Subgroups — C₃×AGL(1,𝔽₅)×C₄⋊Q₈ #14322312

Order 1920.

1176 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×AGL(1,𝔽₅)	C₂	1	2	yes	maximal
2	C₃×D₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₃×(C₂×AGL(1,𝔽₅))⋊Q₈	C₂	1	2	yes	maximal
4	C₃×#65712	C₂	1	4	yes	maximal
5	C₃×C₄⋊C₄×AGL(1,𝔽₅)	C₂	1	4	yes	maximal
6	C₃×#65688	C₂	1	1	yes	maximal, characteristic
7	C₃×C₄²×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
8	AGL(1,𝔽₅)×C₄⋊Q₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
10	C₃×Q₈×AGL(1,𝔽₅)	—	2	8	no	—
11	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	4	yes	—
12	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
13	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	4	yes	—
14	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
15	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	4	yes	—
17	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
19	C₃×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
20	C₃×#4090	C₄	1	2	yes	complemented
21	C₃×D₅×C₄⋊C₄	C₂²	1	4	yes	—
22	C₃×#4034	C₄	1	4	yes	complemented
23	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
24	C₃×#4015	C₄	1	1	yes	characteristic, complemented
25	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	8	yes	—
26	C₃×C₄×C₄⋊Q₈	—	5	1	no	maximal, Hall
27	C₂×Q₈×AGL(1,𝔽₅)	C₂×C₃	1	2	yes	—
28	D₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
29	(C₂×AGL(1,𝔽₅))⋊Q₈	C₂×C₃	1	2	yes	—
30	#65712	C₂×C₃	1	4	yes	—
31	C₄⋊C₄×AGL(1,𝔽₅)	C₂×C₃	1	4	yes	—
32	#65688	C₂×C₃	1	1	yes	characteristic
33	C₄²×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic
34	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	4	yes	—
35	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
36	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
37	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
38	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
39	C₃×Q₈×D₅	—	2	4	no	—
40	C₃×Q₈×D₅	—	2	4	no	—
41	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
42	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
43	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
44	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
45	C₂×C₃×Dic₁₀	C₂×C₄	1	4	yes	—
46	C₃×C₄⋊AGL(1,𝔽₅)	—	2	8	no	—
47	C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
48	C₃×C₄⋊AGL(1,𝔽₅)	—	2	8	no	—
49	C₃×C₄×AGL(1,𝔽₅)	—	2	8	no	—
50	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
51	C₃×C₄×AGL(1,𝔽₅)	—	2	4	no	—
52	C₃×C₄×AGL(1,𝔽₅)	D₄	1	4	yes	—
53	C₃×C₄×AGL(1,𝔽₅)	Q₈	1	8	yes	complemented
54	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
55	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
56	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	—
57	C₃×#683	C₂×C₄	1	8	yes	—
58	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
59	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
60	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
61	C₂×C₃×C₄×Q₈	—	5	2	no	—
62	C₃×#391	—	5	2	no	—
63	C₃×#389	—	5	4	no	—
64	C₃×#384	—	5	1	no	—
65	C₃×C₄×C₄⋊C₄	—	5	4	no	—
66	C₃×C₄³	—	5	1	no	—
67	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
68	Q₈×AGL(1,𝔽₅)	—	2	8	no	—
69	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	—
70	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
71	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	—
72	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
73	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	—
75	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
77	C₅×C₄⋊Q₈	C₃×C₄	1	1	yes	characteristic, complemented
78	#4090	C₃×C₄	1	2	yes	complemented
79	D₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
80	#4034	C₃×C₄	1	4	yes	complemented
81	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
82	#4015	C₃×C₄	1	1	yes	characteristic, complemented
83	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	8	yes	—
84	C₄×C₄⋊Q₈	—	5	1	no	Sylow
85	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
86	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
87	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
88	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
89	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
90	C₂×C₃×AGL(1,𝔽₅)	—	2	8	no	—
91	C₂×C₃×AGL(1,𝔽₅)	C₂×D₄	1	2	yes	—
92	C₂×C₃×AGL(1,𝔽₅)	C₂×D₄	1	2	yes	—
93	C₂×C₃×AGL(1,𝔽₅)	C₂×Q₈	1	4	yes	—
94	C₂×C₃×AGL(1,𝔽₅)	C₂×Q₈	1	4	yes	—
95	C₃×C₅×Q₈	—	2	4	no	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
100	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
102	C₃×C₄×D₅	—	2	4	no	—
103	C₃×C₄×D₅	—	2	4	no	—
104	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
105	C₃×C₄×D₅	C₂×Q₈	1	4	yes	—
106	C₃×C₄×D₅	#41	1	2	yes	—
107	C₃×C₄×D₅	#41	1	4	yes	—
108	C₃×Dic₁₀	—	2	4	no	—
109	C₃×Dic₁₀	—	2	8	no	—
110	C₂²×C₃×Q₈	—	5	2	no	—
111	C₃×C₄⋊Q₈	—	5	2	no	—
112	C₃×C₄⋊Q₈	—	5	4	no	—
113	C₃×C₄⋊Q₈	—	5	1	no	—
114	C₃×C₄⋊Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
115	C₃×C₄×Q₈	—	10	8	no	—
116	C₂×C₃×C₄⋊C₄	—	5	4	no	—
117	C₂×C₃×C₄⋊C₄	—	5	4	no	—
118	C₂×C₃×C₄⋊C₄	—	5	2	no	—
119	C₂×C₃×C₄⋊C₄	—	5	4	no	—
120	C₂×C₃×C₄²	—	5	2	no	—
121	C₂×C₃×C₄²	—	5	1	no	—
122	C₂×C₃×C₄²	—	5	1	no	—
123	C₂×C₃×C₄²	—	5	2	no	—
124	C₂×C₃×C₄²	—	5	1	no	—
125	C₂×C₃×C₄²	—	5	4	no	—
126	C₃×#95	—	5	8	no	—
127	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	4	yes	—
128	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
129	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
130	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
131	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
132	Q₈×D₅	—	2	4	no	—
133	Q₈×D₅	—	2	4	no	—
134	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
135	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
136	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
137	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
138	C₂×Dic₁₀	C₂×C₃×C₄	1	4	yes	—
139	C₄⋊AGL(1,𝔽₅)	—	2	8	no	—
140	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
141	C₄⋊AGL(1,𝔽₅)	—	2	8	no	—
142	C₄×AGL(1,𝔽₅)	—	2	8	no	—
143	C₄×AGL(1,𝔽₅)	—	2	2	no	—
144	C₄×AGL(1,𝔽₅)	—	2	4	no	—
145	C₄×AGL(1,𝔽₅)	C₃×D₄	1	4	yes	—
146	C₄×AGL(1,𝔽₅)	C₃×Q₈	1	8	yes	complemented
147	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
148	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
149	C₄⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
150	#683	C₂×C₃×C₄	1	8	yes	—
151	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
152	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
153	C₂×C₄⋊Q₈	—	5	1	no	—
154	C₂×C₄×Q₈	—	5	2	no	—
155	#391	—	5	2	no	—
156	#389	—	5	4	no	—
157	#384	—	5	1	no	—
158	C₄×C₄⋊C₄	—	5	4	no	—
159	C₄³	—	5	1	no	—
160	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₃×D₅	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₃×D₅	C₂²×Q₈	1	2	yes	—
163	C₂×C₃×D₅	C₂×#41	1	2	yes	—
164	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
165	C₃×AGL(1,𝔽₅)	—	2	2	no	—
166	C₃×AGL(1,𝔽₅)	—	2	4	no	—
167	C₃×AGL(1,𝔽₅)	—	4	4	no	—
168	C₃×AGL(1,𝔽₅)	C₄⋊Q₈	1	4	yes	direct product factor
169	C₃×C₄×C₅	—	2	4	no	—
170	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
171	C₃×C₄×C₅	C₄×Q₈	1	4	yes	complemented
172	C₃×Dic₅	—	2	4	no	—
173	C₃×Dic₅	C₄×D₄	1	2	yes	—
174	C₃×Dic₅	C₄×Q₈	1	4	yes	complemented
175	C₂×C₃×Q₈	—	5	4	no	—
176	C₂×C₃×Q₈	—	5	2	no	—
177	C₂×C₃×Q₈	—	10	4	no	—
178	C₂×C₃×Q₈	—	10	4	no	—
179	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	2	yes	—
180	C₂²×C₃×C₄	—	5	1	no	—
181	C₂²×C₃×C₄	—	5	2	no	—
182	C₂²×C₃×C₄	—	5	1	no	—
183	C₂²×C₃×C₄	—	5	2	no	—
184	C₂²×C₃×C₄	—	5	1	no	—
185	C₂²×C₃×C₄	—	5	4	no	—
186	C₂²×C₃×C₄	—	5	4	no	—
187	C₃×C₄⋊C₄	—	5	8	no	—
188	C₃×C₄⋊C₄	—	5	4	no	—
189	C₃×C₄⋊C₄	—	10	8	no	—
190	C₃×C₄⋊C₄	—	10	4	no	—
191	C₃×C₄⋊C₄	—	10	8	no	—
192	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	4	yes	—
193	C₃×C₄²	—	5	4	no	—
194	C₃×C₄²	—	5	8	no	—
195	C₃×C₄²	—	5	1	no	—
196	C₃×C₄²	—	5	2	no	—
197	C₃×C₄²	—	10	2	no	—
198	C₃×C₄²	—	10	4	no	—
199	C₃×C₄²	—	10	8	no	—
200	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
201	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
202	C₂×AGL(1,𝔽₅)	—	2	2	no	—
203	C₂×AGL(1,𝔽₅)	—	2	2	no	—
204	C₂×AGL(1,𝔽₅)	—	2	2	no	—
205	C₂×AGL(1,𝔽₅)	—	2	4	no	—
206	C₂×AGL(1,𝔽₅)	—	2	8	no	—
207	C₂×AGL(1,𝔽₅)	C₂×C₃×D₄	1	2	yes	—
208	C₂×AGL(1,𝔽₅)	C₂×C₃×D₄	1	2	yes	—
209	C₂×AGL(1,𝔽₅)	C₂×C₃×Q₈	1	4	yes	—
210	C₂×AGL(1,𝔽₅)	C₂×C₃×Q₈	1	4	yes	—
211	C₅×Q₈	—	2	4	no	—
212	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
213	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
215	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
216	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
217	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
218	C₄×D₅	—	2	4	no	—
219	C₄×D₅	—	2	4	no	—
220	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
221	C₄×D₅	C₂×C₃×Q₈	1	4	yes	—
222	C₄×D₅	C₃×#41	1	2	yes	—
223	C₄×D₅	C₃×#41	1	4	yes	—
224	Dic₁₀	—	2	4	no	—
225	Dic₁₀	—	2	8	no	—
226	C₂²×Q₈	—	5	2	no	—
227	C₄⋊Q₈	—	5	2	no	—
228	C₄⋊Q₈	—	5	4	no	—
229	C₄⋊Q₈	—	5	1	no	—
230	C₄⋊Q₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
231	C₄×Q₈	—	10	8	no	—
232	C₂×C₄⋊C₄	—	5	4	no	—
233	C₂×C₄⋊C₄	—	5	2	no	—
234	C₂×C₄⋊C₄	—	5	4	no	—
235	C₂×C₄⋊C₄	—	5	4	no	—
236	C₂×C₄²	—	5	1	no	—
237	C₂×C₄²	—	5	2	no	—
238	C₂×C₄²	—	5	1	no	—
239	C₂×C₄²	—	5	4	no	—
240	C₂×C₄²	—	5	2	no	—
241	C₂×C₄²	—	5	1	no	—
242	#95	—	5	8	no	—
243	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
244	C₂×C₃×C₅	C₂×C₄×Q₈	1	2	yes	—
245	C₃×D₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
246	C₃×D₅	#532	1	1	yes	characteristic
247	C₃×D₅	#533	1	2	yes	—
248	C₂³×C₃	—	5	1	no	—
249	C₃×Q₈	—	2	4	no	—
250	C₃×Q₈	—	10	8	no	—
251	C₃×Q₈	—	10	4	no	—
252	C₂×C₃×C₄	—	5	2	no	—
253	C₂×C₃×C₄	—	5	4	no	—
254	C₂×C₃×C₄	—	5	2	no	—
255	C₂×C₃×C₄	—	5	1	no	—
256	C₂×C₃×C₄	—	5	2	no	—
257	C₂×C₃×C₄	—	5	2	no	—
258	C₂×C₃×C₄	—	5	4	no	—
259	C₂×C₃×C₄	—	5	4	no	—
260	C₂×C₃×C₄	—	5	2	no	—
261	C₂×C₃×C₄	—	5	4	no	—
262	C₂×C₃×C₄	—	5	4	no	—
263	C₂×C₃×C₄	—	10	4	no	—
264	C₂×C₃×C₄	—	10	4	no	—
265	C₂×C₃×C₄	—	10	2	no	—
266	C₂×C₃×C₄	—	10	2	no	—
267	C₂×C₃×C₄	—	10	2	no	—
268	C₂×C₃×C₄	—	10	4	no	—
269	C₂×C₃×C₄	—	10	8	no	—
270	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	4	yes	—
271	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
273	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
274	C₂×D₅	C₂²×C₃×D₄	1	1	yes	characteristic
275	C₂×D₅	C₂²×C₃×Q₈	1	2	yes	—
276	C₂×D₅	C₂×C₃×#41	1	2	yes	—
277	C₂×D₅	C₂×C₃×#41	1	1	yes	characteristic
278	AGL(1,𝔽₅)	—	2	2	no	—
279	AGL(1,𝔽₅)	—	2	4	no	—
280	AGL(1,𝔽₅)	—	4	4	no	—
281	AGL(1,𝔽₅)	C₃×C₄⋊Q₈	1	4	yes	direct product factor
282	C₄×C₅	—	2	4	no	—
283	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
284	C₄×C₅	C₃×C₄×Q₈	1	4	yes	complemented
285	Dic₅	—	2	4	no	—
286	Dic₅	C₃×C₄×D₄	1	2	yes	—
287	Dic₅	C₃×C₄×Q₈	1	4	yes	complemented
288	C₂×Q₈	—	5	4	no	—
289	C₂×Q₈	—	5	2	no	—
290	C₂×Q₈	—	10	4	no	—
291	C₂×Q₈	—	10	4	no	—
292	C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
293	C₂²×C₄	—	5	1	no	—
294	C₂²×C₄	—	5	2	no	—
295	C₂²×C₄	—	5	1	no	—
296	C₂²×C₄	—	5	2	no	—
297	C₂²×C₄	—	5	1	no	—
298	C₂²×C₄	—	5	4	no	—
299	C₂²×C₄	—	5	4	no	—
300	C₄⋊C₄	—	5	8	no	—
301	C₄⋊C₄	—	5	4	no	—
302	C₄⋊C₄	—	10	4	no	—
303	C₄⋊C₄	—	10	8	no	—
304	C₄⋊C₄	—	10	8	no	—
305	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	4	yes	—
306	C₄²	—	5	4	no	—
307	C₄²	—	5	8	no	—
308	C₄²	—	5	1	no	—
309	C₄²	—	5	2	no	—
310	C₄²	—	10	8	no	—
311	C₄²	—	10	2	no	—
312	C₄²	—	10	4	no	—
313	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
314	C₃×C₅	C₄×C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
315	C₂²×C₃	—	5	1	no	—
316	C₂²×C₃	—	5	1	no	—
317	C₂²×C₃	—	5	2	no	—
318	C₂²×C₃	—	5	2	no	—
319	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
320	C₃×C₄	—	2	4	no	—
321	C₃×C₄	—	5	4	no	—
322	C₃×C₄	—	5	2	no	—
323	C₃×C₄	—	5	4	no	—
324	C₃×C₄	—	10	2	no	—
325	C₃×C₄	—	10	4	no	—
326	C₃×C₄	—	10	4	no	—
327	C₃×C₄	—	20	4	no	—
328	C₃×C₄	D₄×AGL(1,𝔽₅)	1	2	yes	—
329	C₃×C₄	Q₈×AGL(1,𝔽₅)	1	4	yes	complemented
330	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
331	C₂×C₅	C₂×C₃×C₄×Q₈	1	2	yes	—
332	D₅	C₂×C₃×C₄⋊Q₈	1	1	yes	characteristic
333	D₅	C₃×#532	1	1	yes	characteristic
334	D₅	C₃×#533	1	2	yes	—
335	C₂³	—	5	1	no	—
336	Q₈	—	2	4	no	—
337	Q₈	—	10	8	no	—
338	Q₈	—	10	4	no	—
339	C₂×C₄	—	5	2	no	—
340	C₂×C₄	—	5	4	no	—
341	C₂×C₄	—	5	2	no	—
342	C₂×C₄	—	5	1	no	—
343	C₂×C₄	—	5	2	no	—
344	C₂×C₄	—	5	2	no	—
345	C₂×C₄	—	5	4	no	—
346	C₂×C₄	—	5	4	no	—
347	C₂×C₄	—	5	2	no	—
348	C₂×C₄	—	5	4	no	—
349	C₂×C₄	—	5	4	no	—
350	C₂×C₄	—	10	4	no	—
351	C₂×C₄	—	10	4	no	—
352	C₂×C₄	—	10	2	no	—
353	C₂×C₄	—	10	2	no	—
354	C₂×C₄	—	10	2	no	—
355	C₂×C₄	—	10	4	no	—
356	C₂×C₄	—	10	8	no	—
357	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	4	yes	—
358	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
359	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
360	C₂×C₃	—	5	1	no	—
361	C₂×C₃	—	5	1	no	—
362	C₂×C₃	—	5	2	no	—
363	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
364	C₂×C₃	C₂×Q₈×AGL(1,𝔽₅)	1	2	yes	—
365	C₅	C₃×C₄×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
366	C₂²	—	5	1	no	—
367	C₂²	—	5	1	no	—
368	C₂²	—	5	2	no	—
369	C₂²	—	5	2	no	—
370	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
371	C₄	—	2	4	no	—
372	C₄	—	5	4	no	—
373	C₄	—	5	2	no	—
374	C₄	—	5	4	no	—
375	C₄	—	10	2	no	—
376	C₄	—	10	4	no	—
377	C₄	—	10	4	no	—
378	C₄	—	20	4	no	—
379	C₄	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
380	C₄	C₃×Q₈×AGL(1,𝔽₅)	1	4	yes	complemented
381	C₃	AGL(1,𝔽₅)×C₄⋊Q₈	1	1	yes	characteristic, direct product factor, Sylow
382	C₂	—	5	1	no	—
383	C₂	—	5	1	no	—
384	C₂	—	5	2	no	—
385	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
386	C₂	C₂×C₃×Q₈×AGL(1,𝔽₅)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂³×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×C₄⋊Q₈	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×C₃×D₅	C₂⁴
cosocle	C₂²×D₅	C₂⁴×C₃
hypercenter	C₃×C₄⋊Q₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×C₄×C₄⋊Q₈
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
8. AGL(1,𝔽₅)×C₄⋊Q₈	C₃	direct (N × H)
19. C₃×C₅×C₄⋊Q₈	C₄	semidirect
20. C₃×#4090	C₄	semidirect
22. C₃×#4034	C₄	semidirect
24. C₃×#4015	C₄	semidirect
53. C₃×C₄×AGL(1,𝔽₅)	Q₈	semidirect
77. C₅×C₄⋊Q₈	C₃×C₄	semidirect
78. #4090	C₃×C₄	semidirect
80. #4034	C₃×C₄	semidirect
82. #4015	C₃×C₄	semidirect
114. C₃×C₄⋊Q₈	AGL(1,𝔽₅)	direct (N × H)
146. C₄×AGL(1,𝔽₅)	C₃×Q₈	semidirect
168. C₃×AGL(1,𝔽₅)	C₄⋊Q₈	direct (N × H)
171. C₃×C₄×C₅	C₄×Q₈	semidirect
174. C₃×Dic₅	C₄×Q₈	semidirect
230. C₄⋊Q₈	C₃×AGL(1,𝔽₅)	direct (N × H)
281. AGL(1,𝔽₅)	C₃×C₄⋊Q₈	direct (N × H)
284. C₄×C₅	C₃×C₄×Q₈	semidirect
287. Dic₅	C₃×C₄×Q₈	semidirect
314. C₃×C₅	C₄×C₄⋊Q₈	semidirect
329. C₃×C₄	Q₈×AGL(1,𝔽₅)	semidirect
365. C₅	C₃×C₄×C₄⋊Q₈	semidirect
380. C₄	C₃×Q₈×AGL(1,𝔽₅)	semidirect
381. C₃	AGL(1,𝔽₅)×C₄⋊Q₈	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×Q₈×AGL(1,𝔽₅)	2
C₃×D₅×C₄⋊Q₈	2
C₃×(C₂×AGL(1,𝔽₅))⋊Q₈	2
C₃×#65712	2
C₃×C₄⋊C₄×AGL(1,𝔽₅)	2
C₃×#65688	2
C₃×C₄²×AGL(1,𝔽₅)	2
AGL(1,𝔽₅)×C₄⋊Q₈	3
C₃×C₄×C₄⋊Q₈	5

Subgroups — C3×AGL(1,𝔽5)×C4⋊Q8 #14322312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×AGL(1,𝔽₅)×C₄⋊Q₈ #14322312