Subgroups — C₃×#10599033 #14282406

Order 1920.

464 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65912	C₂	1	1	yes	maximal, characteristic
2	C₃×#65126	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic
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×#64704	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64676	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599033	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₃×#4092	C₄	1	1	yes	characteristic
11	C₃×#4090	C₄	1	1	yes	characteristic
12	C₂×C₃×#676	—	2	1	no	—
13	C₂×C₃×C₈×D₅	—	2	1	no	—
14	C₃×#4043	C₄	1	1	yes	characteristic
15	C₃×#4042	—	2	1	no	—
16	C₃×#4035	—	2	1	no	—
17	C₃×#4034	C₄	1	1	yes	characteristic
18	C₃×#4018	—	2	1	no	—
19	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
20	C₃×C₄×Dic₁₀	—	2	1	no	—
21	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
22	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₃×#3946	—	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×#1493	—	5	1	no	maximal, Hall
29	#65912	C₂×C₃	1	1	yes	characteristic
30	#65126	C₂×C₃	1	1	yes	characteristic
31	C₄×C₈×D₅	C₂×C₃	1	1	yes	characteristic
32	C₅×Q₈⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
33	Q₈⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
34	#64704	C₂×C₃	1	1	yes	characteristic, complemented
35	#64676	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
39	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
40	C₂×C₃×Dic₁₀	—	2	1	no	—
41	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃×C₅×C₈	—	2	1	no	—
43	C₂×C₃×C₅×C₈	—	2	1	no	—
44	C₃×C₅×C₄⋊C₄	—	2	1	no	—
45	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
46	C₃×C₄²×C₅	—	2	1	no	—
47	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
48	C₃×#685	—	2	1	no	—
49	C₃×#685	—	2	1	no	—
50	C₃×C₄⋊Dic₅	—	2	1	no	—
51	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
52	C₃×#683	—	2	1	no	—
53	C₃×#683	—	2	1	no	—
54	C₃×#683	—	2	1	no	—
55	C₃×#683	—	2	1	no	—
56	C₃×#683	—	2	1	no	—
57	C₃×C₄×Dic₅	—	2	1	no	—
58	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
59	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
60	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
61	C₂×C₃×#168	—	2	1	no	—
62	C₂×C₃×#168	—	2	1	no	—
63	C₃×#676	—	4	2	no	—
64	C₃×C₈×D₅	—	2	4	no	—
65	C₃×#533	—	5	1	no	—
66	C₃×#423	—	5	1	no	—
67	C₂×C₃×C₄×C₈	—	5	1	no	—
68	C₃×Q₈⋊C₈	—	5	1	no	—
69	C₃×Q₈⋊C₈	—	5	1	no	—
70	C₃×Q₈⋊C₈	—	5	1	no	—
71	C₃×Q₈⋊C₈	D₅	1	1	yes	characteristic, complemented
72	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
73	#4092	C₃×C₄	1	1	yes	characteristic
74	#4090	C₃×C₄	1	1	yes	characteristic
75	C₂×#676	—	2	1	no	—
76	C₂×C₈×D₅	—	2	1	no	—
77	#4043	C₃×C₄	1	1	yes	characteristic
78	#4042	—	2	1	no	—
79	#4035	—	2	1	no	—
80	#4034	C₃×C₄	1	1	yes	characteristic
81	#4018	—	2	1	no	—
82	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
83	C₄×Dic₁₀	—	2	1	no	—
84	C₄×Dic₁₀	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	#3946	—	2	1	no	—
88	C₈×Dic₅	—	2	1	no	—
89	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
90	C₄×#168	C₂²×C₃	1	1	yes	characteristic
91	#1493	—	5	1	no	Sylow
92	C₂²×C₃×D₅	C₂²⋊C₄	1	1	yes	characteristic
93	C₃×C₅×Q₈	—	2	1	no	—
94	C₃×C₅×Q₈	—	2	1	no	—
95	C₂×C₃×C₄×C₅	—	2	1	no	—
96	C₂×C₃×C₄×C₅	—	2	1	no	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×Dic₅	—	2	1	no	—
101	C₂×C₃×Dic₅	—	2	1	no	—
102	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
105	C₃×C₄×D₅	—	2	1	no	—
106	C₃×C₄×D₅	—	2	1	no	—
107	C₃×C₄×D₅	—	2	2	no	—
108	C₃×C₄×D₅	SD₁₆	1	2	yes	—
109	C₃×C₄×D₅	Q₁₆	1	2	yes	—
110	C₃×Dic₁₀	—	2	1	no	—
111	C₃×Dic₁₀	—	2	1	no	—
112	C₃×Dic₁₀	—	4	2	no	—
113	C₃×C₅×C₈	—	2	2	no	—
114	C₃×C₅×C₈	—	4	1	no	—
115	C₃×#168	—	2	2	no	—
116	C₃×#168	—	4	1	no	—
117	C₂×C₃×M₁₆	—	10	1	no	—
118	C₂²×C₃×C₈	—	10	1	no	—
119	C₃×C₄⋊Q₈	—	5	1	no	—
120	C₃×C₄⋊Q₈	—	5	1	no	—
121	C₃×#125	—	10	1	no	—
122	C₃×C₂²⋊Q₈	—	5	1	no	—
123	C₃×C₂²⋊Q₈	—	5	1	no	—
124	C₃×C₂²⋊Q₈	—	10	1	no	—
125	C₃×C₄×Q₈	—	5	1	no	—
126	C₃×C₄×Q₈	—	10	1	no	—
127	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
128	C₃×#117	—	10	1	no	—
129	C₂×C₃×C₄²	—	5	1	no	—
130	C₃×C₄⋊C₈	—	5	1	no	—
131	C₃×C₄⋊C₈	—	10	1	no	—
132	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
133	C₃×C₄×C₈	—	5	1	no	—
134	C₃×C₄×C₈	—	10	1	no	—
135	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
136	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
137	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
138	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
139	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
140	C₂×Dic₁₀	—	2	1	no	—
141	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	2	1	no	—
144	C₅×C₄⋊C₄	—	2	1	no	—
145	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
146	C₄²×C₅	—	2	1	no	—
147	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
148	#685	—	2	1	no	—
149	#685	—	2	1	no	—
150	C₄⋊Dic₅	—	2	1	no	—
151	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
152	#683	—	2	1	no	—
153	#683	—	2	1	no	—
154	#683	—	2	1	no	—
155	#683	—	2	1	no	—
156	#683	—	2	1	no	—
157	C₄×Dic₅	—	2	1	no	—
158	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
159	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
160	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
161	C₂×#168	—	2	1	no	—
162	C₂×#168	—	2	1	no	—
163	#676	—	4	2	no	—
164	C₈×D₅	—	2	4	no	—
165	#533	—	5	1	no	—
166	#423	—	5	1	no	—
167	C₂×C₄×C₈	—	5	1	no	—
168	Q₈⋊C₈	—	5	1	no	—
169	Q₈⋊C₈	—	5	1	no	—
170	Q₈⋊C₈	—	5	1	no	—
171	Q₈⋊C₈	C₃×D₅	1	1	yes	characteristic, complemented
172	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₃×D₅	—	2	1	no	—
174	C₂×C₃×D₅	—	2	1	no	—
175	C₂×C₃×D₅	#103	1	2	yes	—
176	C₃×C₄×C₅	—	2	1	no	—
177	C₃×C₄×C₅	—	4	1	no	—
178	C₃×C₄×C₅	—	4	1	no	—
179	C₃×C₄×C₅	#131	1	1	yes	characteristic
180	C₃×C₄×C₅	#131	1	1	yes	characteristic
181	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
182	C₃×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
183	C₃×Dic₅	—	2	1	no	—
184	C₃×Dic₅	—	4	1	no	—
185	C₃×Dic₅	—	4	1	no	—
186	C₃×Dic₅	#103	1	2	yes	—
187	C₃×Dic₅	#104	1	2	yes	—
188	C₂×C₃×Q₈	—	5	1	no	—
189	C₂×C₃×Q₈	—	10	1	no	—
190	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
191	C₂²×C₃×C₄	—	5	1	no	—
192	C₂²×C₃×C₄	—	5	1	no	—
193	C₂²×C₃×C₄	—	5	1	no	—
194	C₃×M₁₆	—	20	2	no	—
195	C₂×C₃×C₈	—	2	1	no	—
196	C₂×C₃×C₈	—	2	1	no	—
197	C₂×C₃×C₈	—	10	4	no	—
198	C₂×C₃×C₈	—	10	1	no	—
199	C₂×C₃×C₈	—	10	1	no	—
200	C₃×C₄⋊C₄	—	2	1	no	—
201	C₃×C₄⋊C₄	—	5	1	no	—
202	C₃×C₄⋊C₄	—	10	1	no	—
203	C₃×C₄⋊C₄	—	10	1	no	—
204	C₃×C₄⋊C₄	—	10	1	no	—
205	C₃×C₄⋊C₄	—	10	1	no	—
206	C₃×C₄⋊C₄	—	10	1	no	—
207	C₃×C₄⋊C₄	—	10	1	no	—
208	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
209	C₃×C₂²⋊C₄	—	10	1	no	—
210	C₃×C₂²⋊C₄	—	10	1	no	—
211	C₃×C₄²	—	2	1	no	—
212	C₃×C₄²	—	5	1	no	—
213	C₃×C₄²	—	5	1	no	—
214	C₃×C₄²	—	5	1	no	—
215	C₃×C₄²	—	10	1	no	—
216	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
217	C₂²×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
218	C₅×Q₈	—	2	1	no	—
219	C₅×Q₈	—	2	1	no	—
220	C₂×C₄×C₅	—	2	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
225	C₂×Dic₅	—	2	1	no	—
226	C₂×Dic₅	—	2	1	no	—
227	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
230	C₄×D₅	—	2	1	no	—
231	C₄×D₅	—	2	1	no	—
232	C₄×D₅	—	2	2	no	—
233	C₄×D₅	C₃×SD₁₆	1	2	yes	—
234	C₄×D₅	C₃×Q₁₆	1	2	yes	—
235	Dic₁₀	—	2	1	no	—
236	Dic₁₀	—	2	1	no	—
237	Dic₁₀	—	4	2	no	—
238	C₅×C₈	—	2	2	no	—
239	C₅×C₈	—	4	1	no	—
240	#168	—	2	2	no	—
241	#168	—	4	1	no	—
242	C₂×M₁₆	—	10	1	no	—
243	C₂²×C₈	—	10	1	no	—
244	C₄⋊Q₈	—	5	1	no	—
245	C₄⋊Q₈	—	5	1	no	—
246	#125	—	10	1	no	—
247	C₂²⋊Q₈	—	5	1	no	—
248	C₂²⋊Q₈	—	5	1	no	—
249	C₂²⋊Q₈	—	10	1	no	—
250	C₄×Q₈	—	5	1	no	—
251	C₄×Q₈	—	10	1	no	—
252	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
253	#117	—	10	1	no	—
254	C₂×C₄²	—	5	1	no	—
255	C₄⋊C₈	—	5	1	no	—
256	C₄⋊C₈	—	10	1	no	—
257	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
258	C₄×C₈	—	5	1	no	—
259	C₄×C₈	—	10	1	no	—
260	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
261	C₂×C₃×C₅	#408	1	1	yes	characteristic
262	C₂×C₃×C₅	C₂×#103	1	1	yes	characteristic
263	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
264	C₃×D₅	—	2	2	no	—
265	C₂³×C₃	—	5	1	no	—
266	C₃×Q₈	—	2	1	no	—
267	C₃×Q₈	—	2	1	no	—
268	C₃×Q₈	—	10	1	no	—
269	C₃×Q₈	—	10	1	no	—
270	C₃×Q₈	—	20	2	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	5	1	no	—
274	C₂×C₃×C₄	—	5	1	no	—
275	C₂×C₃×C₄	—	5	2	no	—
276	C₂×C₃×C₄	—	5	2	no	—
277	C₂×C₃×C₄	—	5	1	no	—
278	C₂×C₃×C₄	—	10	2	no	—
279	C₂×C₃×C₄	—	10	1	no	—
280	C₂×C₃×C₄	—	10	1	no	—
281	C₂×C₃×C₄	—	10	1	no	—
282	C₂×C₃×C₄	—	10	1	no	—
283	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
284	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
285	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
286	C₃×C₈	—	2	2	no	—
287	C₃×C₈	—	4	1	no	—
288	C₃×C₈	—	10	2	no	—
289	C₃×C₈	—	20	1	no	—
290	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
291	C₂×D₅	—	2	1	no	—
292	C₂×D₅	—	2	1	no	—
293	C₂×D₅	C₃×#103	1	2	yes	—
294	C₄×C₅	—	2	1	no	—
295	C₄×C₅	—	4	1	no	—
296	C₄×C₅	—	4	1	no	—
297	C₄×C₅	C₃×#131	1	1	yes	characteristic
298	C₄×C₅	C₃×#131	1	1	yes	characteristic
299	C₄×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
300	C₄×C₅	C₂×C₃×Q₁₆	1	1	yes	characteristic
301	Dic₅	—	2	1	no	—
302	Dic₅	—	4	1	no	—
303	Dic₅	—	4	1	no	—
304	Dic₅	C₃×#103	1	2	yes	—
305	Dic₅	C₃×#104	1	2	yes	—
306	C₂×Q₈	—	5	1	no	—
307	C₂×Q₈	—	10	1	no	—
308	C₂×Q₈	C₃×C₄×D₅	1	1	yes	characteristic
309	C₂²×C₄	—	5	1	no	—
310	C₂²×C₄	—	5	1	no	—
311	C₂²×C₄	—	5	1	no	—
312	M₁₆	—	20	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	10	4	no	—
316	C₂×C₈	—	10	1	no	—
317	C₂×C₈	—	10	1	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	5	1	no	—
320	C₄⋊C₄	—	10	1	no	—
321	C₄⋊C₄	—	10	1	no	—
322	C₄⋊C₄	—	10	1	no	—
323	C₄⋊C₄	—	10	1	no	—
324	C₄⋊C₄	—	10	1	no	—
325	C₄⋊C₄	—	10	1	no	—
326	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
327	C₂²⋊C₄	—	10	1	no	—
328	C₂²⋊C₄	—	10	1	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	5	1	no	—
331	C₄²	—	5	1	no	—
332	C₄²	—	5	1	no	—
333	C₄²	—	10	1	no	—
334	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
335	C₃×C₅	#1493	1	1	yes	characteristic, complemented, Hall
336	C₂²×C₃	—	5	2	no	—
337	C₂²×C₃	—	10	1	no	—
338	C₂²×C₃	—	10	1	no	—
339	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
340	C₃×C₄	—	2	1	no	—
341	C₃×C₄	—	4	1	no	—
342	C₃×C₄	—	4	1	no	—
343	C₃×C₄	—	5	2	no	—
344	C₃×C₄	—	5	2	no	—
345	C₃×C₄	—	10	1	no	—
346	C₃×C₄	—	20	1	no	—
347	C₃×C₄	—	20	1	no	—
348	C₃×C₄	#4047	1	1	yes	characteristic
349	C₃×C₄	#4053	1	1	yes	characteristic
350	C₃×C₄	D₅×SD₁₆	1	1	yes	characteristic
351	C₃×C₄	D₅×Q₁₆	1	1	yes	characteristic
352	C₂×C₅	C₃×#408	1	1	yes	characteristic
353	C₂×C₅	C₂×C₃×#103	1	1	yes	characteristic
354	C₂×C₅	C₂×C₃×#104	1	1	yes	characteristic
355	D₅	—	2	2	no	—
356	C₂³	—	5	1	no	—
357	Q₈	—	2	1	no	—
358	Q₈	—	2	1	no	—
359	Q₈	—	10	1	no	—
360	Q₈	—	10	1	no	—
361	Q₈	—	20	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	5	1	no	—
365	C₂×C₄	—	5	1	no	—
366	C₂×C₄	—	5	2	no	—
367	C₂×C₄	—	5	2	no	—
368	C₂×C₄	—	5	1	no	—
369	C₂×C₄	—	10	2	no	—
370	C₂×C₄	—	10	1	no	—
371	C₂×C₄	—	10	1	no	—
372	C₂×C₄	—	10	1	no	—
373	C₂×C₄	—	10	1	no	—
374	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
375	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
376	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	4	1	no	—
379	C₈	—	10	2	no	—
380	C₈	—	20	1	no	—
381	C₂×C₃	—	10	2	no	—
382	C₂×C₃	#65016	1	1	yes	characteristic
383	C₂×C₃	D₅×#103	1	1	yes	characteristic
384	C₂×C₃	D₅×#104	1	1	yes	characteristic
385	C₅	C₃×#1493	1	1	yes	characteristic, complemented, Sylow
386	C₂²	—	5	2	no	—
387	C₂²	—	10	1	no	—
388	C₂²	—	10	1	no	—
389	C₂²	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	5	2	no	—
394	C₄	—	5	2	no	—
395	C₄	—	10	1	no	—
396	C₄	—	20	1	no	—
397	C₄	—	20	1	no	—
398	C₄	C₃×#4047	1	1	yes	characteristic
399	C₄	C₃×#4053	1	1	yes	characteristic
400	C₄	C₃×D₅×SD₁₆	1	1	yes	characteristic
401	C₄	C₃×D₅×Q₁₆	1	1	yes	characteristic
402	C₃	#10599033	1	1	yes	characteristic, direct product factor, Sylow
403	C₂	—	10	2	no	—
404	C₂	C₃×#65016	1	1	yes	characteristic
405	C₂	C₃×D₅×#103	1	1	yes	characteristic
406	C₂	C₃×D₅×#104	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₄×D₅
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₄²	C₂²×C₃×D₅
Fitting	C₃×C₅×Q₈⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂²×C₃×D₅	C₂²⋊C₄
cosocle	C₄²×C₅	C₂³×C₃
hypercenter	C₃×Q₈⋊C₈	D₅
hypocenter	C₅	C₃×#1493
LCS	G ▷ C₂×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
4. C₃×C₅×Q₈⋊C₈	C₂	semidirect
5. C₃×Q₈⋊#168	C₂	semidirect
6. C₃×#64704	C₂	semidirect
7. C₃×#64676	C₂	semidirect
8. #10599033	C₃	direct (N × H)
32. C₅×Q₈⋊C₈	C₂×C₃	semidirect
33. Q₈⋊#168	C₂×C₃	semidirect
34. #64704	C₂×C₃	semidirect
35. #64676	C₂×C₃	semidirect
71. C₃×Q₈⋊C₈	D₅	semidirect
171. Q₈⋊C₈	C₃×D₅	semidirect
335. C₃×C₅	#1493	semidirect
385. C₅	C₃×#1493	semidirect
402. C₃	#10599033	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×#65912	2
C₃×#65126	2
C₃×C₄×C₈×D₅	2
C₃×C₅×Q₈⋊C₈	2
C₃×Q₈⋊#168	2
C₃×#64704	2
C₃×#64676	2
#10599033	3
C₃×#1493	5

Subgroups — C3×#10599033 #14282406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10599033 #14282406