Subgroups — C₃×#10602923 #14296832

Order 1920.

1760 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	C₂³×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₃×#65536	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#3966	C₂	1	4	yes	maximal, complemented
4	#10602923	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂⁵×C₃×C₅	C₄	1	1	yes	characteristic, complemented
6	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
7	C₂²×C₃×C₅×D₄	—	2	4	no	—
8	C₂²×C₃×C₅×D₄	—	2	8	no	—
9	C₂²×C₃×C₅×D₄	C₄	1	2	yes	complemented
10	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
11	C₂³×C₃×C₄×C₅	C₄	1	1	yes	characteristic, complemented
12	C₂×C₃×C₂²⋊Dic₅	—	2	4	no	—
13	C₂×C₃×C₂²⋊Dic₅	C₂²	1	4	yes	complemented
14	C₃×#3966	—	2	8	no	—
15	C₃×#1781	—	5	1	no	maximal, Hall
16	C₂³×C₅×D₄	C₂×C₃	1	1	yes	characteristic
17	#65536	C₂×C₃	1	2	yes	complemented
18	C₂×#3966	C₂×C₃	1	4	yes	complemented
19	C₂⁴×C₃×C₅	—	2	2	no	—
20	C₂⁴×C₃×C₅	—	2	4	no	—
21	C₂⁴×C₃×C₅	—	2	4	no	—
22	C₂⁴×C₃×C₅	—	4	4	no	—
23	C₂⁴×C₃×C₅	—	4	4	no	—
24	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
25	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
26	C₂⁴×C₃×C₅	C₂×C₄	1	2	yes	—
27	C₂⁴×C₃×C₅	D₄	1	4	yes	—
28	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
29	C₂×C₃×C₅×D₄	—	2	32	no	—
30	C₂×C₃×C₅×D₄	—	2	4	no	—
31	C₂×C₃×C₅×D₄	—	2	4	no	—
32	C₂×C₃×C₅×D₄	—	2	4	no	—
33	C₂×C₃×C₅×D₄	—	2	4	no	—
34	C₂×C₃×C₅×D₄	—	2	4	no	—
35	C₂×C₃×C₅×D₄	D₄	1	8	yes	—
36	C₂²×C₃×C₄×C₅	—	2	2	no	—
37	C₂²×C₃×C₄×C₅	—	2	4	no	—
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
39	C₂²×C₃×Dic₅	—	2	4	no	—
40	C₃×C₂²⋊Dic₅	—	2	8	no	—
41	C₃×C₂²⋊Dic₅	—	4	8	no	—
42	C₂³×C₃×D₄	D₅	1	1	yes	characteristic
43	C₂×C₃×#99	—	5	4	no	—
44	C₃×#379	—	5	2	no	—
45	C₂⁵×C₅	C₃×C₄	1	1	yes	characteristic, complemented
46	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
47	C₂²×C₅×D₄	—	2	4	no	—
48	C₂²×C₅×D₄	—	2	8	no	—
49	C₂²×C₅×D₄	C₃×C₄	1	2	yes	complemented
50	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
51	C₂³×C₄×C₅	C₃×C₄	1	1	yes	characteristic, complemented
52	C₂×C₂²⋊Dic₅	—	2	4	no	—
53	C₂×C₂²⋊Dic₅	C₂²×C₃	1	4	yes	complemented
54	#3966	—	2	8	no	—
55	#1781	—	5	1	no	Sylow
56	C₂³×C₃×C₅	—	2	4	no	—
57	C₂³×C₃×C₅	—	2	2	no	—
58	C₂³×C₃×C₅	—	2	8	no	—
59	C₂³×C₃×C₅	—	2	8	no	—
60	C₂³×C₃×C₅	—	2	2	no	—
61	C₂³×C₃×C₅	—	2	2	no	—
62	C₂³×C₃×C₅	—	2	2	no	—
63	C₂³×C₃×C₅	—	2	8	no	—
64	C₂³×C₃×C₅	—	4	2	no	—
65	C₂³×C₃×C₅	—	4	4	no	—
66	C₂³×C₃×C₅	—	4	2	no	—
67	C₂³×C₃×C₅	—	4	16	no	—
68	C₂³×C₃×C₅	—	4	16	no	—
69	C₂³×C₃×C₅	—	4	4	no	—
70	C₂³×C₃×C₅	—	4	4	no	—
71	C₂³×C₃×C₅	—	4	4	no	—
72	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
73	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
74	C₂³×C₃×C₅	C₂²⋊C₄	1	4	yes	complemented
75	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
76	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
77	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
78	C₃×C₅×D₄	—	2	16	no	—
79	C₃×C₅×D₄	—	2	16	no	—
80	C₂×C₃×C₄×C₅	—	2	8	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	2	2	no	—
83	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	complemented
84	C₂×C₃×Dic₅	—	4	8	no	—
85	C₂×C₃×Dic₅	—	4	4	no	—
86	C₂⁵×C₃	Dic₅	1	1	yes	characteristic, complemented
87	C₂⁵×C₃	C₂×D₅	1	1	yes	characteristic
88	C₂²×C₃×D₄	—	2	4	no	—
89	C₂²×C₃×D₄	—	2	8	no	—
90	C₂²×C₃×D₄	Dic₅	1	2	yes	complemented
91	C₂²×C₃×D₄	C₂×D₅	1	2	yes	—
92	C₂³×C₃×C₄	Dic₅	1	1	yes	characteristic, complemented
93	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
94	C₂×C₃×C₂²⋊C₄	—	10	4	no	—
95	C₃×#99	—	10	8	no	—
96	C₂⁴×C₅	—	2	2	no	—
97	C₂⁴×C₅	—	2	4	no	—
98	C₂⁴×C₅	—	2	4	no	—
99	C₂⁴×C₅	—	4	4	no	—
100	C₂⁴×C₅	—	4	4	no	—
101	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
102	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
103	C₂⁴×C₅	C₂×C₃×C₄	1	2	yes	—
104	C₂⁴×C₅	C₃×D₄	1	4	yes	—
105	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
106	C₂×C₅×D₄	—	2	32	no	—
107	C₂×C₅×D₄	—	2	4	no	—
108	C₂×C₅×D₄	—	2	4	no	—
109	C₂×C₅×D₄	—	2	4	no	—
110	C₂×C₅×D₄	—	2	4	no	—
111	C₂×C₅×D₄	—	2	4	no	—
112	C₂×C₅×D₄	C₃×D₄	1	8	yes	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	2	4	no	—
115	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
116	C₂²×Dic₅	—	2	4	no	—
117	C₂²⋊Dic₅	—	2	8	no	—
118	C₂²⋊Dic₅	—	4	8	no	—
119	C₂³×D₄	C₃×D₅	1	1	yes	characteristic
120	C₂×#99	—	5	4	no	—
121	#379	—	5	2	no	—
122	C₂²×C₃×C₅	—	2	8	no	—
123	C₂²×C₃×C₅	—	2	2	no	—
124	C₂²×C₃×C₅	—	2	4	no	—
125	C₂²×C₃×C₅	—	2	2	no	—
126	C₂²×C₃×C₅	—	2	2	no	—
127	C₂²×C₃×C₅	—	2	2	no	—
128	C₂²×C₃×C₅	—	2	4	no	—
129	C₂²×C₃×C₅	—	2	4	no	—
130	C₂²×C₃×C₅	—	4	4	no	—
131	C₂²×C₃×C₅	—	4	16	no	—
132	C₂²×C₃×C₅	—	4	4	no	—
133	C₂²×C₃×C₅	—	4	16	no	—
134	C₂²×C₃×C₅	—	4	4	no	—
135	C₂²×C₃×C₅	—	4	4	no	—
136	C₂²×C₃×C₅	—	4	4	no	—
137	C₂²×C₃×C₅	#99	1	4	yes	complemented
138	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
139	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂²×C₃×C₅	#120	1	4	yes	—
141	C₃×C₄×C₅	—	2	4	no	—
142	C₃×Dic₅	—	8	4	no	—
143	C₂⁴×C₃	—	2	2	no	—
144	C₂⁴×C₃	—	2	4	no	—
145	C₂⁴×C₃	—	2	4	no	—
146	C₂⁴×C₃	—	4	4	no	—
147	C₂⁴×C₃	—	4	4	no	—
148	C₂⁴×C₃	C₂×Dic₅	1	1	yes	characteristic
149	C₂⁴×C₃	C₂×Dic₅	1	1	yes	characteristic
150	C₂⁴×C₃	C₂×Dic₅	1	2	yes	—
151	C₂⁴×C₃	C₂²⋊D₅	1	4	yes	—
152	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
153	C₂×C₃×D₄	—	2	32	no	—
154	C₂×C₃×D₄	—	2	4	no	—
155	C₂×C₃×D₄	—	2	4	no	—
156	C₂×C₃×D₄	—	2	4	no	—
157	C₂×C₃×D₄	—	2	4	no	—
158	C₂×C₃×D₄	—	2	4	no	—
159	C₂×C₃×D₄	C₂²⋊D₅	1	8	yes	—
160	C₂²×C₃×C₄	—	2	2	no	—
161	C₂²×C₃×C₄	—	2	4	no	—
162	C₂²×C₃×C₄	—	10	4	no	—
163	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
164	C₃×C₂²⋊C₄	—	10	8	no	—
165	C₃×C₂²⋊C₄	—	20	8	no	—
166	C₂³×C₅	—	2	4	no	—
167	C₂³×C₅	—	2	2	no	—
168	C₂³×C₅	—	2	8	no	—
169	C₂³×C₅	—	2	8	no	—
170	C₂³×C₅	—	2	2	no	—
171	C₂³×C₅	—	2	2	no	—
172	C₂³×C₅	—	2	2	no	—
173	C₂³×C₅	—	2	8	no	—
174	C₂³×C₅	—	4	2	no	—
175	C₂³×C₅	—	4	4	no	—
176	C₂³×C₅	—	4	2	no	—
177	C₂³×C₅	—	4	4	no	—
178	C₂³×C₅	—	4	16	no	—
179	C₂³×C₅	—	4	16	no	—
180	C₂³×C₅	—	4	4	no	—
181	C₂³×C₅	—	4	4	no	—
182	C₂³×C₅	C₃×C₂²⋊C₄	1	2	yes	—
183	C₂³×C₅	C₃×C₂²⋊C₄	1	2	yes	—
184	C₂³×C₅	C₃×C₂²⋊C₄	1	4	yes	complemented
185	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
186	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
187	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
188	C₅×D₄	—	2	16	no	—
189	C₅×D₄	—	2	16	no	—
190	C₂×C₄×C₅	—	2	8	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	4	yes	complemented
194	C₂×Dic₅	—	4	8	no	—
195	C₂×Dic₅	—	4	4	no	—
196	C₂⁵	C₃×Dic₅	1	1	yes	characteristic, complemented
197	C₂⁵	C₂×C₃×D₅	1	1	yes	characteristic
198	C₂²×D₄	—	2	4	no	—
199	C₂²×D₄	—	2	8	no	—
200	C₂²×D₄	C₃×Dic₅	1	2	yes	complemented
201	C₂²×D₄	C₂×C₃×D₅	1	2	yes	—
202	C₂³×C₄	C₃×Dic₅	1	1	yes	characteristic, complemented
203	C₂×C₂²⋊C₄	—	5	4	no	—
204	C₂×C₂²⋊C₄	—	10	4	no	—
205	#99	—	10	8	no	—
206	C₂×C₃×C₅	—	2	4	no	—
207	C₂×C₃×C₅	—	2	4	no	—
208	C₂×C₃×C₅	—	2	2	no	—
209	C₂×C₃×C₅	—	4	2	no	—
210	C₂×C₃×C₅	—	4	4	no	—
211	C₂×C₃×C₅	#379	1	1	yes	characteristic
212	C₂×C₃×C₅	C₂×#99	1	2	yes	—
213	C₂³×C₃	—	2	2	no	—
214	C₂³×C₃	—	2	4	no	—
215	C₂³×C₃	—	2	8	no	—
216	C₂³×C₃	—	2	2	no	—
217	C₂³×C₃	—	2	2	no	—
218	C₂³×C₃	—	2	2	no	—
219	C₂³×C₃	—	2	8	no	—
220	C₂³×C₃	—	2	8	no	—
221	C₂³×C₃	—	4	2	no	—
222	C₂³×C₃	—	4	4	no	—
223	C₂³×C₃	—	4	2	no	—
224	C₂³×C₃	—	4	4	no	—
225	C₂³×C₃	—	4	16	no	—
226	C₂³×C₃	—	4	16	no	—
227	C₂³×C₃	—	4	4	no	—
228	C₂³×C₃	—	4	4	no	—
229	C₂³×C₃	C₂²⋊Dic₅	1	2	yes	—
230	C₂³×C₃	C₂²⋊Dic₅	1	2	yes	—
231	C₂³×C₃	C₂²⋊Dic₅	1	4	yes	complemented
232	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
233	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
234	C₂³×C₃	C₂×C₂²⋊D₅	1	4	yes	—
235	C₃×D₄	—	2	16	no	—
236	C₃×D₄	—	2	16	no	—
237	C₂×C₃×C₄	—	2	8	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	20	8	no	—
241	C₂×C₃×C₄	—	20	4	no	—
242	C₂×C₃×C₄	C₂²⋊Dic₅	1	4	yes	complemented
243	C₂²×C₅	—	2	8	no	—
244	C₂²×C₅	—	2	2	no	—
245	C₂²×C₅	—	2	4	no	—
246	C₂²×C₅	—	2	2	no	—
247	C₂²×C₅	—	2	2	no	—
248	C₂²×C₅	—	2	2	no	—
249	C₂²×C₅	—	2	4	no	—
250	C₂²×C₅	—	2	4	no	—
251	C₂²×C₅	—	4	4	no	—
252	C₂²×C₅	—	4	16	no	—
253	C₂²×C₅	—	4	4	no	—
254	C₂²×C₅	—	4	16	no	—
255	C₂²×C₅	—	4	4	no	—
256	C₂²×C₅	—	4	4	no	—
257	C₂²×C₅	—	4	4	no	—
258	C₂²×C₅	C₃×#99	1	4	yes	complemented
259	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
260	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×C₅	C₃×#120	1	4	yes	—
262	C₄×C₅	—	2	4	no	—
263	Dic₅	—	8	4	no	—
264	C₂⁴	—	2	2	no	—
265	C₂⁴	—	2	4	no	—
266	C₂⁴	—	2	4	no	—
267	C₂⁴	—	4	4	no	—
268	C₂⁴	—	4	4	no	—
269	C₂⁴	C₂×C₃×Dic₅	1	1	yes	characteristic
270	C₂⁴	C₂×C₃×Dic₅	1	1	yes	characteristic
271	C₂⁴	C₂×C₃×Dic₅	1	2	yes	—
272	C₂⁴	C₃×C₂²⋊D₅	1	4	yes	—
273	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
274	C₂×D₄	—	2	32	no	—
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	—	2	4	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	C₃×C₂²⋊D₅	1	8	yes	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	10	4	no	—
284	C₂²×C₄	C₂×C₃×Dic₅	1	2	yes	—
285	C₂²⋊C₄	—	10	8	no	—
286	C₂²⋊C₄	—	20	8	no	—
287	C₃×C₅	#1781	1	1	yes	characteristic, complemented, Hall
288	C₂²×C₃	—	2	8	no	—
289	C₂²×C₃	—	2	2	no	—
290	C₂²×C₃	—	2	4	no	—
291	C₂²×C₃	—	2	2	no	—
292	C₂²×C₃	—	2	2	no	—
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	—	2	4	no	—
295	C₂²×C₃	—	2	4	no	—
296	C₂²×C₃	—	4	4	no	—
297	C₂²×C₃	—	4	16	no	—
298	C₂²×C₃	—	4	4	no	—
299	C₂²×C₃	—	4	4	no	—
300	C₂²×C₃	—	4	4	no	—
301	C₂²×C₃	—	4	16	no	—
302	C₂²×C₃	—	4	4	no	—
303	C₂²×C₃	#3966	1	4	yes	complemented
304	C₂²×C₃	C₂×C₂²⋊Dic₅	1	2	yes	—
305	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
306	C₂²×C₃	#4099	1	4	yes	—
307	C₃×C₄	—	2	4	no	—
308	C₃×C₄	—	40	4	no	—
309	C₂×C₅	—	2	4	no	—
310	C₂×C₅	—	2	4	no	—
311	C₂×C₅	—	2	2	no	—
312	C₂×C₅	—	4	2	no	—
313	C₂×C₅	—	4	4	no	—
314	C₂×C₅	C₃×#379	1	1	yes	characteristic
315	C₂×C₅	C₂×C₃×#99	1	2	yes	—
316	C₂³	—	2	2	no	—
317	C₂³	—	2	4	no	—
318	C₂³	—	2	8	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	8	no	—
323	C₂³	—	2	8	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	4	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	4	no	—
328	C₂³	—	4	16	no	—
329	C₂³	—	4	16	no	—
330	C₂³	—	4	4	no	—
331	C₂³	—	4	4	no	—
332	C₂³	C₃×C₂²⋊Dic₅	1	2	yes	—
333	C₂³	C₃×C₂²⋊Dic₅	1	2	yes	—
334	C₂³	C₃×C₂²⋊Dic₅	1	4	yes	complemented
335	C₂³	C₂²×C₃×Dic₅	1	1	yes	characteristic
336	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
337	C₂³	C₂×C₃×C₂²⋊D₅	1	4	yes	—
338	D₄	—	2	16	no	—
339	D₄	—	2	16	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	20	8	no	—
344	C₂×C₄	—	20	4	no	—
345	C₂×C₄	C₃×C₂²⋊Dic₅	1	4	yes	complemented
346	C₂×C₃	—	2	4	no	—
347	C₂×C₃	—	2	2	no	—
348	C₂×C₃	—	2	4	no	—
349	C₂×C₃	—	4	2	no	—
350	C₂×C₃	—	4	4	no	—
351	C₂×C₃	C₂×#3966	1	2	yes	—
352	C₂×C₃	#65536	1	1	yes	characteristic
353	C₅	C₃×#1781	1	1	yes	characteristic, complemented, Sylow
354	C₂²	—	2	8	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	4	no	—
361	C₂²	—	2	4	no	—
362	C₂²	—	4	4	no	—
363	C₂²	—	4	16	no	—
364	C₂²	—	4	4	no	—
365	C₂²	—	4	4	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	16	no	—
368	C₂²	—	4	4	no	—
369	C₂²	C₃×#3966	1	4	yes	complemented
370	C₂²	C₂×C₃×C₂²⋊Dic₅	1	2	yes	—
371	C₂²	C₂×C₃×C₂²⋊Dic₅	1	1	yes	characteristic
372	C₂²	C₃×#4099	1	4	yes	—
373	C₄	—	2	4	no	—
374	C₄	—	40	4	no	—
375	C₃	#10602923	1	1	yes	characteristic, direct product factor, Sylow
376	C₂	—	2	4	no	—
377	C₂	—	2	2	no	—
378	C₂	—	2	4	no	—
379	C₂	—	4	2	no	—
380	C₂	—	4	4	no	—
381	C₂	C₂×C₃×#3966	1	2	yes	—
382	C₂	C₃×#65536	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×C₂²⋊Dic₅
commutator	C₂³×C₅	C₂²×C₃×C₄
Frattini	C₂⁴	C₂²×C₃×D₅
Fitting, prime radical	C₂³×C₃×C₅×D₄	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
cosocle	C₂⁴×C₅	C₂³×C₃
hypercenter	C₂³×C₃×D₄	D₅
hypocenter	C₅	C₃×#1781
LCS	G ▷ C₂³×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂⁵×C₃ ◁ C₂³×C₃×D₄

Complements

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

N	H ≅ G/N	type
2. C₃×#65536	C₂	semidirect
3. C₂×C₃×#3966	C₂	semidirect
4. #10602923	C₃	direct (N × H)
5. C₂⁵×C₃×C₅	C₄	semidirect
9. C₂²×C₃×C₅×D₄	C₄	semidirect
11. C₂³×C₃×C₄×C₅	C₄	semidirect
13. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
17. #65536	C₂×C₃	semidirect
18. C₂×#3966	C₂×C₃	semidirect
45. C₂⁵×C₅	C₃×C₄	semidirect
49. C₂²×C₅×D₄	C₃×C₄	semidirect
51. C₂³×C₄×C₅	C₃×C₄	semidirect
53. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
74. C₂³×C₃×C₅	C₂²⋊C₄	semidirect
83. C₂×C₃×C₄×C₅	C₂²⋊C₄	semidirect
86. C₂⁵×C₃	Dic₅	semidirect
90. C₂²×C₃×D₄	Dic₅	semidirect
92. C₂³×C₃×C₄	Dic₅	semidirect
137. C₂²×C₃×C₅	#99	semidirect
184. C₂³×C₅	C₃×C₂²⋊C₄	semidirect
193. C₂×C₄×C₅	C₃×C₂²⋊C₄	semidirect
196. C₂⁵	C₃×Dic₅	semidirect
200. C₂²×D₄	C₃×Dic₅	semidirect
202. C₂³×C₄	C₃×Dic₅	semidirect
231. C₂³×C₃	C₂²⋊Dic₅	semidirect
242. C₂×C₃×C₄	C₂²⋊Dic₅	semidirect
258. C₂²×C₅	C₃×#99	semidirect
287. C₃×C₅	#1781	semidirect
303. C₂²×C₃	#3966	semidirect
334. C₂³	C₃×C₂²⋊Dic₅	semidirect
345. C₂×C₄	C₃×C₂²⋊Dic₅	semidirect
353. C₅	C₃×#1781	semidirect
369. C₂²	C₃×#3966	semidirect
375. C₃	#10602923	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅×D₄	2
C₃×#65536	2
C₂×C₃×#3966	2
#10602923	3
C₃×#1781	5

Subgroups — C3×#10602923 #14296832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10602923 #14296832