Subgroups — C₃×#10602711 #14288891

Order 1920.

556 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#65362	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65316	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65304	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64764	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×Q₈⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×D₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
8	#10602711	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	—	2	1	no	—
10	C₃×C₅×#127	—	2	1	no	—
11	C₃×C₅×#127	C₂²	1	1	yes	characteristic
12	C₃×C₅×#121	—	2	2	no	—
13	C₃×C₅×#121	—	2	1	no	—
14	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	—	2	1	no	—
16	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×#688	—	2	1	no	—
18	C₂×C₃×#686	—	2	1	no	—
19	C₂×C₃×#686	—	2	2	no	—
20	C₃×#4020	C₂²	1	1	yes	characteristic
21	C₃×#3941	—	2	1	no	—
22	C₃×#3941	—	2	1	no	—
23	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
24	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
25	C₃×C₄×#168	C₂²	1	1	yes	characteristic
26	C₃×#1621	—	5	1	no	maximal, Hall
27	C₅×#550	C₂×C₃	1	1	yes	characteristic, complemented
28	#65362	C₂×C₃	1	1	yes	characteristic, complemented
29	#65316	C₂×C₃	1	1	yes	characteristic, complemented
30	#65304	C₂×C₃	1	1	yes	characteristic, complemented
31	#64764	C₂×C₃	1	1	yes	characteristic, complemented
32	Q₈⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
33	D₄⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
34	C₃×C₅×#41	—	4	2	no	—
35	C₃×C₅×#41	—	4	2	no	—
36	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
37	C₂×C₃×C₅×D₄	—	2	2	no	—
38	C₂×C₃×C₅×D₄	—	2	2	no	—
39	C₂×C₃×C₅×D₄	—	2	1	no	—
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
42	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
43	C₂²×C₃×C₄×C₅	—	2	2	no	—
44	C₂²×C₃×C₄×C₅	—	2	1	no	—
45	C₂×C₃×D₂₀	—	2	1	no	—
46	C₂×C₃×D₂₀	—	2	1	no	—
47	C₂×C₃×D₂₀	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
50	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
51	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
52	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
53	C₃×C₄²×C₅	—	2	1	no	—
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₃×#688	—	4	2	no	—
56	C₃×#686	—	4	4	no	—
57	C₃×#686	—	4	2	no	—
58	C₂×C₃×#168	—	2	1	no	—
59	C₂×C₃×#168	—	2	1	no	—
60	C₂×C₃×#168	—	2	1	no	—
61	C₃×#550	D₅	1	1	yes	characteristic, complemented
62	C₃×#493	—	5	1	no	—
63	C₃×#460	—	5	1	no	—
64	C₃×#459	—	5	1	no	—
65	C₃×#331	—	5	1	no	—
66	C₃×Q₈⋊C₈	—	5	1	no	—
67	C₃×D₄⋊C₈	—	5	1	no	—
68	C₂×C₅×#41	—	2	1	no	—
69	C₅×#127	—	2	1	no	—
70	C₅×#127	C₂²×C₃	1	1	yes	characteristic
71	C₅×#121	—	2	2	no	—
72	C₅×#121	—	2	1	no	—
73	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
74	C₄×C₅×D₄	—	2	1	no	—
75	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
76	C₂×#688	—	2	1	no	—
77	C₂×#686	—	2	1	no	—
78	C₂×#686	—	2	2	no	—
79	#4020	C₂²×C₃	1	1	yes	characteristic
80	#3941	—	2	1	no	—
81	#3941	—	2	1	no	—
82	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
83	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
84	C₄×#168	C₂²×C₃	1	1	yes	characteristic
85	#1621	—	5	1	no	Sylow
86	C₂³×C₃×C₅	—	2	1	no	—
87	C₂³×C₃×C₅	—	2	2	no	—
88	C₂²×C₃×D₅	—	4	1	no	—
89	C₃×C₅×Q₈	—	2	1	no	—
90	C₃×C₅×Q₈	D₈	1	2	yes	complemented
91	C₃×C₅×D₄	—	2	1	no	—
92	C₃×C₅×D₄	—	2	1	no	—
93	C₃×C₅×D₄	—	4	4	no	—
94	C₃×C₅×D₄	—	4	2	no	—
95	C₃×C₅×D₄	—	4	1	no	—
96	C₃×C₅×D₄	—	4	1	no	—
97	C₃×C₅×D₄	—	4	1	no	—
98	C₃×C₅×D₄	—	4	1	no	—
99	C₃×C₅×D₄	—	8	2	no	—
100	C₂×C₃×C₄×C₅	—	2	1	no	—
101	C₂×C₃×C₄×C₅	—	2	1	no	—
102	C₂×C₃×C₄×C₅	—	2	1	no	—
103	C₂×C₃×C₄×C₅	—	4	4	no	—
104	C₂×C₃×C₄×C₅	—	4	1	no	—
105	C₂×C₃×C₄×C₅	—	4	1	no	—
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₃×D₂₀	—	4	2	no	—
110	C₃×D₂₀	—	4	1	no	—
111	C₃×D₂₀	—	4	1	no	—
112	C₃×D₂₀	—	4	1	no	—
113	C₃×D₂₀	—	4	1	no	—
114	C₃×#168	—	2	2	no	—
115	C₃×#168	—	4	1	no	—
116	C₃×#168	—	4	1	no	—
117	C₂×C₃×#41	—	2	1	no	—
118	C₂×C₃×SD₁₆	—	10	1	no	—
119	C₂×C₃×D₈	—	10	1	no	—
120	C₂×C₃×D₈	—	10	2	no	—
121	C₃×#127	—	2	1	no	—
122	C₃×#127	—	5	1	no	—
123	C₃×#127	C₂×D₅	1	1	yes	characteristic
124	C₃×#121	—	2	2	no	—
125	C₃×#121	—	2	1	no	—
126	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
127	C₃×C₄×D₄	—	2	1	no	—
128	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
129	C₃×C₄⋊C₈	—	5	1	no	—
130	C₃×C₄⋊C₈	—	5	1	no	—
131	C₃×#102	—	10	1	no	—
132	C₃×#102	—	10	1	no	—
133	C₃×C₄×C₈	—	5	1	no	—
134	C₅×#41	—	4	2	no	—
135	C₅×#41	—	4	2	no	—
136	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
137	C₂×C₅×D₄	—	2	2	no	—
138	C₂×C₅×D₄	—	2	2	no	—
139	C₂×C₅×D₄	—	2	1	no	—
140	C₂×C₅×D₄	—	2	1	no	—
141	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
142	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
143	C₂²×C₄×C₅	—	2	2	no	—
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂×D₂₀	—	2	1	no	—
146	C₂×D₂₀	—	2	1	no	—
147	C₂×D₂₀	—	2	1	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
150	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
151	C₅×C₂²⋊C₄	—	2	2	no	—
152	C₅×C₂²⋊C₄	—	2	1	no	—
153	C₄²×C₅	—	2	1	no	—
154	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
155	#688	—	4	2	no	—
156	#686	—	4	4	no	—
157	#686	—	4	2	no	—
158	C₂×#168	—	2	1	no	—
159	C₂×#168	—	2	1	no	—
160	C₂×#168	—	2	1	no	—
161	#550	C₃×D₅	1	1	yes	characteristic, complemented
162	#493	—	5	1	no	—
163	#460	—	5	1	no	—
164	#459	—	5	1	no	—
165	#331	—	5	1	no	—
166	Q₈⋊C₈	—	5	1	no	—
167	D₄⋊C₈	—	5	1	no	—
168	C₂²×C₃×C₅	—	4	2	no	—
169	C₂²×C₃×C₅	—	4	1	no	—
170	C₂²×C₃×C₅	—	4	1	no	—
171	C₂²×C₃×C₅	—	4	2	no	—
172	C₂²×C₃×C₅	—	4	2	no	—
173	C₂²×C₃×C₅	—	4	1	no	—
174	C₂²×C₃×C₅	#120	1	1	yes	characteristic
175	C₂×C₃×D₅	—	8	1	no	—
176	C₂×C₃×D₅	—	8	1	no	—
177	C₂×C₃×D₅	—	8	1	no	—
178	C₃×C₄×C₅	—	2	2	no	—
179	C₃×C₄×C₅	—	2	1	no	—
180	C₃×C₄×C₅	—	4	1	no	—
181	C₃×C₄×C₅	—	4	1	no	—
182	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
183	C₃×C₄×C₅	#135	1	1	yes	characteristic
184	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₃×#41	—	4	2	no	—
187	C₃×#41	—	4	2	no	—
188	C₂×C₃×Q₈	C₂²⋊D₅	1	1	yes	characteristic
189	C₂×C₃×D₄	—	2	2	no	—
190	C₂×C₃×D₄	—	2	2	no	—
191	C₂×C₃×D₄	—	2	1	no	—
192	C₂×C₃×D₄	—	2	1	no	—
193	C₂×C₃×D₄	—	10	1	no	—
194	C₂×C₃×D₄	—	10	1	no	—
195	C₂×C₃×D₄	—	10	1	no	—
196	C₂×C₃×D₄	C₂²⋊D₅	1	1	yes	characteristic
197	C₂×C₃×D₄	C₂²⋊D₅	1	2	yes	—
198	C₂²×C₃×C₄	—	2	2	no	—
199	C₂²×C₃×C₄	—	2	1	no	—
200	C₃×SD₁₆	—	20	2	no	—
201	C₃×D₈	—	20	4	no	—
202	C₃×D₈	—	20	2	no	—
203	C₂×C₃×C₈	—	10	1	no	—
204	C₂×C₃×C₈	—	10	1	no	—
205	C₂×C₃×C₈	—	10	1	no	—
206	C₃×C₄⋊C₄	—	2	1	no	—
207	C₃×C₄⋊C₄	C₂²⋊D₅	1	1	yes	characteristic
208	C₃×C₄⋊C₄	C₂²⋊D₅	1	1	yes	characteristic
209	C₃×C₂²⋊C₄	—	2	2	no	—
210	C₃×C₂²⋊C₄	—	2	1	no	—
211	C₃×C₄²	—	2	1	no	—
212	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
213	C₂³×C₅	—	2	1	no	—
214	C₂³×C₅	—	2	2	no	—
215	C₂²×D₅	—	4	1	no	—
216	C₅×Q₈	—	2	1	no	—
217	C₅×Q₈	C₃×D₈	1	2	yes	complemented
218	C₅×D₄	—	2	1	no	—
219	C₅×D₄	—	2	1	no	—
220	C₅×D₄	—	4	2	no	—
221	C₅×D₄	—	4	4	no	—
222	C₅×D₄	—	4	1	no	—
223	C₅×D₄	—	4	1	no	—
224	C₅×D₄	—	4	1	no	—
225	C₅×D₄	—	4	1	no	—
226	C₅×D₄	—	8	2	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	4	4	no	—
231	C₂×C₄×C₅	—	4	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
236	D₂₀	—	4	2	no	—
237	D₂₀	—	4	1	no	—
238	D₂₀	—	4	1	no	—
239	D₂₀	—	4	1	no	—
240	D₂₀	—	4	1	no	—
241	#168	—	2	2	no	—
242	#168	—	4	1	no	—
243	#168	—	4	1	no	—
244	C₂×#41	—	2	1	no	—
245	C₂×SD₁₆	—	10	1	no	—
246	C₂×D₈	—	10	1	no	—
247	C₂×D₈	—	10	2	no	—
248	#127	—	2	1	no	—
249	#127	—	5	1	no	—
250	#127	C₂×C₃×D₅	1	1	yes	characteristic
251	#121	—	2	2	no	—
252	#121	—	2	1	no	—
253	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
256	C₄⋊C₈	—	5	1	no	—
257	C₄⋊C₈	—	5	1	no	—
258	#102	—	10	1	no	—
259	#102	—	10	1	no	—
260	C₄×C₈	—	5	1	no	—
261	C₂×C₃×C₅	—	8	1	no	—
262	C₂×C₃×C₅	—	8	2	no	—
263	C₂×C₃×C₅	#447	1	1	yes	characteristic
264	C₂×C₃×C₅	#449	1	1	yes	characteristic
265	C₂×C₃×C₅	#453	1	1	yes	characteristic
266	C₃×D₅	—	16	1	no	—
267	C₂³×C₃	—	2	1	no	—
268	C₂³×C₃	—	2	2	no	—
269	C₂³×C₃	—	20	1	no	—
270	C₃×Q₈	—	2	1	no	—
271	C₃×Q₈	#686	1	2	yes	complemented
272	C₃×D₄	—	2	1	no	—
273	C₃×D₄	—	2	1	no	—
274	C₃×D₄	—	4	2	no	—
275	C₃×D₄	—	4	4	no	—
276	C₃×D₄	—	4	1	no	—
277	C₃×D₄	—	4	1	no	—
278	C₃×D₄	—	4	1	no	—
279	C₃×D₄	—	4	1	no	—
280	C₃×D₄	—	8	2	no	—
281	C₃×D₄	—	20	2	no	—
282	C₃×D₄	—	20	1	no	—
283	C₃×D₄	—	20	1	no	—
284	C₃×D₄	—	20	1	no	—
285	C₃×D₄	—	20	1	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	1	no	—
289	C₂×C₃×C₄	—	4	4	no	—
290	C₂×C₃×C₄	—	4	1	no	—
291	C₂×C₃×C₄	—	4	1	no	—
292	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
295	C₃×C₈	—	10	2	no	—
296	C₃×C₈	—	20	1	no	—
297	C₃×C₈	—	20	1	no	—
298	C₂²×C₅	—	4	2	no	—
299	C₂²×C₅	—	4	1	no	—
300	C₂²×C₅	—	4	1	no	—
301	C₂²×C₅	—	4	2	no	—
302	C₂²×C₅	—	4	2	no	—
303	C₂²×C₅	—	4	1	no	—
304	C₂²×C₅	C₃×#120	1	1	yes	characteristic
305	C₂×D₅	—	8	1	no	—
306	C₂×D₅	—	8	1	no	—
307	C₂×D₅	—	8	1	no	—
308	C₄×C₅	—	2	2	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	4	1	no	—
311	C₄×C₅	—	4	1	no	—
312	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
313	C₄×C₅	C₃×#135	1	1	yes	characteristic
314	C₄×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
315	C₄×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	C₂×Q₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	10	1	no	—
324	C₂×D₄	—	10	1	no	—
325	C₂×D₄	—	10	1	no	—
326	C₂×D₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
327	C₂×D₄	C₃×C₂²⋊D₅	1	2	yes	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	1	no	—
330	SD₁₆	—	20	2	no	—
331	D₈	—	20	4	no	—
332	D₈	—	20	2	no	—
333	C₂×C₈	—	10	1	no	—
334	C₂×C₈	—	10	1	no	—
335	C₂×C₈	—	10	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
338	C₄⋊C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
343	C₃×C₅	#1621	1	1	yes	characteristic, complemented, Hall
344	C₂²×C₃	—	4	2	no	—
345	C₂²×C₃	—	4	1	no	—
346	C₂²×C₃	—	4	1	no	—
347	C₂²×C₃	—	4	2	no	—
348	C₂²×C₃	—	4	2	no	—
349	C₂²×C₃	—	4	1	no	—
350	C₂²×C₃	—	40	1	no	—
351	C₂²×C₃	—	40	1	no	—
352	C₂²×C₃	—	40	1	no	—
353	C₂²×C₃	#4099	1	1	yes	characteristic
354	C₃×C₄	—	2	2	no	—
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	—	4	1	no	—
357	C₃×C₄	—	4	1	no	—
358	C₃×C₄	C₂×#686	1	1	yes	characteristic
359	C₃×C₄	#4078	1	1	yes	characteristic
360	C₃×C₄	#4095	1	1	yes	characteristic
361	C₃×C₄	#4096	1	1	yes	characteristic
362	C₂×C₅	—	8	1	no	—
363	C₂×C₅	—	8	2	no	—
364	C₂×C₅	C₃×#447	1	1	yes	characteristic
365	C₂×C₅	C₃×#449	1	1	yes	characteristic
366	C₂×C₅	C₃×#453	1	1	yes	characteristic
367	D₅	—	16	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	20	1	no	—
371	Q₈	—	2	1	no	—
372	Q₈	C₃×#686	1	2	yes	complemented
373	D₄	—	2	1	no	—
374	D₄	—	2	1	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	4	no	—
377	D₄	—	4	1	no	—
378	D₄	—	4	1	no	—
379	D₄	—	4	1	no	—
380	D₄	—	4	1	no	—
381	D₄	—	8	2	no	—
382	D₄	—	20	2	no	—
383	D₄	—	20	1	no	—
384	D₄	—	20	1	no	—
385	D₄	—	20	1	no	—
386	D₄	—	20	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
394	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
395	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
396	C₈	—	10	2	no	—
397	C₈	—	20	1	no	—
398	C₈	—	20	1	no	—
399	C₂×C₃	—	8	1	no	—
400	C₂×C₃	—	8	2	no	—
401	C₂×C₃	—	80	1	no	—
402	C₂×C₃	#65506	1	1	yes	characteristic
403	C₂×C₃	#65527	1	1	yes	characteristic
404	C₂×C₃	#65530	1	1	yes	characteristic
405	C₅	C₃×#1621	1	1	yes	characteristic, complemented, Sylow
406	C₂²	—	4	2	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	40	1	no	—
413	C₂²	—	40	1	no	—
414	C₂²	—	40	1	no	—
415	C₂²	C₃×#4099	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	C₂×C₃×#686	1	1	yes	characteristic
421	C₄	C₃×#4078	1	1	yes	characteristic
422	C₄	C₃×#4095	1	1	yes	characteristic
423	C₄	C₃×#4096	1	1	yes	characteristic
424	C₃	#10602711	1	1	yes	characteristic, direct product factor, Sylow
425	C₂	—	8	1	no	—
426	C₂	—	8	2	no	—
427	C₂	—	80	1	no	—
428	C₂	C₃×#65506	1	1	yes	characteristic
429	C₂	C₃×#65527	1	1	yes	characteristic
430	C₂	C₃×#65530	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#4099
commutator, cosocle	C₄²×C₅	C₂³×C₃
Frattini	C₄²	C₂²×C₃×D₅
Fitting	C₃×C₅×#550	C₂
socle	C₂²×C₃×C₅	#120
hypercenter	C₃×#550	D₅
hypocenter	C₅	C₃×#1621
LCS	G ▷ C₄²×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#550

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#550	C₂	semidirect
2. C₃×#65362	C₂	semidirect
3. C₃×#65316	C₂	semidirect
4. C₃×#65304	C₂	semidirect
5. C₃×#64764	C₂	semidirect
6. C₃×Q₈⋊#168	C₂	semidirect
7. C₃×D₄⋊#168	C₂	semidirect
8. #10602711	C₃	direct (N × H)
27. C₅×#550	C₂×C₃	semidirect
28. #65362	C₂×C₃	semidirect
29. #65316	C₂×C₃	semidirect
30. #65304	C₂×C₃	semidirect
31. #64764	C₂×C₃	semidirect
32. Q₈⋊#168	C₂×C₃	semidirect
33. D₄⋊#168	C₂×C₃	semidirect
61. C₃×#550	D₅	semidirect
90. C₃×C₅×Q₈	D₈	semidirect
161. #550	C₃×D₅	semidirect
217. C₅×Q₈	C₃×D₈	semidirect
271. C₃×Q₈	#686	semidirect
343. C₃×C₅	#1621	semidirect
372. Q₈	C₃×#686	semidirect
405. C₅	C₃×#1621	semidirect
424. C₃	#10602711	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×C₅×#550	2
C₃×#65362	2
C₃×#65316	2
C₃×#65304	2
C₃×#64764	2
C₃×Q₈⋊#168	2
C₃×D₄⋊#168	2
#10602711	3
C₃×#1621	5

Subgroups — C3×#10602711 #14288891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10602711 #14288891