Subgroups — C₃×#10617262 #14418583

Order 1920.

696 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65956	C₂	1	1	yes	maximal, characteristic
2	C₃×#65788	C₂	1	2	yes	maximal, complemented
3	C₃×#65758	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#4002	C₂	1	1	yes	maximal, characteristic
5	C₃×#65709	C₂	1	2	yes	maximal, complemented
6	C₃×#65707	C₂	1	2	yes	maximal, complemented
7	C₃×#65707	C₂	1	2	yes	maximal, complemented
8	C₃×#65696	C₂	1	2	yes	maximal
9	C₃×#65691	C₂	1	2	yes	maximal
10	#10617262	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×#704	C₂²	1	2	yes	—
12	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
13	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
14	C₃×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
15	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic
16	C₃×#4090	C₄	1	1	yes	characteristic
17	C₃×#4070	C₄	1	1	yes	characteristic
18	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
19	C₃×#4035	C₄	1	2	yes	—
20	C₃×#4034	C₄	1	1	yes	characteristic
21	C₃×#4033	C₂²	1	1	yes	characteristic
22	C₃×#4033	C₂²	1	2	yes	—
23	C₃×#4024	C₄	1	2	yes	—
24	C₃×#4023	C₂²	1	2	yes	—
25	C₃×#4004	C₂²	1	2	yes	—
26	C₃×#4004	C₂²	1	2	yes	—
27	C₃×#4004	C₂²	1	2	yes	—
28	C₃×#4002	C₂²	1	2	yes	—
29	C₃×#4002	C₂²	1	2	yes	—
30	C₃×#4002	C₂²	1	2	yes	—
31	C₃×#4002	C₂²	1	2	yes	—
32	C₃×C₄⋊#170	C₂²	1	2	yes	—
33	C₃×C₄⋊#170	C₂²	1	2	yes	—
34	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic
35	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic
36	C₃×C₄×#170	C₂²	1	2	yes	—
37	C₃×C₄×#170	C₂²	1	2	yes	—
38	C₃×#2961	—	5	1	no	maximal, Hall
39	#65956	C₂×C₃	1	1	yes	characteristic
40	#65788	C₂×C₃	1	2	yes	complemented
41	#65758	C₂×C₃	1	1	yes	characteristic
42	C₂×#4002	C₂×C₃	1	1	yes	characteristic
43	#65709	C₂×C₃	1	2	yes	complemented
44	#65707	C₂×C₃	1	2	yes	complemented
45	#65707	C₂×C₃	1	2	yes	complemented
46	#65696	C₂×C₃	1	2	yes	—
47	#65691	C₂×C₃	1	2	yes	—
48	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
52	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
53	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
54	C₃×#704	—	2	4	no	—
55	C₂×C₃×#170	—	2	2	no	—
56	C₂×C₃×#170	Q₈	1	4	yes	complemented
57	C₂×C₃×#170	C₂³	1	2	yes	—
58	C₂×C₃×#170	C₂³	1	2	yes	—
59	C₂×C₃×#170	C₂³	1	2	yes	—
60	C₂×C₃×#170	C₂³	1	2	yes	—
61	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
63	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
64	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
65	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
66	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
67	C₃×#683	C₂×C₄	1	2	yes	—
68	C₃×#683	C₂×C₄	1	2	yes	—
69	C₃×#683	C₂×C₄	1	2	yes	—
70	C₃×#683	C₂×C₄	1	2	yes	—
71	C₃×#683	C₂×C₄	1	2	yes	—
72	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
73	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
74	C₃×C₄×Dic₅	C₂³	1	2	yes	—
75	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
76	C₃×C₄×Dic₅	C₂³	1	2	yes	—
77	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
78	C₃×#533	—	5	1	no	—
79	C₃×#446	—	5	2	no	—
80	C₃×#446	—	5	2	no	—
81	C₃×#446	—	5	2	no	—
82	C₃×#446	—	5	2	no	—
83	C₃×#424	—	5	2	no	—
84	C₃×#423	—	5	1	no	—
85	C₃×#405	—	5	2	no	—
86	C₂×C₃×#97	—	5	1	no	—
87	C₂×#704	C₂²×C₃	1	2	yes	—
88	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
89	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
90	C₅×C₂²⋊Q₈	C₃×C₄	1	1	yes	characteristic
91	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
92	#4090	C₃×C₄	1	1	yes	characteristic
93	#4070	C₃×C₄	1	1	yes	characteristic
94	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
95	#4035	C₃×C₄	1	2	yes	—
96	#4034	C₃×C₄	1	1	yes	characteristic
97	#4033	C₂²×C₃	1	1	yes	characteristic
98	#4033	C₂²×C₃	1	2	yes	—
99	#4024	C₃×C₄	1	2	yes	—
100	#4023	C₂²×C₃	1	2	yes	—
101	#4004	C₂²×C₃	1	2	yes	—
102	#4004	C₂²×C₃	1	2	yes	—
103	#4004	C₂²×C₃	1	2	yes	—
104	#4002	C₂²×C₃	1	2	yes	—
105	#4002	C₂²×C₃	1	2	yes	—
106	#4002	C₂²×C₃	1	2	yes	—
107	#4002	C₂²×C₃	1	2	yes	—
108	C₄⋊#170	C₂²×C₃	1	2	yes	—
109	C₄⋊#170	C₂²×C₃	1	2	yes	—
110	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic
111	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic
112	C₄×#170	C₂²×C₃	1	2	yes	—
113	C₄×#170	C₂²×C₃	1	2	yes	—
114	#2961	—	5	1	no	Sylow
115	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₃×C₅×Q₈	—	4	1	no	—
117	C₂×C₃×C₄×C₅	—	4	1	no	—
118	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
122	C₂×C₃×Dic₅	—	4	1	no	—
123	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
126	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
127	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₃×Dic₅	C₂×Q₈	1	2	yes	—
129	C₂×C₃×Dic₅	#41	1	2	yes	—
130	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
131	C₃×Dic₁₀	—	4	2	no	—
132	C₃×Dic₁₀	—	4	1	no	—
133	C₃×#170	—	2	2	no	—
134	C₃×#170	—	2	2	no	—
135	C₃×#170	—	2	2	no	—
136	C₃×#170	C₂×Q₈	1	4	yes	—
137	C₂×C₃×M₁₆	—	5	2	no	—
138	C₂²×C₃×C₈	—	5	1	no	—
139	C₂²×C₃×C₈	—	5	1	no	—
140	C₃×C₄⋊Q₈	—	5	1	no	—
141	C₃×C₄⋊Q₈	—	5	1	no	—
142	C₃×#125	—	5	2	no	—
143	C₃×C₂²⋊Q₈	—	5	1	no	—
144	C₃×C₂²⋊Q₈	—	5	2	no	—
145	C₃×C₂²⋊Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic
146	C₃×C₄×Q₈	—	5	1	no	—
147	C₃×C₄×Q₈	—	5	1	no	—
148	C₃×C₄×Q₈	—	5	2	no	—
149	C₃×#117	—	5	2	no	—
150	C₂×C₃×C₄²	—	5	1	no	—
151	C₃×C₄⋊C₈	—	5	1	no	—
152	C₃×C₄⋊C₈	—	5	1	no	—
153	C₃×C₄⋊C₈	—	5	2	no	—
154	C₃×C₄⋊C₈	—	5	2	no	—
155	C₃×C₄⋊C₈	—	5	2	no	—
156	C₃×C₄⋊C₈	—	5	2	no	—
157	C₃×C₄⋊C₈	—	5	2	no	—
158	C₃×#97	—	5	2	no	—
159	C₃×#97	—	5	2	no	—
160	C₃×#97	—	5	2	no	—
161	C₃×#97	—	5	2	no	—
162	C₃×C₄×C₈	—	5	2	no	—
163	C₃×C₄×C₈	—	5	2	no	—
164	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
166	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
167	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
168	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
169	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
170	#704	—	2	4	no	—
171	C₂×#170	—	2	2	no	—
172	C₂×#170	C₃×Q₈	1	4	yes	complemented
173	C₂×#170	C₂³×C₃	1	2	yes	—
174	C₂×#170	C₂³×C₃	1	2	yes	—
175	C₂×#170	C₂³×C₃	1	2	yes	—
176	C₂×#170	C₂³×C₃	1	2	yes	—
177	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
178	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
179	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
180	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
181	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
182	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
183	#683	C₂×C₃×C₄	1	2	yes	—
184	#683	C₂×C₃×C₄	1	2	yes	—
185	#683	C₂×C₃×C₄	1	2	yes	—
186	#683	C₂×C₃×C₄	1	2	yes	—
187	#683	C₂×C₃×C₄	1	2	yes	—
188	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
189	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
190	C₄×Dic₅	C₂³×C₃	1	2	yes	—
191	C₄×Dic₅	C₂³×C₃	1	2	yes	—
192	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
193	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
194	#533	—	5	1	no	—
195	#446	—	5	2	no	—
196	#446	—	5	2	no	—
197	#446	—	5	2	no	—
198	#446	—	5	2	no	—
199	#424	—	5	2	no	—
200	#423	—	5	1	no	—
201	#405	—	5	2	no	—
202	C₂×#97	—	5	1	no	—
203	C₂²×C₃×C₅	—	2	1	no	—
204	C₂²×C₃×C₅	—	2	1	no	—
205	C₂²×C₃×C₅	C₄×Q₈	1	2	yes	—
206	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
207	C₃×C₄×C₅	—	2	1	no	—
208	C₃×C₄×C₅	—	2	2	no	—
209	C₃×C₄×C₅	—	2	1	no	—
210	C₃×C₄×C₅	—	2	2	no	—
211	C₃×Dic₅	—	2	1	no	—
212	C₃×Dic₅	—	2	2	no	—
213	C₃×Dic₅	—	2	2	no	—
214	C₃×Dic₅	—	2	1	no	—
215	C₃×Dic₅	C₄×Q₈	1	2	yes	—
216	C₃×Dic₅	C₂²×Q₈	1	1	yes	characteristic
217	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
218	C₂×C₃×Q₈	—	5	2	no	—
219	C₂×C₃×Q₈	—	5	1	no	—
220	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
221	C₂²×C₃×C₄	—	5	1	no	—
222	C₂²×C₃×C₄	—	5	1	no	—
223	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
224	C₃×M₁₆	—	10	4	no	—
225	C₂×C₃×C₈	—	5	2	no	—
226	C₂×C₃×C₈	—	5	4	no	—
227	C₂×C₃×C₈	—	5	2	no	—
228	C₂×C₃×C₈	—	5	2	no	—
229	C₂×C₃×C₈	—	5	2	no	—
230	C₂×C₃×C₈	—	10	2	no	—
231	C₃×C₄⋊C₄	—	5	2	no	—
232	C₃×C₄⋊C₄	—	5	2	no	—
233	C₃×C₄⋊C₄	—	5	2	no	—
234	C₃×C₄⋊C₄	—	5	2	no	—
235	C₃×C₄⋊C₄	—	5	2	no	—
236	C₃×C₄⋊C₄	—	5	2	no	—
237	C₃×C₄⋊C₄	—	5	1	no	—
238	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
239	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
240	C₃×C₂²⋊C₄	—	5	2	no	—
241	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
242	C₃×C₄²	—	5	1	no	—
243	C₃×C₄²	—	5	1	no	—
244	C₃×C₄²	—	5	2	no	—
245	C₃×C₄²	—	5	2	no	—
246	C₃×C₄²	—	5	1	no	—
247	C₃×C₄²	—	5	1	no	—
248	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
249	C₅×Q₈	—	4	1	no	—
250	C₂×C₄×C₅	—	4	1	no	—
251	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
252	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
254	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
255	C₂×Dic₅	—	4	1	no	—
256	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
257	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
258	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
259	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
260	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
261	C₂×Dic₅	C₂×C₃×Q₈	1	2	yes	—
262	C₂×Dic₅	C₃×#41	1	2	yes	—
263	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
264	Dic₁₀	—	4	2	no	—
265	Dic₁₀	—	4	1	no	—
266	#170	—	2	2	no	—
267	#170	—	2	2	no	—
268	#170	—	2	2	no	—
269	#170	C₂×C₃×Q₈	1	4	yes	—
270	C₂×M₁₆	—	5	2	no	—
271	C₂²×C₈	—	5	1	no	—
272	C₂²×C₈	—	5	1	no	—
273	C₄⋊Q₈	—	5	1	no	—
274	C₄⋊Q₈	—	5	1	no	—
275	#125	—	5	2	no	—
276	C₂²⋊Q₈	—	5	1	no	—
277	C₂²⋊Q₈	—	5	2	no	—
278	C₂²⋊Q₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
279	C₄×Q₈	—	5	1	no	—
280	C₄×Q₈	—	5	1	no	—
281	C₄×Q₈	—	5	2	no	—
282	#117	—	5	2	no	—
283	C₂×C₄²	—	5	1	no	—
284	C₄⋊C₈	—	5	1	no	—
285	C₄⋊C₈	—	5	1	no	—
286	C₄⋊C₈	—	5	2	no	—
287	C₄⋊C₈	—	5	2	no	—
288	C₄⋊C₈	—	5	2	no	—
289	C₄⋊C₈	—	5	2	no	—
290	C₄⋊C₈	—	5	2	no	—
291	#97	—	5	2	no	—
292	#97	—	5	2	no	—
293	#97	—	5	2	no	—
294	#97	—	5	2	no	—
295	C₄×C₈	—	5	2	no	—
296	C₄×C₈	—	5	2	no	—
297	C₂×C₃×C₅	—	2	2	no	—
298	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
299	C₂×C₃×C₅	#568	1	1	yes	characteristic
300	C₂×C₃×C₅	#568	1	1	yes	characteristic
301	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
302	C₃×Q₈	—	4	1	no	—
303	C₃×Q₈	—	20	1	no	—
304	C₃×Q₈	—	20	2	no	—
305	C₂×C₃×C₄	—	4	1	no	—
306	C₂×C₃×C₄	—	5	2	no	—
307	C₂×C₃×C₄	—	5	2	no	—
308	C₂×C₃×C₄	—	5	1	no	—
309	C₂×C₃×C₄	—	5	1	no	—
310	C₂×C₃×C₄	—	5	1	no	—
311	C₂×C₃×C₄	—	5	1	no	—
312	C₂×C₃×C₄	—	5	2	no	—
313	C₂×C₃×C₄	—	5	2	no	—
314	C₂×C₃×C₄	—	20	1	no	—
315	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
316	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
317	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
318	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
319	C₃×C₈	—	5	4	no	—
320	C₃×C₈	—	10	2	no	—
321	C₃×C₈	—	10	2	no	—
322	C₃×C₈	—	10	2	no	—
323	C₂²×C₅	—	2	1	no	—
324	C₂²×C₅	—	2	1	no	—
325	C₂²×C₅	C₃×C₄×Q₈	1	2	yes	—
326	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
327	C₄×C₅	—	2	1	no	—
328	C₄×C₅	—	2	2	no	—
329	C₄×C₅	—	2	1	no	—
330	C₄×C₅	—	2	2	no	—
331	Dic₅	—	2	1	no	—
332	Dic₅	—	2	2	no	—
333	Dic₅	—	2	2	no	—
334	Dic₅	—	2	1	no	—
335	Dic₅	C₃×C₄×Q₈	1	2	yes	—
336	Dic₅	C₂²×C₃×Q₈	1	1	yes	characteristic
337	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
338	C₂×Q₈	—	5	2	no	—
339	C₂×Q₈	—	5	1	no	—
340	C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
341	C₂²×C₄	—	5	1	no	—
342	C₂²×C₄	—	5	1	no	—
343	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
344	M₁₆	—	10	4	no	—
345	C₂×C₈	—	5	2	no	—
346	C₂×C₈	—	5	4	no	—
347	C₂×C₈	—	5	2	no	—
348	C₂×C₈	—	5	2	no	—
349	C₂×C₈	—	5	2	no	—
350	C₂×C₈	—	10	2	no	—
351	C₄⋊C₄	—	5	2	no	—
352	C₄⋊C₄	—	5	2	no	—
353	C₄⋊C₄	—	5	2	no	—
354	C₄⋊C₄	—	5	2	no	—
355	C₄⋊C₄	—	5	2	no	—
356	C₄⋊C₄	—	5	2	no	—
357	C₄⋊C₄	—	5	1	no	—
358	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
359	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
360	C₂²⋊C₄	—	5	2	no	—
361	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
362	C₄²	—	5	2	no	—
363	C₄²	—	5	2	no	—
364	C₄²	—	5	1	no	—
365	C₄²	—	5	1	no	—
366	C₄²	—	5	1	no	—
367	C₄²	—	5	1	no	—
368	C₃×C₅	#2961	1	1	yes	characteristic, complemented, Hall
369	C₂²×C₃	—	2	1	no	—
370	C₂²×C₃	—	2	1	no	—
371	C₂²×C₃	Q₈×AGL(1,𝔽₅)	1	2	yes	—
372	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
373	C₃×C₄	—	2	1	no	—
374	C₃×C₄	—	2	1	no	—
375	C₃×C₄	—	2	2	no	—
376	C₃×C₄	—	2	2	no	—
377	C₃×C₄	—	5	2	no	—
378	C₃×C₄	—	5	1	no	—
379	C₃×C₄	—	5	1	no	—
380	C₃×C₄	—	10	2	no	—
381	C₃×C₄	—	10	1	no	—
382	C₃×C₄	—	10	1	no	—
383	C₃×C₄	—	10	2	no	—
384	C₂×C₅	—	2	2	no	—
385	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
386	C₂×C₅	C₃×#568	1	1	yes	characteristic
387	C₂×C₅	C₃×#568	1	1	yes	characteristic
388	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
389	Q₈	—	4	1	no	—
390	Q₈	—	20	1	no	—
391	Q₈	—	20	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	5	2	no	—
394	C₂×C₄	—	5	2	no	—
395	C₂×C₄	—	5	1	no	—
396	C₂×C₄	—	5	1	no	—
397	C₂×C₄	—	5	1	no	—
398	C₂×C₄	—	5	1	no	—
399	C₂×C₄	—	5	2	no	—
400	C₂×C₄	—	5	2	no	—
401	C₂×C₄	—	20	1	no	—
402	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
404	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
405	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
406	C₈	—	5	4	no	—
407	C₈	—	10	2	no	—
408	C₈	—	10	2	no	—
409	C₈	—	10	2	no	—
410	C₂×C₃	—	2	2	no	—
411	C₂×C₃	#66256	1	1	yes	characteristic
412	C₂×C₃	C₂×Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
413	C₂×C₃	#66264	1	1	yes	characteristic
414	C₅	C₃×#2961	1	1	yes	characteristic, complemented, Sylow
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	C₃×Q₈×AGL(1,𝔽₅)	1	2	yes	—
418	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	5	1	no	—
424	C₄	—	5	1	no	—
425	C₄	—	5	2	no	—
426	C₄	—	10	2	no	—
427	C₄	—	10	1	no	—
428	C₄	—	10	1	no	—
429	C₄	—	10	2	no	—
430	C₃	#10617262	1	1	yes	characteristic, direct product factor, Sylow
431	C₂	—	2	2	no	—
432	C₂	C₃×#66256	1	1	yes	characteristic
433	C₂	C₂×C₃×Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
434	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×C₅×C₂²⋊Q₈	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×C₂²⋊Q₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2961
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₃×#65788	C₂	semidirect
5. C₃×#65709	C₂	semidirect
6. C₃×#65707	C₂	semidirect
7. C₃×#65707	C₂	semidirect
10. #10617262	C₃	direct (N × H)
40. #65788	C₂×C₃	semidirect
43. #65709	C₂×C₃	semidirect
44. #65707	C₂×C₃	semidirect
45. #65707	C₂×C₃	semidirect
56. C₂×C₃×#170	Q₈	semidirect
172. C₂×#170	C₃×Q₈	semidirect
368. C₃×C₅	#2961	semidirect
414. C₅	C₃×#2961	semidirect
430. C₃	#10617262	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×#65956	2
C₃×#65788	2
C₃×#65758	2
C₂×C₃×#4002	2
C₃×#65709	2
C₃×#65707	2
C₃×#65696	2
C₃×#65691	2
#10617262	3
C₃×#2961	5

Subgroups — C3×#10617262 #14418583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617262 #14418583