Subgroups — C₃×#10608225 #14329828

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4090	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic
3	C₃×#65519	C₂	1	1	yes	maximal, characteristic
4	C₃×#65261	C₂	1	2	yes	maximal
5	C₃×C₄×#683	C₂	1	2	yes	maximal
6	C₃×#64938	C₂	1	2	yes	maximal
7	C₃×#64938	C₂	1	2	yes	maximal
8	C₃×#64936	C₂	1	2	yes	maximal
9	C₃×#64935	C₂	1	2	yes	maximal
10	#10608225	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₃×#4090	C₄	1	8	yes	complemented
16	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×#683	C₂²	1	2	yes	—
18	C₂×C₃×#683	C₂²	1	2	yes	—
19	C₂×C₃×#683	C₂²	1	2	yes	—
20	C₂×C₃×#683	C₂²	1	2	yes	—
21	C₂×C₃×#683	C₂²	1	2	yes	—
22	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
23	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
24	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
25	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×C₅×#95	C₂²	1	2	yes	—
29	C₃×#3963	C₂²	1	2	yes	—
30	C₃×#3963	C₂²	1	2	yes	—
31	C₃×#3963	C₂²	1	2	yes	—
32	C₃×#3963	C₂²	1	2	yes	—
33	C₃×#2369	—	5	1	no	maximal, Hall
34	C₂×#4090	C₂×C₃	1	1	yes	characteristic
35	C₅×#391	C₂×C₃	1	1	yes	characteristic
36	#65519	C₂×C₃	1	1	yes	characteristic
37	#65261	C₂×C₃	1	2	yes	—
38	C₄×#683	C₂×C₃	1	2	yes	—
39	#64938	C₂×C₃	1	2	yes	—
40	#64938	C₂×C₃	1	2	yes	—
41	#64936	C₂×C₃	1	2	yes	—
42	#64935	C₂×C₃	1	2	yes	—
43	C₂×C₃×C₅×Q₈	—	4	1	no	—
44	C₂×C₃×C₅×Q₈	—	4	1	no	—
45	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
52	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
53	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
54	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
55	C₂×C₃×Dic₁₀	—	4	1	no	—
56	C₂×C₃×Dic₁₀	—	4	1	no	—
57	C₂×C₃×Dic₁₀	C₂×C₄	1	4	yes	—
58	C₃×C₅×C₄⋊C₄	—	4	1	no	—
59	C₃×C₄²×C₅	—	4	1	no	—
60	C₃×C₄⋊Dic₅	—	4	1	no	—
61	C₃×#683	—	2	4	no	—
62	C₃×#683	—	4	2	no	—
63	C₃×#683	C₂×C₄	1	8	yes	—
64	C₃×#683	C₂×C₄	1	8	yes	—
65	C₃×#683	Q₈	1	8	yes	complemented
66	C₃×C₄×Dic₅	—	2	4	no	—
67	C₃×C₄×Dic₅	—	2	4	no	—
68	C₃×C₄×Dic₅	—	4	1	no	—
69	C₃×C₄×Dic₅	—	4	2	no	—
70	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
71	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
72	C₃×#391	—	5	1	no	—
73	C₃×#391	—	5	2	no	—
74	C₃×#391	D₅	1	1	yes	characteristic
75	C₃×#389	—	5	2	no	—
76	C₃×#389	—	5	2	no	—
77	C₃×C₄×C₄⋊C₄	—	5	2	no	—
78	C₃×C₄×C₄⋊C₄	—	5	2	no	—
79	C₃×C₄×C₄⋊C₄	—	5	2	no	—
80	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
81	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
84	#4090	C₃×C₄	1	8	yes	complemented
85	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
86	C₂×#683	C₂²×C₃	1	2	yes	—
87	C₂×#683	C₂²×C₃	1	2	yes	—
88	C₂×#683	C₂²×C₃	1	2	yes	—
89	C₂×#683	C₂²×C₃	1	2	yes	—
90	C₂×#683	C₂²×C₃	1	2	yes	—
91	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
92	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
93	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
94	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
96	C₅×#95	C₂²×C₃	1	2	yes	—
97	C₅×#95	C₂²×C₃	1	2	yes	—
98	#3963	C₂²×C₃	1	2	yes	—
99	#3963	C₂²×C₃	1	2	yes	—
100	#3963	C₂²×C₃	1	2	yes	—
101	#3963	C₂²×C₃	1	2	yes	—
102	#2369	—	5	1	no	Sylow
103	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
104	C₃×C₅×Q₈	—	4	4	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	1	no	—
108	C₂×C₃×C₄×C₅	—	2	1	no	—
109	C₂×C₃×C₄×C₅	—	2	1	no	—
110	C₂×C₃×C₄×C₅	—	2	1	no	—
111	C₂×C₃×C₄×C₅	—	2	1	no	—
112	C₂×C₃×C₄×C₅	—	2	1	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
120	C₂×C₃×Dic₅	—	2	2	no	—
121	C₂×C₃×Dic₅	—	2	2	no	—
122	C₂×C₃×Dic₅	—	2	2	no	—
123	C₂×C₃×Dic₅	—	2	2	no	—
124	C₂×C₃×Dic₅	—	2	2	no	—
125	C₂×C₃×Dic₅	—	2	2	no	—
126	C₂×C₃×Dic₅	—	2	2	no	—
127	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
128	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
129	C₂×C₃×Dic₅	C₂×Q₈	1	4	yes	—
130	C₂×C₃×Dic₅	C₂×Q₈	1	4	yes	—
131	C₂×C₃×Dic₅	#41	1	4	yes	—
132	C₃×Dic₁₀	—	4	4	no	—
133	C₂²×C₃×Q₈	—	5	1	no	—
134	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
135	C₃×C₄⋊Q₈	—	5	8	no	—
136	C₂×C₃×C₄⋊C₄	—	5	2	no	—
137	C₂×C₃×C₄⋊C₄	—	5	2	no	—
138	C₂×C₃×C₄⋊C₄	—	5	2	no	—
139	C₂×C₃×C₄⋊C₄	—	5	2	no	—
140	C₂×C₃×C₄⋊C₄	—	5	2	no	—
141	C₂×C₃×C₄⋊C₄	—	5	1	no	—
142	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
143	C₂×C₃×C₄²	—	5	1	no	—
144	C₂×C₃×C₄²	—	5	2	no	—
145	C₂×C₃×C₄²	—	5	2	no	—
146	C₂×C₃×C₄²	—	5	1	no	—
147	C₂×C₃×C₄²	—	5	2	no	—
148	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
149	C₃×#95	—	5	2	no	—
150	C₃×#95	—	5	2	no	—
151	C₃×#95	—	5	2	no	—
152	C₃×#95	—	5	2	no	—
153	C₃×#95	C₂×D₅	1	2	yes	—
154	C₃×#95	C₂×D₅	1	2	yes	—
155	C₂×C₅×Q₈	—	4	1	no	—
156	C₂×C₅×Q₈	—	4	1	no	—
157	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	—
158	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
159	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
163	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
164	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
165	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
166	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
167	C₂×Dic₁₀	—	4	1	no	—
168	C₂×Dic₁₀	—	4	1	no	—
169	C₂×Dic₁₀	C₂×C₃×C₄	1	4	yes	—
170	C₅×C₄⋊C₄	—	4	1	no	—
171	C₄²×C₅	—	4	1	no	—
172	C₄⋊Dic₅	—	4	1	no	—
173	#683	—	2	4	no	—
174	#683	—	4	2	no	—
175	#683	C₂×C₃×C₄	1	8	yes	—
176	#683	C₂×C₃×C₄	1	8	yes	—
177	#683	C₃×Q₈	1	8	yes	complemented
178	C₄×Dic₅	—	2	4	no	—
179	C₄×Dic₅	—	2	4	no	—
180	C₄×Dic₅	—	4	1	no	—
181	C₄×Dic₅	—	4	2	no	—
182	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
183	C₂×C₄⋊Q₈	—	5	1	no	—
184	#391	—	5	1	no	—
185	#391	—	5	2	no	—
186	#391	C₃×D₅	1	1	yes	characteristic
187	#389	—	5	2	no	—
188	#389	—	5	2	no	—
189	C₄×C₄⋊C₄	—	5	2	no	—
190	C₄×C₄⋊C₄	—	5	2	no	—
191	C₄×C₄⋊C₄	—	5	2	no	—
192	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
193	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
194	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
195	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
197	C₃×C₄×C₅	—	2	2	no	—
198	C₃×C₄×C₅	—	2	2	no	—
199	C₃×C₄×C₅	—	2	2	no	—
200	C₃×C₄×C₅	—	2	4	no	—
201	C₃×C₄×C₅	—	4	2	no	—
202	C₃×Dic₅	—	2	4	no	—
203	C₃×Dic₅	—	2	4	no	—
204	C₃×Dic₅	—	4	2	no	—
205	C₃×Dic₅	C₄×Q₈	1	8	yes	—
206	C₂×C₃×Q₈	—	4	1	no	—
207	C₂×C₃×Q₈	—	4	1	no	—
208	C₂×C₃×Q₈	—	5	4	no	—
209	C₂×C₃×Q₈	—	20	1	no	—
210	C₂×C₃×Q₈	—	20	1	no	—
211	C₂×C₃×Q₈	C₄×D₅	1	4	yes	—
212	C₂²×C₃×C₄	—	5	2	no	—
213	C₂²×C₃×C₄	—	5	2	no	—
214	C₂²×C₃×C₄	—	5	2	no	—
215	C₂²×C₃×C₄	—	5	2	no	—
216	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
217	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
221	C₃×C₄⋊C₄	—	4	1	no	—
222	C₃×C₄⋊C₄	—	5	8	no	—
223	C₃×C₄⋊C₄	—	5	8	no	—
224	C₃×C₄⋊C₄	—	5	8	no	—
225	C₃×C₄⋊C₄	—	10	4	no	—
226	C₃×C₄⋊C₄	—	20	2	no	—
227	C₃×C₄⋊C₄	—	20	1	no	—
228	C₃×C₄²	—	4	1	no	—
229	C₃×C₄²	—	5	4	no	—
230	C₃×C₄²	—	10	4	no	—
231	C₃×C₄²	—	10	4	no	—
232	C₃×C₄²	—	20	2	no	—
233	C₃×C₄²	—	20	1	no	—
234	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
235	C₅×Q₈	—	4	4	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	2	1	no	—
241	C₂×C₄×C₅	—	2	1	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	2	1	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
248	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
249	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
250	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
251	C₂×Dic₅	—	2	2	no	—
252	C₂×Dic₅	—	2	2	no	—
253	C₂×Dic₅	—	2	2	no	—
254	C₂×Dic₅	—	2	2	no	—
255	C₂×Dic₅	—	2	2	no	—
256	C₂×Dic₅	—	2	2	no	—
257	C₂×Dic₅	—	2	2	no	—
258	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
259	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
260	C₂×Dic₅	C₂×C₃×Q₈	1	4	yes	—
261	C₂×Dic₅	C₂×C₃×Q₈	1	4	yes	—
262	C₂×Dic₅	C₃×#41	1	4	yes	—
263	Dic₁₀	—	4	4	no	—
264	C₂²×Q₈	—	5	1	no	—
265	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
266	C₄⋊Q₈	—	5	8	no	—
267	C₂×C₄⋊C₄	—	5	2	no	—
268	C₂×C₄⋊C₄	—	5	2	no	—
269	C₂×C₄⋊C₄	—	5	2	no	—
270	C₂×C₄⋊C₄	—	5	2	no	—
271	C₂×C₄⋊C₄	—	5	2	no	—
272	C₂×C₄⋊C₄	—	5	1	no	—
273	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
274	C₂×C₄²	—	5	1	no	—
275	C₂×C₄²	—	5	2	no	—
276	C₂×C₄²	—	5	2	no	—
277	C₂×C₄²	—	5	1	no	—
278	C₂×C₄²	—	5	2	no	—
279	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
280	#95	—	5	2	no	—
281	#95	—	5	2	no	—
282	#95	—	5	2	no	—
283	#95	—	5	2	no	—
284	#95	C₂×C₃×D₅	1	2	yes	—
285	#95	C₂×C₃×D₅	1	2	yes	—
286	C₂×C₃×C₅	C₂×C₄×Q₈	1	2	yes	—
287	C₂×C₃×C₅	#518	1	1	yes	characteristic
288	C₂×C₃×C₅	#554	1	2	yes	—
289	C₂×C₃×C₅	#555	1	1	yes	characteristic
290	C₂×C₃×C₅	Q₈²	1	1	yes	characteristic
291	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
292	C₃×Q₈	—	4	4	no	—
293	C₃×Q₈	—	20	4	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	2	1	no	—
297	C₂×C₃×C₄	—	2	1	no	—
298	C₂×C₃×C₄	—	2	1	no	—
299	C₂×C₃×C₄	—	2	1	no	—
300	C₂×C₃×C₄	—	2	1	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	2	2	no	—
305	C₂×C₃×C₄	—	5	4	no	—
306	C₂×C₃×C₄	—	5	4	no	—
307	C₂×C₃×C₄	—	5	4	no	—
308	C₂×C₃×C₄	—	5	4	no	—
309	C₂×C₃×C₄	—	5	4	no	—
310	C₂×C₃×C₄	—	10	2	no	—
311	C₂×C₃×C₄	—	10	2	no	—
312	C₂×C₃×C₄	—	10	2	no	—
313	C₂×C₃×C₄	—	10	2	no	—
314	C₂×C₃×C₄	—	10	2	no	—
315	C₂×C₃×C₄	—	10	2	no	—
316	C₂×C₃×C₄	—	10	2	no	—
317	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
318	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
319	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
320	C₂×C₃×C₄	Q₈×D₅	1	4	yes	—
321	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
322	C₂²×C₅	C₂²×C₃×Q₈	1	2	yes	—
323	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
324	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
325	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
326	C₄×C₅	—	2	2	no	—
327	C₄×C₅	—	2	2	no	—
328	C₄×C₅	—	2	2	no	—
329	C₄×C₅	—	2	4	no	—
330	C₄×C₅	—	4	2	no	—
331	Dic₅	—	2	4	no	—
332	Dic₅	—	2	4	no	—
333	Dic₅	—	4	2	no	—
334	Dic₅	C₃×C₄×Q₈	1	8	yes	—
335	C₂×Q₈	—	4	1	no	—
336	C₂×Q₈	—	4	1	no	—
337	C₂×Q₈	—	5	4	no	—
338	C₂×Q₈	—	20	1	no	—
339	C₂×Q₈	—	20	1	no	—
340	C₂×Q₈	C₃×C₄×D₅	1	4	yes	—
341	C₂²×C₄	—	5	2	no	—
342	C₂²×C₄	—	5	2	no	—
343	C₂²×C₄	—	5	2	no	—
344	C₂²×C₄	—	5	2	no	—
345	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
346	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
347	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
348	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	—	5	8	no	—
352	C₄⋊C₄	—	5	8	no	—
353	C₄⋊C₄	—	5	8	no	—
354	C₄⋊C₄	—	10	4	no	—
355	C₄⋊C₄	—	20	2	no	—
356	C₄⋊C₄	—	20	1	no	—
357	C₄²	—	4	1	no	—
358	C₄²	—	5	4	no	—
359	C₄²	—	10	4	no	—
360	C₄²	—	10	4	no	—
361	C₄²	—	20	2	no	—
362	C₄²	—	20	1	no	—
363	C₃×C₅	#2369	1	1	yes	characteristic, complemented, Hall
364	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
365	C₂²×C₃	#4144	1	1	yes	characteristic
366	C₂²×C₃	#4144	1	1	yes	characteristic
367	C₂²×C₃	C₂×Q₈×D₅	1	2	yes	—
368	C₂²×C₃	D₅×#41	1	2	yes	—
369	C₃×C₄	—	2	2	no	—
370	C₃×C₄	—	2	2	no	—
371	C₃×C₄	—	2	2	no	—
372	C₃×C₄	—	2	4	no	—
373	C₃×C₄	—	4	2	no	—
374	C₃×C₄	—	5	8	no	—
375	C₃×C₄	—	10	4	no	—
376	C₃×C₄	—	10	4	no	—
377	C₃×C₄	—	20	2	no	—
378	C₂×C₅	C₂×C₃×C₄×Q₈	1	2	yes	—
379	C₂×C₅	C₃×#518	1	1	yes	characteristic
380	C₂×C₅	C₃×#554	1	2	yes	—
381	C₂×C₅	C₃×#555	1	1	yes	characteristic
382	C₂×C₅	C₃×Q₈²	1	1	yes	characteristic
383	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
384	Q₈	—	4	4	no	—
385	Q₈	—	20	4	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	5	4	no	—
398	C₂×C₄	—	5	4	no	—
399	C₂×C₄	—	5	4	no	—
400	C₂×C₄	—	5	4	no	—
401	C₂×C₄	—	5	4	no	—
402	C₂×C₄	—	10	2	no	—
403	C₂×C₄	—	10	2	no	—
404	C₂×C₄	—	10	2	no	—
405	C₂×C₄	—	10	2	no	—
406	C₂×C₄	—	10	2	no	—
407	C₂×C₄	—	10	2	no	—
408	C₂×C₄	—	10	2	no	—
409	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
410	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
411	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
412	C₂×C₄	C₃×Q₈×D₅	1	4	yes	—
413	C₂×C₃	#65820	1	1	yes	characteristic
414	C₂×C₃	C₄×Q₈×D₅	1	2	yes	—
415	C₂×C₃	#65970	1	2	yes	—
416	C₂×C₃	#66004	1	1	yes	characteristic
417	C₂×C₃	#66056	1	1	yes	characteristic
418	C₅	C₃×#2369	1	1	yes	characteristic, complemented, Sylow
419	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
420	C₂²	C₃×#4144	1	1	yes	characteristic
421	C₂²	C₃×#4144	1	1	yes	characteristic
422	C₂²	C₂×C₃×Q₈×D₅	1	2	yes	—
423	C₂²	C₃×D₅×#41	1	2	yes	—
424	C₄	—	2	4	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	5	8	no	—
430	C₄	—	10	4	no	—
431	C₄	—	10	4	no	—
432	C₄	—	20	2	no	—
433	C₃	#10608225	1	1	yes	characteristic, direct product factor, Sylow
434	C₂	C₃×#65820	1	1	yes	characteristic
435	C₂	C₃×C₄×Q₈×D₅	1	2	yes	—
436	C₂	C₃×#65970	1	2	yes	—
437	C₂	C₃×#66004	1	1	yes	characteristic
438	C₂	C₃×#66056	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×C₅×#391	C₂
socle, prime radical	C₂³×C₃×C₅	C₂⁴
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×#391	D₅
hypocenter	C₅	C₃×#2369
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×#391

Complements

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

N	H ≅ G/N	type
10. #10608225	C₃	direct (N × H)
15. C₃×#4090	C₄	semidirect
65. C₃×#683	Q₈	semidirect
84. #4090	C₃×C₄	semidirect
177. #683	C₃×Q₈	semidirect
363. C₃×C₅	#2369	semidirect
418. C₅	C₃×#2369	semidirect
433. C₃	#10608225	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×#4090	2
C₃×C₅×#391	2
C₃×#65519	2
C₃×#65261	2
C₃×C₄×#683	2
C₃×#64938	2
C₃×#64936	2
C₃×#64935	2
#10608225	3
C₃×#2369	5

Subgroups — C3×#10608225 #14329828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10608225 #14329828