	8	no	—
307	C₂²×C₃	C₅×#121	1	2	yes	—
308	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
309	C₂²×C₃	C₅×#135	1	2	yes	—
310	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
311	C₂×D₃	—	2	8	no	—
312	C₂×D₃	—	2	2	no	—
313	C₂×D₃	—	2	2	no	—
314	C₂×D₃	C₂×C₅×D₈	1	4	yes	complemented
315	C₃×C₄	C₅×#121	1	2	yes	—
316	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
317	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
318	Dic₃	—	2	2	no	—
319	Dic₃	—	4	4	no	—
320	C₂×C₅	—	6	4	no	—
321	C₂×C₅	—	8	4	no	—
322	C₂×C₅	#5157	1	4	yes	direct product factor
323	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
324	C₂×C₅	C₂×#912	1	1	yes	characteristic
325	C₂×C₅	C₂×#938	1	1	yes	characteristic
326	C₂³	—	2	4	no	—
327	C₂³	—	3	4	no	—
328	C₂³	—	3	2	no	—
329	C₂³	—	4	4	no	—
330	C₂³	—	4	4	no	—
331	C₂³	—	4	4	no	—
332	C₂³	—	6	2	no	—
333	C₂³	—	6	2	no	—
334	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
335	D₄	—	2	4	no	—
336	D₄	—	2	4	no	—
337	D₄	—	4	4	no	—
338	D₄	—	12	16	no	—
339	C₂×C₄	—	3	2	no	—
340	C₂×C₄	—	6	2	no	—
341	C₂×C₄	—	6	4	no	—
342	C₂×C₄	—	6	2	no	—
343	C₂×C₄	—	6	2	no	—
344	C₂×C₄	—	6	4	no	—
345	C₂×C₄	—	12	4	no	—
346	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
347	C₂×C₄	C₅×#237	1	2	yes	—
348	C₂×C₄	C₂×C₅×#67	1	2	yes	—
349	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
350	C₈	—	6	2	no	—
351	C₈	C₂×C₅×#67	1	4	yes	complemented
352	C₂×C₃	—	8	4	no	—
353	C₂×C₃	C₅×#466	1	4	yes	complemented
354	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
355	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
356	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
357	D₃	—	2	4	no	—
358	C₅	C₂×#5157	1	1	yes	characteristic, direct product factor, Sylow
359	C₂²	—	3	4	no	—
360	C₂²	—	4	4	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	4	4	no	—
363	C₂²	—	6	8	no	—
364	C₂²	—	6	2	no	—
365	C₂²	—	6	2	no	—
366	C₂²	—	8	8	no	—
367	C₂²	C₅×D₃×D₈	1	2	yes	—
368	C₂²	C₅×#912	1	2	yes	—
369	C₂²	C₅×#938	1	2	yes	—
370	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
371	C₄	—	6	2	no	—
372	C₄	—	12	4	no	—
373	C₄	C₅×#938	1	2	yes	—
374	C₄	C₂×C₅×#237	1	1	yes	characteristic
375	C₄	C₂²×C₅×#67	1	1	yes	characteristic
376	C₃	C₂×C₅×#466	1	1	yes	characteristic, complemented, Sylow
377	C₂	—	6	4	no	—
378	C₂	—	8	4	no	—
379	C₂	C₅×#5157	1	4	yes	direct product factor
380	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic
381	C₂	C₂×C₅×#912	1	1	yes	characteristic
382	C₂	C₂×C₅×#938	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×D₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂²×C₅×D₈	D₃
hypocenter	C₃	C₂×C₅×#466
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×D₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×D₈	C₂	semidirect
2. C₂×C₅×#938	C₂	semidirect
3. C₂²×C₅×D₃×C₈	C₂	semidirect
4. C₂×C₅×#832	C₂	semidirect
5. C₅×#5157	C₂	direct (N × H)
6. C₂×C₅×#818	C₂	semidirect
12. C₂×C₃×C₅×D₈	C₂²	semidirect
16. C₅×#938	C₂²	semidirect
20. C₂×C₅×D₃×C₈	C₂²	semidirect
21. C₅×#832	C₂²	semidirect
22. C₅×#818	C₂²	semidirect
23. C₂×#5157	C₅	direct (N × H)
24. C₂²×C₅×D₈	D₃	semidirect
46. C₂×C₃×C₅×C₈	D₄	semidirect
54. C₂²×C₃×D₈	C₂×C₅	semidirect
55. C₂×#938	C₂×C₅	semidirect
56. C₂²×D₃×C₈	C₂×C₅	semidirect
57. C₂×#832	C₂×C₅	semidirect
58. #5157	C₂×C₅	direct (N × H)
59. C₂×#818	C₂×C₅	semidirect
64. C₂×C₅×D₈	C₂×D₃	semidirect
83. C₂²×C₅×D₃	D₈	semidirect
100. C₃×C₅×C₈	C₂×D₄	semidirect
106. C₂×C₃×D₈	C₂²×C₅	semidirect
110. #938	C₂²×C₅	semidirect
114. C₂×D₃×C₈	C₂²×C₅	semidirect
115. #832	C₂²×C₅	semidirect
116. #818	C₂²×C₅	semidirect
136. C₂×C₅×C₈	#67	semidirect
141. C₂²×D₈	C₅×D₃	semidirect
158. C₂×C₅×D₃	C₂×D₈	semidirect
180. C₂×C₃×C₈	C₅×D₄	semidirect
213. C₅×C₈	C₂×#67	semidirect
218. C₂×D₈	C₂×C₅×D₃	semidirect
230. C₂×C₃×C₅	#466	semidirect
242. C₂²×D₃	C₅×D₈	semidirect
259. C₃×C₈	C₂×C₅×D₄	semidirect
297. C₂×C₈	C₅×#67	semidirect
302. C₃×C₅	C₂×#466	semidirect
314. C₂×D₃	C₂×C₅×D₈	semidirect
322. C₂×C₅	#5157	direct (N × H)
351. C₈	C₂×C₅×#67	semidirect
353. C₂×C₃	C₅×#466	semidirect
358. C₅	C₂×#5157	direct (N × H)
376. C₃	C₂×C₅×#466	semidirect
379. C₂	C₅×#5157	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×D₈	2
C₂×C₅×#938	2
C₂²×C₅×D₃×C₈	2
C₂×C₅×#832	2
C₅×#5157	2
C₂×C₅×#818	2
C₂×C₅×#466	3
C₂×#5157	5

Subgroups — C2×C5×#5157 #14427675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5157 #14427675