Subgroups — #14299450

Order 1920.

632 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91781	C₂	1	1	yes	maximal, characteristic
2	C₂×#91104	C₂	1	1	yes	maximal, characteristic
3	C₂×#91101	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751088	C₂	1	1	yes	maximal, characteristic
5	C₂×#91091	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#340	C₂	1	1	yes	maximal, characteristic, complemented
7	#11746350	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599669	—	3	1	no	maximal, Hall
9	C₂²×C₄×D₁₅	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×#6714	—	2	1	no	—
14	C₂×#6714	—	2	1	no	—
15	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
17	C₂×C₄×Dic₁₅	—	2	1	no	—
18	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
19	#91781	—	2	2	no	—
20	#91781	—	2	2	no	—
21	#91115	—	2	1	no	—
22	#91104	C₄	1	4	yes	complemented
23	#91101	—	2	2	no	—
24	#91091	—	2	2	no	—
25	#68876	—	5	1	no	maximal, Hall
26	C₂×#4038	—	3	1	no	—
27	C₂×#3952	—	3	1	no	—
28	C₂×#3949	—	3	1	no	—
29	#65276	—	3	1	no	—
30	C₂×#3939	—	3	1	no	—
31	C₅×#340	D₃	1	1	yes	characteristic, complemented
32	#64749	—	3	1	no	—
33	C₂³×D₁₅	D₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	—	2	1	no	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×Dic₁₅	—	2	1	no	—
38	C₂²×Dic₁₅	—	2	1	no	—
39	C₂²×Dic₁₅	D₄	1	1	yes	characteristic
40	C₂×C₄×D₁₅	—	2	1	no	—
41	C₂×C₄×D₁₅	—	2	1	no	—
42	C₂×C₄×D₁₅	—	2	1	no	—
43	C₂×C₄×D₁₅	—	2	1	no	—
44	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
45	C₂×C₄×D₁₅	Q₈	1	2	yes	—
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
49	C₃×C₅×C₄⋊C₄	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	—	2	1	no	—
51	C₃×C₅×C₄⋊C₄	—	2	1	no	—
52	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
53	#6714	—	2	4	no	—
54	#6714	—	4	2	no	—
55	C₄⋊Dic₁₅	—	2	1	no	—
56	C₄⋊Dic₁₅	—	2	1	no	—
57	C₄⋊Dic₁₅	—	2	1	no	—
58	C₄⋊Dic₁₅	D₄	1	2	yes	—
59	C₄×Dic₁₅	—	2	4	no	—
60	C₂×C₃⋊#168	—	2	1	no	—
61	C₂×C₃⋊#168	—	2	1	no	—
62	C₂×C₃⋊#168	C₂×C₄	1	2	yes	—
63	C₂×#892	—	5	1	no	—
64	C₂×(C₂×D₃)⋊C₈	—	5	1	no	—
65	C₂×#817	—	5	1	no	—
66	#4987	—	5	1	no	—
67	C₂×#807	—	5	1	no	—
68	C₃×#340	D₅	1	1	yes	characteristic, complemented
69	#4529	—	5	1	no	—
70	C₂²×C₄×D₅	—	3	1	no	—
71	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
72	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
73	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
74	C₂×#685	—	6	1	no	—
75	C₂×#685	—	6	1	no	—
76	C₂×C₄⋊Dic₅	—	3	1	no	—
77	C₂×C₄⋊Dic₅	—	3	1	no	—
78	C₂×C₄×Dic₅	—	6	1	no	—
79	C₂²×#168	—	3	1	no	—
80	#4038	—	6	2	no	—
81	#4038	—	6	2	no	—
82	#3963	—	6	1	no	—
83	#3952	—	3	4	no	—
84	#3949	—	6	2	no	—
85	#3939	—	6	2	no	—
86	#1854	—	15	1	no	Sylow
87	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂²×D₁₅	—	2	1	no	—
89	C₂²×D₁₅	—	2	1	no	—
90	C₂²×D₁₅	—	2	1	no	—
91	C₂²×D₁₅	—	2	1	no	—
92	C₂²×D₁₅	—	2	1	no	—
93	C₂²×D₁₅	—	2	1	no	—
94	C₂²×D₁₅	C₄⋊C₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	4	1	no	—
97	C₂×C₃×C₄×C₅	—	4	1	no	—
98	C₂×C₃×C₄×C₅	—	4	1	no	—
99	C₂×C₃×C₄×C₅	—	4	1	no	—
100	C₂×C₃×C₄×C₅	—	4	1	no	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
107	C₂×Dic₁₅	—	2	1	no	—
108	C₂×Dic₁₅	—	2	1	no	—
109	C₂×Dic₁₅	—	2	2	no	—
110	C₂×Dic₁₅	—	4	1	no	—
111	C₂×Dic₁₅	—	4	1	no	—
112	C₂×Dic₁₅	—	4	1	no	—
113	C₂×Dic₁₅	—	4	1	no	—
114	C₂×Dic₁₅	—	4	1	no	—
115	C₂×Dic₁₅	C₄⋊C₄	1	2	yes	—
116	C₄×D₁₅	—	2	2	no	—
117	C₄×D₁₅	—	2	2	no	—
118	C₄×D₁₅	—	2	2	no	—
119	C₄×D₁₅	—	2	2	no	—
120	C₃×C₅×C₈	—	2	2	no	—
121	C₃⋊#168	—	2	2	no	—
122	C₂²×C₄×D₃	—	5	1	no	—
123	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
124	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
125	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
126	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
127	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
128	C₂×C₄⋊Dic₃	—	5	1	no	—
129	C₂×C₄⋊Dic₃	—	5	1	no	—
130	C₂×C₄×Dic₃	—	10	1	no	—
131	C₂²×C₃⋊C₈	—	5	1	no	—
132	#892	—	10	2	no	—
133	#892	—	10	2	no	—
134	C₃⋊#95	—	10	1	no	—
135	(C₂×D₃)⋊C₈	—	5	4	no	—
136	#817	—	10	2	no	—
137	#807	—	10	2	no	—
138	C₂³×D₅	—	3	1	no	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
142	C₂²×Dic₅	—	3	1	no	—
143	C₂²×Dic₅	—	6	1	no	—
144	C₂²×Dic₅	—	6	1	no	—
145	C₂×C₄×D₅	—	3	2	no	—
146	C₂×C₄×D₅	—	3	2	no	—
147	C₂×C₄×D₅	—	6	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×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	2	1	no	—
153	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	—	2	1	no	—
156	C₅×C₄⋊C₄	—	2	1	no	—
157	C₅×C₄⋊C₄	D₁₂	1	2	yes	—
158	#685	—	6	4	no	—
159	#685	—	12	2	no	—
160	C₄⋊Dic₅	—	3	2	no	—
161	C₄⋊Dic₅	—	6	1	no	—
162	C₄⋊Dic₅	—	6	1	no	—
163	C₄⋊Dic₅	—	6	1	no	—
164	C₄×Dic₅	—	6	4	no	—
165	C₂×#168	—	3	2	no	—
166	C₂×#168	—	6	1	no	—
167	C₂×#168	—	6	1	no	—
168	C₂×#117	—	15	1	no	—
169	C₂×#107	—	15	1	no	—
170	C₂×#106	—	15	1	no	—
171	C₂×C₂²⋊C₈	—	15	1	no	—
172	#380	—	15	1	no	—
173	#340	—	15	1	no	—
174	#340	D₁₅	1	1	yes	characteristic, complemented
175	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂²×C₃×C₅	#120	1	1	yes	characteristic
177	C₂²×C₃×C₅	#123	1	1	yes	characteristic
178	C₂²×C₃×C₅	#135	1	1	yes	characteristic
179	C₂²×C₃×C₅	#135	1	1	yes	characteristic
180	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₂²×C₃×C₅	#137	1	1	yes	characteristic
182	C₂×D₁₅	—	2	2	no	—
183	C₂×D₁₅	—	2	2	no	—
184	C₂×D₁₅	—	2	2	no	—
185	C₂×D₁₅	—	4	1	no	—
186	C₂×D₁₅	—	4	1	no	—
187	C₂×D₁₅	—	4	1	no	—
188	C₂×D₁₅	—	4	1	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	—	8	1	no	—
191	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
192	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
193	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
194	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
195	Dic₁₅	—	2	2	no	—
196	Dic₁₅	—	4	2	no	—
197	Dic₁₅	—	8	1	no	—
198	C₂³×D₃	—	5	1	no	—
199	C₂²×C₃×C₄	—	2	1	no	—
200	C₂²×C₃×C₄	—	2	1	no	—
201	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
202	C₂²×Dic₃	—	5	1	no	—
203	C₂²×Dic₃	—	10	1	no	—
204	C₂²×Dic₃	—	10	1	no	—
205	C₂×C₄×D₃	—	5	2	no	—
206	C₂×C₄×D₃	—	5	2	no	—
207	C₂×C₄×D₃	—	10	1	no	—
208	C₂×C₄×D₃	—	10	1	no	—
209	C₂×C₄×D₃	—	10	1	no	—
210	C₂×C₄×D₃	—	10	1	no	—
211	C₂×C₃×C₈	—	2	1	no	—
212	C₂×C₃×C₈	—	2	1	no	—
213	C₂×C₃×C₈	C₄×D₅	1	2	yes	—
214	C₃×C₄⋊C₄	—	2	1	no	—
215	C₃×C₄⋊C₄	—	2	1	no	—
216	C₃×C₄⋊C₄	—	2	1	no	—
217	C₃×C₄⋊C₄	D₂₀	1	2	yes	—
218	(C₂×D₃)⋊C₄	—	10	4	no	—
219	(C₂×D₃)⋊C₄	—	20	2	no	—
220	C₄⋊Dic₃	—	5	2	no	—
221	C₄⋊Dic₃	—	10	1	no	—
222	C₄⋊Dic₃	—	10	1	no	—
223	C₄⋊Dic₃	—	10	1	no	—
224	C₄×Dic₃	—	10	4	no	—
225	C₂×C₃⋊C₈	—	5	2	no	—
226	C₂×C₃⋊C₈	—	10	1	no	—
227	C₂×C₃⋊C₈	—	10	1	no	—
228	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
229	C₂²×D₅	—	3	2	no	—
230	C₂²×D₅	—	6	1	no	—
231	C₂²×D₅	—	6	1	no	—
232	C₂²×D₅	—	6	1	no	—
233	C₂²×D₅	—	6	1	no	—
234	C₂²×D₅	—	6	1	no	—
235	C₂²×D₅	—	6	1	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	—	4	1	no	—
239	C₂×C₄×C₅	—	4	1	no	—
240	C₂×C₄×C₅	—	4	1	no	—
241	C₂×C₄×C₅	—	4	1	no	—
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	#235	1	1	yes	characteristic
245	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
246	C₂×C₄×C₅	#237	1	1	yes	characteristic
247	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
248	C₂×Dic₅	—	3	2	no	—
249	C₂×Dic₅	—	6	1	no	—
250	C₂×Dic₅	—	6	1	no	—
251	C₂×Dic₅	—	6	2	no	—
252	C₂×Dic₅	—	12	1	no	—
253	C₂×Dic₅	—	12	1	no	—
254	C₂×Dic₅	—	12	1	no	—
255	C₂×Dic₅	—	12	1	no	—
256	C₂×Dic₅	—	12	1	no	—
257	C₄×D₅	—	6	2	no	—
258	C₄×D₅	—	6	2	no	—
259	C₄×D₅	—	6	2	no	—
260	C₄×D₅	—	6	2	no	—
261	C₅×C₈	—	2	2	no	—
262	#168	—	6	2	no	—
263	C₂³×C₄	—	15	1	no	—
264	C₂²×C₈	—	15	1	no	—
265	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
266	#117	—	30	2	no	—
267	#117	—	30	2	no	—
268	C₂×C₄⋊C₄	—	15	1	no	—
269	C₂×C₄⋊C₄	—	15	1	no	—
270	C₂×C₄⋊C₄	C₂×D₁₅	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂×D₁₅	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	—	30	1	no	—
273	C₂×C₂²⋊C₄	—	30	1	no	—
274	C₂×C₄²	—	30	1	no	—
275	#107	—	30	2	no	—
276	#106	—	30	2	no	—
277	C₂²⋊C₈	—	15	4	no	—
278	#95	—	30	1	no	—
279	C₂×C₃×C₅	#385	1	1	yes	characteristic
280	C₂×C₃×C₅	#427	1	1	yes	characteristic
281	C₂×C₃×C₅	#428	1	1	yes	characteristic
282	C₂×C₃×C₅	#449	1	1	yes	characteristic
283	C₂×C₃×C₅	#452	1	1	yes	characteristic
284	C₂×C₃×C₅	#482	1	1	yes	characteristic
285	C₂×C₃×C₅	#485	1	1	yes	characteristic
286	D₁₅	—	4	2	no	—
287	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
288	C₂²×D₃	—	5	2	no	—
289	C₂²×D₃	—	10	1	no	—
290	C₂²×D₃	—	10	1	no	—
291	C₂²×D₃	—	10	1	no	—
292	C₂²×D₃	—	10	1	no	—
293	C₂²×D₃	—	10	1	no	—
294	C₂²×D₃	—	10	1	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	4	1	no	—
297	C₂×C₃×C₄	—	4	1	no	—
298	C₂×C₃×C₄	—	4	1	no	—
299	C₂×C₃×C₄	—	4	1	no	—
300	C₂×C₃×C₄	—	4	1	no	—
301	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
303	C₂×C₃×C₄	#709	1	1	yes	characteristic
304	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
305	C₂×C₃×C₄	#711	1	1	yes	characteristic
306	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
307	C₂×Dic₃	—	5	2	no	—
308	C₂×Dic₃	—	10	1	no	—
309	C₂×Dic₃	—	10	1	no	—
310	C₂×Dic₃	—	10	2	no	—
311	C₂×Dic₃	—	20	1	no	—
312	C₂×Dic₃	—	20	1	no	—
313	C₂×Dic₃	—	20	1	no	—
314	C₂×Dic₃	—	20	1	no	—
315	C₂×Dic₃	—	20	1	no	—
316	C₄×D₃	—	10	2	no	—
317	C₄×D₃	—	10	2	no	—
318	C₄×D₃	—	10	2	no	—
319	C₄×D₃	—	10	2	no	—
320	C₃×C₈	—	2	2	no	—
321	C₃⋊C₈	—	10	2	no	—
322	C₂²×C₅	#882	1	1	yes	characteristic
323	C₂²×C₅	#883	1	1	yes	characteristic
324	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
325	C₂²×C₅	#911	1	1	yes	characteristic
326	C₂²×C₅	#916	1	1	yes	characteristic
327	C₂²×C₅	#916	1	1	yes	characteristic
328	C₂²×C₅	#918	1	1	yes	characteristic
329	C₂×D₅	—	6	2	no	—
330	C₂×D₅	—	6	2	no	—
331	C₂×D₅	—	6	2	no	—
332	C₂×D₅	—	12	1	no	—
333	C₂×D₅	—	12	1	no	—
334	C₂×D₅	—	12	1	no	—
335	C₂×D₅	—	12	1	no	—
336	C₄×C₅	—	4	2	no	—
337	C₄×C₅	—	8	1	no	—
338	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
339	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
340	C₄×C₅	#896	1	1	yes	characteristic
341	C₄×C₅	#897	1	1	yes	characteristic
342	Dic₅	—	6	2	no	—
343	Dic₅	—	12	2	no	—
344	Dic₅	—	24	1	no	—
345	C₂⁴	—	15	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	15	1	no	—
349	C₂²×C₄	—	15	2	no	—
350	C₂²×C₄	—	15	2	no	—
351	C₂²×C₄	—	30	1	no	—
352	C₂²×C₄	—	30	1	no	—
353	C₂²×C₄	—	30	1	no	—
354	C₂²×C₄	—	30	1	no	—
355	C₂²×C₄	—	30	1	no	—
356	C₂²×C₄	—	30	1	no	—
357	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	15	2	no	—
361	C₂×C₈	—	30	1	no	—
362	C₂×C₈	—	30	1	no	—
363	C₂×C₈	C₄×D₁₅	1	2	yes	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	15	2	no	—
368	C₄⋊C₄	—	30	1	no	—
369	C₄⋊C₄	—	30	1	no	—
370	C₄⋊C₄	—	30	1	no	—
371	C₄⋊C₄	D₆₀	1	2	yes	—
372	C₂²⋊C₄	—	30	4	no	—
373	C₂²⋊C₄	—	60	2	no	—
374	C₄²	—	30	4	no	—
375	C₃×C₅	#1854	1	1	yes	characteristic, complemented, Hall
376	C₂²×C₃	#4028	1	1	yes	characteristic
377	C₂²×C₃	#4029	1	1	yes	characteristic
378	C₂²×C₃	D₅×C₄⋊C₄	1	1	yes	characteristic
379	C₂²×C₃	#4057	1	1	yes	characteristic
380	C₂²×C₃	#4062	1	1	yes	characteristic
381	C₂²×C₃	#4062	1	1	yes	characteristic
382	C₂²×C₃	#4064	1	1	yes	characteristic
383	C₂×D₃	—	10	2	no	—
384	C₂×D₃	—	10	2	no	—
385	C₂×D₃	—	10	2	no	—
386	C₂×D₃	—	20	1	no	—
387	C₂×D₃	—	20	1	no	—
388	C₂×D₃	—	20	1	no	—
389	C₂×D₃	—	20	1	no	—
390	C₃×C₄	—	4	2	no	—
391	C₃×C₄	—	8	1	no	—
392	C₃×C₄	C₄×D₂₀	1	1	yes	characteristic
393	C₃×C₄	#4027	1	1	yes	characteristic
394	C₃×C₄	#4042	1	1	yes	characteristic
395	C₃×C₄	#4043	1	1	yes	characteristic
396	Dic₃	—	10	2	no	—
397	Dic₃	—	20	2	no	—
398	Dic₃	—	40	1	no	—
399	C₂×C₅	#4668	1	1	yes	characteristic
400	C₂×C₅	#4779	1	1	yes	characteristic
401	C₂×C₅	#4781	1	1	yes	characteristic
402	C₂×C₅	#4808	1	1	yes	characteristic
403	C₂×C₅	#4815	1	1	yes	characteristic
404	C₂×C₅	#4860	1	1	yes	characteristic
405	C₂×C₅	#4881	1	1	yes	characteristic
406	D₅	—	12	2	no	—
407	C₂³	—	15	2	no	—
408	C₂³	—	30	1	no	—
409	C₂³	—	30	1	no	—
410	C₂³	—	30	1	no	—
411	C₂³	—	30	1	no	—
412	C₂³	—	30	1	no	—
413	C₂³	—	30	1	no	—
414	C₂³	D₄×D₁₅	1	1	yes	characteristic
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	15	2	no	—
422	C₂×C₄	—	30	1	no	—
423	C₂×C₄	—	30	1	no	—
424	C₂×C₄	—	30	2	no	—
425	C₂×C₄	—	30	2	no	—
426	C₂×C₄	—	30	2	no	—
427	C₂×C₄	—	30	2	no	—
428	C₂×C₄	—	30	2	no	—
429	C₂×C₄	—	60	1	no	—
430	C₂×C₄	—	60	1	no	—
431	C₂×C₄	—	60	1	no	—
432	C₂×C₄	—	60	1	no	—
433	C₂×C₄	—	60	1	no	—
434	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
435	C₂×C₄	C₂×D₆₀	1	1	yes	characteristic
436	C₂×C₄	#6817	1	1	yes	characteristic
437	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
438	C₂×C₄	#6819	1	1	yes	characteristic
439	C₂×C₄	Q₈×D₁₅	1	1	yes	characteristic
440	C₈	—	2	2	no	—
441	C₈	—	30	2	no	—
442	C₂×C₃	#64957	1	1	yes	characteristic
443	C₂×C₃	#65068	1	1	yes	characteristic
444	C₂×C₃	#65070	1	1	yes	characteristic
445	C₂×C₃	#65099	1	1	yes	characteristic
446	C₂×C₃	#65104	1	1	yes	characteristic
447	C₂×C₃	#65149	1	1	yes	characteristic
448	C₂×C₃	#65170	1	1	yes	characteristic
449	D₃	—	20	2	no	—
450	C₅	#68876	1	1	yes	characteristic, complemented, Sylow
451	C₂²	—	30	2	no	—
452	C₂²	—	30	2	no	—
453	C₂²	—	30	2	no	—
454	C₂²	—	60	1	no	—
455	C₂²	—	60	1	no	—
456	C₂²	—	60	1	no	—
457	C₂²	—	60	1	no	—
458	C₂²	#91771	1	1	yes	characteristic
459	C₂²	#91772	1	1	yes	characteristic
460	C₂²	C₄⋊C₄×D₁₅	1	1	yes	characteristic
461	C₂²	#91800	1	1	yes	characteristic
462	C₂²	#91805	1	1	yes	characteristic
463	C₂²	#91805	1	1	yes	characteristic
464	C₂²	#91807	1	1	yes	characteristic
465	C₄	—	4	2	no	—
466	C₄	—	8	1	no	—
467	C₄	—	30	2	no	—
468	C₄	—	60	2	no	—
469	C₄	—	120	1	no	—
470	C₄	C₄×D₆₀	1	1	yes	characteristic
471	C₄	#91770	1	1	yes	characteristic
472	C₄	#91785	1	1	yes	characteristic
473	C₄	#91786	1	1	yes	characteristic
474	C₃	#10599669	1	1	yes	characteristic, complemented, Sylow
475	C₂	—	60	2	no	—
476	C₂	#11750769	1	1	yes	characteristic
477	C₂	#11750880	1	1	yes	characteristic
478	C₂	#11750882	1	1	yes	characteristic
479	C₂	#11750909	1	1	yes	characteristic
480	C₂	#11750916	1	1	yes	characteristic
481	C₂	#11750961	1	1	yes	characteristic
482	C₂	#11750982	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₅
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₅
Fitting	C₃×C₅×#340	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂³×D₁₅	D₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	#340	D₁₅
hypocenter	C₃×C₅	#1854
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

Complements

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

N	H ≅ G/N	type
3. C₂×#91101	C₂	semidirect
5. C₂×#91091	C₂	semidirect
6. C₃×C₅×#340	C₂	semidirect
7. #11746350	C₂	semidirect
22. #91104	C₄	semidirect
31. C₅×#340	D₃	semidirect
68. C₃×#340	D₅	semidirect
174. #340	D₁₅	semidirect
375. C₃×C₅	#1854	semidirect
450. C₅	#68876	semidirect
474. C₃	#10599669	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91781	2
C₂×#91104	2
C₂×#91101	2
#11751088	2
C₂×#91091	2
C₃×C₅×#340	2
#11746350	2
#10599669	3
#68876	5