Subgroups — C₃×C₄×C₄⋊#170 #14296100

Order 1920.

632 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄⋊#170	C₂	1	2	yes	maximal
2	C₂×C₃×C₄×#170	C₂	1	2	yes	maximal
3	C₃×C₄²×Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₃×#64918	C₂	1	2	yes	maximal
5	C₄×C₄⋊#170	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×#170	C₂²	1	4	yes	—
7	C₂×C₃×C₄²×C₅	C₄	1	1	yes	characteristic
8	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
9	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
10	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
11	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
14	C₃×C₄⋊#170	C₄	1	8	yes	direct product factor
15	C₃×C₄×#170	—	2	4	no	—
16	C₃×C₄×C₄⋊C₈	—	5	1	no	maximal, Hall
17	C₂×C₄⋊#170	C₂×C₃	1	2	yes	—
18	C₂×C₄×#170	C₂×C₃	1	2	yes	—
19	C₄²×Dic₅	C₂×C₃	1	1	yes	characteristic
20	#64918	C₂×C₃	1	2	yes	—
21	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
28	C₂×C₃×#170	—	2	4	no	—
29	C₂×C₃×#170	—	2	4	no	—
30	C₂×C₃×#170	C₂×C₄	1	8	yes	—
31	C₃×C₄²×C₅	C₈	1	4	yes	complemented
32	C₃×C₄×Dic₅	—	2	2	no	—
33	C₃×C₄×Dic₅	—	2	2	no	—
34	C₃×C₄×Dic₅	—	2	2	no	—
35	C₃×C₄×Dic₅	C₈	1	4	yes	complemented
36	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
37	C₃×C₄×Dic₅	D₄	1	2	yes	—
38	C₃×C₄×Dic₅	Q₈	1	2	yes	—
39	C₂×C₃×C₄⋊C₈	—	5	2	no	—
40	C₂×C₃×C₄×C₈	—	5	2	no	—
41	C₃×C₄³	—	5	1	no	—
42	C₃×#336	—	5	2	no	—
43	C₂²×#170	C₂²×C₃	1	4	yes	—
44	C₂×C₄²×C₅	C₃×C₄	1	1	yes	characteristic
45	C₂×C₄×Dic₅	C₃×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₅	C₃×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₅	C₃×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
49	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
50	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
51	C₄⋊#170	C₃×C₄	1	8	yes	direct product factor
52	C₄×#170	—	2	4	no	—
53	C₄×C₄⋊C₈	—	5	1	no	Sylow
54	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₃×C₄×C₅	—	2	1	no	—
56	C₂×C₃×C₄×C₅	—	2	1	no	—
57	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
58	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
59	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
60	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
61	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
62	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
63	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
64	C₂×C₃×Dic₅	—	2	1	no	—
65	C₂×C₃×Dic₅	—	2	1	no	—
66	C₂×C₃×Dic₅	—	2	1	no	—
67	C₂×C₃×Dic₅	—	2	1	no	—
68	C₂×C₃×Dic₅	C₄²	1	2	yes	—
69	C₂×C₃×Dic₅	C₄⋊C₄	1	2	yes	—
70	C₂×C₃×Dic₅	C₂×C₈	1	2	yes	—
71	C₂×C₃×Dic₅	C₂×C₈	1	2	yes	—
72	C₂×C₃×Dic₅	M₁₆	1	2	yes	—
73	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
74	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
75	C₂×C₃×Dic₅	C₂×Q₈	1	1	yes	characteristic
76	C₂×C₃×Dic₅	#41	1	2	yes	—
77	C₃×#170	—	2	8	no	—
78	C₂²×C₃×C₈	—	5	4	no	—
79	C₂×C₃×C₄²	—	5	1	no	—
80	C₂×C₃×C₄²	—	5	1	no	—
81	C₂×C₃×C₄²	—	5	1	no	—
82	C₂×C₃×C₄²	—	5	1	no	—
83	C₂×C₃×C₄²	—	5	1	no	—
84	C₂×C₃×C₄²	—	5	1	no	—
85	C₂×C₃×C₄²	AGL(1,𝔽₅)	1	1	yes	characteristic
86	C₃×C₄⋊C₈	—	5	8	no	—
87	C₃×C₄×C₈	—	10	4	no	—
88	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
91	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
92	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
93	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
94	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
95	C₂×#170	—	2	4	no	—
96	C₂×#170	—	2	4	no	—
97	C₂×#170	C₂×C₃×C₄	1	8	yes	—
98	C₄²×C₅	C₃×C₈	1	4	yes	complemented
99	C₄×Dic₅	—	2	2	no	—
100	C₄×Dic₅	—	2	2	no	—
101	C₄×Dic₅	—	2	2	no	—
102	C₄×Dic₅	C₃×C₈	1	4	yes	complemented
103	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
104	C₄×Dic₅	C₃×D₄	1	2	yes	—
105	C₄×Dic₅	C₃×Q₈	1	2	yes	—
106	C₂×C₄⋊C₈	—	5	2	no	—
107	C₂×C₄×C₈	—	5	2	no	—
108	C₄³	—	5	1	no	—
109	#336	—	5	2	no	—
110	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
111	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
112	C₂²×C₃×C₅	#117	1	1	yes	characteristic
113	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
114	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
115	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
116	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
117	C₃×C₄×C₅	—	2	2	no	—
118	C₃×C₄×C₅	C₄×C₈	1	4	yes	complemented
119	C₃×C₄×C₅	C₄⋊C₈	1	4	yes	complemented
120	C₃×Dic₅	—	2	2	no	—
121	C₃×Dic₅	—	2	2	no	—
122	C₃×Dic₅	C₄⋊C₈	1	4	yes	complemented
123	C₃×Dic₅	C₄×D₄	1	2	yes	—
124	C₃×Dic₅	C₄×Q₈	1	2	yes	—
125	C₂²×C₃×C₄	—	5	1	no	—
126	C₂²×C₃×C₄	—	5	1	no	—
127	C₂²×C₃×C₄	—	5	1	no	—
128	C₂²×C₃×C₄	—	5	1	no	—
129	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
130	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
131	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
132	C₂×C₃×C₈	—	5	8	no	—
133	C₂×C₃×C₈	—	10	4	no	—
134	C₂×C₃×C₈	—	10	4	no	—
135	C₃×C₄²	—	5	4	no	—
136	C₃×C₄²	—	5	4	no	—
137	C₃×C₄²	—	5	2	no	—
138	C₃×C₄²	—	5	2	no	—
139	C₃×C₄²	—	10	2	no	—
140	C₃×C₄²	—	10	2	no	—
141	C₃×C₄²	—	10	2	no	—
142	C₃×C₄²	#170	1	4	yes	complemented
143	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
144	C₂×C₄×C₅	—	2	1	no	—
145	C₂×C₄×C₅	—	2	1	no	—
146	C₂×C₄×C₅	C₃×C₄²	1	2	yes	—
147	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
148	C₂×C₄×C₅	C₂×C₃×C₈	1	2	yes	—
149	C₂×C₄×C₅	C₂×C₃×C₈	1	2	yes	—
150	C₂×C₄×C₅	C₂×C₃×C₈	1	2	yes	—
151	C₂×C₄×C₅	C₂×C₃×C₈	1	2	yes	—
152	C₂×C₄×C₅	C₃×M₁₆	1	2	yes	—
153	C₂×Dic₅	—	2	1	no	—
154	C₂×Dic₅	—	2	1	no	—
155	C₂×Dic₅	—	2	1	no	—
156	C₂×Dic₅	—	2	1	no	—
157	C₂×Dic₅	C₃×C₄²	1	2	yes	—
158	C₂×Dic₅	C₃×C₄⋊C₄	1	2	yes	—
159	C₂×Dic₅	C₂×C₃×C₈	1	2	yes	—
160	C₂×Dic₅	C₂×C₃×C₈	1	2	yes	—
161	C₂×Dic₅	C₃×M₁₆	1	2	yes	—
162	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
163	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
164	C₂×Dic₅	C₂×C₃×Q₈	1	1	yes	characteristic
165	C₂×Dic₅	C₃×#41	1	2	yes	—
166	#170	—	2	8	no	—
167	C₂²×C₈	—	5	4	no	—
168	C₂×C₄²	—	5	1	no	—
169	C₂×C₄²	—	5	1	no	—
170	C₂×C₄²	—	5	1	no	—
171	C₂×C₄²	—	5	1	no	—
172	C₂×C₄²	—	5	1	no	—
173	C₂×C₄²	—	5	1	no	—
174	C₂×C₄²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
175	C₄⋊C₈	—	5	8	no	—
176	C₄×C₈	—	10	4	no	—
177	C₂×C₃×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₃×C₅	C₂×C₄×C₈	1	1	yes	characteristic
179	C₂×C₃×C₅	C₄×M₁₆	1	1	yes	characteristic
180	C₂×C₃×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
181	C₂×C₃×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
182	C₂×C₃×C₅	#431	1	1	yes	characteristic
183	C₂×C₃×C₅	#431	1	1	yes	characteristic
184	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
185	C₂×C₃×C₄	—	2	1	no	—
186	C₂×C₃×C₄	—	2	1	no	—
187	C₂×C₃×C₄	—	5	2	no	—
188	C₂×C₃×C₄	—	5	2	no	—
189	C₂×C₃×C₄	—	5	2	no	—
190	C₂×C₃×C₄	—	5	2	no	—
191	C₂×C₃×C₄	—	5	1	no	—
192	C₂×C₃×C₄	—	5	1	no	—
193	C₂×C₃×C₄	—	5	2	no	—
194	C₂×C₃×C₄	—	5	2	no	—
195	C₂×C₃×C₄	—	5	2	no	—
196	C₂×C₃×C₄	—	10	1	no	—
197	C₂×C₃×C₄	—	10	1	no	—
198	C₂×C₃×C₄	—	10	1	no	—
199	C₂×C₃×C₄	—	10	1	no	—
200	C₂×C₃×C₄	D₅⋊C₈	1	2	yes	—
201	C₂×C₃×C₄	#700	1	2	yes	—
202	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	2	yes	—
203	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	2	yes	—
204	C₂×C₃×C₄	C₂×#170	1	2	yes	—
205	C₂×C₃×C₄	C₂×#170	1	2	yes	—
206	C₂×C₃×C₄	C₂×#170	1	2	yes	—
207	C₃×C₈	—	10	8	no	—
208	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
209	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
210	C₂²×C₅	C₃×#117	1	1	yes	characteristic
211	C₂²×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
212	C₂²×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
213	C₂²×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
214	C₂²×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
215	C₄×C₅	—	2	2	no	—
216	C₄×C₅	C₃×C₄×C₈	1	4	yes	complemented
217	C₄×C₅	C₃×C₄⋊C₈	1	4	yes	complemented
218	Dic₅	—	2	2	no	—
219	Dic₅	—	2	2	no	—
220	Dic₅	C₃×C₄⋊C₈	1	4	yes	complemented
221	Dic₅	C₃×C₄×D₄	1	2	yes	—
222	Dic₅	C₃×C₄×Q₈	1	2	yes	—
223	C₂²×C₄	—	5	1	no	—
224	C₂²×C₄	—	5	1	no	—
225	C₂²×C₄	—	5	1	no	—
226	C₂²×C₄	—	5	1	no	—
227	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
228	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
229	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
230	C₂×C₈	—	5	8	no	—
231	C₂×C₈	—	10	4	no	—
232	C₂×C₈	—	10	4	no	—
233	C₄²	—	5	4	no	—
234	C₄²	—	5	4	no	—
235	C₄²	—	5	2	no	—
236	C₄²	—	5	2	no	—
237	C₄²	—	10	2	no	—
238	C₄²	—	10	2	no	—
239	C₄²	—	10	2	no	—
240	C₄²	C₃×#170	1	4	yes	complemented
241	C₃×C₅	C₄×C₄⋊C₈	1	1	yes	characteristic, complemented, Hall
242	C₂²×C₃	C₂×D₅⋊C₈	1	1	yes	characteristic
243	C₂²×C₃	C₂×#700	1	1	yes	characteristic
244	C₂²×C₃	D₅⋊M₁₆	1	1	yes	characteristic
245	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
246	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
247	C₂²×C₃	#4130	1	1	yes	characteristic
248	C₂²×C₃	C₂²×#170	1	1	yes	characteristic
249	C₃×C₄	—	2	2	no	—
250	C₃×C₄	—	5	4	no	—
251	C₃×C₄	—	5	2	no	—
252	C₃×C₄	—	5	2	no	—
253	C₃×C₄	—	10	2	no	—
254	C₃×C₄	—	10	2	no	—
255	C₃×C₄	C₄×#170	1	4	yes	complemented
256	C₃×C₄	C₄⋊#170	1	4	yes	direct product factor
257	C₂×C₅	C₃×C₄×C₄⋊C₄	1	1	yes	characteristic
258	C₂×C₅	C₂×C₃×C₄×C₈	1	1	yes	characteristic
259	C₂×C₅	C₃×C₄×M₁₆	1	1	yes	characteristic
260	C₂×C₅	C₂×C₃×C₄⋊C₈	1	1	yes	characteristic
261	C₂×C₅	C₂×C₃×C₄⋊C₈	1	1	yes	characteristic
262	C₂×C₅	C₃×#431	1	1	yes	characteristic
263	C₂×C₅	C₃×#431	1	1	yes	characteristic
264	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
265	C₂×C₄	—	2	1	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	5	2	no	—
268	C₂×C₄	—	5	2	no	—
269	C₂×C₄	—	5	2	no	—
270	C₂×C₄	—	5	1	no	—
271	C₂×C₄	—	5	2	no	—
272	C₂×C₄	—	5	1	no	—
273	C₂×C₄	—	5	2	no	—
274	C₂×C₄	—	5	2	no	—
275	C₂×C₄	—	5	2	no	—
276	C₂×C₄	—	10	1	no	—
277	C₂×C₄	—	10	1	no	—
278	C₂×C₄	—	10	1	no	—
279	C₂×C₄	—	10	1	no	—
280	C₂×C₄	C₃×D₅⋊C₈	1	2	yes	—
281	C₂×C₄	C₃×#700	1	2	yes	—
282	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
283	C₂×C₄	C₃×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
284	C₂×C₄	C₂×C₃×#170	1	2	yes	—
285	C₂×C₄	C₂×C₃×#170	1	2	yes	—
286	C₂×C₄	C₂×C₃×#170	1	2	yes	—
287	C₈	—	10	8	no	—
288	C₂×C₃	C₄×#700	1	1	yes	characteristic
289	C₂×C₃	D₅⋊(C₄⋊C₈)	1	1	yes	characteristic
290	C₂×C₃	#65680	1	1	yes	characteristic
291	C₂×C₃	C₄×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
292	C₂×C₃	C₂×C₄×#170	1	1	yes	characteristic
293	C₂×C₃	C₂×C₄⋊#170	1	1	yes	characteristic
294	C₂×C₃	#65748	1	1	yes	characteristic
295	C₅	C₃×C₄×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
296	C₂²	C₂×C₃×D₅⋊C₈	1	1	yes	characteristic
297	C₂²	C₂×C₃×#700	1	1	yes	characteristic
298	C₂²	C₃×D₅⋊M₁₆	1	1	yes	characteristic
299	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
300	C₂²	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
301	C₂²	C₃×#4130	1	1	yes	characteristic
302	C₂²	C₂²×C₃×#170	1	1	yes	characteristic
303	C₄	—	2	2	no	—
304	C₄	—	5	4	no	—
305	C₄	—	5	2	no	—
306	C₄	—	5	2	no	—
307	C₄	—	10	2	no	—
308	C₄	—	10	2	no	—
309	C₄	C₃×C₄×#170	1	4	yes	complemented
310	C₄	C₃×C₄⋊#170	1	4	yes	direct product factor
311	C₃	C₄×C₄⋊#170	1	1	yes	characteristic, direct product factor, Sylow
312	C₂	C₃×C₄×#700	1	1	yes	characteristic
313	C₂	C₃×D₅⋊(C₄⋊C₈)	1	1	yes	characteristic
314	C₂	C₃×#65680	1	1	yes	characteristic
315	C₂	C₃×C₄×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
316	C₂	C₂×C₃×C₄×#170	1	1	yes	characteristic
317	C₂	C₂×C₃×C₄⋊#170	1	1	yes	characteristic
318	C₂	C₃×#65748	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂×C₃×C₄×C₈
Frattini	C₂³	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₄²×C₅	C₄
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂²×Dic₅	C₂³×C₃
hypercenter	C₂×C₃×C₄²	AGL(1,𝔽₅)
hypocenter	C₅	C₃×C₄×C₄⋊C₈
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×C₄²

Complements

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

N	H ≅ G/N	type
5. C₄×C₄⋊#170	C₃	direct (N × H)
14. C₃×C₄⋊#170	C₄	direct (N × H)
31. C₃×C₄²×C₅	C₈	semidirect
35. C₃×C₄×Dic₅	C₈	semidirect
51. C₄⋊#170	C₃×C₄	direct (N × H)
98. C₄²×C₅	C₃×C₈	semidirect
102. C₄×Dic₅	C₃×C₈	semidirect
118. C₃×C₄×C₅	C₄×C₈	semidirect
119. C₃×C₄×C₅	C₄⋊C₈	semidirect
122. C₃×Dic₅	C₄⋊C₈	semidirect
142. C₃×C₄²	#170	semidirect
216. C₄×C₅	C₃×C₄×C₈	semidirect
217. C₄×C₅	C₃×C₄⋊C₈	semidirect
220. Dic₅	C₃×C₄⋊C₈	semidirect
240. C₄²	C₃×#170	semidirect
241. C₃×C₅	C₄×C₄⋊C₈	semidirect
255. C₃×C₄	C₄×#170	semidirect
256. C₃×C₄	C₄⋊#170	direct (N × H)
295. C₅	C₃×C₄×C₄⋊C₈	semidirect
309. C₄	C₃×C₄×#170	semidirect
310. C₄	C₃×C₄⋊#170	direct (N × H)
311. C₃	C₄×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
C₂×C₃×C₄⋊#170	2
C₂×C₃×C₄×#170	2
C₃×C₄²×Dic₅	2
C₃×#64918	2
C₄×C₄⋊#170	3
C₃×C₄×C₄⋊C₈	5

Subgroups — C3×C4×C4⋊#170 #14296100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₄⋊#170 #14296100