Subgroups — C₃×#10599022 #14281561

Order 1920.

552 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	C₃×C₄×#713	C₂	1	1	yes	maximal, characteristic
2	C₃×#65122	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×Q₈⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64703	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64679	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599022	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×#713	C₄	1	1	yes	characteristic
10	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₃×Q₈×Dic₅	C₄	1	1	yes	characteristic
12	C₂×C₃×C₈×D₅	—	2	1	no	—
13	C₃×#4039	—	2	1	no	—
14	C₃×#4039	C₄	1	1	yes	characteristic
15	C₃×#4038	—	2	1	no	—
16	C₃×#4038	C₄	1	1	yes	characteristic
17	C₃×C₄×D₂₀	—	2	1	no	—
18	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
19	C₃×C₄²×D₅	—	2	1	no	—
20	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₃×#3952	—	2	1	no	—
24	C₃×C₈×Dic₅	—	2	1	no	—
25	C₃×C₈×Dic₅	—	2	1	no	—
26	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
27	C₃×C₄×#168	C₂²	1	1	yes	characteristic
28	C₃×#1476	—	5	1	no	maximal, Hall
29	C₄×#713	C₂×C₃	1	1	yes	characteristic
30	#65122	C₂×C₃	1	1	yes	characteristic, complemented
31	C₄×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
32	C₅×Q₈⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
33	Q₈⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
34	#64703	C₂×C₃	1	1	yes	characteristic, complemented
35	#64679	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
37	C₃×#713	—	2	2	no	—
38	C₃×#713	C₈	1	4	yes	complemented
39	C₂×C₃×D₂₀	—	2	1	no	—
40	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₄×D₅	—	2	1	no	—
42	C₂×C₃×C₄×D₅	—	2	1	no	—
43	C₂×C₃×C₄×D₅	—	2	1	no	—
44	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
46	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₂×C₃×C₅×C₈	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	—	2	1	no	—
52	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₃×#685	—	2	1	no	—
54	C₃×#685	—	2	1	no	—
55	C₃×#685	—	2	1	no	—
56	C₃×C₄⋊Dic₅	—	2	1	no	—
57	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
58	C₃×C₄×Dic₅	—	2	1	no	—
59	C₃×C₄×Dic₅	—	2	1	no	—
60	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
61	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
62	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
63	C₂×C₃×#168	—	2	1	no	—
64	C₂×C₃×#168	—	2	1	no	—
65	C₃×C₈×D₅	—	2	4	no	—
66	C₃×C₄×#41	—	5	1	no	—
67	C₃×#431	—	5	1	no	—
68	C₂×C₃×C₄×C₈	—	5	1	no	—
69	C₃×Q₈⋊C₈	—	5	1	no	—
70	C₃×Q₈⋊C₈	D₅	1	1	yes	characteristic, complemented
71	C₃×D₄⋊C₈	—	5	1	no	—
72	C₃×D₄⋊C₈	—	5	1	no	—
73	C₂×#713	C₃×C₄	1	1	yes	characteristic
74	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
75	Q₈×Dic₅	C₃×C₄	1	1	yes	characteristic
76	C₂×C₈×D₅	—	2	1	no	—
77	#4039	—	2	1	no	—
78	#4039	C₃×C₄	1	1	yes	characteristic
79	#4038	—	2	1	no	—
80	#4038	C₃×C₄	1	1	yes	characteristic
81	C₄×D₂₀	—	2	1	no	—
82	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
83	C₄²×D₅	—	2	1	no	—
84	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
85	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
86	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
87	#3952	—	2	1	no	—
88	C₈×Dic₅	—	2	1	no	—
89	C₈×Dic₅	—	2	1	no	—
90	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
91	C₄×#168	C₂²×C₃	1	1	yes	characteristic
92	#1476	—	5	1	no	Sylow
93	C₂²×C₃×D₅	—	2	1	no	—
94	C₂²×C₃×D₅	C₂²⋊C₄	1	1	yes	characteristic
95	C₃×C₅×Q₈	—	2	1	no	—
96	C₃×C₅×Q₈	C₂×C₈	1	2	yes	complemented
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	—	2	1	no	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×Dic₅	—	2	1	no	—
103	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
106	C₃×D₂₀	—	2	4	no	—
107	C₃×D₂₀	—	2	1	no	—
108	C₃×D₂₀	C₂×C₈	1	2	yes	complemented
109	C₃×C₄×D₅	—	2	1	no	—
110	C₃×C₄×D₅	—	2	1	no	—
111	C₃×C₄×D₅	—	2	4	no	—
112	C₃×C₄×D₅	—	2	2	no	—
113	C₃×C₄×D₅	—	4	1	no	—
114	C₃×C₄×D₅	—	4	1	no	—
115	C₃×C₄×D₅	—	4	2	no	—
116	C₃×C₄×D₅	C₂×C₈	1	2	yes	—
117	C₃×C₄×D₅	M₁₆	1	2	yes	—
118	C₃×C₅×C₈	—	2	2	no	—
119	C₃×C₅×C₈	—	4	1	no	—
120	C₃×#168	—	2	2	no	—
121	C₃×#168	—	4	1	no	—
122	C₂×C₃×#41	—	5	1	no	—
123	C₂²×C₃×C₈	—	10	1	no	—
124	C₃×C₄×Q₈	—	5	1	no	—
125	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
126	C₃×C₄×D₄	—	5	1	no	—
127	C₃×C₄×D₄	—	5	1	no	—
128	C₃×C₄×D₄	—	10	1	no	—
129	C₃×C₄×D₄	—	10	1	no	—
130	C₃×#117	—	5	1	no	—
131	C₃×#117	—	10	1	no	—
132	C₂×C₃×C₄²	—	5	1	no	—
133	C₂×C₃×C₄²	—	10	1	no	—
134	C₃×C₄⋊C₈	—	5	1	no	—
135	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
136	C₃×C₂²⋊C₈	—	10	1	no	—
137	C₃×C₄×C₈	—	5	1	no	—
138	C₃×C₄×C₈	—	10	1	no	—
139	C₃×C₄×C₈	—	10	1	no	—
140	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
141	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
142	#713	—	2	2	no	—
143	#713	C₃×C₈	1	4	yes	complemented
144	C₂×D₂₀	—	2	1	no	—
145	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
146	C₂×C₄×D₅	—	2	1	no	—
147	C₂×C₄×D₅	—	2	1	no	—
148	C₂×C₄×D₅	—	2	1	no	—
149	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
150	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
151	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
152	C₂×C₅×C₈	—	2	1	no	—
153	C₂×C₅×C₈	—	2	1	no	—
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
156	C₄²×C₅	—	2	1	no	—
157	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
158	#685	—	2	1	no	—
159	#685	—	2	1	no	—
160	#685	—	2	1	no	—
161	C₄⋊Dic₅	—	2	1	no	—
162	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
163	C₄×Dic₅	—	2	1	no	—
164	C₄×Dic₅	—	2	1	no	—
165	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
166	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
167	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
168	C₂×#168	—	2	1	no	—
169	C₂×#168	—	2	1	no	—
170	C₈×D₅	—	2	4	no	—
171	C₄×#41	—	5	1	no	—
172	#431	—	5	1	no	—
173	C₂×C₄×C₈	—	5	1	no	—
174	Q₈⋊C₈	—	5	1	no	—
175	Q₈⋊C₈	C₃×D₅	1	1	yes	characteristic, complemented
176	D₄⋊C₈	—	5	1	no	—
177	D₄⋊C₈	—	5	1	no	—
178	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₃×D₅	—	2	1	no	—
180	C₂×C₃×D₅	—	2	1	no	—
181	C₂×C₃×D₅	—	2	2	no	—
182	C₂×C₃×D₅	—	4	1	no	—
183	C₂×C₃×D₅	—	4	1	no	—
184	C₂×C₃×D₅	C₂²⋊C₈	1	2	yes	—
185	C₃×C₄×C₅	—	2	2	no	—
186	C₃×C₄×C₅	—	2	1	no	—
187	C₃×C₄×C₅	—	4	1	no	—
188	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
189	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
190	C₃×C₄×C₅	#135	1	1	yes	characteristic
191	C₃×C₄×C₅	#135	1	1	yes	characteristic
192	C₃×Dic₅	—	2	1	no	—
193	C₃×Dic₅	—	4	1	no	—
194	C₃×Dic₅	C₂²⋊C₈	1	2	yes	—
195	C₃×Dic₅	#104	1	2	yes	—
196	C₃×#41	—	5	4	no	—
197	C₃×#41	—	10	2	no	—
198	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
199	C₂×C₃×D₄	—	5	1	no	—
200	C₂×C₃×D₄	—	10	1	no	—
201	C₂²×C₃×C₄	—	5	1	no	—
202	C₂²×C₃×C₄	—	5	1	no	—
203	C₂²×C₃×C₄	—	5	1	no	—
204	C₂²×C₃×C₄	—	10	1	no	—
205	C₂²×C₃×C₄	—	10	1	no	—
206	C₂²×C₃×C₄	—	10	1	no	—
207	C₂×C₃×C₈	—	2	1	no	—
208	C₂×C₃×C₈	—	2	1	no	—
209	C₂×C₃×C₈	—	10	4	no	—
210	C₂×C₃×C₈	—	10	1	no	—
211	C₂×C₃×C₈	—	10	1	no	—
212	C₃×C₄⋊C₄	—	2	1	no	—
213	C₃×C₄⋊C₄	—	5	1	no	—
214	C₃×C₄⋊C₄	—	10	1	no	—
215	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
216	C₃×C₂²⋊C₄	—	10	1	no	—
217	C₃×C₂²⋊C₄	—	10	1	no	—
218	C₃×C₂²⋊C₄	—	10	1	no	—
219	C₃×C₄²	—	2	1	no	—
220	C₃×C₄²	—	5	1	no	—
221	C₃×C₄²	—	5	1	no	—
222	C₃×C₄²	—	5	1	no	—
223	C₃×C₄²	—	10	1	no	—
224	C₃×C₄²	—	10	1	no	—
225	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
226	C₂²×D₅	—	2	1	no	—
227	C₂²×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
228	C₅×Q₈	—	2	1	no	—
229	C₅×Q₈	C₂×C₃×C₈	1	2	yes	complemented
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
235	C₂×Dic₅	—	2	1	no	—
236	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
239	D₂₀	—	2	4	no	—
240	D₂₀	—	2	1	no	—
241	D₂₀	C₂×C₃×C₈	1	2	yes	complemented
242	C₄×D₅	—	2	1	no	—
243	C₄×D₅	—	2	1	no	—
244	C₄×D₅	—	2	4	no	—
245	C₄×D₅	—	2	2	no	—
246	C₄×D₅	—	4	1	no	—
247	C₄×D₅	—	4	1	no	—
248	C₄×D₅	—	4	2	no	—
249	C₄×D₅	C₂×C₃×C₈	1	2	yes	—
250	C₄×D₅	C₃×M₁₆	1	2	yes	—
251	C₅×C₈	—	2	2	no	—
252	C₅×C₈	—	4	1	no	—
253	#168	—	2	2	no	—
254	#168	—	4	1	no	—
255	C₂×#41	—	5	1	no	—
256	C₂²×C₈	—	10	1	no	—
257	C₄×Q₈	—	5	1	no	—
258	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
259	C₄×D₄	—	5	1	no	—
260	C₄×D₄	—	5	1	no	—
261	C₄×D₄	—	10	1	no	—
262	C₄×D₄	—	10	1	no	—
263	#117	—	5	1	no	—
264	#117	—	10	1	no	—
265	C₂×C₄²	—	5	1	no	—
266	C₂×C₄²	—	10	1	no	—
267	C₄⋊C₈	—	5	1	no	—
268	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
269	C₂²⋊C₈	—	10	1	no	—
270	C₄×C₈	—	5	1	no	—
271	C₄×C₈	—	10	1	no	—
272	C₄×C₈	—	10	1	no	—
273	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
274	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
275	C₂×C₃×C₅	#416	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
277	C₃×D₅	—	2	2	no	—
278	C₃×D₅	—	4	2	no	—
279	C₂³×C₃	—	5	1	no	—
280	C₂³×C₃	—	10	1	no	—
281	C₃×Q₈	—	2	1	no	—
282	C₃×Q₈	C₈×D₅	1	2	yes	complemented
283	C₃×D₄	—	5	2	no	—
284	C₃×D₄	—	10	4	no	—
285	C₃×D₄	—	10	1	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	5	1	no	—
289	C₂×C₃×C₄	—	5	1	no	—
290	C₂×C₃×C₄	—	5	2	no	—
291	C₂×C₃×C₄	—	5	2	no	—
292	C₂×C₃×C₄	—	5	1	no	—
293	C₂×C₃×C₄	—	10	2	no	—
294	C₂×C₃×C₄	—	10	4	no	—
295	C₂×C₃×C₄	—	10	1	no	—
296	C₂×C₃×C₄	—	10	1	no	—
297	C₂×C₃×C₄	—	10	1	no	—
298	C₂×C₃×C₄	—	20	2	no	—
299	C₂×C₃×C₄	—	20	1	no	—
300	C₂×C₃×C₄	—	20	1	no	—
301	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
302	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
303	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
304	C₃×C₈	—	2	2	no	—
305	C₃×C₈	—	4	1	no	—
306	C₃×C₈	—	10	2	no	—
307	C₃×C₈	—	20	1	no	—
308	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
309	C₂×D₅	—	2	1	no	—
310	C₂×D₅	—	2	1	no	—
311	C₂×D₅	—	2	2	no	—
312	C₂×D₅	—	4	1	no	—
313	C₂×D₅	—	4	1	no	—
314	C₂×D₅	C₃×C₂²⋊C₈	1	2	yes	—
315	C₄×C₅	—	2	2	no	—
316	C₄×C₅	—	2	1	no	—
317	C₄×C₅	—	4	1	no	—
318	C₄×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
319	C₄×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
320	C₄×C₅	C₃×#135	1	1	yes	characteristic
321	C₄×C₅	C₃×#135	1	1	yes	characteristic
322	Dic₅	—	2	1	no	—
323	Dic₅	—	4	1	no	—
324	Dic₅	C₃×C₂²⋊C₈	1	2	yes	—
325	Dic₅	C₃×#104	1	2	yes	—
326	#41	—	5	4	no	—
327	#41	—	10	2	no	—
328	C₂×Q₈	C₃×C₄×D₅	1	1	yes	characteristic
329	C₂×D₄	—	5	1	no	—
330	C₂×D₄	—	10	1	no	—
331	C₂²×C₄	—	5	1	no	—
332	C₂²×C₄	—	5	1	no	—
333	C₂²×C₄	—	5	1	no	—
334	C₂²×C₄	—	10	1	no	—
335	C₂²×C₄	—	10	1	no	—
336	C₂²×C₄	—	10	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	10	4	no	—
340	C₂×C₈	—	10	1	no	—
341	C₂×C₈	—	10	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	5	1	no	—
344	C₄⋊C₄	—	10	1	no	—
345	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
346	C₂²⋊C₄	—	10	1	no	—
347	C₂²⋊C₄	—	10	1	no	—
348	C₂²⋊C₄	—	10	1	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	5	1	no	—
351	C₄²	—	5	1	no	—
352	C₄²	—	5	1	no	—
353	C₄²	—	10	1	no	—
354	C₄²	—	10	1	no	—
355	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
356	C₃×C₅	#1476	1	1	yes	characteristic, complemented, Hall
357	C₂²×C₃	—	5	2	no	—
358	C₂²×C₃	—	10	1	no	—
359	C₂²×C₃	—	10	1	no	—
360	C₂²×C₃	—	10	2	no	—
361	C₂²×C₃	—	20	1	no	—
362	C₂²×C₃	—	20	1	no	—
363	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
364	C₃×C₄	—	2	1	no	—
365	C₃×C₄	—	2	2	no	—
366	C₃×C₄	—	4	1	no	—
367	C₃×C₄	—	5	2	no	—
368	C₃×C₄	—	5	2	no	—
369	C₃×C₄	—	10	1	no	—
370	C₃×C₄	—	20	1	no	—
371	C₃×C₄	C₂×C₈×D₅	1	1	yes	characteristic
372	C₃×C₄	D₅×M₁₆	1	1	yes	characteristic
373	C₃×C₄	#4062	1	1	yes	characteristic
374	C₃×C₄	#4065	1	1	yes	characteristic
375	C₂×C₅	C₂×C₃×C₂²⋊C₈	1	1	yes	characteristic
376	C₂×C₅	C₃×#416	1	1	yes	characteristic
377	C₂×C₅	C₂×C₃×#104	1	1	yes	characteristic
378	D₅	—	2	2	no	—
379	D₅	—	4	2	no	—
380	C₂³	—	5	1	no	—
381	C₂³	—	10	1	no	—
382	Q₈	—	2	1	no	—
383	Q₈	C₃×C₈×D₅	1	2	yes	complemented
384	D₄	—	5	2	no	—
385	D₄	—	10	4	no	—
386	D₄	—	10	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	5	1	no	—
390	C₂×C₄	—	5	1	no	—
391	C₂×C₄	—	5	2	no	—
392	C₂×C₄	—	5	2	no	—
393	C₂×C₄	—	5	1	no	—
394	C₂×C₄	—	10	2	no	—
395	C₂×C₄	—	10	4	no	—
396	C₂×C₄	—	10	1	no	—
397	C₂×C₄	—	10	1	no	—
398	C₂×C₄	—	10	1	no	—
399	C₂×C₄	—	20	2	no	—
400	C₂×C₄	—	20	1	no	—
401	C₂×C₄	—	20	1	no	—
402	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
403	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
404	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
405	C₈	—	2	2	no	—
406	C₈	—	4	1	no	—
407	C₈	—	10	2	no	—
408	C₈	—	20	1	no	—
409	C₂×C₃	—	10	2	no	—
410	C₂×C₃	—	20	2	no	—
411	C₂×C₃	D₅×C₂²⋊C₈	1	1	yes	characteristic
412	C₂×C₃	#65093	1	1	yes	characteristic
413	C₂×C₃	D₅×#104	1	1	yes	characteristic
414	C₅	C₃×#1476	1	1	yes	characteristic, complemented, Sylow
415	C₂²	—	5	2	no	—
416	C₂²	—	10	1	no	—
417	C₂²	—	10	1	no	—
418	C₂²	—	10	2	no	—
419	C₂²	—	20	1	no	—
420	C₂²	—	20	1	no	—
421	C₂²	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
422	C₄	—	2	1	no	—
423	C₄	—	2	2	no	—
424	C₄	—	4	1	no	—
425	C₄	—	5	2	no	—
426	C₄	—	5	2	no	—
427	C₄	—	10	1	no	—
428	C₄	—	20	1	no	—
429	C₄	C₂×C₃×C₈×D₅	1	1	yes	characteristic
430	C₄	C₃×D₅×M₁₆	1	1	yes	characteristic
431	C₄	C₃×#4062	1	1	yes	characteristic
432	C₄	C₃×#4065	1	1	yes	characteristic
433	C₃	#10599022	1	1	yes	characteristic, direct product factor, Sylow
434	C₂	—	10	2	no	—
435	C₂	—	20	2	no	—
436	C₂	C₃×D₅×C₂²⋊C₈	1	1	yes	characteristic
437	C₂	C₃×#65093	1	1	yes	characteristic
438	C₂	C₃×D₅×#104	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₄×D₅
commutator	C₄×C₅	C₂²×C₃×C₈
Frattini	C₄²	C₂²×C₃×D₅
Fitting	C₃×C₅×Q₈⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×#713	C₄
cosocle	C₄²×C₅	C₂³×C₃
hypercenter	C₃×Q₈⋊C₈	D₅
hypocenter	C₅	C₃×#1476
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄² ◁ C₃×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₃×#65122	C₂	semidirect
3. C₃×C₄×C₈×D₅	C₂	semidirect
4. C₃×C₅×Q₈⋊C₈	C₂	semidirect
5. C₃×Q₈⋊#168	C₂	semidirect
6. C₃×#64703	C₂	semidirect
7. C₃×#64679	C₂	semidirect
8. #10599022	C₃	direct (N × H)
30. #65122	C₂×C₃	semidirect
31. C₄×C₈×D₅	C₂×C₃	semidirect
32. C₅×Q₈⋊C₈	C₂×C₃	semidirect
33. Q₈⋊#168	C₂×C₃	semidirect
34. #64703	C₂×C₃	semidirect
35. #64679	C₂×C₃	semidirect
38. C₃×#713	C₈	semidirect
70. C₃×Q₈⋊C₈	D₅	semidirect
96. C₃×C₅×Q₈	C₂×C₈	semidirect
108. C₃×D₂₀	C₂×C₈	semidirect
143. #713	C₃×C₈	semidirect
175. Q₈⋊C₈	C₃×D₅	semidirect
229. C₅×Q₈	C₂×C₃×C₈	semidirect
241. D₂₀	C₂×C₃×C₈	semidirect
282. C₃×Q₈	C₈×D₅	semidirect
356. C₃×C₅	#1476	semidirect
383. Q₈	C₃×C₈×D₅	semidirect
414. C₅	C₃×#1476	semidirect
433. C₃	#10599022	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×#713	2
C₃×#65122	2
C₃×C₄×C₈×D₅	2
C₃×C₅×Q₈⋊C₈	2
C₃×Q₈⋊#168	2
C₃×#64703	2
C₃×#64679	2
#10599022	3
C₃×#1476	5

Subgroups — C3×#10599022 #14281561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10599022 #14281561