Subgroups — C₃×C₄⋊C₄×Dic₁₀ #14327218

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×Dic₁₀	C₂	1	2	yes	maximal
2	C₂×C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₃×#65265	C₂	1	2	yes	maximal
5	C₃×C₄⋊C₄×Dic₅	C₂	1	2	yes	maximal
6	C₃×#65224	C₂	1	1	yes	maximal, characteristic
7	C₃×#65217	C₂	1	2	yes	maximal
8	C₃×#64936	C₂	1	4	yes	maximal
9	C₄⋊C₄×Dic₁₀	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
16	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
17	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×#683	C₂²	1	4	yes	—
20	C₂×C₃×#683	C₂²	1	4	yes	—
21	C₂×C₃×#683	C₂²	1	2	yes	—
22	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	—
23	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
24	C₃×C₄×Dic₁₀	—	2	8	no	—
25	C₃×C₄×Dic₁₀	C₄	1	8	yes	complemented
26	C₃×C₅×#95	C₂²	1	2	yes	—
27	C₃×#3963	C₂²	1	4	yes	—
28	C₃×Q₈×C₄⋊C₄	—	5	1	no	maximal, Hall
29	C₂×C₄×Dic₁₀	C₂×C₃	1	2	yes	—
30	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic
31	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
32	#65265	C₂×C₃	1	2	yes	—
33	C₄⋊C₄×Dic₅	C₂×C₃	1	2	yes	—
34	#65224	C₂×C₃	1	1	yes	characteristic
35	#65217	C₂×C₃	1	2	yes	—
36	#64936	C₂×C₃	1	4	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
43	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
44	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
45	C₂×C₃×Dic₁₀	C₂×C₄	1	4	yes	—
46	C₂×C₃×Dic₁₀	D₄	1	4	yes	—
47	C₂×C₃×Dic₁₀	Q₈	1	4	yes	—
48	C₃×C₅×C₄⋊C₄	—	2	2	no	—
49	C₃×C₅×C₄⋊C₄	Q₈	1	4	yes	complemented
50	C₃×C₄²×C₅	—	2	4	no	—
51	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
52	C₃×C₄⋊Dic₅	—	2	4	no	—
53	C₃×C₄⋊Dic₅	—	2	4	no	—
54	C₃×C₄⋊Dic₅	—	4	2	no	—
55	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	—
56	C₃×#683	—	2	8	no	—
57	C₃×#683	—	4	4	no	—
58	C₃×#683	C₂×C₄	1	8	yes	—
59	C₃×C₄×Dic₅	—	2	8	no	—
60	C₃×C₄×Dic₅	C₂×C₄	1	8	yes	—
61	C₂×C₃×C₄×Q₈	—	5	1	no	—
62	C₂×C₃×C₄×Q₈	—	5	2	no	—
63	C₃×#389	—	5	2	no	—
64	C₃×#389	—	5	4	no	—
65	C₃×#384	—	5	2	no	—
66	C₃×#384	—	5	1	no	—
67	C₃×C₄×C₄⋊C₄	—	5	2	no	—
68	C₃×C₄×C₄⋊C₄	D₅	1	1	yes	characteristic
69	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
73	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
75	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
76	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
77	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
78	C₂×#683	C₂²×C₃	1	4	yes	—
79	C₂×#683	C₂²×C₃	1	4	yes	—
80	C₂×#683	C₂²×C₃	1	2	yes	—
81	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	—
82	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
83	C₄×Dic₁₀	—	2	8	no	—
84	C₄×Dic₁₀	C₃×C₄	1	8	yes	complemented
85	C₅×#95	C₂²×C₃	1	2	yes	—
86	#3963	C₂²×C₃	1	4	yes	—
87	Q₈×C₄⋊C₄	—	5	1	no	Sylow
88	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	2	1	no	—
91	C₂×C₃×C₄×C₅	—	2	1	no	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
101	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
103	C₂×C₃×C₄×C₅	#41	1	2	yes	—
104	C₂×C₃×Dic₅	—	2	2	no	—
105	C₂×C₃×Dic₅	—	2	2	no	—
106	C₂×C₃×Dic₅	—	2	4	no	—
107	C₂×C₃×Dic₅	—	2	4	no	—
108	C₂×C₃×Dic₅	—	2	4	no	—
109	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
110	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
111	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
112	C₂×C₃×Dic₅	C₂×Q₈	1	4	yes	—
113	C₃×Dic₁₀	C₄⋊C₄	1	16	yes	direct product factor
114	C₂²×C₃×Q₈	—	5	1	no	—
115	C₃×C₄×Q₈	—	5	8	no	—
116	C₃×C₄×Q₈	—	10	8	no	—
117	C₂×C₃×C₄⋊C₄	—	5	2	no	—
118	C₂×C₃×C₄⋊C₄	—	5	1	no	—
119	C₂×C₃×C₄⋊C₄	—	5	2	no	—
120	C₂×C₃×C₄⋊C₄	—	5	4	no	—
121	C₂×C₃×C₄⋊C₄	—	5	2	no	—
122	C₂×C₃×C₄⋊C₄	—	5	4	no	—
123	C₂×C₃×C₄⋊C₄	—	5	2	no	—
124	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
125	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
126	C₂×C₃×C₄²	—	5	2	no	—
127	C₂×C₃×C₄²	—	5	4	no	—
128	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
129	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
130	C₃×#95	—	5	4	no	—
131	C₃×#95	C₂×D₅	1	2	yes	—
132	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
133	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
135	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
137	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
138	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
139	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
140	C₂×Dic₁₀	C₂×C₃×C₄	1	4	yes	—
141	C₂×Dic₁₀	C₃×D₄	1	4	yes	—
142	C₂×Dic₁₀	C₃×Q₈	1	4	yes	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	C₃×Q₈	1	4	yes	complemented
145	C₄²×C₅	—	2	4	no	—
146	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
147	C₄⋊Dic₅	—	2	4	no	—
148	C₄⋊Dic₅	—	2	4	no	—
149	C₄⋊Dic₅	—	4	2	no	—
150	C₄⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
151	#683	—	2	8	no	—
152	#683	—	4	4	no	—
153	#683	C₂×C₃×C₄	1	8	yes	—
154	C₄×Dic₅	—	2	8	no	—
155	C₄×Dic₅	C₂×C₃×C₄	1	8	yes	—
156	C₂×C₄×Q₈	—	5	1	no	—
157	C₂×C₄×Q₈	—	5	2	no	—
158	#389	—	5	2	no	—
159	#389	—	5	4	no	—
160	#384	—	5	2	no	—
161	#384	—	5	1	no	—
162	C₄×C₄⋊C₄	—	5	2	no	—
163	C₄×C₄⋊C₄	C₃×D₅	1	1	yes	characteristic
164	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
165	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
166	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
167	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
168	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
169	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
171	C₃×C₄×C₅	—	2	2	no	—
172	C₃×C₄×C₅	—	2	4	no	—
173	C₃×C₄×C₅	—	4	2	no	—
174	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
175	C₃×C₄×C₅	C₄×Q₈	1	4	yes	complemented
176	C₃×Dic₅	—	2	4	no	—
177	C₃×Dic₅	—	4	4	no	—
178	C₃×Dic₅	C₂×C₄⋊C₄	1	8	yes	—
179	C₂×C₃×Q₈	—	5	4	no	—
180	C₂×C₃×Q₈	—	5	4	no	—
181	C₂×C₃×Q₈	—	5	4	no	—
182	C₂²×C₃×C₄	—	5	2	no	—
183	C₂²×C₃×C₄	—	5	2	no	—
184	C₂²×C₃×C₄	—	5	4	no	—
185	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
186	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
187	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
188	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
190	C₃×C₄⋊C₄	—	2	2	no	—
191	C₃×C₄⋊C₄	—	5	8	no	—
192	C₃×C₄⋊C₄	—	5	4	no	—
193	C₃×C₄⋊C₄	—	10	8	no	—
194	C₃×C₄⋊C₄	—	10	4	no	—
195	C₃×C₄⋊C₄	—	10	4	no	—
196	C₃×C₄⋊C₄	—	20	4	no	—
197	C₃×C₄⋊C₄	—	20	2	no	—
198	C₃×C₄⋊C₄	Dic₁₀	1	4	yes	direct product factor
199	C₃×C₄²	—	2	4	no	—
200	C₃×C₄²	—	5	8	no	—
201	C₃×C₄²	—	10	8	no	—
202	C₃×C₄²	C₄×D₅	1	4	yes	—
203	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
212	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
213	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
214	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
215	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
216	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
217	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
218	C₂×C₄×C₅	C₃×#41	1	2	yes	—
219	C₂×Dic₅	—	2	2	no	—
220	C₂×Dic₅	—	2	2	no	—
221	C₂×Dic₅	—	2	4	no	—
222	C₂×Dic₅	—	2	4	no	—
223	C₂×Dic₅	—	2	4	no	—
224	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
225	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
226	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
227	C₂×Dic₅	C₂×C₃×Q₈	1	4	yes	—
228	Dic₁₀	C₃×C₄⋊C₄	1	16	yes	direct product factor
229	C₂²×Q₈	—	5	1	no	—
230	C₄×Q₈	—	5	8	no	—
231	C₄×Q₈	—	10	8	no	—
232	C₂×C₄⋊C₄	—	5	2	no	—
233	C₂×C₄⋊C₄	—	5	1	no	—
234	C₂×C₄⋊C₄	—	5	4	no	—
235	C₂×C₄⋊C₄	—	5	2	no	—
236	C₂×C₄⋊C₄	—	5	2	no	—
237	C₂×C₄⋊C₄	—	5	4	no	—
238	C₂×C₄⋊C₄	—	5	2	no	—
239	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
241	C₂×C₄²	—	5	2	no	—
242	C₂×C₄²	—	5	4	no	—
243	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
244	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
245	#95	—	5	4	no	—
246	#95	C₂×C₃×D₅	1	2	yes	—
247	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
248	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
249	C₂×C₃×C₅	#520	1	1	yes	characteristic
250	C₂×C₃×C₅	D₄×Q₈	1	1	yes	characteristic
251	C₂×C₃×C₅	#550	1	1	yes	characteristic
252	C₂×C₃×C₅	#557	1	1	yes	characteristic
253	C₂×C₃×C₅	Q₈²	1	1	yes	characteristic
254	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
255	C₃×Q₈	—	5	16	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	5	4	no	—
264	C₂×C₃×C₄	—	5	4	no	—
265	C₂×C₃×C₄	—	5	4	no	—
266	C₂×C₃×C₄	—	5	4	no	—
267	C₂×C₃×C₄	—	10	2	no	—
268	C₂×C₃×C₄	—	10	2	no	—
269	C₂×C₃×C₄	—	10	4	no	—
270	C₂×C₃×C₄	—	10	4	no	—
271	C₂×C₃×C₄	—	10	4	no	—
272	C₂×C₃×C₄	C₂×Dic₁₀	1	4	yes	—
273	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
274	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
275	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
276	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
277	C₂×C₃×C₄	#709	1	2	yes	—
278	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
279	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
280	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
281	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
282	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
283	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
284	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
285	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
286	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
287	C₄×C₅	—	2	2	no	—
288	C₄×C₅	—	2	4	no	—
289	C₄×C₅	—	4	2	no	—
290	C₄×C₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
291	C₄×C₅	C₃×C₄×Q₈	1	4	yes	complemented
292	Dic₅	—	2	4	no	—
293	Dic₅	—	4	4	no	—
294	Dic₅	C₂×C₃×C₄⋊C₄	1	8	yes	—
295	C₂×Q₈	—	5	4	no	—
296	C₂×Q₈	—	5	4	no	—
297	C₂×Q₈	—	5	4	no	—
298	C₂²×C₄	—	5	2	no	—
299	C₂²×C₄	—	5	2	no	—
300	C₂²×C₄	—	5	4	no	—
301	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
302	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
303	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	5	8	no	—
308	C₄⋊C₄	—	5	4	no	—
309	C₄⋊C₄	—	10	8	no	—
310	C₄⋊C₄	—	10	4	no	—
311	C₄⋊C₄	—	10	4	no	—
312	C₄⋊C₄	—	20	4	no	—
313	C₄⋊C₄	—	20	2	no	—
314	C₄⋊C₄	C₃×Dic₁₀	1	4	yes	direct product factor
315	C₄²	—	2	4	no	—
316	C₄²	—	5	8	no	—
317	C₄²	—	10	8	no	—
318	C₄²	C₃×C₄×D₅	1	4	yes	—
319	C₃×C₅	Q₈×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
320	C₂²×C₃	C₂²×Dic₁₀	1	1	yes	characteristic
321	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
322	C₂²×C₃	C₂×#709	1	1	yes	characteristic
323	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
324	C₂²×C₃	C₂×Q₈×D₅	1	1	yes	characteristic
325	C₂²×C₃	#4149	1	1	yes	characteristic
326	C₂²×C₃	#4150	1	1	yes	characteristic
327	C₃×C₄	—	2	2	no	—
328	C₃×C₄	—	2	4	no	—
329	C₃×C₄	—	4	2	no	—
330	C₃×C₄	—	5	8	no	—
331	C₃×C₄	—	10	4	no	—
332	C₃×C₄	—	20	4	no	—
333	C₃×C₄	C₄×Dic₁₀	1	4	yes	complemented
334	C₃×C₄	D₅×C₄⋊C₄	1	4	yes	—
335	C₂×C₅	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
336	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
337	C₂×C₅	C₃×#520	1	1	yes	characteristic
338	C₂×C₅	C₃×D₄×Q₈	1	1	yes	characteristic
339	C₂×C₅	C₃×#550	1	1	yes	characteristic
340	C₂×C₅	C₃×#557	1	1	yes	characteristic
341	C₂×C₅	C₃×Q₈²	1	1	yes	characteristic
342	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
343	Q₈	—	5	16	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	5	4	no	—
352	C₂×C₄	—	5	4	no	—
353	C₂×C₄	—	5	4	no	—
354	C₂×C₄	—	5	4	no	—
355	C₂×C₄	—	10	2	no	—
356	C₂×C₄	—	10	2	no	—
357	C₂×C₄	—	10	4	no	—
358	C₂×C₄	—	10	4	no	—
359	C₂×C₄	—	10	4	no	—
360	C₂×C₄	C₂×C₃×Dic₁₀	1	4	yes	—
361	C₂×C₄	C₂×C₃×Dic₁₀	1	2	yes	—
362	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
363	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
364	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
365	C₂×C₄	C₃×#709	1	2	yes	—
366	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
367	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
368	C₂×C₃	C₂×C₄×Dic₁₀	1	1	yes	characteristic
369	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
370	C₂×C₃	#65857	1	1	yes	characteristic
371	C₂×C₃	D₄×Dic₁₀	1	1	yes	characteristic
372	C₂×C₃	#65887	1	1	yes	characteristic
373	C₂×C₃	Q₈×Dic₁₀	1	1	yes	characteristic
374	C₂×C₃	#65901	1	1	yes	characteristic
375	C₅	C₃×Q₈×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
376	C₂²	C₂²×C₃×Dic₁₀	1	1	yes	characteristic
377	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
378	C₂²	C₂×C₃×#709	1	1	yes	characteristic
379	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
380	C₂²	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
381	C₂²	C₃×#4149	1	1	yes	characteristic
382	C₂²	C₃×#4150	1	1	yes	characteristic
383	C₄	—	2	2	no	—
384	C₄	—	2	4	no	—
385	C₄	—	4	2	no	—
386	C₄	—	5	8	no	—
387	C₄	—	10	4	no	—
388	C₄	—	20	4	no	—
389	C₄	C₃×C₄×Dic₁₀	1	4	yes	complemented
390	C₄	C₃×D₅×C₄⋊C₄	1	4	yes	—
391	C₃	C₄⋊C₄×Dic₁₀	1	1	yes	characteristic, direct product factor, Sylow
392	C₂	C₂×C₃×C₄×Dic₁₀	1	1	yes	characteristic
393	C₂	C₂×C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
394	C₂	C₃×#65857	1	1	yes	characteristic
395	C₂	C₃×D₄×Dic₁₀	1	1	yes	characteristic
396	C₂	C₃×#65887	1	1	yes	characteristic
397	C₂	C₃×Q₈×Dic₁₀	1	1	yes	characteristic
398	C₂	C₃×#65901	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×C₄⋊C₄	C₂
socle, prime radical	C₂³×C₃×C₅	C₂⁴
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×C₄⋊C₄	D₅
hypocenter	C₅	C₃×Q₈×C₄⋊C₄
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
9. C₄⋊C₄×Dic₁₀	C₃	direct (N × H)
25. C₃×C₄×Dic₁₀	C₄	semidirect
49. C₃×C₅×C₄⋊C₄	Q₈	semidirect
84. C₄×Dic₁₀	C₃×C₄	semidirect
113. C₃×Dic₁₀	C₄⋊C₄	direct (N × H)
144. C₅×C₄⋊C₄	C₃×Q₈	semidirect
175. C₃×C₄×C₅	C₄×Q₈	semidirect
198. C₃×C₄⋊C₄	Dic₁₀	direct (N × H)
228. Dic₁₀	C₃×C₄⋊C₄	direct (N × H)
291. C₄×C₅	C₃×C₄×Q₈	semidirect
314. C₄⋊C₄	C₃×Dic₁₀	direct (N × H)
319. C₃×C₅	Q₈×C₄⋊C₄	semidirect
333. C₃×C₄	C₄×Dic₁₀	semidirect
375. C₅	C₃×Q₈×C₄⋊C₄	semidirect
389. C₄	C₃×C₄×Dic₁₀	semidirect
391. C₃	C₄⋊C₄×Dic₁₀	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×Dic₁₀	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×#65265	2
C₃×C₄⋊C₄×Dic₅	2
C₃×#65224	2
C₃×#65217	2
C₃×#64936	2
C₄⋊C₄×Dic₁₀	3
C₃×Q₈×C₄⋊C₄	5

Subgroups — C3×C4⋊C4×Dic10 #14327218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄⋊C₄×Dic₁₀ #14327218