Subgroups — #14281657

Order 1920.

528 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	C₄×#6765	C₂	1	1	yes	maximal, characteristic
2	C₅×#4685	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
4	#11746277	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64679	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745844	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745835	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601548	—	3	1	no	maximal, Hall
9	C₂×#6765	C₄	1	1	yes	characteristic
10	C₄×Dic₃₀	C₂²	1	1	yes	characteristic
11	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
12	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
13	#91441	—	2	1	no	—
14	C₄×#1201	—	2	1	no	—
15	Dic₃×D₂₀	C₄	1	1	yes	characteristic
16	#91393	—	2	1	no	—
17	C₄×D₅×Dic₃	—	2	1	no	—
18	#91340	C₄	1	1	yes	characteristic
19	#91338	C₄	1	1	yes	characteristic
20	C₂×D₃×#168	—	2	1	no	—
21	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
23	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
24	C₅×Dic₃⋊C₈	—	2	1	no	—
25	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
27	Dic₃⋊#168	—	2	1	no	—
28	#68166	—	5	1	no	maximal, Hall
29	C₄×#709	—	3	1	no	—
30	C₅×#431	—	3	1	no	—
31	C₂×C₄⋊#168	—	3	1	no	—
32	#64679	—	3	1	no	—
33	#64679	D₃	1	1	yes	characteristic, complemented
34	#64676	—	3	1	no	—
35	#64676	—	3	1	no	—
36	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
39	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
40	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₄×D₅	—	2	1	no	—
42	C₂×#1201	—	2	1	no	—
43	C₂×D₅×Dic₃	—	2	1	no	—
44	C₂×D₅×Dic₃	—	2	1	no	—
45	#6765	—	2	2	no	—
46	#6765	C₈	1	4	yes	complemented
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
49	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
50	#6712	—	2	1	no	—
51	C₄×Dic₁₅	—	2	1	no	—
52	C₂×C₃⋊#168	—	2	1	no	—
53	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
54	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
55	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
56	C₂×C₅×C₃⋊C₈	—	2	1	no	—
57	C₃×#685	—	2	1	no	—
58	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×#168	—	2	1	no	—
60	#6669	—	2	1	no	—
61	(C₂×D₃)⋊Dic₅	—	2	1	no	—
62	#6665	—	2	1	no	—
63	Dic₃×Dic₅	—	2	1	no	—
64	Dic₃×Dic₅	—	2	1	no	—
65	D₃×#168	—	4	2	no	—
66	C₄×#237	—	5	1	no	—
67	D₃×C₄⋊C₈	—	5	1	no	—
68	#4685	D₅	1	1	yes	characteristic, complemented
69	C₃×D₄⋊C₈	—	5	1	no	—
70	D₄⋊(C₃⋊C₈)	—	5	1	no	—
71	#4484	—	5	1	no	—
72	#4456	—	5	1	no	—
73	C₂×#709	—	3	1	no	—
74	C₂×C₄²×C₅	—	3	1	no	—
75	C₄×C₂²⋊D₅	—	6	1	no	—
76	C₄×C₂²⋊D₅	—	6	1	no	—
77	#4072	—	3	1	no	—
78	C₂²×#168	—	6	1	no	—
79	C₄×D₂₀	—	3	1	no	—
80	C₄×D₂₀	C₂×D₃	1	1	yes	characteristic
81	#4018	—	6	1	no	—
82	C₄²×D₅	—	6	1	no	—
83	C₄×Dic₁₀	—	3	1	no	—
84	C₄×Dic₁₀	—	3	1	no	—
85	C₅×C₄⋊C₈	—	6	1	no	—
86	C₅×C₂²⋊C₈	—	6	1	no	—
87	C₄×C₅×C₈	—	3	1	no	—
88	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
89	C₄⋊#168	—	3	1	no	—
90	C₄⋊#168	—	6	1	no	—
91	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
92	#1477	—	15	1	no	Sylow
93	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₃×D₅	—	2	1	no	—
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂×Dic₁₅	—	2	1	no	—
99	C₂×Dic₁₅	—	2	1	no	—
100	Dic₃₀	—	2	1	no	—
101	Dic₃₀	C₂×C₈	1	2	yes	complemented
102	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₄×C₅×D₃	—	2	1	no	—
106	C₄×C₅×D₃	—	2	1	no	—
107	C₄×C₅×D₃	—	4	1	no	—
108	C₄×C₅×D₃	C₂×C₈	1	2	yes	—
109	C₄×C₅×D₃	M₁₆	1	2	yes	—
110	C₂×C₃×Dic₅	—	2	1	no	—
111	C₃×D₂₀	—	2	1	no	—
112	C₃×D₂₀	C₂×C₈	1	2	yes	complemented
113	C₃×C₄×D₅	—	4	1	no	—
114	C₃×C₄×D₅	—	4	1	no	—
115	#1201	—	2	4	no	—
116	D₅×Dic₃	—	2	4	no	—
117	D₅×Dic₃	—	4	2	no	—
118	C₃×C₅×C₈	—	4	1	no	—
119	C₃⋊#168	—	4	1	no	—
120	C₃×#168	—	4	1	no	—
121	C₅×C₃⋊C₈	—	4	1	no	—
122	C₂×#237	—	5	1	no	—
123	C₃×C₄×D₄	—	5	1	no	—
124	D₄×Dic₃	—	5	1	no	—
125	C₄×#67	—	10	1	no	—
126	C₂×C₄×Dic₃	—	10	1	no	—
127	C₂×D₃×C₈	—	10	1	no	—
128	#892	—	5	1	no	—
129	#887	—	5	1	no	—
130	#67⋊C₄	—	10	1	no	—
131	#877	—	10	1	no	—
132	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
133	C₄×Dic₆	—	5	1	no	—
134	C₃×C₄⋊C₈	—	5	1	no	—
135	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
136	(C₂×D₃)⋊C₈	—	2	1	no	—
137	Dic₃⋊C₈	—	2	1	no	—
138	Dic₃⋊C₈	—	10	1	no	—
139	C₄⋊(C₃⋊C₈)	—	5	1	no	—
140	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
141	C₂²×C₄×C₅	—	3	1	no	—
142	C₂²×C₄×C₅	—	3	1	no	—
143	C₂²×C₄×C₅	—	3	1	no	—
144	C₂×C₂²⋊D₅	—	6	1	no	—
145	#709	—	3	4	no	—
146	#709	—	6	2	no	—
147	C₂×D₂₀	C₄×D₃	1	1	yes	characteristic
148	C₂×C₄×D₅	—	2	1	no	—
149	C₂×C₄×D₅	—	6	1	no	—
150	C₂×C₄×D₅	—	6	1	no	—
151	C₂×Dic₁₀	—	3	1	no	—
152	C₂×C₅×C₈	—	2	1	no	—
153	C₂×C₅×C₈	—	6	1	no	—
154	C₄²×C₅	—	3	1	no	—
155	C₄²×C₅	—	3	1	no	—
156	C₄²×C₅	—	3	1	no	—
157	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
158	C₂²⋊Dic₅	—	6	1	no	—
159	#685	—	2	1	no	—
160	#685	—	6	1	no	—
161	C₄⋊Dic₅	—	3	1	no	—
162	C₄⋊Dic₅	C₄×D₃	1	1	yes	characteristic
163	#683	—	6	1	no	—
164	#683	—	6	1	no	—
165	C₄×Dic₅	—	6	1	no	—
166	C₄×Dic₅	—	6	1	no	—
167	C₄×Dic₅	—	6	1	no	—
168	C₂×#168	—	2	1	no	—
169	C₂×#168	—	6	1	no	—
170	C₂×#168	—	12	2	no	—
171	C₄×#41	—	15	1	no	—
172	#431	—	3	1	no	—
173	C₂×C₄⋊C₈	—	15	1	no	—
174	Q₈⋊C₈	—	15	1	no	—
175	Q₈⋊C₈	—	15	1	no	—
176	D₄⋊C₈	—	5	1	no	—
177	D₄⋊C₈	—	15	1	no	—
178	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₅×D₃	—	2	1	no	—
180	C₂×C₅×D₃	—	2	1	no	—
181	C₂×C₅×D₃	C₂²⋊C₈	1	2	yes	—
182	C₂×C₃×D₅	—	2	2	no	—
183	C₂×C₃×D₅	—	4	1	no	—
184	C₂×C₃×D₅	—	4	1	no	—
185	C₃×C₄×C₅	—	2	1	no	—
186	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
187	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
188	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₃×C₄×C₅	#137	1	1	yes	characteristic
190	Dic₁₅	—	2	2	no	—
191	Dic₁₅	—	4	1	no	—
192	C₃×Dic₅	—	4	1	no	—
193	C₅×Dic₃	—	2	1	no	—
194	C₅×Dic₃	—	2	1	no	—
195	C₅×Dic₃	C₂²⋊C₈	1	2	yes	—
196	C₂×C₃×D₄	—	5	1	no	—
197	C₂²×C₃×C₄	—	10	1	no	—
198	C₂×#67	—	10	1	no	—
199	C₂²×Dic₃	—	10	1	no	—
200	C₂²×Dic₃	—	10	1	no	—
201	#237	—	5	4	no	—
202	#237	—	10	2	no	—
203	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
204	C₂×C₄×D₃	D₂₀	1	1	yes	characteristic
205	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
206	C₂×Dic₆	—	5	1	no	—
207	C₂×C₃×C₈	—	2	1	no	—
208	C₂×C₃×C₈	—	10	1	no	—
209	C₃×C₄⋊C₄	—	5	1	no	—
210	C₃×C₂²⋊C₄	—	10	1	no	—
211	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
212	#217	—	10	1	no	—
213	(C₂×D₃)⋊C₄	—	10	1	no	—
214	C₄⋊Dic₃	—	5	1	no	—
215	Dic₃⋊C₄	—	10	1	no	—
216	Dic₃⋊C₄	—	10	1	no	—
217	C₄×Dic₃	—	10	1	no	—
218	C₄×Dic₃	—	10	1	no	—
219	C₄×Dic₃	—	10	1	no	—
220	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
221	C₄×Dic₃	D₂₀	1	1	yes	characteristic
222	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
223	C₂×C₃⋊C₈	—	2	1	no	—
224	C₂×C₃⋊C₈	—	10	1	no	—
225	D₃×C₈	—	20	2	no	—
226	C₂³×C₅	—	3	1	no	—
227	C₂²×D₅	—	2	1	no	—
228	C₂×C₄×C₅	—	3	1	no	—
229	C₂×C₄×C₅	—	3	2	no	—
230	C₂×C₄×C₅	—	3	2	no	—
231	C₂×C₄×C₅	—	3	1	no	—
232	C₂×C₄×C₅	—	3	1	no	—
233	C₂×C₄×C₅	—	6	1	no	—
234	C₂×C₄×C₅	—	6	1	no	—
235	C₂×C₄×C₅	—	12	1	no	—
236	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
237	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
238	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
239	C₂²⋊D₅	—	6	4	no	—
240	C₂×Dic₅	—	2	1	no	—
241	C₂×Dic₅	—	6	1	no	—
242	C₂×Dic₅	—	6	1	no	—
243	D₂₀	—	2	1	no	—
244	D₂₀	D₃×C₈	1	2	yes	complemented
245	C₄×D₅	—	4	1	no	—
246	C₄×D₅	—	4	1	no	—
247	C₄×D₅	—	6	4	no	—
248	C₄×D₅	—	12	2	no	—
249	Dic₁₀	—	3	2	no	—
250	Dic₁₀	—	6	1	no	—
251	C₅×C₈	—	4	1	no	—
252	C₅×C₈	—	12	1	no	—
253	#168	—	4	1	no	—
254	#168	—	12	1	no	—
255	C₂×#41	—	15	1	no	—
256	C₂²×C₈	—	30	1	no	—
257	C₄×Q₈	—	15	1	no	—
258	C₄×Q₈	—	15	1	no	—
259	C₄×D₄	—	5	1	no	—
260	C₄×D₄	—	15	1	no	—
261	C₄×D₄	—	30	1	no	—
262	C₄×D₄	—	30	1	no	—
263	#117	—	15	1	no	—
264	#117	—	30	1	no	—
265	C₂×C₄²	—	3	1	no	—
266	C₂×C₄²	—	30	1	no	—
267	C₄⋊C₈	—	5	1	no	—
268	C₄⋊C₈	—	6	1	no	—
269	C₄⋊C₈	—	15	1	no	—
270	C₄⋊C₈	—	30	1	no	—
271	C₂²⋊C₈	—	6	1	no	—
272	C₄×C₈	—	3	1	no	—
273	C₄×C₈	D₃×D₅	1	1	yes	characteristic
274	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
275	C₂×C₃×C₅	#417	1	1	yes	characteristic
276	C₂×C₃×C₅	#421	1	1	yes	characteristic
277	C₃×D₅	—	4	2	no	—
278	C₅×D₃	—	2	2	no	—
279	C₂³×C₃	—	10	1	no	—
280	C₂²×D₃	#685	1	1	yes	characteristic
281	C₃×D₄	—	5	2	no	—
282	C₃×D₄	—	10	1	no	—
283	C₂×C₃×C₄	—	10	1	no	—
284	C₂×C₃×C₄	—	20	1	no	—
285	C₂×C₃×C₄	—	20	1	no	—
286	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
289	#67	—	10	4	no	—
290	C₂×Dic₃	—	10	1	no	—
291	C₂×Dic₃	—	10	4	no	—
292	C₂×Dic₃	—	10	1	no	—
293	C₂×Dic₃	—	20	2	no	—
294	C₂×Dic₃	#685	1	1	yes	characteristic
295	C₂×Dic₃	#685	1	1	yes	characteristic
296	C₂×Dic₃	#685	1	1	yes	characteristic
297	C₄×D₃	—	2	1	no	—
298	C₄×D₃	—	2	1	no	—
299	C₄×D₃	—	4	1	no	—
300	C₄×D₃	C₈×D₅	1	2	yes	—
301	C₄×D₃	#676	1	2	yes	—
302	Dic₆	—	5	2	no	—
303	Dic₆	—	10	1	no	—
304	C₃×C₈	—	4	1	no	—
305	C₃×C₈	—	20	1	no	—
306	C₃⋊C₈	—	4	1	no	—
307	C₃⋊C₈	—	20	1	no	—
308	C₂²×C₅	—	3	2	no	—
309	C₂²×C₅	—	6	1	no	—
310	C₂²×C₅	—	6	1	no	—
311	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
312	C₂×D₅	—	2	2	no	—
313	C₂×D₅	—	4	1	no	—
314	C₂×D₅	—	4	1	no	—
315	C₄×C₅	—	2	1	no	—
316	C₄×C₅	—	3	2	no	—
317	C₄×C₅	—	6	1	no	—
318	C₄×C₅	—	6	1	no	—
319	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
320	C₄×C₅	D₃×M₁₆	1	1	yes	characteristic
321	C₄×C₅	#911	1	1	yes	characteristic
322	C₄×C₅	#915	1	1	yes	characteristic
323	Dic₅	—	4	1	no	—
324	Dic₅	—	6	2	no	—
325	Dic₅	—	12	1	no	—
326	#41	—	15	4	no	—
327	#41	—	30	2	no	—
328	C₂×Q₈	—	15	1	no	—
329	C₂×D₄	—	5	1	no	—
330	C₂×D₄	—	30	1	no	—
331	C₂²×C₄	—	3	1	no	—
332	C₂²×C₄	—	3	1	no	—
333	C₂²×C₄	—	3	1	no	—
334	C₂²×C₄	—	10	1	no	—
335	C₂²×C₄	—	30	1	no	—
336	C₂²×C₄	—	30	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	6	1	no	—
339	C₂×C₈	—	10	1	no	—
340	C₂×C₈	—	30	1	no	—
341	C₂×C₈	—	60	2	no	—
342	C₄⋊C₄	—	5	1	no	—
343	C₄⋊C₄	—	15	1	no	—
344	C₄⋊C₄	—	30	1	no	—
345	C₄⋊C₄	—	30	1	no	—
346	C₂²⋊C₄	—	10	1	no	—
347	C₂²⋊C₄	—	30	1	no	—
348	C₂²⋊C₄	—	30	1	no	—
349	C₄²	—	3	1	no	—
350	C₄²	—	3	1	no	—
351	C₄²	—	3	1	no	—
352	C₄²	—	30	1	no	—
353	C₄²	—	30	1	no	—
354	C₄²	—	30	1	no	—
355	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
356	C₃×C₅	#1477	1	1	yes	characteristic, complemented, Hall
357	C₂²×C₃	—	10	2	no	—
358	C₂²×C₃	—	20	1	no	—
359	C₂²×C₃	—	20	1	no	—
360	C₂²×C₃	C₂×#685	1	1	yes	characteristic
361	C₂×D₃	—	2	1	no	—
362	C₂×D₃	—	2	1	no	—
363	C₂×D₃	#3952	1	2	yes	—
364	C₃×C₄	—	2	1	no	—
365	C₃×C₄	—	20	1	no	—
366	C₃×C₄	C₂×C₈×D₅	1	1	yes	characteristic
367	C₃×C₄	C₂×#676	1	1	yes	characteristic
368	C₃×C₄	#4054	1	1	yes	characteristic
369	C₃×C₄	#4055	1	1	yes	characteristic
370	Dic₃	—	2	1	no	—
371	Dic₃	—	2	1	no	—
372	Dic₃	—	10	2	no	—
373	Dic₃	—	20	1	no	—
374	Dic₃	#3952	1	2	yes	—
375	C₂×C₅	—	6	2	no	—
376	C₂×C₅	D₃×C₂²⋊C₈	1	1	yes	characteristic
377	C₂×C₅	#4771	1	1	yes	characteristic
378	C₂×C₅	#4821	1	1	yes	characteristic
379	D₅	—	4	2	no	—
380	C₂³	—	3	1	no	—
381	C₂³	—	10	1	no	—
382	Q₈	—	15	2	no	—
383	Q₈	—	30	1	no	—
384	D₄	—	5	2	no	—
385	D₄	—	10	1	no	—
386	D₄	—	30	4	no	—
387	C₂×C₄	—	3	1	no	—
388	C₂×C₄	—	3	2	no	—
389	C₂×C₄	—	3	2	no	—
390	C₂×C₄	—	3	1	no	—
391	C₂×C₄	—	3	1	no	—
392	C₂×C₄	—	6	1	no	—
393	C₂×C₄	—	6	1	no	—
394	C₂×C₄	—	10	1	no	—
395	C₂×C₄	—	12	1	no	—
396	C₂×C₄	—	20	1	no	—
397	C₂×C₄	—	20	1	no	—
398	C₂×C₄	—	30	4	no	—
399	C₂×C₄	—	30	1	no	—
400	C₂×C₄	—	30	1	no	—
401	C₂×C₄	—	60	2	no	—
402	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
403	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
404	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
405	C₈	—	4	1	no	—
406	C₈	—	12	1	no	—
407	C₈	—	20	1	no	—
408	C₈	—	60	1	no	—
409	C₂×C₃	—	20	2	no	—
410	C₂×C₃	#65294	1	1	yes	characteristic
411	C₂×C₃	C₂×#3952	1	1	yes	characteristic
412	C₂×C₃	#65422	1	1	yes	characteristic
413	D₃	—	2	2	no	—
414	C₅	#68166	1	1	yes	characteristic, complemented, Sylow
415	C₂²	—	3	2	no	—
416	C₂²	—	6	1	no	—
417	C₂²	—	6	1	no	—
418	C₂²	—	10	2	no	—
419	C₂²	—	20	1	no	—
420	C₂²	—	20	1	no	—
421	C₂²	D₃×#685	1	1	yes	characteristic
422	C₄	—	2	1	no	—
423	C₄	—	3	2	no	—
424	C₄	—	6	1	no	—
425	C₄	—	6	1	no	—
426	C₄	—	20	1	no	—
427	C₄	—	30	2	no	—
428	C₄	—	60	1	no	—
429	C₄	D₃×C₈×D₅	1	1	yes	characteristic
430	C₄	D₃×#676	1	1	yes	characteristic
431	C₄	#91254	1	1	yes	characteristic
432	C₄	#91274	1	1	yes	characteristic
433	C₃	#10601548	1	1	yes	characteristic, complemented, Sylow
434	C₂	—	6	2	no	—
435	C₂	—	20	2	no	—
436	C₂	#11747111	1	1	yes	characteristic
437	C₂	D₃×#3952	1	1	yes	characteristic
438	C₂	#11748138	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₃×D₂₀
commutator	C₃×C₄×C₅	C₂²×C₈
Frattini	C₄²	C₂×D₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×#6765	C₄
cosocle	C₃×C₄²×C₅	C₂³
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	#1477
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₅×#4685	C₂	semidirect
3. D₃×C₄⋊#168	C₂	semidirect
4. #11746277	C₂	semidirect
5. C₃×#64679	C₂	semidirect
6. #11745844	C₂	semidirect
7. #11745835	C₂	semidirect
33. #64679	D₃	semidirect
46. #6765	C₈	semidirect
68. #4685	D₅	semidirect
101. Dic₃₀	C₂×C₈	semidirect
112. C₃×D₂₀	C₂×C₈	semidirect
244. D₂₀	D₃×C₈	semidirect
356. C₃×C₅	#1477	semidirect
414. C₅	#68166	semidirect
433. C₃	#10601548	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×#6765	2
C₅×#4685	2
D₃×C₄⋊#168	2
#11746277	2
C₃×#64679	2
#11745844	2
#11745835	2
#10601548	3
#68166	5