Subgroups — C₃×#10617193 #14418824

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×Q₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃×#65788	C₂	1	2	yes	maximal, complemented
3	C₃×#65707	C₂	1	4	yes	maximal, complemented
4	C₃×#65703	C₂	1	2	yes	maximal, complemented
5	C₃×#65682	C₂	1	2	yes	maximal
6	C₃×#65681	C₂	1	1	yes	maximal, characteristic
7	C₃×C₄×#700	C₂	1	2	yes	maximal
8	C₃×C₄×#700	C₂	1	1	yes	maximal, characteristic
9	#10617193	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×Q₈×D₅	C₄	1	1	yes	characteristic
11	C₂×C₃×#700	C₂²	1	2	yes	—
12	C₂×C₃×#700	C₂²	1	1	yes	characteristic
13	C₂×C₃×#700	C₂²	1	1	yes	characteristic
14	C₃×C₄×C₅×Q₈	C₄	1	1	yes	characteristic
15	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic
16	C₃×D₅×C₄⋊C₄	C₄	1	1	yes	characteristic
17	C₃×D₅×C₄⋊C₄	C₄	1	2	yes	—
18	C₃×#4033	C₂²	1	1	yes	characteristic
19	C₃×#4033	C₂²	1	2	yes	—
20	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
21	C₃×C₄²×D₅	C₂²	1	2	yes	—
22	C₃×C₄×Dic₁₀	C₄	1	2	yes	—
23	C₃×C₄×Dic₁₀	C₄	1	1	yes	characteristic
24	C₃×#4004	C₂²	1	4	yes	—
25	C₃×#4004	C₂²	1	4	yes	—
26	C₃×#4002	C₂²	1	2	yes	—
27	C₃×#4002	C₂²	1	4	yes	—
28	C₃×C₄⋊#170	C₂²	1	2	yes	—
29	C₃×C₄⋊#170	C₂²	1	2	yes	—
30	C₃×C₄×#170	C₂²	1	4	yes	—
31	C₃×C₄×#170	C₂²	1	2	yes	—
32	C₃×Q₈×M₁₆	—	5	1	no	maximal, Hall
33	C₄×Q₈×D₅	C₂×C₃	1	1	yes	characteristic
34	#65788	C₂×C₃	1	2	yes	complemented
35	#65707	C₂×C₃	1	4	yes	complemented
36	#65703	C₂×C₃	1	2	yes	complemented
37	#65682	C₂×C₃	1	2	yes	—
38	#65681	C₂×C₃	1	1	yes	characteristic
39	C₄×#700	C₂×C₃	1	2	yes	—
40	C₄×#700	C₂×C₃	1	1	yes	characteristic
41	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
42	C₃×Q₈×D₅	—	2	4	no	—
43	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
45	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
47	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
48	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
49	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×#170	C₂³	1	4	yes	—
51	C₂×C₃×#170	C₂³	1	2	yes	—
52	C₂×C₃×#170	C₂³	1	2	yes	—
53	C₃×#700	—	2	4	no	—
54	C₃×#700	—	2	2	no	—
55	C₃×#700	Q₈	1	4	yes	complemented
56	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
57	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
59	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
60	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
61	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
62	C₃×#683	C₂×C₄	1	2	yes	—
63	C₃×#683	C₂×C₄	1	2	yes	—
64	C₃×#683	C₂×C₄	1	2	yes	—
65	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
66	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
67	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
68	C₃×C₄×Dic₅	C₂³	1	2	yes	—
69	C₃×C₄×Dic₅	C₂³	1	2	yes	—
70	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₄×Q₈	—	5	1	no	—
72	C₃×#446	—	5	4	no	—
73	C₃×#446	—	5	2	no	—
74	C₃×C₈×Q₈	—	5	2	no	—
75	C₃×#423	—	5	1	no	—
76	C₃×#423	—	5	2	no	—
77	C₃×C₄×M₁₆	—	5	2	no	—
78	C₃×C₄×M₁₆	—	5	1	no	—
79	C₂×Q₈×D₅	C₃×C₄	1	1	yes	characteristic
80	C₂×#700	C₂²×C₃	1	2	yes	—
81	C₂×#700	C₂²×C₃	1	1	yes	characteristic
82	C₂×#700	C₂²×C₃	1	1	yes	characteristic
83	C₄×C₅×Q₈	C₃×C₄	1	1	yes	characteristic
84	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
85	D₅×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
86	D₅×C₄⋊C₄	C₃×C₄	1	2	yes	—
87	#4033	C₂²×C₃	1	1	yes	characteristic
88	#4033	C₂²×C₃	1	2	yes	—
89	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
90	C₄²×D₅	C₂²×C₃	1	2	yes	—
91	C₄×Dic₁₀	C₃×C₄	1	2	yes	—
92	C₄×Dic₁₀	C₃×C₄	1	1	yes	characteristic
93	#4004	C₂²×C₃	1	4	yes	—
94	#4004	C₂²×C₃	1	4	yes	—
95	#4002	C₂²×C₃	1	2	yes	—
96	#4002	C₂²×C₃	1	4	yes	—
97	C₄⋊#170	C₂²×C₃	1	2	yes	—
98	C₄⋊#170	C₂²×C₃	1	2	yes	—
99	C₄×#170	C₂²×C₃	1	4	yes	—
100	C₄×#170	C₂²×C₃	1	2	yes	—
101	Q₈×M₁₆	—	5	1	no	Sylow
102	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
103	C₃×C₅×Q₈	—	2	2	no	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
111	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
113	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
114	C₃×C₄×D₅	—	2	2	no	—
115	C₃×C₄×D₅	—	2	4	no	—
116	C₃×C₄×D₅	—	4	1	no	—
117	C₃×C₄×D₅	—	4	2	no	—
118	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
119	C₃×C₄×D₅	#41	1	2	yes	—
120	C₃×Dic₁₀	—	2	4	no	—
121	C₃×Dic₁₀	M₁₆	1	4	yes	complemented
122	C₃×#170	—	2	4	no	—
123	C₃×#170	—	2	2	no	—
124	C₃×#170	C₂×Q₈	1	4	yes	complemented
125	C₂²×C₃×Q₈	—	5	1	no	—
126	C₂×C₃×M₁₆	—	5	1	no	—
127	C₂×C₃×M₁₆	—	5	2	no	—
128	C₂×C₃×M₁₆	—	5	1	no	—
129	C₃×C₄×Q₈	—	5	1	no	—
130	C₃×C₄×Q₈	—	5	1	no	—
131	C₃×C₄×Q₈	—	5	2	no	—
132	C₃×C₄×Q₈	—	5	1	no	—
133	C₃×C₄×Q₈	—	5	2	no	—
134	C₃×C₄×Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic
135	C₂×C₃×C₄⋊C₄	—	5	2	no	—
136	C₂×C₃×C₄⋊C₄	—	5	1	no	—
137	C₂×C₃×C₄²	—	5	1	no	—
138	C₂×C₃×C₄²	—	5	2	no	—
139	C₃×C₄⋊C₈	—	5	2	no	—
140	C₃×C₄⋊C₈	—	5	2	no	—
141	C₃×C₄⋊C₈	—	5	4	no	—
142	C₃×C₄⋊C₈	—	5	4	no	—
143	C₃×#97	—	5	2	no	—
144	C₃×#97	—	5	4	no	—
145	C₃×C₄×C₈	—	5	4	no	—
146	C₃×C₄×C₈	—	5	2	no	—
147	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
148	Q₈×D₅	—	2	4	no	—
149	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
150	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
151	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
152	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
153	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
154	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
155	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
156	C₂×#170	C₂³×C₃	1	4	yes	—
157	C₂×#170	C₂³×C₃	1	2	yes	—
158	C₂×#170	C₂³×C₃	1	2	yes	—
159	#700	—	2	4	no	—
160	#700	—	2	2	no	—
161	#700	C₃×Q₈	1	4	yes	complemented
162	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
163	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
164	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
165	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
166	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
167	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
168	#683	C₂×C₃×C₄	1	2	yes	—
169	#683	C₂×C₃×C₄	1	2	yes	—
170	#683	C₂×C₃×C₄	1	2	yes	—
171	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
172	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
173	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
174	C₄×Dic₅	C₂³×C₃	1	2	yes	—
175	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
176	C₄×Dic₅	C₂³×C₃	1	2	yes	—
177	C₂×C₄×Q₈	—	5	1	no	—
178	#446	—	5	4	no	—
179	#446	—	5	2	no	—
180	C₈×Q₈	—	5	2	no	—
181	#423	—	5	1	no	—
182	#423	—	5	2	no	—
183	C₄×M₁₆	—	5	2	no	—
184	C₄×M₁₆	—	5	1	no	—
185	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₃×D₅	—	2	1	no	—
187	C₂×C₃×D₅	—	2	1	no	—
188	C₂×C₃×D₅	C₄×Q₈	1	2	yes	—
189	C₃×C₄×C₅	—	2	2	no	—
190	C₃×C₄×C₅	—	2	2	no	—
191	C₃×C₄×C₅	—	2	1	no	—
192	C₃×C₄×C₅	C₄×Q₈	1	2	yes	—
193	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
194	C₃×Dic₅	—	2	1	no	—
195	C₃×Dic₅	—	2	1	no	—
196	C₃×Dic₅	—	2	2	no	—
197	C₃×Dic₅	C₂×M₁₆	1	4	yes	—
198	C₃×Dic₅	C₂²×Q₈	1	1	yes	characteristic
199	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
200	C₂×C₃×Q₈	—	5	1	no	—
201	C₂×C₃×Q₈	—	5	2	no	—
202	C₂×C₃×Q₈	—	10	4	no	—
203	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
204	C₂²×C₃×C₄	—	5	1	no	—
205	C₂²×C₃×C₄	—	5	2	no	—
206	C₂²×C₃×C₄	—	5	1	no	—
207	C₂²×C₃×C₄	—	5	1	no	—
208	C₂²×C₃×C₄	—	5	2	no	—
209	C₃×M₁₆	—	5	4	no	—
210	C₃×M₁₆	—	10	4	no	—
211	C₃×M₁₆	—	10	2	no	—
212	C₂×C₃×C₈	—	5	2	no	—
213	C₂×C₃×C₈	—	5	4	no	—
214	C₂×C₃×C₈	—	5	2	no	—
215	C₃×C₄⋊C₄	—	5	2	no	—
216	C₃×C₄⋊C₄	—	5	2	no	—
217	C₃×C₄⋊C₄	—	5	2	no	—
218	C₃×C₄⋊C₄	—	5	2	no	—
219	C₃×C₄⋊C₄	—	5	1	no	—
220	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
221	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
222	C₃×C₄²	—	5	2	no	—
223	C₃×C₄²	—	5	1	no	—
224	C₃×C₄²	—	5	2	no	—
225	C₃×C₄²	—	5	1	no	—
226	C₃×C₄²	—	5	2	no	—
227	C₃×C₄²	—	5	1	no	—
228	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	2	yes	—
229	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
230	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
231	C₅×Q₈	—	2	2	no	—
232	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
233	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
235	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
237	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
238	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
239	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
240	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
241	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
242	C₄×D₅	—	2	2	no	—
243	C₄×D₅	—	2	4	no	—
244	C₄×D₅	—	4	1	no	—
245	C₄×D₅	—	4	2	no	—
246	C₄×D₅	C₂×C₃×Q₈	1	2	yes	—
247	C₄×D₅	C₃×#41	1	2	yes	—
248	Dic₁₀	—	2	4	no	—
249	Dic₁₀	C₃×M₁₆	1	4	yes	complemented
250	#170	—	2	4	no	—
251	#170	—	2	2	no	—
252	#170	C₂×C₃×Q₈	1	4	yes	complemented
253	C₂²×Q₈	—	5	1	no	—
254	C₂×M₁₆	—	5	1	no	—
255	C₂×M₁₆	—	5	2	no	—
256	C₂×M₁₆	—	5	1	no	—
257	C₄×Q₈	—	5	1	no	—
258	C₄×Q₈	—	5	1	no	—
259	C₄×Q₈	—	5	2	no	—
260	C₄×Q₈	—	5	1	no	—
261	C₄×Q₈	—	5	2	no	—
262	C₄×Q₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
263	C₂×C₄⋊C₄	—	5	2	no	—
264	C₂×C₄⋊C₄	—	5	1	no	—
265	C₂×C₄²	—	5	1	no	—
266	C₂×C₄²	—	5	2	no	—
267	C₄⋊C₈	—	5	2	no	—
268	C₄⋊C₈	—	5	2	no	—
269	C₄⋊C₈	—	5	4	no	—
270	C₄⋊C₈	—	5	4	no	—
271	#97	—	5	2	no	—
272	#97	—	5	4	no	—
273	C₄×C₈	—	5	4	no	—
274	C₄×C₈	—	5	2	no	—
275	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
277	C₂×C₃×C₅	#568	1	1	yes	characteristic
278	C₃×D₅	—	2	2	no	—
279	C₂³×C₃	—	5	1	no	—
280	C₃×Q₈	—	2	2	no	—
281	C₃×Q₈	—	5	4	no	—
282	C₃×Q₈	—	10	4	no	—
283	C₂×C₃×C₄	—	5	2	no	—
284	C₂×C₃×C₄	—	5	1	no	—
285	C₂×C₃×C₄	—	5	2	no	—
286	C₂×C₃×C₄	—	5	2	no	—
287	C₂×C₃×C₄	—	5	1	no	—
288	C₂×C₃×C₄	—	5	2	no	—
289	C₂×C₃×C₄	—	5	1	no	—
290	C₂×C₃×C₄	—	10	4	no	—
291	C₂×C₃×C₄	—	10	2	no	—
292	C₂×C₃×C₄	—	20	2	no	—
293	C₂×C₃×C₄	—	20	1	no	—
294	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
295	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
297	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
299	C₃×C₈	—	5	4	no	—
300	C₃×C₈	—	10	4	no	—
301	C₃×C₈	—	10	2	no	—
302	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
303	C₂×D₅	—	2	1	no	—
304	C₂×D₅	—	2	1	no	—
305	C₂×D₅	C₃×C₄×Q₈	1	2	yes	—
306	C₄×C₅	—	2	2	no	—
307	C₄×C₅	—	2	2	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	C₃×C₄×Q₈	1	2	yes	—
310	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	—
311	Dic₅	—	2	1	no	—
312	Dic₅	—	2	1	no	—
313	Dic₅	—	2	2	no	—
314	Dic₅	C₂×C₃×M₁₆	1	4	yes	—
315	Dic₅	C₂²×C₃×Q₈	1	1	yes	characteristic
316	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
317	C₂×Q₈	—	5	1	no	—
318	C₂×Q₈	—	5	2	no	—
319	C₂×Q₈	—	10	4	no	—
320	C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
321	C₂²×C₄	—	5	1	no	—
322	C₂²×C₄	—	5	2	no	—
323	C₂²×C₄	—	5	1	no	—
324	C₂²×C₄	—	5	1	no	—
325	C₂²×C₄	—	5	2	no	—
326	M₁₆	—	5	4	no	—
327	M₁₆	—	10	4	no	—
328	M₁₆	—	10	2	no	—
329	C₂×C₈	—	5	2	no	—
330	C₂×C₈	—	5	4	no	—
331	C₂×C₈	—	5	2	no	—
332	C₄⋊C₄	—	5	2	no	—
333	C₄⋊C₄	—	5	2	no	—
334	C₄⋊C₄	—	5	2	no	—
335	C₄⋊C₄	—	5	2	no	—
336	C₄⋊C₄	—	5	1	no	—
337	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
338	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
339	C₄²	—	5	2	no	—
340	C₄²	—	5	1	no	—
341	C₄²	—	5	2	no	—
342	C₄²	—	5	1	no	—
343	C₄²	—	5	2	no	—
344	C₄²	—	5	1	no	—
345	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
346	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
347	C₃×C₅	Q₈×M₁₆	1	1	yes	characteristic, complemented, Hall
348	C₂²×C₃	—	5	2	no	—
349	C₂²×C₃	—	10	1	no	—
350	C₂²×C₃	—	10	1	no	—
351	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
352	C₃×C₄	—	2	2	no	—
353	C₃×C₄	—	2	2	no	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	5	4	no	—
356	C₃×C₄	—	5	1	no	—
357	C₃×C₄	—	5	1	no	—
358	C₃×C₄	—	10	1	no	—
359	C₃×C₄	—	10	1	no	—
360	C₃×C₄	—	10	2	no	—
361	C₃×C₄	D₅⋊M₁₆	1	2	yes	—
362	C₃×C₄	Q₈×AGL(1,𝔽₅)	1	2	yes	—
363	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
364	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
365	C₂×C₅	C₃×#568	1	1	yes	characteristic
366	D₅	—	2	2	no	—
367	C₂³	—	5	1	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	5	4	no	—
370	Q₈	—	10	4	no	—
371	C₂×C₄	—	5	1	no	—
372	C₂×C₄	—	5	2	no	—
373	C₂×C₄	—	5	2	no	—
374	C₂×C₄	—	5	2	no	—
375	C₂×C₄	—	5	1	no	—
376	C₂×C₄	—	5	2	no	—
377	C₂×C₄	—	5	1	no	—
378	C₂×C₄	—	10	4	no	—
379	C₂×C₄	—	10	2	no	—
380	C₂×C₄	—	20	2	no	—
381	C₂×C₄	—	20	1	no	—
382	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
383	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
384	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
385	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
386	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
387	C₈	—	5	4	no	—
388	C₈	—	10	4	no	—
389	C₈	—	10	2	no	—
390	C₂×C₃	—	10	2	no	—
391	C₂×C₃	C₂×D₅⋊M₁₆	1	1	yes	characteristic
392	C₂×C₃	C₂×Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
393	C₂×C₃	#66264	1	1	yes	characteristic
394	C₅	C₃×Q₈×M₁₆	1	1	yes	characteristic, complemented, Sylow
395	C₂²	—	5	2	no	—
396	C₂²	—	10	1	no	—
397	C₂²	—	10	1	no	—
398	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	1	no	—
402	C₄	—	5	4	no	—
403	C₄	—	5	1	no	—
404	C₄	—	5	1	no	—
405	C₄	—	10	1	no	—
406	C₄	—	10	1	no	—
407	C₄	—	10	2	no	—
408	C₄	C₃×D₅⋊M₁₆	1	2	yes	—
409	C₄	C₃×Q₈×AGL(1,𝔽₅)	1	2	yes	—
410	C₃	#10617193	1	1	yes	characteristic, direct product factor, Sylow
411	C₂	—	10	2	no	—
412	C₂	C₂×C₃×D₅⋊M₁₆	1	1	yes	characteristic
413	C₂	C₂×C₃×Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
414	C₂	C₃×#66264	1	1	yes	characteristic

	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×C₄×C₅×Q₈	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×C₃×D₅	C₂²×C₄
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×C₄×Q₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×Q₈×M₁₆
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
2. C₃×#65788	C₂	semidirect
3. C₃×#65707	C₂	semidirect
4. C₃×#65703	C₂	semidirect
9. #10617193	C₃	direct (N × H)
34. #65788	C₂×C₃	semidirect
35. #65707	C₂×C₃	semidirect
36. #65703	C₂×C₃	semidirect
55. C₃×#700	Q₈	semidirect
121. C₃×Dic₁₀	M₁₆	semidirect
124. C₃×#170	C₂×Q₈	semidirect
161. #700	C₃×Q₈	semidirect
249. Dic₁₀	C₃×M₁₆	semidirect
252. #170	C₂×C₃×Q₈	semidirect
347. C₃×C₅	Q₈×M₁₆	semidirect
394. C₅	C₃×Q₈×M₁₆	semidirect
410. C₃	#10617193	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₄×Q₈×D₅	2
C₃×#65788	2
C₃×#65707	2
C₃×#65703	2
C₃×#65682	2
C₃×#65681	2
C₃×C₄×#700	2
#10617193	3
C₃×Q₈×M₁₆	5

Subgroups — C3×#10617193 #14418824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617193 #14418824