Subgroups — C₃×C₂²⋊C₄×#170 #14295158

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×#170	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₂²⋊#170	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×#170	C₂	1	2	yes	maximal, complemented
4	C₃×C₂²⋊C₄×Dic₅	C₂	1	1	yes	maximal, characteristic
5	C₃×#64918	C₂	1	2	yes	maximal, complemented
6	C₂²⋊C₄×#170	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
8	C₂²×C₃×#170	—	2	4	no	—
9	C₂²×C₃×#170	C₄	1	4	yes	complemented
10	C₂²×C₃×#170	C₂²	1	2	yes	—
11	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
12	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
14	C₂×C₃×C₂²⋊Dic₅	C₄	1	1	yes	characteristic
15	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
16	C₃×C₂²⋊#170	C₄	1	4	yes	complemented
17	C₃×C₄×#170	—	2	4	no	—
18	C₃×#3963	C₄	1	2	yes	—
19	C₃×C₈×C₂²⋊C₄	—	5	1	no	maximal, Hall
20	C₂³×#170	C₂×C₃	1	1	yes	characteristic
21	C₂×C₂²⋊#170	C₂×C₃	1	1	yes	characteristic
22	C₂×C₄×#170	C₂×C₃	1	2	yes	complemented
23	C₂²⋊C₄×Dic₅	C₂×C₃	1	1	yes	characteristic
24	#64918	C₂×C₃	1	2	yes	complemented
25	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
27	C₂²×C₃×Dic₅	—	2	2	no	—
28	C₂²×C₃×Dic₅	—	2	2	no	—
29	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
31	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
32	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
33	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
34	C₂×C₃×#170	—	2	2	no	—
35	C₂×C₃×#170	—	2	2	no	—
36	C₂×C₃×#170	—	2	2	no	—
37	C₂×C₃×#170	—	2	8	no	—
38	C₂×C₃×#170	C₂×C₄	1	2	yes	—
39	C₂×C₃×#170	C₂×C₄	1	4	yes	—
40	C₂×C₃×#170	C₂×C₄	1	2	yes	—
41	C₂×C₃×#170	D₄	1	4	yes	—
42	C₃×C₅×C₂²⋊C₄	C₈	1	4	yes	complemented
43	C₃×C₂²⋊Dic₅	C₈	1	4	yes	complemented
44	C₃×C₄×Dic₅	—	2	2	no	—
45	C₃×C₄×Dic₅	—	2	2	no	—
46	C₂³×C₃×C₈	—	5	1	no	—
47	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
48	C₂×C₃×C₄×C₈	—	5	2	no	—
49	C₃×C₄×C₂²⋊C₄	—	5	1	no	—
50	C₃×#336	—	5	2	no	—
51	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
52	C₂²×#170	—	2	4	no	—
53	C₂²×#170	C₃×C₄	1	4	yes	complemented
54	C₂²×#170	C₂²×C₃	1	2	yes	—
55	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
56	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
57	C₂×C₅×C₂²⋊C₄	C₃×C₄	1	1	yes	characteristic
58	C₂×C₂²⋊Dic₅	C₃×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
60	C₂²⋊#170	C₃×C₄	1	4	yes	complemented
61	C₄×#170	—	2	4	no	—
62	#3963	C₃×C₄	1	2	yes	—
63	C₈×C₂²⋊C₄	—	5	1	no	Sylow
64	C₂³×C₃×C₅	—	2	2	no	—
65	C₂³×C₃×C₅	—	2	2	no	—
66	C₂³×C₃×C₅	C₄²	1	2	yes	—
67	C₂³×C₃×C₅	C₂×C₈	1	2	yes	—
68	C₂³×C₃×C₅	C₂×C₈	1	2	yes	—
69	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₃×C₄×C₅	—	2	2	no	—
71	C₂×C₃×C₄×C₅	—	2	2	no	—
72	C₂×C₃×C₄×C₅	C₂×C₈	1	4	yes	complemented
73	C₂×C₃×Dic₅	—	2	2	no	—
74	C₂×C₃×Dic₅	—	2	2	no	—
75	C₂×C₃×Dic₅	—	2	2	no	—
76	C₂×C₃×Dic₅	—	2	2	no	—
77	C₂×C₃×Dic₅	—	2	2	no	—
78	C₂×C₃×Dic₅	—	2	4	no	—
79	C₂×C₃×Dic₅	C₄²	1	2	yes	—
80	C₂×C₃×Dic₅	C₂×C₈	1	4	yes	complemented
81	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
84	C₂×C₃×Dic₅	#41	1	2	yes	—
85	C₃×#170	—	2	2	no	—
86	C₃×#170	—	2	4	no	—
87	C₃×#170	C₂²⋊C₄	1	4	yes	direct product factor
88	C₂³×C₃×C₄	—	5	1	no	—
89	C₂²×C₃×C₈	—	5	1	no	—
90	C₂²×C₃×C₈	—	5	4	no	—
91	C₂²×C₃×C₈	—	5	1	no	—
92	C₂²×C₃×C₈	—	5	2	no	—
93	C₂²×C₃×C₈	—	10	4	no	—
94	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
95	C₂×C₃×C₂²⋊C₄	AGL(1,𝔽₅)	1	1	yes	characteristic
96	C₂×C₃×C₄²	—	5	2	no	—
97	C₃×C₂²⋊C₈	—	5	4	no	—
98	C₃×C₄×C₈	—	10	4	no	—
99	C₃×#95	—	5	2	no	—
100	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
102	C₂²×Dic₅	—	2	2	no	—
103	C₂²×Dic₅	—	2	2	no	—
104	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
105	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
106	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
107	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
108	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
109	C₂×#170	—	2	2	no	—
110	C₂×#170	—	2	2	no	—
111	C₂×#170	—	2	2	no	—
112	C₂×#170	—	2	8	no	—
113	C₂×#170	C₂×C₃×C₄	1	2	yes	—
114	C₂×#170	C₂×C₃×C₄	1	4	yes	—
115	C₂×#170	C₂×C₃×C₄	1	2	yes	—
116	C₂×#170	C₃×D₄	1	4	yes	—
117	C₅×C₂²⋊C₄	C₃×C₈	1	4	yes	complemented
118	C₂²⋊Dic₅	C₃×C₈	1	4	yes	complemented
119	C₄×Dic₅	—	2	2	no	—
120	C₄×Dic₅	—	2	2	no	—
121	C₂³×C₈	—	5	1	no	—
122	C₂×C₂²⋊C₈	—	5	1	no	—
123	C₂×C₄×C₈	—	5	2	no	—
124	C₄×C₂²⋊C₄	—	5	1	no	—
125	#336	—	5	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	C₄×C₈	1	4	yes	complemented
131	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
132	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
133	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
134	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
135	C₂²×C₃×C₅	#131	1	2	yes	—
136	C₃×C₄×C₅	—	2	4	no	—
137	C₃×Dic₅	—	2	2	no	—
138	C₃×Dic₅	—	2	4	no	—
139	C₃×Dic₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₃×Dic₅	#117	1	1	yes	characteristic
141	C₃×Dic₅	C₄×D₄	1	2	yes	—
142	C₂⁴×C₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
143	C₂²×C₃×C₄	—	5	1	no	—
144	C₂²×C₃×C₄	—	5	2	no	—
145	C₂²×C₃×C₄	—	5	2	no	—
146	C₂²×C₃×C₄	—	5	1	no	—
147	C₂²×C₃×C₄	—	5	2	no	—
148	C₂²×C₃×C₄	—	10	2	no	—
149	C₂²×C₃×C₄	—	10	2	no	—
150	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
151	C₂×C₃×C₈	—	5	4	no	—
152	C₂×C₃×C₈	—	5	2	no	—
153	C₂×C₃×C₈	—	5	4	no	—
154	C₂×C₃×C₈	—	5	2	no	—
155	C₂×C₃×C₈	—	10	8	no	—
156	C₂×C₃×C₈	—	10	2	no	—
157	C₂×C₃×C₈	—	10	2	no	—
158	C₂×C₃×C₈	—	10	2	no	—
159	C₃×C₂²⋊C₄	—	5	4	no	—
160	C₃×C₂²⋊C₄	#170	1	4	yes	direct product factor
161	C₃×C₄²	—	10	2	no	—
162	C₃×C₄²	—	10	2	no	—
163	C₂³×C₅	—	2	2	no	—
164	C₂³×C₅	—	2	2	no	—
165	C₂³×C₅	C₃×C₄²	1	2	yes	—
166	C₂³×C₅	C₂×C₃×C₈	1	2	yes	—
167	C₂³×C₅	C₂×C₃×C₈	1	2	yes	—
168	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
169	C₂×C₄×C₅	—	2	2	no	—
170	C₂×C₄×C₅	—	2	2	no	—
171	C₂×C₄×C₅	C₂×C₃×C₈	1	4	yes	complemented
172	C₂×Dic₅	—	2	2	no	—
173	C₂×Dic₅	—	2	2	no	—
174	C₂×Dic₅	—	2	2	no	—
175	C₂×Dic₅	—	2	2	no	—
176	C₂×Dic₅	—	2	2	no	—
177	C₂×Dic₅	—	2	4	no	—
178	C₂×Dic₅	C₃×C₄²	1	2	yes	—
179	C₂×Dic₅	C₂×C₃×C₈	1	4	yes	complemented
180	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
181	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
182	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
183	C₂×Dic₅	C₃×#41	1	2	yes	—
184	#170	—	2	2	no	—
185	#170	—	2	4	no	—
186	#170	C₃×C₂²⋊C₄	1	4	yes	direct product factor
187	C₂³×C₄	—	5	1	no	—
188	C₂²×C₈	—	5	1	no	—
189	C₂²×C₈	—	5	4	no	—
190	C₂²×C₈	—	5	1	no	—
191	C₂²×C₈	—	5	2	no	—
192	C₂²×C₈	—	10	4	no	—
193	C₂×C₂²⋊C₄	—	5	1	no	—
194	C₂×C₂²⋊C₄	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
195	C₂×C₄²	—	5	2	no	—
196	C₂²⋊C₈	—	5	4	no	—
197	C₄×C₈	—	10	4	no	—
198	#95	—	5	2	no	—
199	C₂×C₃×C₅	—	2	4	no	—
200	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₃×C₅	C₂×C₄×C₈	1	1	yes	characteristic
202	C₂×C₃×C₅	#405	1	1	yes	characteristic
203	C₂×C₃×C₅	C₈×D₄	1	2	yes	—
204	C₂×C₃×C₅	C₈×D₄	1	2	yes	—
205	C₂³×C₃	—	2	2	no	—
206	C₂³×C₃	—	2	2	no	—
207	C₂³×C₃	D₅⋊C₈	1	2	yes	—
208	C₂³×C₃	C₄×AGL(1,𝔽₅)	1	2	yes	—
209	C₂³×C₃	C₂×#170	1	2	yes	—
210	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
211	C₂×C₃×C₄	—	2	2	no	—
212	C₂×C₃×C₄	—	2	2	no	—
213	C₂×C₃×C₄	—	5	1	no	—
214	C₂×C₃×C₄	—	5	1	no	—
215	C₂×C₃×C₄	—	5	2	no	—
216	C₂×C₃×C₄	—	5	2	no	—
217	C₂×C₃×C₄	—	5	4	no	—
218	C₂×C₃×C₄	—	5	2	no	—
219	C₂×C₃×C₄	—	10	2	no	—
220	C₂×C₃×C₄	—	10	2	no	—
221	C₂×C₃×C₄	—	10	4	no	—
222	C₂×C₃×C₄	—	10	2	no	—
223	C₂×C₃×C₄	—	10	2	no	—
224	C₂×C₃×C₄	—	10	2	no	—
225	C₂×C₃×C₄	C₂×#170	1	4	yes	complemented
226	C₃×C₈	—	5	4	no	—
227	C₃×C₈	—	10	4	no	—
228	C₃×C₈	—	10	2	no	—
229	C₂²×C₅	—	2	2	no	—
230	C₂²×C₅	—	2	2	no	—
231	C₂²×C₅	—	2	4	no	—
232	C₂²×C₅	—	2	4	no	—
233	C₂²×C₅	C₃×C₄×C₈	1	4	yes	complemented
234	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
235	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
236	C₂²×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
237	C₂²×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
238	C₂²×C₅	C₃×#131	1	2	yes	—
239	C₄×C₅	—	2	4	no	—
240	Dic₅	—	2	2	no	—
241	Dic₅	—	2	4	no	—
242	Dic₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
243	Dic₅	C₃×#117	1	1	yes	characteristic
244	Dic₅	C₃×C₄×D₄	1	2	yes	—
245	C₂⁴	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
246	C₂²×C₄	—	5	1	no	—
247	C₂²×C₄	—	5	2	no	—
248	C₂²×C₄	—	5	2	no	—
249	C₂²×C₄	—	5	1	no	—
250	C₂²×C₄	—	5	2	no	—
251	C₂²×C₄	—	10	2	no	—
252	C₂²×C₄	—	10	2	no	—
253	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
254	C₂×C₈	—	5	4	no	—
255	C₂×C₈	—	5	2	no	—
256	C₂×C₈	—	5	4	no	—
257	C₂×C₈	—	5	2	no	—
258	C₂×C₈	—	10	8	no	—
259	C₂×C₈	—	10	2	no	—
260	C₂×C₈	—	10	2	no	—
261	C₂×C₈	—	10	2	no	—
262	C₂²⋊C₄	—	5	4	no	—
263	C₂²⋊C₄	C₃×#170	1	4	yes	direct product factor
264	C₄²	—	10	2	no	—
265	C₄²	—	10	2	no	—
266	C₃×C₅	C₈×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
267	C₂²×C₃	—	2	2	no	—
268	C₂²×C₃	—	2	4	no	—
269	C₂²×C₃	—	2	2	no	—
270	C₂²×C₃	—	2	4	no	—
271	C₂²×C₃	C₄×#170	1	4	yes	complemented
272	C₂²×C₃	C₂×D₅⋊C₈	1	1	yes	characteristic
273	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
274	C₂²×C₃	#4131	1	2	yes	—
275	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	2	yes	—
276	C₂²×C₃	C₂²×#170	1	1	yes	characteristic
277	C₃×C₄	—	2	4	no	—
278	C₃×C₄	—	5	1	no	—
279	C₃×C₄	—	5	1	no	—
280	C₃×C₄	—	5	2	no	—
281	C₃×C₄	—	10	4	no	—
282	C₃×C₄	—	10	2	no	—
283	C₂×C₅	—	2	4	no	—
284	C₂×C₅	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
285	C₂×C₅	C₂×C₃×C₄×C₈	1	1	yes	characteristic
286	C₂×C₅	C₃×#405	1	1	yes	characteristic
287	C₂×C₅	C₃×C₈×D₄	1	2	yes	—
288	C₂×C₅	C₃×C₈×D₄	1	2	yes	—
289	C₂³	—	2	2	no	—
290	C₂³	—	2	2	no	—
291	C₂³	C₃×D₅⋊C₈	1	2	yes	—
292	C₂³	C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
293	C₂³	C₂×C₃×#170	1	2	yes	—
294	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	5	1	no	—
298	C₂×C₄	—	5	1	no	—
299	C₂×C₄	—	5	2	no	—
300	C₂×C₄	—	5	2	no	—
301	C₂×C₄	—	5	4	no	—
302	C₂×C₄	—	5	2	no	—
303	C₂×C₄	—	10	2	no	—
304	C₂×C₄	—	10	4	no	—
305	C₂×C₄	—	10	2	no	—
306	C₂×C₄	—	10	2	no	—
307	C₂×C₄	—	10	2	no	—
308	C₂×C₄	—	10	2	no	—
309	C₂×C₄	C₂×C₃×#170	1	4	yes	complemented
310	C₈	—	5	4	no	—
311	C₈	—	10	2	no	—
312	C₈	—	10	4	no	—
313	C₂×C₃	—	2	4	no	—
314	C₂×C₃	#65691	1	1	yes	characteristic
315	C₂×C₃	#65692	1	2	yes	—
316	C₂×C₃	C₂²⋊C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
317	C₂×C₃	C₂×C₄×#170	1	1	yes	characteristic
318	C₂×C₃	D₄×#170	1	2	yes	—
319	C₅	C₃×C₈×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
320	C₂²	—	2	2	no	—
321	C₂²	—	2	4	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	4	no	—
324	C₂²	C₃×C₄×#170	1	4	yes	complemented
325	C₂²	C₂×C₃×D₅⋊C₈	1	1	yes	characteristic
326	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
327	C₂²	C₃×#4131	1	2	yes	—
328	C₂²	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
329	C₂²	C₂²×C₃×#170	1	1	yes	characteristic
330	C₄	—	2	4	no	—
331	C₄	—	5	1	no	—
332	C₄	—	5	2	no	—
333	C₄	—	5	1	no	—
334	C₄	—	10	4	no	—
335	C₄	—	10	2	no	—
336	C₃	C₂²⋊C₄×#170	1	1	yes	characteristic, direct product factor, Sylow
337	C₂	—	2	4	no	—
338	C₂	C₃×#65691	1	1	yes	characteristic
339	C₂	C₃×#65692	1	2	yes	—
340	C₂	C₃×C₂²⋊C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
341	C₂	C₂×C₃×C₄×#170	1	1	yes	characteristic
342	C₂	C₃×D₄×#170	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂²×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂×C₃×C₄×C₈
Frattini	C₂³	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×C₂²⋊C₄	C₄
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂⁴×C₃×C₅	C₂×C₄
cosocle	C₂²×Dic₅	C₂³×C₃
hypercenter	C₂×C₃×C₂²⋊C₄	AGL(1,𝔽₅)
hypocenter	C₅	C₃×C₈×C₂²⋊C₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×C₄×#170	C₂	semidirect
5. C₃×#64918	C₂	semidirect
6. C₂²⋊C₄×#170	C₃	direct (N × H)
9. C₂²×C₃×#170	C₄	semidirect
16. C₃×C₂²⋊#170	C₄	semidirect
22. C₂×C₄×#170	C₂×C₃	semidirect
24. #64918	C₂×C₃	semidirect
42. C₃×C₅×C₂²⋊C₄	C₈	semidirect
43. C₃×C₂²⋊Dic₅	C₈	semidirect
53. C₂²×#170	C₃×C₄	semidirect
60. C₂²⋊#170	C₃×C₄	semidirect
72. C₂×C₃×C₄×C₅	C₂×C₈	semidirect
80. C₂×C₃×Dic₅	C₂×C₈	semidirect
87. C₃×#170	C₂²⋊C₄	direct (N × H)
117. C₅×C₂²⋊C₄	C₃×C₈	semidirect
118. C₂²⋊Dic₅	C₃×C₈	semidirect
130. C₂²×C₃×C₅	C₄×C₈	semidirect
160. C₃×C₂²⋊C₄	#170	direct (N × H)
171. C₂×C₄×C₅	C₂×C₃×C₈	semidirect
179. C₂×Dic₅	C₂×C₃×C₈	semidirect
186. #170	C₃×C₂²⋊C₄	direct (N × H)
225. C₂×C₃×C₄	C₂×#170	semidirect
233. C₂²×C₅	C₃×C₄×C₈	semidirect
263. C₂²⋊C₄	C₃×#170	direct (N × H)
266. C₃×C₅	C₈×C₂²⋊C₄	semidirect
271. C₂²×C₃	C₄×#170	semidirect
309. C₂×C₄	C₂×C₃×#170	semidirect
319. C₅	C₃×C₈×C₂²⋊C₄	semidirect
324. C₂²	C₃×C₄×#170	semidirect
336. C₃	C₂²⋊C₄×#170	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×#170	2
C₂×C₃×C₂²⋊#170	2
C₂×C₃×C₄×#170	2
C₃×C₂²⋊C₄×Dic₅	2
C₃×#64918	2
C₂²⋊C₄×#170	3
C₃×C₈×C₂²⋊C₄	5

Subgroups — C3×C22⋊C4×#170 #14295158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂²⋊C₄×#170 #14295158