Subgroups — #14297818

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6817	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#91089	C₂	1	2	yes	maximal
4	#11751025	C₂	1	1	yes	maximal, characteristic, complemented
5	#11746344	C₂	1	2	yes	maximal, complemented
6	#10600287	—	3	1	no	maximal, Hall
7	C₂×#6817	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
9	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₄×#1220	—	2	1	no	—
12	C₄×#1220	—	2	1	no	—
13	#91815	C₂²	1	1	yes	characteristic
14	C₂×#6710	C₂²	1	2	yes	—
15	C₄×D₆₀	C₄	1	1	yes	characteristic, complemented
16	C₄×D₆₀	C₄	1	1	yes	characteristic, complemented
17	#91761	—	2	1	no	—
18	C₄²×D₁₅	—	2	1	no	—
19	C₄×Dic₃₀	C₄	1	1	yes	characteristic, complemented
20	C₄×Dic₃₀	C₄	1	1	yes	characteristic, complemented
21	C₃×C₅×#95	—	2	1	no	—
22	#91089	—	2	4	no	—
23	C₄⋊(C₃⋊#168)	—	2	1	no	—
24	C₄⋊(C₃⋊#168)	—	2	1	no	—
25	#69494	—	5	1	no	maximal, Hall
26	C₄×#709	—	3	1	no	—
27	C₄×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
28	C₂×#3937	—	3	2	no	—
29	#65213	—	3	1	no	—
30	#64743	—	3	2	no	—
31	C₂²×C₃×C₄×C₅	—	2	2	no	—
32	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂×#1220	—	2	1	no	—
36	#6817	—	2	1	no	—
37	#6817	—	2	1	no	—
38	#6817	D₄	1	2	yes	—
39	#6817	Q₈	1	2	yes	—
40	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×D₁₅	—	2	1	no	—
42	C₂×C₄×D₁₅	—	2	1	no	—
43	C₂×C₄×D₁₅	—	2	1	no	—
44	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
45	C₃×C₅×C₄⋊C₄	—	2	4	no	—
46	C₃×C₄²×C₅	—	2	2	no	—
47	C₃×C₄²×C₅	—	2	2	no	—
48	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
49	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
50	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
52	#6719	—	2	1	no	—
53	#6714	—	2	1	no	—
54	#6714	—	2	1	no	—
55	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
56	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
57	#6712	—	2	1	no	—
58	#6712	—	2	1	no	—
59	C₄×Dic₁₅	—	2	1	no	—
60	C₄×Dic₁₅	—	2	1	no	—
61	C₄×Dic₁₅	—	2	1	no	—
62	#6710	—	2	2	no	—
63	#6710	—	2	2	no	—
64	C₂×C₃⋊#168	—	2	2	no	—
65	C₄×#235	—	5	1	no	—
66	C₃×C₄×C₄⋊C₄	D₅	1	1	yes	characteristic, complemented
67	C₂×#805	—	5	2	no	—
68	#4924	—	5	1	no	—
69	#4523	—	5	2	no	—
70	C₂×#709	—	3	1	no	—
71	C₂×C₅×C₄⋊C₄	—	2	1	no	—
72	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
73	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
74	C₄×C₂²⋊D₅	—	6	1	no	—
75	C₄×C₂²⋊D₅	—	6	1	no	—
76	#4072	—	3	1	no	—
77	C₂×#681	—	3	2	no	—
78	C₄×D₂₀	—	3	1	no	—
79	C₄×D₂₀	—	3	1	no	—
80	#4018	—	6	1	no	—
81	C₄²×D₅	—	6	1	no	—
82	C₄×Dic₁₀	—	3	1	no	—
83	C₄×Dic₁₀	—	3	1	no	—
84	C₅×#95	—	2	1	no	—
85	#3937	—	6	4	no	—
86	C₄⋊#168	—	6	1	no	—
87	C₄⋊#168	—	6	1	no	—
88	#1806	—	15	1	no	Sylow
89	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂²×D₁₅	—	2	1	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	4	1	no	—
94	C₂×C₃×C₄×C₅	—	4	2	no	—
95	C₂×C₃×C₄×C₅	—	4	2	no	—
96	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
106	#1220	—	2	2	no	—
107	#1220	—	2	2	no	—
108	C₂×Dic₁₅	—	2	1	no	—
109	C₂×Dic₁₅	—	2	1	no	—
110	C₂×Dic₁₅	—	2	1	no	—
111	D₆₀	—	2	1	no	—
112	D₆₀	C₄⋊C₄	1	2	yes	complemented
113	C₄×D₁₅	—	2	2	no	—
114	C₄×D₁₅	—	2	2	no	—
115	C₄×D₁₅	—	4	2	no	—
116	C₄×D₁₅	—	4	2	no	—
117	Dic₃₀	—	2	1	no	—
118	Dic₃₀	C₄⋊C₄	1	2	yes	complemented
119	C₃⋊#168	—	4	2	no	—
120	C₂×#235	—	5	1	no	—
121	C₂×C₃×C₄⋊C₄	—	2	1	no	—
122	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
123	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
124	C₄×#67	—	10	1	no	—
125	C₄×#67	—	10	1	no	—
126	#926	—	5	1	no	—
127	C₂×#208	—	5	2	no	—
128	C₄×D₁₂	—	5	1	no	—
129	C₄×D₁₂	—	5	1	no	—
130	#872	—	10	1	no	—
131	C₄²×D₃	—	10	1	no	—
132	C₄×Dic₆	—	5	1	no	—
133	C₄×Dic₆	—	5	1	no	—
134	C₃×#95	—	2	1	no	—
135	#805	—	10	4	no	—
136	C₄⋊(C₃⋊C₈)	—	10	1	no	—
137	C₄⋊(C₃⋊C₈)	—	10	1	no	—
138	C₂²×C₄×C₅	—	2	2	no	—
139	C₂²×C₄×C₅	#67	1	1	yes	characteristic
140	C₂²×C₄×C₅	#67	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
142	C₂×C₂²⋊D₅	—	6	1	no	—
143	#709	—	3	2	no	—
144	#709	—	3	2	no	—
145	#709	—	6	1	no	—
146	#709	—	6	1	no	—
147	C₂×D₂₀	—	3	1	no	—
148	C₂×C₄×D₅	—	6	1	no	—
149	C₂×C₄×D₅	—	6	1	no	—
150	C₂×C₄×D₅	—	6	1	no	—
151	C₂×Dic₁₀	—	3	1	no	—
152	C₅×C₄⋊C₄	—	2	4	no	—
153	C₄²×C₅	—	2	2	no	—
154	C₄²×C₅	—	2	2	no	—
155	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
156	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
157	C₄²×C₅	D₁₂	1	1	yes	characteristic
158	C₄²×C₅	D₁₂	1	1	yes	characteristic
159	C₂²⋊Dic₅	—	6	1	no	—
160	#685	—	6	1	no	—
161	#685	—	6	1	no	—
162	C₄⋊Dic₅	—	3	1	no	—
163	C₄⋊Dic₅	—	3	1	no	—
164	#683	—	6	1	no	—
165	#683	—	6	1	no	—
166	C₄×Dic₅	—	6	1	no	—
167	C₄×Dic₅	—	6	1	no	—
168	C₄×Dic₅	—	6	1	no	—
169	#681	—	6	2	no	—
170	#681	—	6	2	no	—
171	C₂×#168	—	6	2	no	—
172	C₄×#41	—	15	1	no	—
173	#423	—	15	1	no	—
174	C₂×#104	—	15	2	no	—
175	C₄×C₄⋊C₄	D₁₅	1	1	yes	characteristic, complemented
176	#339	—	15	2	no	—
177	C₂²×C₃×C₅	—	2	1	no	—
178	C₂²×C₃×C₅	—	2	1	no	—
179	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₂²×C₃×C₅	#121	1	1	yes	characteristic
181	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
182	C₂×D₁₅	—	2	2	no	—
183	C₂×D₁₅	—	4	1	no	—
184	C₂×D₁₅	—	4	1	no	—
185	C₃×C₄×C₅	—	2	1	no	—
186	C₃×C₄×C₅	—	2	1	no	—
187	C₃×C₄×C₅	—	2	1	no	—
188	C₃×C₄×C₅	—	4	4	no	—
189	C₃×C₄×C₅	#104	1	2	yes	complemented
190	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₃×C₄×C₅	#117	1	1	yes	characteristic
192	C₃×C₄×C₅	#121	1	1	yes	characteristic
193	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
194	Dic₁₅	—	2	2	no	—
195	Dic₁₅	—	4	1	no	—
196	Dic₁₅	—	4	1	no	—
197	C₂²×C₃×C₄	—	2	2	no	—
198	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
201	C₂×#67	—	10	1	no	—
202	#235	—	5	2	no	—
203	#235	—	5	2	no	—
204	#235	—	10	1	no	—
205	#235	—	10	1	no	—
206	C₂×D₁₂	—	5	1	no	—
207	C₂×C₄×D₃	—	10	1	no	—
208	C₂×C₄×D₃	—	10	1	no	—
209	C₂×C₄×D₃	—	10	1	no	—
210	C₂×Dic₆	—	5	1	no	—
211	C₃×C₄⋊C₄	—	2	4	no	—
212	C₃×C₄²	—	2	2	no	—
213	C₃×C₄²	—	2	2	no	—
214	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
215	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
216	C₃×C₄²	D₂₀	1	1	yes	characteristic
217	C₃×C₄²	D₂₀	1	1	yes	characteristic
218	#217	—	10	1	no	—
219	(C₂×D₃)⋊C₄	—	10	1	no	—
220	(C₂×D₃)⋊C₄	—	10	1	no	—
221	C₄⋊Dic₃	—	5	1	no	—
222	C₄⋊Dic₃	—	5	1	no	—
223	Dic₃⋊C₄	—	10	1	no	—
224	Dic₃⋊C₄	—	10	1	no	—
225	C₄×Dic₃	—	10	1	no	—
226	C₄×Dic₃	—	10	1	no	—
227	C₄×Dic₃	—	10	1	no	—
228	#208	—	10	2	no	—
229	#208	—	10	2	no	—
230	C₂×C₃⋊C₈	—	10	2	no	—
231	C₂³×C₅	C₂×#67	1	1	yes	characteristic
232	C₂²×D₅	—	6	1	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	—	4	2	no	—
237	C₂×C₄×C₅	—	4	2	no	—
238	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
244	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
245	C₂×C₄×C₅	#237	1	1	yes	characteristic
246	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
247	C₂×C₄×C₅	#239	1	1	yes	characteristic
248	C₂²⋊D₅	—	6	2	no	—
249	C₂²⋊D₅	—	6	2	no	—
250	C₂×Dic₅	—	6	1	no	—
251	C₂×Dic₅	—	6	1	no	—
252	C₂×Dic₅	—	6	1	no	—
253	D₂₀	—	3	2	no	—
254	D₂₀	—	6	1	no	—
255	C₄×D₅	—	6	2	no	—
256	C₄×D₅	—	6	2	no	—
257	C₄×D₅	—	12	2	no	—
258	C₄×D₅	—	12	2	no	—
259	Dic₁₀	—	3	2	no	—
260	Dic₁₀	—	6	1	no	—
261	#168	—	12	2	no	—
262	C₂×#41	—	15	1	no	—
263	C₂×M₁₆	—	15	2	no	—
264	C₄×Q₈	—	15	1	no	—
265	C₄×Q₈	—	15	1	no	—
266	C₄×D₄	—	15	1	no	—
267	C₄×D₄	—	15	1	no	—
268	C₄×D₄	—	30	1	no	—
269	C₄×D₄	—	30	1	no	—
270	#117	—	15	1	no	—
271	#117	—	30	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄²	—	30	1	no	—
274	C₂×C₄²	C₂×D₁₅	1	2	yes	—
275	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
276	C₄⋊C₈	—	30	1	no	—
277	C₄⋊C₈	—	30	1	no	—
278	#104	—	30	4	no	—
279	#95	—	2	1	no	—
280	C₂×C₃×C₅	—	2	1	no	—
281	C₂×C₃×C₅	—	2	1	no	—
282	C₂×C₃×C₅	#380	1	1	yes	characteristic
283	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
284	C₂×C₃×C₅	#421	1	1	yes	characteristic
285	D₁₅	—	4	2	no	—
286	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
287	C₂²×D₃	—	10	1	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	4	no	—
290	C₂×C₃×C₄	—	4	1	no	—
291	C₂×C₃×C₄	—	4	2	no	—
292	C₂×C₃×C₄	—	4	2	no	—
293	C₂×C₃×C₄	#685	1	1	yes	characteristic
294	C₂×C₃×C₄	#685	1	1	yes	characteristic
295	C₂×C₃×C₄	#685	1	1	yes	characteristic
296	C₂×C₃×C₄	#685	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
299	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
300	C₂×C₃×C₄	#711	1	1	yes	characteristic
301	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
302	C₂×C₃×C₄	#713	1	1	yes	characteristic
303	#67	—	10	2	no	—
304	#67	—	10	2	no	—
305	C₂×Dic₃	—	10	1	no	—
306	C₂×Dic₃	—	10	1	no	—
307	C₂×Dic₃	—	10	1	no	—
308	D₁₂	—	5	2	no	—
309	D₁₂	—	10	1	no	—
310	C₄×D₃	—	10	2	no	—
311	C₄×D₃	—	10	2	no	—
312	C₄×D₃	—	20	2	no	—
313	C₄×D₃	—	20	2	no	—
314	Dic₆	—	5	2	no	—
315	Dic₆	—	10	1	no	—
316	C₃⋊C₈	—	20	2	no	—
317	C₂²×C₅	—	2	1	no	—
318	C₂²×C₅	—	2	1	no	—
319	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
320	C₂²×C₅	#938	1	1	yes	characteristic
321	C₂²×C₅	#946	1	1	yes	characteristic
322	C₂×D₅	—	6	2	no	—
323	C₂×D₅	—	12	1	no	—
324	C₂×D₅	—	12	1	no	—
325	C₄×C₅	—	2	1	no	—
326	C₄×C₅	—	2	1	no	—
327	C₄×C₅	—	2	1	no	—
328	C₄×C₅	—	4	4	no	—
329	C₄×C₅	#805	1	2	yes	complemented
330	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
331	C₄×C₅	#892	1	1	yes	characteristic
332	C₄×C₅	#895	1	1	yes	characteristic
333	C₄×C₅	#897	1	1	yes	characteristic
334	Dic₅	—	6	2	no	—
335	Dic₅	—	12	1	no	—
336	Dic₅	—	12	1	no	—
337	#41	—	15	2	no	—
338	#41	—	15	2	no	—
339	#41	—	30	1	no	—
340	#41	—	30	1	no	—
341	C₂×Q₈	—	15	1	no	—
342	C₂×D₄	—	15	1	no	—
343	C₂×D₄	—	30	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	30	1	no	—
346	C₂²×C₄	—	30	1	no	—
347	C₂²×C₄	—	30	1	no	—
348	C₂²×C₄	#1220	1	1	yes	characteristic
349	C₂²×C₄	#1220	1	1	yes	characteristic
350	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
351	M₁₆	—	30	2	no	—
352	M₁₆	—	30	2	no	—
353	C₂×C₈	—	30	2	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	15	1	no	—
356	C₄⋊C₄	—	15	1	no	—
357	C₄⋊C₄	—	30	1	no	—
358	C₄⋊C₄	—	30	1	no	—
359	C₂²⋊C₄	—	30	1	no	—
360	C₂²⋊C₄	—	30	1	no	—
361	C₂²⋊C₄	—	30	1	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	30	1	no	—
365	C₄²	—	30	1	no	—
366	C₄²	—	30	1	no	—
367	C₄²	C₄×D₁₅	1	1	yes	characteristic
368	C₄²	C₄×D₁₅	1	1	yes	characteristic
369	C₄²	D₆₀	1	1	yes	characteristic
370	C₄²	D₆₀	1	1	yes	characteristic
371	C₃×C₅	#1806	1	1	yes	characteristic, complemented, Hall
372	C₂²×C₃	—	2	1	no	—
373	C₂²×C₃	—	2	1	no	—
374	C₂²×C₃	C₂×#685	1	1	yes	characteristic
375	C₂²×C₃	#4084	1	1	yes	characteristic
376	C₂²×C₃	#4092	1	1	yes	characteristic
377	C₂×D₃	—	10	2	no	—
378	C₂×D₃	—	20	1	no	—
379	C₂×D₃	—	20	1	no	—
380	C₃×C₄	—	2	1	no	—
381	C₃×C₄	—	2	1	no	—
382	C₃×C₄	—	2	1	no	—
383	C₃×C₄	—	4	4	no	—
384	C₃×C₄	#3937	1	2	yes	complemented
385	C₃×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
386	C₃×C₄	#4038	1	1	yes	characteristic
387	C₃×C₄	#4041	1	1	yes	characteristic
388	C₃×C₄	#4043	1	1	yes	characteristic
389	Dic₃	—	10	2	no	—
390	Dic₃	—	20	1	no	—
391	Dic₃	—	20	1	no	—
392	C₂×C₅	—	2	1	no	—
393	C₂×C₅	—	2	1	no	—
394	C₂×C₅	C₂×#805	1	1	yes	characteristic
395	C₂×C₅	#4987	1	1	yes	characteristic
396	C₂×C₅	#5005	1	1	yes	characteristic
397	D₅	—	12	2	no	—
398	C₂³	—	30	1	no	—
399	C₂³	C₂×#1220	1	1	yes	characteristic
400	Q₈	—	15	2	no	—
401	Q₈	—	30	1	no	—
402	D₄	—	15	2	no	—
403	D₄	—	30	2	no	—
404	D₄	—	30	2	no	—
405	D₄	—	30	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	30	1	no	—
412	C₂×C₄	—	30	2	no	—
413	C₂×C₄	—	30	2	no	—
414	C₂×C₄	—	30	1	no	—
415	C₂×C₄	—	30	1	no	—
416	C₂×C₄	—	60	2	no	—
417	C₂×C₄	—	60	2	no	—
418	C₂×C₄	#6714	1	1	yes	characteristic
419	C₂×C₄	#6714	1	1	yes	characteristic
420	C₂×C₄	#6714	1	1	yes	characteristic
421	C₂×C₄	#6714	1	1	yes	characteristic
422	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
423	C₂×C₄	C₂×D₆₀	1	1	yes	characteristic
424	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
425	C₂×C₄	#6819	1	1	yes	characteristic
426	C₂×C₄	Q₈×D₁₅	1	1	yes	characteristic
427	C₂×C₄	#6821	1	1	yes	characteristic
428	C₈	—	60	2	no	—
429	C₂×C₃	—	2	1	no	—
430	C₂×C₃	—	2	1	no	—
431	C₂×C₃	C₂×#3937	1	1	yes	characteristic
432	C₂×C₃	#65276	1	1	yes	characteristic
433	C₂×C₃	#65294	1	1	yes	characteristic
434	D₃	—	20	2	no	—
435	C₅	#69494	1	1	yes	characteristic, complemented, Sylow
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	30	2	no	—
439	C₂²	—	60	1	no	—
440	C₂²	—	60	1	no	—
441	C₂²	C₂×#6714	1	1	yes	characteristic
442	C₂²	#91827	1	1	yes	characteristic
443	C₂²	#91835	1	1	yes	characteristic
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	4	4	no	—
448	C₄	—	30	2	no	—
449	C₄	—	60	1	no	—
450	C₄	—	60	1	no	—
451	C₄	#91089	1	2	yes	complemented
452	C₄	C₄⋊C₄×D₁₅	1	1	yes	characteristic
453	C₄	#91781	1	1	yes	characteristic
454	C₄	#91784	1	1	yes	characteristic
455	C₄	#91786	1	1	yes	characteristic
456	C₃	#10600287	1	1	yes	characteristic, complemented, Sylow
457	C₂	—	2	1	no	—
458	C₂	—	2	1	no	—
459	C₂	—	60	2	no	—
460	C₂	C₂×#91089	1	1	yes	characteristic
461	C₂	#11751088	1	1	yes	characteristic
462	C₂	#11751106	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₆₀
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₅
Fitting	C₃×C₄×C₅×C₄⋊C₄	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×#6817	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₄×C₄⋊C₄	D₁₅
hypocenter	C₃×C₅	#1806
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
4. #11751025	C₂	semidirect
5. #11746344	C₂	semidirect
15. C₄×D₆₀	C₄	semidirect
16. C₄×D₆₀	C₄	semidirect
19. C₄×Dic₃₀	C₄	semidirect
20. C₄×Dic₃₀	C₄	semidirect
27. C₄×C₅×C₄⋊C₄	D₃	semidirect
66. C₃×C₄×C₄⋊C₄	D₅	semidirect
112. D₆₀	C₄⋊C₄	semidirect
118. Dic₃₀	C₄⋊C₄	semidirect
175. C₄×C₄⋊C₄	D₁₅	semidirect
189. C₃×C₄×C₅	#104	semidirect
329. C₄×C₅	#805	semidirect
371. C₃×C₅	#1806	semidirect
384. C₃×C₄	#3937	semidirect
435. C₅	#69494	semidirect
451. C₄	#91089	semidirect
456. C₃	#10600287	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6817	2
C₃×C₄×C₅×C₄⋊C₄	2
C₂×#91089	2
#11751025	2
#11746344	2
#10600287	3
#69494	5