Subgroups — C₂×C₃×#65154 #14427988

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×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#676	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4041	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3941	C₂	1	2	yes	maximal, complemented
6	C₃×#65154	C₂	1	8	yes	maximal, direct product factor
7	C₂×#65154	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×#676	—	2	4	no	—
18	C₂×C₃×#676	C₂²	1	4	yes	complemented
19	C₃×#4041	—	2	4	no	—
20	C₃×#4041	C₂²	1	8	yes	complemented
21	C₃×C₅×#106	C₂²	1	4	yes	complemented
22	C₃×#3941	C₂²	1	8	yes	complemented
23	C₂×C₃×#469	—	5	1	no	maximal, Hall
24	C₂²×D₄₀	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂²×#676	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×#4041	C₂×C₃	1	2	yes	complemented
27	C₂×C₅×#106	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×#3941	C₂×C₃	1	2	yes	complemented
29	#65154	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×#676	—	2	8	no	—
54	C₂²×C₃×D₈	—	5	1	no	—
55	C₂²×C₃×M₁₆	—	5	1	no	—
56	C₂×C₃×#121	—	5	2	no	—
57	C₃×#469	—	5	8	no	—
58	C₂×C₃×#106	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×#676	—	2	4	no	—
70	C₂×#676	C₂²×C₃	1	4	yes	complemented
71	#4041	—	2	4	no	—
72	#4041	C₂²×C₃	1	8	yes	complemented
73	C₅×#106	C₂²×C₃	1	4	yes	complemented
74	#3941	C₂²×C₃	1	8	yes	complemented
75	C₂×#469	—	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	4	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	C₂×D₄	1	2	yes	—
84	C₂×C₃×C₄×C₅	—	2	4	no	—
85	C₂×C₃×C₄×C₅	—	4	4	no	—
86	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	#41	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
90	C₂×C₃×Dic₅	—	2	2	no	—
91	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
92	C₃×D₂₀	—	2	4	no	—
93	C₃×D₂₀	—	2	4	no	—
94	C₃×D₂₀	—	4	16	no	—
95	C₃×D₂₀	—	4	4	no	—
96	C₃×C₄×D₅	—	2	4	no	—
97	C₃×C₄×D₅	—	2	2	no	—
98	C₃×C₄×D₅	—	2	2	no	—
99	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
100	C₃×#168	—	2	2	no	—
101	C₂²×C₃×D₄	—	5	2	no	—
102	C₂²×C₃×D₄	—	10	2	no	—
103	C₂³×C₃×C₄	—	5	1	no	—
104	C₂×C₃×D₈	—	5	4	no	—
105	C₂×C₃×D₈	—	10	4	no	—
106	C₂×C₃×M₁₆	—	5	4	no	—
107	C₂×C₃×M₁₆	—	10	4	no	—
108	C₂²×C₃×C₈	—	5	1	no	—
109	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
110	C₃×#121	—	5	8	no	—
111	C₃×#121	—	10	4	no	—
112	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
113	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
114	C₃×#106	C₂×D₅	1	4	yes	complemented
115	C₃×#102	—	5	8	no	—
116	C₂³×D₅	—	2	2	no	—
117	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
120	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
121	C₂×D₂₀	—	2	4	no	—
122	C₂×D₂₀	—	2	4	no	—
123	C₂×D₂₀	—	2	8	no	—
124	C₂×D₂₀	—	2	2	no	—
125	C₂×D₂₀	—	4	8	no	—
126	C₂×D₂₀	C₂³×C₃	1	4	yes	—
127	C₂×C₄×D₅	—	2	2	no	—
128	C₂×C₄×D₅	—	2	2	no	—
129	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
130	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
131	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
132	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
133	C₅×C₄⋊C₄	—	2	2	no	—
134	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
135	#685	—	2	8	no	—
136	C₂×#168	—	2	2	no	—
137	C₂×#168	C₂³×C₃	1	2	yes	—
138	D₄₀	—	2	8	no	—
139	#676	—	2	8	no	—
140	C₂²×D₈	—	5	1	no	—
141	C₂²×M₁₆	—	5	1	no	—
142	C₂×#121	—	5	2	no	—
143	#469	—	5	8	no	—
144	C₂×#106	C₃×D₅	1	1	yes	characteristic, complemented
145	C₂×#102	—	5	2	no	—
146	C₂²×C₃×C₅	#121	1	2	yes	—
147	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	4	yes	—
148	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₃×D₅	—	2	2	no	—
150	C₂×C₃×D₅	—	2	4	no	—
151	C₂×C₃×D₅	—	4	4	no	—
152	C₂×C₃×D₅	—	4	4	no	—
153	C₂×C₃×D₅	—	4	4	no	—
154	C₂×C₃×D₅	—	4	4	no	—
155	C₂×C₃×D₅	—	8	8	no	—
156	C₃×C₄×C₅	—	4	4	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	C₃×Dic₅	—	2	2	no	—
161	C₂⁴×C₃	—	5	1	no	—
162	C₂⁴×C₃	—	10	2	no	—
163	C₂×C₃×D₄	—	5	4	no	—
164	C₂×C₃×D₄	—	10	8	no	—
165	C₂×C₃×D₄	—	10	4	no	—
166	C₂×C₃×D₄	—	10	2	no	—
167	C₂×C₃×D₄	—	10	4	no	—
168	C₂×C₃×D₄	—	20	8	no	—
169	C₂²×C₃×C₄	—	2	2	no	—
170	C₂²×C₃×C₄	—	5	1	no	—
171	C₂²×C₃×C₄	—	5	2	no	—
172	C₂²×C₃×C₄	—	5	2	no	—
173	C₂²×C₃×C₄	—	10	2	no	—
174	C₂²×C₃×C₄	—	10	2	no	—
175	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
176	C₃×D₈	—	10	8	no	—
177	C₃×M₁₆	—	10	8	no	—
178	C₂×C₃×C₈	—	5	2	no	—
179	C₂×C₃×C₈	—	10	2	no	—
180	C₂×C₃×C₈	D₂₀	1	4	yes	complemented
181	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
182	C₃×C₄⋊C₄	—	2	2	no	—
183	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
184	C₃×C₂²⋊C₄	—	10	8	no	—
185	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
186	C₂²×D₅	—	2	2	no	—
187	C₂²×D₅	—	2	4	no	—
188	C₂²×D₅	—	2	4	no	—
189	C₂²×D₅	—	4	4	no	—
190	C₂²×D₅	—	4	4	no	—
191	C₂²×D₅	—	4	4	no	—
192	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
193	C₂×C₄×C₅	—	2	4	no	—
194	C₂×C₄×C₅	—	4	4	no	—
195	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
196	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
197	C₂×C₄×C₅	C₃×#41	1	2	yes	—
198	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
199	C₂×Dic₅	—	2	2	no	—
200	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
201	D₂₀	—	2	4	no	—
202	D₂₀	—	2	4	no	—
203	D₂₀	—	4	16	no	—
204	D₂₀	—	4	4	no	—
205	C₄×D₅	—	2	4	no	—
206	C₄×D₅	—	2	2	no	—
207	C₄×D₅	—	2	2	no	—
208	C₅×C₈	C₂×C₃×D₄	1	4	yes	complemented
209	#168	—	2	2	no	—
210	C₂²×D₄	—	5	2	no	—
211	C₂²×D₄	—	10	2	no	—
212	C₂³×C₄	—	5	1	no	—
213	C₂×D₈	—	5	4	no	—
214	C₂×D₈	—	10	4	no	—
215	C₂×M₁₆	—	5	4	no	—
216	C₂×M₁₆	—	10	4	no	—
217	C₂²×C₈	—	5	1	no	—
218	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
219	#121	—	5	8	no	—
220	#121	—	10	4	no	—
221	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
222	C₂×C₂²⋊C₄	—	10	2	no	—
223	#106	C₂×C₃×D₅	1	4	yes	complemented
224	#102	—	5	8	no	—
225	C₂×C₃×C₅	#469	1	4	yes	complemented
226	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
227	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
228	C₃×D₅	—	4	2	no	—
229	C₃×D₅	—	8	4	no	—
230	C₂³×C₃	—	5	2	no	—
231	C₂³×C₃	—	10	2	no	—
232	C₂³×C₃	—	10	4	no	—
233	C₂³×C₃	—	10	4	no	—
234	C₂³×C₃	—	20	4	no	—
235	C₂³×C₃	—	20	4	no	—
236	C₂³×C₃	—	20	4	no	—
237	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
238	C₃×D₄	—	10	4	no	—
239	C₃×D₄	—	10	4	no	—
240	C₃×D₄	—	20	16	no	—
241	C₃×D₄	—	20	4	no	—
242	C₂×C₃×C₄	—	2	4	no	—
243	C₂×C₃×C₄	—	4	4	no	—
244	C₂×C₃×C₄	—	5	2	no	—
245	C₂×C₃×C₄	—	10	2	no	—
246	C₂×C₃×C₄	—	10	2	no	—
247	C₂×C₃×C₄	—	10	2	no	—
248	C₂×C₃×C₄	—	10	4	no	—
249	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
250	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
251	C₂×C₃×C₄	#713	1	2	yes	—
252	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
253	C₃×C₈	—	10	2	no	—
254	C₃×C₈	C₂×D₂₀	1	4	yes	complemented
255	C₂²×C₅	C₃×#121	1	2	yes	—
256	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	4	yes	—
257	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
258	C₂×D₅	—	2	4	no	—
259	C₂×D₅	—	2	2	no	—
260	C₂×D₅	—	4	4	no	—
261	C₂×D₅	—	4	4	no	—
262	C₂×D₅	—	4	4	no	—
263	C₂×D₅	—	4	4	no	—
264	C₂×D₅	—	8	8	no	—
265	C₄×C₅	—	4	4	no	—
266	C₄×C₅	C₃×#121	1	2	yes	—
267	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
268	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
269	Dic₅	—	2	2	no	—
270	C₂⁴	—	5	1	no	—
271	C₂⁴	—	10	2	no	—
272	C₂×D₄	—	5	4	no	—
273	C₂×D₄	—	10	8	no	—
274	C₂×D₄	—	10	4	no	—
275	C₂×D₄	—	10	2	no	—
276	C₂×D₄	—	10	4	no	—
277	C₂×D₄	—	20	8	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	5	1	no	—
280	C₂²×C₄	—	5	2	no	—
281	C₂²×C₄	—	5	2	no	—
282	C₂²×C₄	—	10	2	no	—
283	C₂²×C₄	—	10	2	no	—
284	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
285	D₈	—	10	8	no	—
286	M₁₆	—	10	8	no	—
287	C₂×C₈	—	5	2	no	—
288	C₂×C₈	—	10	2	no	—
289	C₂×C₈	C₃×D₂₀	1	4	yes	complemented
290	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
293	C₂²⋊C₄	—	10	8	no	—
294	C₃×C₅	C₂×#469	1	1	yes	characteristic, complemented, Hall
295	C₂²×C₃	—	10	4	no	—
296	C₂²×C₃	—	10	2	no	—
297	C₂²×C₃	—	20	4	no	—
298	C₂²×C₃	—	20	4	no	—
299	C₂²×C₃	—	20	4	no	—
300	C₂²×C₃	—	20	4	no	—
301	C₂²×C₃	—	40	8	no	—
302	C₂²×C₃	#4041	1	2	yes	—
303	C₂²×C₃	#4060	1	4	yes	—
304	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
305	C₃×C₄	—	4	4	no	—
306	C₃×C₄	—	10	2	no	—
307	C₃×C₄	#4041	1	2	yes	—
308	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
309	C₃×C₄	C₂×#713	1	1	yes	characteristic
310	C₂×C₅	C₃×#469	1	4	yes	complemented
311	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
312	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
313	D₅	—	4	2	no	—
314	D₅	—	8	4	no	—
315	C₂³	—	5	2	no	—
316	C₂³	—	10	2	no	—
317	C₂³	—	10	4	no	—
318	C₂³	—	10	4	no	—
319	C₂³	—	20	4	no	—
320	C₂³	—	20	4	no	—
321	C₂³	—	20	4	no	—
322	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
323	D₄	—	10	4	no	—
324	D₄	—	10	4	no	—
325	D₄	—	20	16	no	—
326	D₄	—	20	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	5	2	no	—
330	C₂×C₄	—	10	2	no	—
331	C₂×C₄	—	10	2	no	—
332	C₂×C₄	—	10	2	no	—
333	C₂×C₄	—	10	4	no	—
334	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
335	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
336	C₂×C₄	C₃×#713	1	2	yes	—
337	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
338	C₈	—	10	2	no	—
339	C₈	C₂×C₃×D₂₀	1	4	yes	complemented
340	C₂×C₃	—	20	2	no	—
341	C₂×C₃	—	40	4	no	—
342	C₂×C₃	#65154	1	4	yes	direct product factor
343	C₂×C₃	C₂×#4041	1	1	yes	characteristic
344	C₂×C₃	C₂×#4060	1	2	yes	—
345	C₅	C₂×C₃×#469	1	1	yes	characteristic, complemented, Sylow
346	C₂²	—	10	4	no	—
347	C₂²	—	10	2	no	—
348	C₂²	—	20	4	no	—
349	C₂²	—	20	4	no	—
350	C₂²	—	20	4	no	—
351	C₂²	—	20	4	no	—
352	C₂²	—	40	8	no	—
353	C₂²	C₃×#4041	1	2	yes	—
354	C₂²	C₃×#4060	1	4	yes	—
355	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
356	C₄	—	4	4	no	—
357	C₄	—	10	2	no	—
358	C₄	C₃×#4041	1	2	yes	—
359	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
360	C₄	C₂×C₃×#713	1	1	yes	characteristic
361	C₃	C₂×#65154	1	1	yes	characteristic, direct product factor, Sylow
362	C₂	—	20	2	no	—
363	C₂	—	40	4	no	—
364	C₂	C₃×#65154	1	4	yes	direct product factor
365	C₂	C₂×C₃×#4041	1	1	yes	characteristic
366	C₂	C₂×C₃×#4060	1	2	yes	—

	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×#106	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₃×#106	D₅
hypocenter	C₅	C₂×C₃×#469
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#106

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×#676	C₂	semidirect
3. C₂×C₃×#4041	C₂	semidirect
4. C₂×C₃×C₅×#106	C₂	semidirect
5. C₂×C₃×#3941	C₂	semidirect
6. C₃×#65154	C₂	direct (N × H)
7. C₂×#65154	C₃	direct (N × H)
16. C₂×C₃×D₄₀	C₂²	semidirect
18. C₂×C₃×#676	C₂²	semidirect
20. C₃×#4041	C₂²	semidirect
21. C₃×C₅×#106	C₂²	semidirect
22. C₃×#3941	C₂²	semidirect
24. C₂²×D₄₀	C₂×C₃	semidirect
25. C₂²×#676	C₂×C₃	semidirect
26. C₂×#4041	C₂×C₃	semidirect
27. C₂×C₅×#106	C₂×C₃	semidirect
28. C₂×#3941	C₂×C₃	semidirect
29. #65154	C₂×C₃	direct (N × H)
45. C₂×C₃×C₅×C₈	D₄	semidirect
58. C₂×C₃×#106	D₅	semidirect
68. C₂×D₄₀	C₂²×C₃	semidirect
70. C₂×#676	C₂²×C₃	semidirect
72. #4041	C₂²×C₃	semidirect
73. C₅×#106	C₂²×C₃	semidirect
74. #3941	C₂²×C₃	semidirect
99. C₃×C₅×C₈	C₂×D₄	semidirect
114. C₃×#106	C₂×D₅	semidirect
131. C₂×C₅×C₈	C₃×D₄	semidirect
144. C₂×#106	C₃×D₅	semidirect
180. C₂×C₃×C₈	D₂₀	semidirect
208. C₅×C₈	C₂×C₃×D₄	semidirect
223. #106	C₂×C₃×D₅	semidirect
225. C₂×C₃×C₅	#469	semidirect
254. C₃×C₈	C₂×D₂₀	semidirect
289. C₂×C₈	C₃×D₂₀	semidirect
294. C₃×C₅	C₂×#469	semidirect
310. C₂×C₅	C₃×#469	semidirect
339. C₈	C₂×C₃×D₂₀	semidirect
342. C₂×C₃	#65154	direct (N × H)
345. C₅	C₂×C₃×#469	semidirect
361. C₃	C₂×#65154	direct (N × H)
364. C₂	C₃×#65154	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×#676	2
C₂×C₃×#4041	2
C₂×C₃×C₅×#106	2
C₂×C₃×#3941	2
C₃×#65154	2
C₂×#65154	3
C₂×C₃×#469	5

Subgroups — C2×C3×#65154 #14427988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65154 #14427988