Subgroups — C₃×#10610225 #14416554

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4050	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×#709	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65402	C₂	1	2	yes	maximal, complemented
5	C₃×#65395	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65005	C₂	1	2	yes	maximal, complemented
7	C₃×#65000	C₂	1	2	yes	maximal, complemented
8	C₃×#64999	C₂	1	4	yes	maximal, complemented
9	#10610225	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×#709	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₃×C₄×C₂²⋊D₅	—	2	4	no	—
15	C₃×#4072	C₂²	1	2	yes	—
16	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic
17	C₃×#4050	C₄	1	8	yes	complemented
18	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
19	C₂×C₃×#677	C₂²	1	2	yes	—
20	C₃×C₄×D₂₀	C₂²	1	4	yes	—
21	C₃×#4018	—	2	2	no	—
22	C₃×C₄²×D₅	—	2	2	no	—
23	C₃×C₄×Dic₁₀	C₂²	1	4	yes	—
24	C₃×C₅×#97	C₂²	1	2	yes	—
25	C₃×C₅×#97	C₂²	1	2	yes	—
26	C₃×#3953	C₂²	1	4	yes	—
27	C₃×#3950	C₂²	1	2	yes	—
28	C₃×#3949	C₂²	1	2	yes	—
29	C₃×#3948	C₂²	1	4	yes	—
30	C₃×#2943	—	5	1	no	maximal, Hall
31	C₂×#4050	C₂×C₃	1	1	yes	characteristic
32	C₄×#709	C₂×C₃	1	2	yes	complemented
33	C₂×C₅×#97	C₂×C₃	1	1	yes	characteristic, complemented
34	#65402	C₂×C₃	1	2	yes	complemented
35	#65395	C₂×C₃	1	1	yes	characteristic, complemented
36	#65005	C₂×C₃	1	2	yes	complemented
37	#65000	C₂×C₃	1	2	yes	complemented
38	#64999	C₂×C₃	1	4	yes	complemented
39	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
42	C₃×#709	—	2	4	no	—
43	C₃×#709	C₂×C₄	1	8	yes	complemented
44	C₂×C₃×D₂₀	C₂³	1	2	yes	—
45	C₂×C₃×C₄×D₅	—	2	2	no	—
46	C₂×C₃×C₄×D₅	—	2	4	no	—
47	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
48	C₂×C₃×C₅×C₈	—	2	2	no	—
49	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
50	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
51	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₃×C₄²×C₅	D₄	1	2	yes	—
54	C₃×C₄²×C₅	C₂³	1	2	yes	—
55	C₃×C₂²⋊Dic₅	—	2	2	no	—
56	C₃×#685	—	2	4	no	—
57	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
58	C₃×#683	—	2	4	no	—
59	C₃×C₄×Dic₅	—	2	4	no	—
60	C₃×C₄×Dic₅	—	2	2	no	—
61	C₃×Dic₂₀	C₂×C₄	1	4	yes	complemented
62	C₃×D₄₀	C₂×C₄	1	4	yes	complemented
63	C₃×#677	C₂×C₄	1	8	yes	complemented
64	C₂×C₃×#135	—	5	1	no	—
65	C₃×C₄×#41	—	5	2	no	—
66	C₃×#442	—	5	2	no	—
67	C₃×#441	—	5	2	no	—
68	C₃×#440	—	5	4	no	—
69	C₃×#427	—	5	1	no	—
70	C₃×#416	—	5	2	no	—
71	C₂×C₃×#97	D₅	1	1	yes	characteristic, complemented
72	C₂×#709	C₂²×C₃	1	2	yes	—
73	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
74	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
76	C₄×C₂²⋊D₅	—	2	4	no	—
77	#4072	C₂²×C₃	1	2	yes	—
78	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic
79	#4050	C₃×C₄	1	8	yes	complemented
80	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
81	C₂×#677	C₂²×C₃	1	2	yes	—
82	C₄×D₂₀	C₂²×C₃	1	4	yes	—
83	#4018	—	2	2	no	—
84	C₄²×D₅	—	2	2	no	—
85	C₄×Dic₁₀	C₂²×C₃	1	4	yes	—
86	C₅×#97	C₂²×C₃	1	2	yes	—
87	C₅×#97	C₂²×C₃	1	2	yes	—
88	#3953	C₂²×C₃	1	4	yes	—
89	#3950	C₂²×C₃	1	2	yes	—
90	#3949	C₂²×C₃	1	2	yes	—
91	#3948	C₂²×C₃	1	4	yes	—
92	#2943	—	5	1	no	Sylow
93	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₃×D₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	4	2	no	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	#41	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
101	C₃×C₂²⋊D₅	—	2	8	no	—
102	C₂×C₃×Dic₅	—	2	2	no	—
103	C₂×C₃×Dic₅	—	2	4	no	—
104	C₃×D₂₀	—	2	2	no	—
105	C₃×D₂₀	C₂²×C₄	1	4	yes	—
106	C₃×C₄×D₅	—	2	8	no	—
107	C₃×C₄×D₅	—	4	8	no	—
108	C₃×Dic₁₀	—	2	2	no	—
109	C₃×Dic₁₀	C₂²×C₄	1	4	yes	—
110	C₃×C₅×C₈	—	2	2	no	—
111	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
112	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
113	C₂×C₃×#41	—	5	2	no	—
114	C₃×#135	—	5	8	no	—
115	C₂×C₃×Q₁₆	—	5	1	no	—
116	C₂×C₃×SD₁₆	—	5	2	no	—
117	C₂×C₃×D₈	—	5	1	no	—
118	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
119	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
120	C₃×C₄×Q₈	—	5	4	no	—
121	C₃×C₄×D₄	—	5	4	no	—
122	C₃×C₄×D₄	—	10	4	no	—
123	C₃×#117	—	5	2	no	—
124	C₃×#117	—	10	2	no	—
125	C₂×C₃×C₄²	—	10	2	no	—
126	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
127	C₃×#107	—	5	2	no	—
128	C₃×#106	—	5	2	no	—
129	C₃×#103	—	5	4	no	—
130	C₃×#102	—	5	4	no	—
131	C₃×#97	C₂×D₅	1	2	yes	—
132	C₃×#97	C₂×D₅	1	2	yes	—
133	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
134	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
135	C₂×C₂²⋊D₅	—	2	2	no	—
136	#709	—	2	4	no	—
137	#709	C₂×C₃×C₄	1	8	yes	complemented
138	C₂×D₂₀	C₂³×C₃	1	2	yes	—
139	C₂×C₄×D₅	—	2	2	no	—
140	C₂×C₄×D₅	—	2	4	no	—
141	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	complemented
144	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
145	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
146	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
147	C₄²×C₅	C₃×D₄	1	2	yes	—
148	C₄²×C₅	C₂³×C₃	1	2	yes	—
149	C₂²⋊Dic₅	—	2	2	no	—
150	#685	—	2	4	no	—
151	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
152	#683	—	2	4	no	—
153	C₄×Dic₅	—	2	4	no	—
154	C₄×Dic₅	—	2	2	no	—
155	Dic₂₀	C₂×C₃×C₄	1	4	yes	complemented
156	D₄₀	C₂×C₃×C₄	1	4	yes	complemented
157	#677	C₂×C₃×C₄	1	8	yes	complemented
158	C₂×#135	—	5	1	no	—
159	C₄×#41	—	5	2	no	—
160	#442	—	5	2	no	—
161	#441	—	5	2	no	—
162	#440	—	5	4	no	—
163	#427	—	5	1	no	—
164	#416	—	5	2	no	—
165	C₂×#97	C₃×D₅	1	1	yes	characteristic, complemented
166	C₂²×C₃×C₅	—	2	2	no	—
167	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
168	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₃×D₅	—	2	4	no	—
170	C₂×C₃×D₅	—	4	4	no	—
171	C₃×C₄×C₅	—	2	4	no	—
172	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
173	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
174	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
175	C₃×Dic₅	—	2	4	no	—
176	C₃×Dic₅	—	4	4	no	—
177	C₃×#41	—	5	8	no	—
178	C₃×#41	—	10	4	no	—
179	C₂×C₃×Q₈	—	5	2	no	—
180	C₂×C₃×D₄	—	5	2	no	—
181	C₂×C₃×D₄	—	10	2	no	—
182	C₂²×C₃×C₄	—	10	2	no	—
183	C₂²×C₃×C₄	—	10	4	no	—
184	C₂²×C₃×C₄	D₂₀	1	2	yes	—
185	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
186	C₃×Q₁₆	—	5	4	no	—
187	C₃×SD₁₆	—	5	8	no	—
188	C₃×D₈	—	5	4	no	—
189	C₂×C₃×C₈	—	2	2	no	—
190	C₂×C₃×C₈	C₄×D₅	1	4	yes	complemented
191	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
192	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
193	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
194	C₃×C₄⋊C₄	—	5	4	no	—
195	C₃×C₄⋊C₄	—	10	4	no	—
196	C₃×C₂²⋊C₄	—	10	2	no	—
197	C₃×C₂²⋊C₄	—	10	4	no	—
198	C₃×C₄²	—	10	4	no	—
199	C₃×C₄²	—	10	2	no	—
200	C₃×C₄²	D₂₀	1	2	yes	—
201	C₃×C₄²	C₂²×D₅	1	2	yes	—
202	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
203	C₂²×D₅	—	2	2	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
206	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
207	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₃×#41	1	2	yes	—
209	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
210	C₂²⋊D₅	—	2	8	no	—
211	C₂×Dic₅	—	2	2	no	—
212	C₂×Dic₅	—	2	4	no	—
213	D₂₀	—	2	2	no	—
214	D₂₀	C₂²×C₃×C₄	1	4	yes	—
215	C₄×D₅	—	2	8	no	—
216	C₄×D₅	—	4	8	no	—
217	Dic₁₀	—	2	2	no	—
218	Dic₁₀	C₂²×C₃×C₄	1	4	yes	—
219	C₅×C₈	—	2	2	no	—
220	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
221	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
222	C₂×#41	—	5	2	no	—
223	#135	—	5	8	no	—
224	C₂×Q₁₆	—	5	1	no	—
225	C₂×SD₁₆	—	5	2	no	—
226	C₂×D₈	—	5	1	no	—
227	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
228	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
229	C₄×Q₈	—	5	4	no	—
230	C₄×D₄	—	5	4	no	—
231	C₄×D₄	—	10	4	no	—
232	#117	—	5	2	no	—
233	#117	—	10	2	no	—
234	C₂×C₄²	—	10	2	no	—
235	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
236	#107	—	5	2	no	—
237	#106	—	5	2	no	—
238	#103	—	5	4	no	—
239	#102	—	5	4	no	—
240	#97	C₂×C₃×D₅	1	2	yes	—
241	#97	C₂×C₃×D₅	1	2	yes	—
242	C₂×C₃×C₅	—	2	2	no	—
243	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
244	C₂×C₃×C₅	#575	1	2	yes	—
245	C₃×D₅	—	4	4	no	—
246	C₂³×C₃	—	10	2	no	—
247	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
248	C₃×Q₈	—	5	4	no	—
249	C₃×Q₈	—	10	2	no	—
250	C₃×D₄	—	5	4	no	—
251	C₃×D₄	—	10	8	no	—
252	C₃×D₄	—	10	2	no	—
253	C₂×C₃×C₄	—	4	2	no	—
254	C₂×C₃×C₄	—	10	2	no	—
255	C₂×C₃×C₄	—	10	8	no	—
256	C₂×C₃×C₄	—	10	4	no	—
257	C₂×C₃×C₄	—	20	8	no	—
258	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
259	C₂×C₃×C₄	C₂×D₂₀	1	4	yes	—
260	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
261	C₂×C₃×C₄	#709	1	2	yes	—
262	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
263	C₃×C₈	—	2	2	no	—
264	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
265	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
266	C₂²×C₅	—	2	2	no	—
267	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
268	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
269	C₂×D₅	—	2	4	no	—
270	C₂×D₅	—	4	4	no	—
271	C₄×C₅	—	2	4	no	—
272	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
273	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
274	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
275	Dic₅	—	2	4	no	—
276	Dic₅	—	4	4	no	—
277	#41	—	5	8	no	—
278	#41	—	10	4	no	—
279	C₂×Q₈	—	5	2	no	—
280	C₂×D₄	—	5	2	no	—
281	C₂×D₄	—	10	2	no	—
282	C₂²×C₄	—	10	2	no	—
283	C₂²×C₄	—	10	4	no	—
284	C₂²×C₄	C₃×D₂₀	1	2	yes	—
285	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
286	Q₁₆	—	5	4	no	—
287	SD₁₆	—	5	8	no	—
288	D₈	—	5	4	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	C₃×C₄×D₅	1	4	yes	complemented
291	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
292	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
293	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
294	C₄⋊C₄	—	5	4	no	—
295	C₄⋊C₄	—	10	4	no	—
296	C₂²⋊C₄	—	10	2	no	—
297	C₂²⋊C₄	—	10	4	no	—
298	C₄²	—	10	2	no	—
299	C₄²	—	10	4	no	—
300	C₄²	C₃×D₂₀	1	2	yes	—
301	C₄²	C₂²×C₃×D₅	1	2	yes	—
302	C₃×C₅	#2943	1	1	yes	characteristic, complemented, Hall
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	—	10	4	no	—
305	C₂²×C₃	—	20	4	no	—
306	C₂²×C₃	C₄×D₂₀	1	2	yes	—
307	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
308	C₃×C₄	—	2	4	no	—
309	C₃×C₄	—	10	4	no	—
310	C₃×C₄	—	20	4	no	—
311	C₃×C₄	C₄×D₂₀	1	2	yes	—
312	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
313	C₃×C₄	C₂×#709	1	1	yes	characteristic
314	C₂×C₅	—	2	2	no	—
315	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
316	C₂×C₅	C₃×#575	1	2	yes	—
317	D₅	—	4	4	no	—
318	C₂³	—	10	2	no	—
319	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
320	Q₈	—	5	4	no	—
321	Q₈	—	10	2	no	—
322	D₄	—	5	4	no	—
323	D₄	—	10	8	no	—
324	D₄	—	10	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	10	2	no	—
327	C₂×C₄	—	10	8	no	—
328	C₂×C₄	—	10	4	no	—
329	C₂×C₄	—	20	8	no	—
330	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
331	C₂×C₄	C₂×C₃×D₂₀	1	4	yes	—
332	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
333	C₂×C₄	C₃×#709	1	2	yes	—
334	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
335	C₈	—	2	2	no	—
336	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
337	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
338	C₂×C₃	—	2	2	no	—
339	C₂×C₃	—	20	4	no	—
340	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
341	C₂×C₃	#66082	1	2	yes	—
342	C₅	C₃×#2943	1	1	yes	characteristic, complemented, Sylow
343	C₂²	—	2	2	no	—
344	C₂²	—	10	4	no	—
345	C₂²	—	20	4	no	—
346	C₂²	C₃×C₄×D₂₀	1	2	yes	—
347	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
348	C₄	—	2	4	no	—
349	C₄	—	10	4	no	—
350	C₄	—	20	4	no	—
351	C₄	C₃×C₄×D₂₀	1	2	yes	—
352	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
353	C₄	C₂×C₃×#709	1	1	yes	characteristic
354	C₃	#10610225	1	1	yes	characteristic, direct product factor, Sylow
355	C₂	—	2	2	no	—
356	C₂	—	20	4	no	—
357	C₂	C₂×C₃×C₄×D₂₀	1	1	yes	characteristic
358	C₂	C₃×#66082	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₂₀
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#97	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4050	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×#97	D₅
hypocenter	C₅	C₃×#2943
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₂×C₃×#97

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×#709	C₂	semidirect
3. C₂×C₃×C₅×#97	C₂	semidirect
4. C₃×#65402	C₂	semidirect
5. C₃×#65395	C₂	semidirect
6. C₃×#65005	C₂	semidirect
7. C₃×#65000	C₂	semidirect
8. C₃×#64999	C₂	semidirect
9. #10610225	C₃	direct (N × H)
17. C₃×#4050	C₄	semidirect
32. C₄×#709	C₂×C₃	semidirect
33. C₂×C₅×#97	C₂×C₃	semidirect
34. #65402	C₂×C₃	semidirect
35. #65395	C₂×C₃	semidirect
36. #65005	C₂×C₃	semidirect
37. #65000	C₂×C₃	semidirect
38. #64999	C₂×C₃	semidirect
43. C₃×#709	C₂×C₄	semidirect
49. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
61. C₃×Dic₂₀	C₂×C₄	semidirect
62. C₃×D₄₀	C₂×C₄	semidirect
63. C₃×#677	C₂×C₄	semidirect
71. C₂×C₃×#97	D₅	semidirect
79. #4050	C₃×C₄	semidirect
137. #709	C₂×C₃×C₄	semidirect
143. C₂×C₅×C₈	C₂×C₃×C₄	semidirect
155. Dic₂₀	C₂×C₃×C₄	semidirect
156. D₄₀	C₂×C₃×C₄	semidirect
157. #677	C₂×C₃×C₄	semidirect
165. C₂×#97	C₃×D₅	semidirect
190. C₂×C₃×C₈	C₄×D₅	semidirect
290. C₂×C₈	C₃×C₄×D₅	semidirect
302. C₃×C₅	#2943	semidirect
342. C₅	C₃×#2943	semidirect
354. C₃	#10610225	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#4050	2
C₃×C₄×#709	2
C₂×C₃×C₅×#97	2
C₃×#65402	2
C₃×#65395	2
C₃×#65005	2
C₃×#65000	2
C₃×#64999	2
#10610225	3
C₃×#2943	5

Subgroups — C3×#10610225 #14416554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610225 #14416554