Subgroups — C₂×C₃×#65172 #14427688

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×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4041	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3941	C₂	1	2	yes	maximal, complemented
6	C₃×#65172	C₂	1	8	yes	maximal, direct product factor
7	C₂×#65172	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×D₂₀	—	2	2	no	—
9	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
10	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×#685	—	2	2	no	—
14	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₄₀	—	2	4	no	—
16	C₂×C₃×D₄₀	C₂²	1	4	yes	complemented
17	C₂×C₃×C₈×D₅	—	2	4	no	—
18	C₂×C₃×C₈×D₅	C₂²	1	4	yes	complemented
19	C₃×#4041	—	2	4	no	—
20	C₃×#4041	C₂²	1	8	yes	complemented
21	C₃×C₅×#107	C₂²	1	4	yes	complemented
22	C₃×#3941	C₂²	1	8	yes	complemented
23	C₂×C₃×#466	—	5	1	no	maximal, Hall
24	C₂²×D₄₀	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂²×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×#4041	C₂×C₃	1	2	yes	complemented
27	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×#3941	C₂×C₃	1	2	yes	complemented
29	#65172	C₂×C₃	1	8	yes	direct product factor
30	C₂³×C₃×D₅	—	2	2	no	—
31	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
35	C₂×C₃×D₂₀	—	2	4	no	—
36	C₂×C₃×D₂₀	—	2	4	no	—
37	C₂×C₃×D₂₀	—	2	8	no	—
38	C₂×C₃×D₂₀	—	2	2	no	—
39	C₂×C₃×D₂₀	—	4	8	no	—
40	C₂×C₃×D₂₀	C₂³	1	4	yes	—
41	C₂×C₃×C₄×D₅	—	2	2	no	—
42	C₂×C₃×C₄×D₅	—	2	2	no	—
43	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
44	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
45	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
46	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
47	C₃×C₅×C₄⋊C₄	—	2	2	no	—
48	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
49	C₃×#685	—	2	8	no	—
50	C₂×C₃×#168	—	2	2	no	—
51	C₂×C₃×#168	C₂³	1	2	yes	—
52	C₃×D₄₀	—	2	8	no	—
53	C₃×C₈×D₅	—	2	8	no	—
54	C₂²×C₃×D₈	—	5	1	no	—
55	C₂³×C₃×C₈	—	5	1	no	—
56	C₂×C₃×#121	—	5	2	no	—
57	C₃×#466	—	5	8	no	—
58	C₂×C₃×#107	D₅	1	1	yes	characteristic, complemented
59	C₂×C₃×#102	—	5	2	no	—
60	C₂²×D₂₀	—	2	2	no	—
61	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
62	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
63	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
65	C₂×#685	—	2	2	no	—
66	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
67	C₂×D₄₀	—	2	4	no	—
68	C₂×D₄₀	C₂²×C₃	1	4	yes	complemented
69	C₂×C₈×D₅	—	2	4	no	—
70	C₂×C₈×D₅	C₂²×C₃	1	4	yes	complemented
71	#4041	—	2	4	no	—
72	#4041	C₂²×C₃	1	8	yes	complemented
73	C₅×#107	C₂²×C₃	1	4	yes	complemented
74	#3941	C₂²×C₃	1	8	yes	complemented
75	C₂×#466	—	5	1	no	Sylow
76	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₃×D₅	—	2	2	no	—
78	C₂²×C₃×D₅	—	2	2	no	—
79	C₂²×C₃×D₅	—	2	4	no	—
80	C₂²×C₃×D₅	—	4	4	no	—
81	C₂²×C₃×D₅	—	4	4	no	—
82	C₂²×C₃×D₅	—	4	4	no	—
83	C₂²×C₃×D₅	D₈	1	4	yes	complemented
84	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
85	C₂×C₃×C₄×C₅	—	2	4	no	—
86	C₂×C₃×C₄×C₅	—	4	4	no	—
87	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	#41	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
91	C₂×C₃×Dic₅	—	2	2	no	—
92	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
93	C₃×D₂₀	—	2	4	no	—
94	C₃×D₂₀	—	2	4	no	—
95	C₃×D₂₀	—	4	16	no	—
96	C₃×D₂₀	—	4	4	no	—
97	C₃×C₄×D₅	—	2	4	no	—
98	C₃×C₄×D₅	—	2	2	no	—
99	C₃×C₄×D₅	—	2	2	no	—
100	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
101	C₃×#168	—	2	2	no	—
102	C₂²×C₃×D₄	—	5	2	no	—
103	C₂²×C₃×D₄	—	10	2	no	—
104	C₂³×C₃×C₄	—	5	1	no	—
105	C₂×C₃×D₈	—	5	4	no	—
106	C₂×C₃×D₈	—	10	4	no	—
107	C₂²×C₃×C₈	—	5	1	no	—
108	C₂²×C₃×C₈	—	5	4	no	—
109	C₂²×C₃×C₈	—	10	4	no	—
110	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
111	C₃×#121	—	5	8	no	—
112	C₃×#121	—	10	4	no	—
113	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
114	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
115	C₃×#107	C₂×D₅	1	4	yes	complemented
116	C₃×#102	—	5	8	no	—
117	C₂³×D₅	—	2	2	no	—
118	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
121	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
122	C₂×D₂₀	—	2	4	no	—
123	C₂×D₂₀	—	2	4	no	—
124	C₂×D₂₀	—	2	8	no	—
125	C₂×D₂₀	—	2	2	no	—
126	C₂×D₂₀	—	4	8	no	—
127	C₂×D₂₀	C₂³×C₃	1	4	yes	—
128	C₂×C₄×D₅	—	2	2	no	—
129	C₂×C₄×D₅	—	2	2	no	—
130	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
131	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
132	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
133	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
134	C₅×C₄⋊C₄	—	2	2	no	—
135	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
136	#685	—	2	8	no	—
137	C₂×#168	—	2	2	no	—
138	C₂×#168	C₂³×C₃	1	2	yes	—
139	D₄₀	—	2	8	no	—
140	C₈×D₅	—	2	8	no	—
141	C₂²×D₈	—	5	1	no	—
142	C₂³×C₈	—	5	1	no	—
143	C₂×#121	—	5	2	no	—
144	#466	—	5	8	no	—
145	C₂×#107	C₃×D₅	1	1	yes	characteristic, complemented
146	C₂×#102	—	5	2	no	—
147	C₂²×C₃×C₅	#121	1	2	yes	—
148	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
149	C₂²×C₃×C₅	#135	1	2	yes	—
150	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₃×D₅	—	2	2	no	—
152	C₂×C₃×D₅	—	2	2	no	—
153	C₂×C₃×D₅	—	2	8	no	—
154	C₂×C₃×D₅	—	4	4	no	—
155	C₂×C₃×D₅	—	4	4	no	—
156	C₂×C₃×D₅	—	4	4	no	—
157	C₂×C₃×D₅	—	8	8	no	—
158	C₂×C₃×D₅	C₂×D₈	1	4	yes	complemented
159	C₃×C₄×C₅	—	4	4	no	—
160	C₃×C₄×C₅	#121	1	2	yes	—
161	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
162	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
163	C₃×Dic₅	—	2	2	no	—
164	C₂⁴×C₃	—	5	1	no	—
165	C₂⁴×C₃	—	10	2	no	—
166	C₂×C₃×D₄	—	5	4	no	—
167	C₂×C₃×D₄	—	10	8	no	—
168	C₂×C₃×D₄	—	10	4	no	—
169	C₂×C₃×D₄	—	10	2	no	—
170	C₂×C₃×D₄	—	10	4	no	—
171	C₂×C₃×D₄	—	20	8	no	—
172	C₂²×C₃×C₄	—	2	2	no	—
173	C₂²×C₃×C₄	—	5	1	no	—
174	C₂²×C₃×C₄	—	5	2	no	—
175	C₂²×C₃×C₄	—	5	2	no	—
176	C₂²×C₃×C₄	—	10	2	no	—
177	C₂²×C₃×C₄	—	10	2	no	—
178	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
179	C₃×D₈	—	10	8	no	—
180	C₂×C₃×C₈	—	5	2	no	—
181	C₂×C₃×C₈	—	10	2	no	—
182	C₂×C₃×C₈	—	10	8	no	—
183	C₂×C₃×C₈	D₂₀	1	4	yes	complemented
184	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
185	C₃×C₄⋊C₄	—	2	2	no	—
186	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
187	C₃×C₂²⋊C₄	—	10	8	no	—
188	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
189	C₂²×D₅	—	2	2	no	—
190	C₂²×D₅	—	2	2	no	—
191	C₂²×D₅	—	2	4	no	—
192	C₂²×D₅	—	4	4	no	—
193	C₂²×D₅	—	4	4	no	—
194	C₂²×D₅	—	4	4	no	—
195	C₂²×D₅	C₃×D₈	1	4	yes	complemented
196	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
197	C₂×C₄×C₅	—	2	4	no	—
198	C₂×C₄×C₅	—	4	4	no	—
199	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
200	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
201	C₂×C₄×C₅	C₃×#41	1	2	yes	—
202	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
203	C₂×Dic₅	—	2	2	no	—
204	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
205	D₂₀	—	2	4	no	—
206	D₂₀	—	2	4	no	—
207	D₂₀	—	4	16	no	—
208	D₂₀	—	4	4	no	—
209	C₄×D₅	—	2	4	no	—
210	C₄×D₅	—	2	2	no	—
211	C₄×D₅	—	2	2	no	—
212	C₅×C₈	C₂×C₃×D₄	1	4	yes	complemented
213	#168	—	2	2	no	—
214	C₂²×D₄	—	5	2	no	—
215	C₂²×D₄	—	10	2	no	—
216	C₂³×C₄	—	5	1	no	—
217	C₂×D₈	—	5	4	no	—
218	C₂×D₈	—	10	4	no	—
219	C₂²×C₈	—	5	1	no	—
220	C₂²×C₈	—	5	4	no	—
221	C₂²×C₈	—	10	4	no	—
222	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
223	#121	—	5	8	no	—
224	#121	—	10	4	no	—
225	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
226	C₂×C₂²⋊C₄	—	10	2	no	—
227	#107	C₂×C₃×D₅	1	4	yes	complemented
228	#102	—	5	8	no	—
229	C₂×C₃×C₅	#466	1	4	yes	complemented
230	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
231	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
232	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
233	C₃×D₅	—	2	4	no	—
234	C₃×D₅	—	8	4	no	—
235	C₂³×C₃	—	5	2	no	—
236	C₂³×C₃	—	5	4	no	—
237	C₂³×C₃	—	10	2	no	—
238	C₂³×C₃	—	10	2	no	—
239	C₂³×C₃	—	10	4	no	—
240	C₂³×C₃	—	20	4	no	—
241	C₂³×C₃	—	20	4	no	—
242	C₂³×C₃	—	20	4	no	—
243	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
244	C₃×D₄	—	10	4	no	—
245	C₃×D₄	—	10	4	no	—
246	C₃×D₄	—	20	16	no	—
247	C₃×D₄	—	20	4	no	—
248	C₂×C₃×C₄	—	2	4	no	—
249	C₂×C₃×C₄	—	4	4	no	—
250	C₂×C₃×C₄	—	5	2	no	—
251	C₂×C₃×C₄	—	10	2	no	—
252	C₂×C₃×C₄	—	10	2	no	—
253	C₂×C₃×C₄	—	10	2	no	—
254	C₂×C₃×C₄	—	10	4	no	—
255	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
256	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
257	C₂×C₃×C₄	#713	1	2	yes	—
258	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
259	C₃×C₈	—	10	2	no	—
260	C₃×C₈	C₂×D₂₀	1	4	yes	complemented
261	C₂²×C₅	C₃×#121	1	2	yes	—
262	C₂²×C₅	C₂×C₃×D₈	1	2	yes	—
263	C₂²×C₅	C₃×#135	1	2	yes	—
264	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
265	C₂×D₅	—	2	2	no	—
266	C₂×D₅	—	2	8	no	—
267	C₂×D₅	—	2	2	no	—
268	C₂×D₅	—	4	4	no	—
269	C₂×D₅	—	4	4	no	—
270	C₂×D₅	—	4	4	no	—
271	C₂×D₅	—	8	8	no	—
272	C₂×D₅	C₂×C₃×D₈	1	4	yes	complemented
273	C₄×C₅	—	4	4	no	—
274	C₄×C₅	C₃×#121	1	2	yes	—
275	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
276	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
277	Dic₅	—	2	2	no	—
278	C₂⁴	—	5	1	no	—
279	C₂⁴	—	10	2	no	—
280	C₂×D₄	—	5	4	no	—
281	C₂×D₄	—	10	8	no	—
282	C₂×D₄	—	10	4	no	—
283	C₂×D₄	—	10	2	no	—
284	C₂×D₄	—	10	4	no	—
285	C₂×D₄	—	20	8	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	5	1	no	—
288	C₂²×C₄	—	5	2	no	—
289	C₂²×C₄	—	5	2	no	—
290	C₂²×C₄	—	10	2	no	—
291	C₂²×C₄	—	10	2	no	—
292	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
293	D₈	—	10	8	no	—
294	C₂×C₈	—	5	2	no	—
295	C₂×C₈	—	10	2	no	—
296	C₂×C₈	—	10	8	no	—
297	C₂×C₈	C₃×D₂₀	1	4	yes	complemented
298	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
301	C₂²⋊C₄	—	10	8	no	—
302	C₃×C₅	C₂×#466	1	1	yes	characteristic, complemented, Hall
303	C₂²×C₃	—	5	4	no	—
304	C₂²×C₃	—	10	2	no	—
305	C₂²×C₃	—	10	2	no	—
306	C₂²×C₃	—	10	8	no	—
307	C₂²×C₃	—	20	4	no	—
308	C₂²×C₃	—	20	4	no	—
309	C₂²×C₃	—	20	4	no	—
310	C₂²×C₃	—	40	8	no	—
311	C₂²×C₃	#4041	1	2	yes	—
312	C₂²×C₃	D₅×D₈	1	2	yes	—
313	C₂²×C₃	#4065	1	2	yes	—
314	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
315	C₃×C₄	—	4	4	no	—
316	C₃×C₄	—	10	2	no	—
317	C₃×C₄	#4041	1	2	yes	—
318	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
319	C₃×C₄	C₂×#713	1	1	yes	characteristic
320	C₂×C₅	C₃×#466	1	4	yes	complemented
321	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
322	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
323	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
324	D₅	—	2	4	no	—
325	D₅	—	8	4	no	—
326	C₂³	—	5	2	no	—
327	C₂³	—	5	4	no	—
328	C₂³	—	10	2	no	—
329	C₂³	—	10	2	no	—
330	C₂³	—	10	4	no	—
331	C₂³	—	20	4	no	—
332	C₂³	—	20	4	no	—
333	C₂³	—	20	4	no	—
334	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
335	D₄	—	10	4	no	—
336	D₄	—	10	4	no	—
337	D₄	—	20	16	no	—
338	D₄	—	20	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	5	2	no	—
342	C₂×C₄	—	10	2	no	—
343	C₂×C₄	—	10	2	no	—
344	C₂×C₄	—	10	2	no	—
345	C₂×C₄	—	10	4	no	—
346	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
347	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
348	C₂×C₄	C₃×#713	1	2	yes	—
349	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
350	C₈	—	10	2	no	—
351	C₈	C₂×C₃×D₂₀	1	4	yes	complemented
352	C₂×C₃	—	10	4	no	—
353	C₂×C₃	—	40	4	no	—
354	C₂×C₃	#65172	1	4	yes	direct product factor
355	C₂×C₃	C₂×#4041	1	1	yes	characteristic
356	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
357	C₂×C₃	C₂×#4065	1	1	yes	characteristic
358	C₅	C₂×C₃×#466	1	1	yes	characteristic, complemented, Sylow
359	C₂²	—	5	4	no	—
360	C₂²	—	10	2	no	—
361	C₂²	—	10	8	no	—
362	C₂²	—	10	2	no	—
363	C₂²	—	20	4	no	—
364	C₂²	—	20	4	no	—
365	C₂²	—	20	4	no	—
366	C₂²	—	40	8	no	—
367	C₂²	C₃×#4041	1	2	yes	—
368	C₂²	C₃×D₅×D₈	1	2	yes	—
369	C₂²	C₃×#4065	1	2	yes	—
370	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
371	C₄	—	4	4	no	—
372	C₄	—	10	2	no	—
373	C₄	C₃×#4041	1	2	yes	—
374	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
375	C₄	C₂×C₃×#713	1	1	yes	characteristic
376	C₃	C₂×#65172	1	1	yes	characteristic, direct product factor, Sylow
377	C₂	—	10	4	no	—
378	C₂	—	40	4	no	—
379	C₂	C₃×#65172	1	4	yes	direct product factor
380	C₂	C₂×C₃×#4041	1	1	yes	characteristic
381	C₂	C₂×C₃×D₅×D₈	1	1	yes	characteristic
382	C₂	C₂×C₃×#4065	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#107	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₃×#107	D₅
hypocenter	C₅	C₂×C₃×#466
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#107

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₄₀	C₂	semidirect
2. C₂²×C₃×C₈×D₅	C₂	semidirect
3. C₂×C₃×#4041	C₂	semidirect
4. C₂×C₃×C₅×#107	C₂	semidirect
5. C₂×C₃×#3941	C₂	semidirect
6. C₃×#65172	C₂	direct (N × H)
7. C₂×#65172	C₃	direct (N × H)
16. C₂×C₃×D₄₀	C₂²	semidirect
18. C₂×C₃×C₈×D₅	C₂²	semidirect
20. C₃×#4041	C₂²	semidirect
21. C₃×C₅×#107	C₂²	semidirect
22. C₃×#3941	C₂²	semidirect
24. C₂²×D₄₀	C₂×C₃	semidirect
25. C₂²×C₈×D₅	C₂×C₃	semidirect
26. C₂×#4041	C₂×C₃	semidirect
27. C₂×C₅×#107	C₂×C₃	semidirect
28. C₂×#3941	C₂×C₃	semidirect
29. #65172	C₂×C₃	direct (N × H)
45. C₂×C₃×C₅×C₈	D₄	semidirect
58. C₂×C₃×#107	D₅	semidirect
68. C₂×D₄₀	C₂²×C₃	semidirect
70. C₂×C₈×D₅	C₂²×C₃	semidirect
72. #4041	C₂²×C₃	semidirect
73. C₅×#107	C₂²×C₃	semidirect
74. #3941	C₂²×C₃	semidirect
83. C₂²×C₃×D₅	D₈	semidirect
100. C₃×C₅×C₈	C₂×D₄	semidirect
115. C₃×#107	C₂×D₅	semidirect
132. C₂×C₅×C₈	C₃×D₄	semidirect
145. C₂×#107	C₃×D₅	semidirect
158. C₂×C₃×D₅	C₂×D₈	semidirect
183. C₂×C₃×C₈	D₂₀	semidirect
195. C₂²×D₅	C₃×D₈	semidirect
212. C₅×C₈	C₂×C₃×D₄	semidirect
227. #107	C₂×C₃×D₅	semidirect
229. C₂×C₃×C₅	#466	semidirect
260. C₃×C₈	C₂×D₂₀	semidirect
272. C₂×D₅	C₂×C₃×D₈	semidirect
297. C₂×C₈	C₃×D₂₀	semidirect
302. C₃×C₅	C₂×#466	semidirect
320. C₂×C₅	C₃×#466	semidirect
351. C₈	C₂×C₃×D₂₀	semidirect
354. C₂×C₃	#65172	direct (N × H)
358. C₅	C₂×C₃×#466	semidirect
376. C₃	C₂×#65172	direct (N × H)
379. C₂	C₃×#65172	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×D₄₀	2
C₂²×C₃×C₈×D₅	2
C₂×C₃×#4041	2
C₂×C₃×C₅×#107	2
C₂×C₃×#3941	2
C₃×#65172	2
C₂×#65172	3
C₂×C₃×#466	5

Subgroups — C2×C3×#65172 #14427688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65172 #14427688