Subgroups — C₂×C₃×D₄⋊#170 #14281480

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄⋊#170	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×#170	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₄⋊#170	C₂	1	4	yes	maximal, direct product factor
5	C₂×D₄⋊#170	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×C₅×D₄	C₄	1	1	yes	characteristic
7	C₂³×C₃×Dic₅	—	2	1	no	—
8	C₂²×C₃×#170	—	2	1	no	—
9	C₂²×C₃×#170	—	2	1	no	—
10	C₂×C₃×C₂²⋊Dic₅	—	2	1	no	—
11	C₃×D₄×Dic₅	—	2	1	no	—
12	C₃×D₄×Dic₅	—	2	1	no	—
13	C₃×D₄×Dic₅	C₄	1	2	yes	—
14	C₃×D₄×Dic₅	C₂²	1	2	yes	—
15	C₂×C₃×C₄⋊Dic₅	C₄	1	1	yes	characteristic
16	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
17	C₃×C₄⋊#170	—	2	1	no	—
18	C₃×C₄⋊#170	C₂²	1	2	yes	complemented
19	C₃×C₄×#170	—	2	1	no	—
20	C₃×C₄×#170	C₂²	1	2	yes	complemented
21	C₂×C₃×D₄⋊C₈	—	5	1	no	maximal, Hall
22	C₂×D₄×Dic₅	C₂×C₃	1	1	yes	characteristic
23	C₂×C₄⋊#170	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×C₄×#170	C₂×C₃	1	1	yes	characteristic, complemented
25	D₄⋊#170	C₂×C₃	1	4	yes	direct product factor
26	C₂⁴×C₃×C₅	—	2	1	no	—
27	C₂×C₃×C₅×D₄	—	2	1	no	—
28	C₂×C₃×C₅×D₄	—	2	2	no	—
29	C₂×C₃×C₅×D₄	C₈	1	4	yes	complemented
30	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×Dic₅	—	2	1	no	—
33	C₂²×C₃×Dic₅	—	2	2	no	—
34	C₂²×C₃×Dic₅	—	2	2	no	—
35	C₂²×C₃×Dic₅	—	4	2	no	—
36	C₂²×C₃×Dic₅	—	4	2	no	—
37	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
38	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
39	C₂×C₃×#170	—	2	4	no	—
40	C₂×C₃×#170	—	2	2	no	—
41	C₂×C₃×#170	—	2	2	no	—
42	C₂×C₃×#170	—	4	2	no	—
43	C₃×C₂²⋊Dic₅	—	2	2	no	—
44	C₃×C₂²⋊Dic₅	—	2	2	no	—
45	C₃×C₄⋊Dic₅	—	2	1	no	—
46	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
47	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
48	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
49	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
50	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₄×D₄	—	5	1	no	—
52	C₂×C₃×C₄⋊C₈	—	5	1	no	—
53	C₂×C₃×C₄×C₈	—	5	1	no	—
54	C₃×D₄⋊C₈	—	5	4	no	—
55	C₂²×C₅×D₄	C₃×C₄	1	1	yes	characteristic
56	C₂³×Dic₅	—	2	1	no	—
57	C₂²×#170	—	2	1	no	—
58	C₂²×#170	—	2	1	no	—
59	C₂×C₂²⋊Dic₅	—	2	1	no	—
60	D₄×Dic₅	—	2	1	no	—
61	D₄×Dic₅	—	2	1	no	—
62	D₄×Dic₅	C₃×C₄	1	2	yes	—
63	D₄×Dic₅	C₂²×C₃	1	2	yes	—
64	C₂×C₄⋊Dic₅	C₃×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
66	C₄⋊#170	—	2	1	no	—
67	C₄⋊#170	C₂²×C₃	1	2	yes	complemented
68	C₄×#170	—	2	1	no	—
69	C₄×#170	C₂²×C₃	1	2	yes	complemented
70	C₂×D₄⋊C₈	—	5	1	no	Sylow
71	C₂³×C₃×C₅	—	2	4	no	—
72	C₂³×C₃×C₅	—	2	2	no	—
73	C₂³×C₃×C₅	—	4	2	no	—
74	C₂³×C₃×C₅	—	4	2	no	—
75	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
76	C₃×C₅×D₄	—	2	4	no	—
77	C₃×C₅×D₄	—	2	2	no	—
78	C₃×C₅×D₄	C₂×C₈	1	4	yes	complemented
79	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
81	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
82	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₃×Dic₅	—	2	2	no	—
84	C₂×C₃×Dic₅	—	2	2	no	—
85	C₂×C₃×Dic₅	—	4	2	no	—
86	C₂×C₃×Dic₅	—	4	4	no	—
87	C₂×C₃×Dic₅	—	4	2	no	—
88	C₂×C₃×Dic₅	—	4	2	no	—
89	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₃×Dic₅	D₈	1	2	yes	—
92	C₂×C₃×Dic₅	SD₁₆	1	2	yes	—
93	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
94	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
95	C₃×#170	—	2	4	no	—
96	C₃×#170	—	4	2	no	—
97	C₂²×C₃×D₄	AGL(1,𝔽₅)	1	1	yes	characteristic
98	C₂³×C₃×C₄	—	10	1	no	—
99	C₂²×C₃×C₈	—	10	1	no	—
100	C₂²×C₃×C₈	—	10	1	no	—
101	C₃×C₄×D₄	—	5	2	no	—
102	C₃×C₄×D₄	—	5	2	no	—
103	C₃×C₄×D₄	—	10	1	no	—
104	C₃×C₄×D₄	—	10	1	no	—
105	C₂×C₃×C₄⋊C₄	—	5	1	no	—
106	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
107	C₂×C₃×C₄²	—	5	1	no	—
108	C₃×C₄⋊C₈	—	5	2	no	—
109	C₃×C₄⋊C₈	—	10	1	no	—
110	C₃×C₄×C₈	—	5	2	no	—
111	C₃×C₄×C₈	—	10	1	no	—
112	C₂⁴×C₅	—	2	1	no	—
113	C₂×C₅×D₄	—	2	1	no	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	C₃×C₈	1	4	yes	complemented
116	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
117	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
118	C₂²×Dic₅	—	2	1	no	—
119	C₂²×Dic₅	—	2	2	no	—
120	C₂²×Dic₅	—	2	2	no	—
121	C₂²×Dic₅	—	4	2	no	—
122	C₂²×Dic₅	—	4	2	no	—
123	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
124	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
125	C₂×#170	—	2	4	no	—
126	C₂×#170	—	2	2	no	—
127	C₂×#170	—	2	2	no	—
128	C₂×#170	—	4	2	no	—
129	C₂²⋊Dic₅	—	2	2	no	—
130	C₂²⋊Dic₅	—	2	2	no	—
131	C₄⋊Dic₅	—	2	1	no	—
132	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
133	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
134	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
135	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
136	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
137	C₂×C₄×D₄	—	5	1	no	—
138	C₂×C₄⋊C₈	—	5	1	no	—
139	C₂×C₄×C₈	—	5	1	no	—
140	D₄⋊C₈	—	5	4	no	—
141	C₂²×C₃×C₅	—	2	4	no	—
142	C₂²×C₃×C₅	—	4	8	no	—
143	C₂²×C₃×C₅	—	4	2	no	—
144	C₂²×C₃×C₅	—	4	2	no	—
145	C₂²×C₃×C₅	C₂²⋊C₈	1	2	yes	—
146	C₂²×C₃×C₅	#102	1	2	yes	—
147	C₂²×C₃×C₅	#104	1	2	yes	—
148	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₃×C₄×C₅	C₂²⋊C₈	1	2	yes	—
150	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
151	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
152	C₃×Dic₅	—	2	1	no	—
153	C₃×Dic₅	—	2	1	no	—
154	C₃×Dic₅	—	4	2	no	—
155	C₃×Dic₅	#102	1	2	yes	—
156	C₃×Dic₅	C₂×D₈	1	1	yes	characteristic
157	C₃×Dic₅	C₂×SD₁₆	1	1	yes	characteristic
158	C₂⁴×C₃	—	2	1	no	—
159	C₂×C₃×D₄	—	2	2	no	—
160	C₂×C₃×D₄	—	2	1	no	—
161	C₂×C₃×D₄	#170	1	4	yes	complemented
162	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
163	C₂²×C₃×C₄	—	5	1	no	—
164	C₂²×C₃×C₄	—	5	1	no	—
165	C₂²×C₃×C₄	—	10	2	no	—
166	C₂²×C₃×C₄	—	10	2	no	—
167	C₂²×C₃×C₄	—	10	1	no	—
168	C₂²×C₃×C₄	—	20	2	no	—
169	C₂²×C₃×C₄	—	20	2	no	—
170	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
171	C₂×C₃×C₈	—	10	2	no	—
172	C₂×C₃×C₈	—	10	4	no	—
173	C₂×C₃×C₈	—	10	2	no	—
174	C₂×C₃×C₈	—	20	2	no	—
175	C₃×C₄⋊C₄	—	5	2	no	—
176	C₃×C₄⋊C₄	—	10	1	no	—
177	C₃×C₂²⋊C₄	—	10	2	no	—
178	C₃×C₂²⋊C₄	—	10	2	no	—
179	C₃×C₄²	—	5	1	no	—
180	C₃×C₄²	—	5	1	no	—
181	C₃×C₄²	—	5	1	no	—
182	C₃×C₄²	—	5	1	no	—
183	C₂³×C₅	—	2	4	no	—
184	C₂³×C₅	—	2	2	no	—
185	C₂³×C₅	—	4	2	no	—
186	C₂³×C₅	—	4	2	no	—
187	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
188	C₅×D₄	—	2	4	no	—
189	C₅×D₄	—	2	2	no	—
190	C₅×D₄	C₂×C₃×C₈	1	4	yes	complemented
191	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×C₃×C₈	1	2	yes	—
193	C₂×C₄×C₅	C₃×M₁₆	1	2	yes	—
194	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
195	C₂×Dic₅	—	2	2	no	—
196	C₂×Dic₅	—	2	2	no	—
197	C₂×Dic₅	—	4	2	no	—
198	C₂×Dic₅	—	4	4	no	—
199	C₂×Dic₅	—	4	2	no	—
200	C₂×Dic₅	—	4	2	no	—
201	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
202	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×Dic₅	C₃×D₈	1	2	yes	—
204	C₂×Dic₅	C₃×SD₁₆	1	2	yes	—
205	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
206	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
207	#170	—	2	4	no	—
208	#170	—	4	2	no	—
209	C₂²×D₄	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
210	C₂³×C₄	—	10	1	no	—
211	C₂²×C₈	—	10	1	no	—
212	C₂²×C₈	—	10	1	no	—
213	C₄×D₄	—	5	2	no	—
214	C₄×D₄	—	5	2	no	—
215	C₄×D₄	—	10	1	no	—
216	C₄×D₄	—	10	1	no	—
217	C₂×C₄⋊C₄	—	5	1	no	—
218	C₂×C₂²⋊C₄	—	10	1	no	—
219	C₂×C₄²	—	5	1	no	—
220	C₄⋊C₈	—	5	2	no	—
221	C₄⋊C₈	—	10	1	no	—
222	C₄×C₈	—	5	2	no	—
223	C₄×C₈	—	10	1	no	—
224	C₂×C₃×C₅	—	4	4	no	—
225	C₂×C₃×C₅	D₄⋊C₈	1	4	yes	complemented
226	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
227	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
228	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
229	C₂³×C₃	—	2	2	no	—
230	C₂³×C₃	—	2	4	no	—
231	C₂³×C₃	—	4	2	no	—
232	C₂³×C₃	—	4	2	no	—
233	C₂³×C₃	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
234	C₃×D₄	—	2	2	no	—
235	C₃×D₄	—	2	4	no	—
236	C₃×D₄	C₂×#170	1	4	yes	complemented
237	C₂×C₃×C₄	—	5	1	no	—
238	C₂×C₃×C₄	—	5	1	no	—
239	C₂×C₃×C₄	—	5	2	no	—
240	C₂×C₃×C₄	—	5	2	no	—
241	C₂×C₃×C₄	—	5	1	no	—
242	C₂×C₃×C₄	—	5	1	no	—
243	C₂×C₃×C₄	—	10	2	no	—
244	C₂×C₃×C₄	—	10	2	no	—
245	C₂×C₃×C₄	—	20	4	no	—
246	C₂×C₃×C₄	—	20	2	no	—
247	C₂×C₃×C₄	—	20	2	no	—
248	C₂×C₃×C₄	—	20	2	no	—
249	C₂×C₃×C₄	C₂×#170	1	2	yes	—
250	C₂×C₃×C₄	#704	1	2	yes	—
251	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
253	C₃×C₈	—	10	4	no	—
254	C₃×C₈	—	20	2	no	—
255	C₂²×C₅	—	2	4	no	—
256	C₂²×C₅	—	4	2	no	—
257	C₂²×C₅	—	4	2	no	—
258	C₂²×C₅	—	4	8	no	—
259	C₂²×C₅	C₃×C₂²⋊C₈	1	2	yes	—
260	C₂²×C₅	C₃×#102	1	2	yes	—
261	C₂²×C₅	C₃×#104	1	2	yes	—
262	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
263	C₄×C₅	C₃×C₂²⋊C₈	1	2	yes	—
264	C₄×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
265	C₄×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
266	Dic₅	—	2	1	no	—
267	Dic₅	—	2	1	no	—
268	Dic₅	—	4	2	no	—
269	Dic₅	C₃×#102	1	2	yes	—
270	Dic₅	C₂×C₃×D₈	1	1	yes	characteristic
271	Dic₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
272	C₂⁴	—	2	1	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	C₃×#170	1	4	yes	complemented
276	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
277	C₂²×C₄	—	5	1	no	—
278	C₂²×C₄	—	5	1	no	—
279	C₂²×C₄	—	10	2	no	—
280	C₂²×C₄	—	10	2	no	—
281	C₂²×C₄	—	10	1	no	—
282	C₂²×C₄	—	20	2	no	—
283	C₂²×C₄	—	20	2	no	—
284	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
285	C₂×C₈	—	10	2	no	—
286	C₂×C₈	—	10	4	no	—
287	C₂×C₈	—	10	2	no	—
288	C₂×C₈	—	20	2	no	—
289	C₄⋊C₄	—	5	2	no	—
290	C₄⋊C₄	—	10	1	no	—
291	C₂²⋊C₄	—	10	2	no	—
292	C₂²⋊C₄	—	10	2	no	—
293	C₄²	—	5	1	no	—
294	C₄²	—	5	1	no	—
295	C₄²	—	5	1	no	—
296	C₄²	—	5	1	no	—
297	C₃×C₅	C₂×D₄⋊C₈	1	1	yes	characteristic, complemented, Hall
298	C₂²×C₃	—	2	4	no	—
299	C₂²×C₃	—	4	8	no	—
300	C₂²×C₃	—	4	2	no	—
301	C₂²×C₃	—	4	2	no	—
302	C₂²×C₃	#4007	1	2	yes	—
303	C₂²×C₃	#4008	1	2	yes	—
304	C₂²×C₃	C₂²⋊#170	1	2	yes	—
305	C₂²×C₃	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
306	C₃×C₄	—	5	2	no	—
307	C₃×C₄	—	5	1	no	—
308	C₃×C₄	—	5	1	no	—
309	C₃×C₄	—	10	1	no	—
310	C₃×C₄	—	10	1	no	—
311	C₃×C₄	—	20	2	no	—
312	C₃×C₄	C₂²⋊#170	1	2	yes	—
313	C₃×C₄	C₂²×#170	1	1	yes	characteristic
314	C₃×C₄	C₂×#704	1	1	yes	characteristic
315	C₂×C₅	—	4	4	no	—
316	C₂×C₅	C₃×D₄⋊C₈	1	4	yes	complemented
317	C₂×C₅	C₂×C₃×C₂²⋊C₈	1	1	yes	characteristic
318	C₂×C₅	C₂×C₃×#102	1	1	yes	characteristic
319	C₂×C₅	C₂×C₃×#104	1	1	yes	characteristic
320	C₂³	—	2	2	no	—
321	C₂³	—	2	4	no	—
322	C₂³	—	4	2	no	—
323	C₂³	—	4	2	no	—
324	C₂³	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
325	D₄	—	2	2	no	—
326	D₄	—	2	4	no	—
327	D₄	C₂×C₃×#170	1	4	yes	complemented
328	C₂×C₄	—	5	2	no	—
329	C₂×C₄	—	5	2	no	—
330	C₂×C₄	—	5	1	no	—
331	C₂×C₄	—	5	1	no	—
332	C₂×C₄	—	5	1	no	—
333	C₂×C₄	—	5	1	no	—
334	C₂×C₄	—	10	2	no	—
335	C₂×C₄	—	10	2	no	—
336	C₂×C₄	—	20	2	no	—
337	C₂×C₄	—	20	4	no	—
338	C₂×C₄	—	20	2	no	—
339	C₂×C₄	—	20	2	no	—
340	C₂×C₄	C₂×C₃×#170	1	2	yes	—
341	C₂×C₄	C₃×#704	1	2	yes	—
342	C₂×C₄	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
343	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
344	C₈	—	10	4	no	—
345	C₈	—	20	2	no	—
346	C₂×C₃	—	4	4	no	—
347	C₂×C₃	D₄⋊#170	1	4	yes	direct product factor
348	C₂×C₃	C₂×#4007	1	1	yes	characteristic
349	C₂×C₃	C₂×#4008	1	1	yes	characteristic
350	C₂×C₃	C₂×C₂²⋊#170	1	1	yes	characteristic
351	C₅	C₂×C₃×D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
352	C₂²	—	2	4	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	8	no	—
356	C₂²	C₃×#4007	1	2	yes	—
357	C₂²	C₃×#4008	1	2	yes	—
358	C₂²	C₃×C₂²⋊#170	1	2	yes	—
359	C₂²	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
360	C₄	—	5	1	no	—
361	C₄	—	5	2	no	—
362	C₄	—	5	1	no	—
363	C₄	—	10	1	no	—
364	C₄	—	10	1	no	—
365	C₄	—	20	2	no	—
366	C₄	C₃×C₂²⋊#170	1	2	yes	—
367	C₄	C₂²×C₃×#170	1	1	yes	characteristic
368	C₄	C₂×C₃×#704	1	1	yes	characteristic
369	C₃	C₂×D₄⋊#170	1	1	yes	characteristic, direct product factor, Sylow
370	C₂	—	4	4	no	—
371	C₂	C₃×D₄⋊#170	1	4	yes	direct product factor
372	C₂	C₂×C₃×#4007	1	1	yes	characteristic
373	C₂	C₂×C₃×#4008	1	1	yes	characteristic
374	C₂	C₂×C₃×C₂²⋊#170	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂²⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂²×C₃×C₈
Frattini	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)
Fitting, prime radical	C₂²×C₃×C₅×D₄	C₄
socle	C₂³×C₃×C₅	C₂²⋊C₄
cosocle	C₄×Dic₅	C₂³×C₃
hypercenter	C₂²×C₃×D₄	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₃×D₄⋊C₈
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄⋊#170	C₂	semidirect
3. C₂×C₃×C₄×#170	C₂	semidirect
4. C₃×D₄⋊#170	C₂	direct (N × H)
5. C₂×D₄⋊#170	C₃	direct (N × H)
18. C₃×C₄⋊#170	C₂²	semidirect
20. C₃×C₄×#170	C₂²	semidirect
23. C₂×C₄⋊#170	C₂×C₃	semidirect
24. C₂×C₄×#170	C₂×C₃	semidirect
25. D₄⋊#170	C₂×C₃	direct (N × H)
29. C₂×C₃×C₅×D₄	C₈	semidirect
67. C₄⋊#170	C₂²×C₃	semidirect
69. C₄×#170	C₂²×C₃	semidirect
78. C₃×C₅×D₄	C₂×C₈	semidirect
115. C₂×C₅×D₄	C₃×C₈	semidirect
161. C₂×C₃×D₄	#170	semidirect
190. C₅×D₄	C₂×C₃×C₈	semidirect
225. C₂×C₃×C₅	D₄⋊C₈	semidirect
236. C₃×D₄	C₂×#170	semidirect
275. C₂×D₄	C₃×#170	semidirect
297. C₃×C₅	C₂×D₄⋊C₈	semidirect
316. C₂×C₅	C₃×D₄⋊C₈	semidirect
327. D₄	C₂×C₃×#170	semidirect
347. C₂×C₃	D₄⋊#170	direct (N × H)
351. C₅	C₂×C₃×D₄⋊C₈	semidirect
369. C₃	C₂×D₄⋊#170	direct (N × H)
371. C₂	C₃×D₄⋊#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×D₄×Dic₅	2
C₂×C₃×C₄⋊#170	2
C₂×C₃×C₄×#170	2
C₃×D₄⋊#170	2
C₂×D₄⋊#170	3
C₂×C₃×D₄⋊C₈	5

Subgroups — C2×C3×D4⋊#170 #14281480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₄⋊#170 #14281480