Subgroups — #14413932

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×D₃×D₅	C₂	1	1	yes	maximal, characteristic
2	#11750786	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4685	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×#676	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748101	C₂	1	2	yes	maximal
6	#11747600	C₂	1	2	yes	maximal, complemented
7	#11747598	C₂	1	2	yes	maximal, complemented
8	#11747596	C₂	1	2	yes	maximal, complemented
9	C₄×#6649	C₂	1	1	yes	maximal, characteristic, complemented
10	#11746937	C₂	1	1	yes	maximal, characteristic, complemented
11	#11746876	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611013	—	3	1	no	maximal, Hall
13	C₂×C₄×D₃×D₅	C₄	1	1	yes	characteristic
14	C₂×C₄×D₃×D₅	C₄	1	1	yes	characteristic
15	C₂×C₄×D₃×D₅	C₂²	1	1	yes	characteristic
16	C₄²×D₁₅	C₂²	1	1	yes	characteristic
17	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₂×C₃×#676	C₂²	1	2	yes	—
19	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
20	C₄×#1200	C₄	1	1	yes	characteristic
21	C₄×#1200	C₄	1	1	yes	characteristic
22	C₄×#1200	C₂²	1	1	yes	characteristic
23	C₄×D₃×Dic₅	C₄	1	1	yes	characteristic
24	C₄×D₃×Dic₅	C₄	1	1	yes	characteristic
25	C₄×D₃×Dic₅	C₂²	1	1	yes	characteristic
26	C₄×D₅×Dic₃	C₄	1	1	yes	characteristic
27	C₄×D₅×Dic₃	C₄	1	1	yes	characteristic
28	C₄×D₅×Dic₃	C₂²	1	1	yes	characteristic
29	C₂×#6649	C₂²	1	2	yes	—
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
31	#91104	C₂²	1	2	yes	—
32	#91098	C₂²	1	2	yes	complemented
33	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic, complemented
34	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
35	C₅×Dic₃⋊C₈	C₂²	1	2	yes	complemented
36	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×#3947	C₂²	1	2	yes	complemented
38	C₃×C₄×#168	C₂²	1	1	yes	characteristic, complemented
39	Dic₃⋊#168	C₂²	1	2	yes	complemented
40	#90983	C₂²	1	2	yes	complemented
41	#90957	C₂²	1	2	yes	—
42	(C₂×D₃)⋊#168	C₂²	1	2	yes	—
43	#90952	C₂²	1	2	yes	complemented
44	#78517	—	5	1	no	maximal, Hall
45	C₂×C₄²×D₅	—	3	1	no	—
46	C₅×#431	—	3	1	no	—
47	#65214	—	3	1	no	—
48	#65126	—	3	2	no	—
49	#65124	—	3	2	no	—
50	#65015	—	3	2	no	—
51	#65008	—	3	2	no	—
52	C₄×#676	—	3	1	no	—
53	C₄×#676	D₃	1	1	yes	characteristic, complemented
54	#64974	—	3	1	no	—
55	#64974	—	3	1	no	—
56	C₂²×D₃×D₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
60	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
66	C₂×#1200	C₂×C₄	1	1	yes	characteristic
67	C₂×#1200	C₂×C₄	1	1	yes	characteristic
68	C₂×#1200	C₂×C₄	1	1	yes	characteristic
69	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
70	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
71	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
72	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
73	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
74	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
75	C₄×D₃×D₅	—	2	4	no	—
76	C₄×D₃×D₅	—	2	4	no	—
77	C₄×D₃×D₅	—	2	4	no	—
78	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
79	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
81	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
82	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
83	C₂×C₃⋊#168	C₂³	1	2	yes	—
84	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
85	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
86	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
88	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
89	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
90	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
91	C₂×C₃×#168	C₂³	1	2	yes	—
92	C₃×#676	—	2	4	no	—
93	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
94	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
95	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
96	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
97	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
98	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
99	#6649	—	2	4	no	—
100	C₂×C₄²×D₃	—	5	1	no	—
101	C₃×C₄×M₁₆	—	5	1	no	—
102	#5126	—	5	2	no	—
103	#5118	—	5	2	no	—
104	C₄×#208	—	5	1	no	—
105	#4705	—	5	2	no	—
106	#4705	—	5	2	no	—
107	#4685	—	5	1	no	—
108	#4685	—	5	1	no	—
109	#4685	—	5	1	no	—
110	#4685	D₅	1	1	yes	characteristic, complemented
111	C₂²×C₄×D₅	—	3	1	no	—
112	C₂²×C₄×D₅	—	3	1	no	—
113	C₂²×C₄×D₅	—	3	1	no	—
114	C₂×C₄²×C₅	—	3	1	no	—
115	C₂×C₄×Dic₅	—	3	1	no	—
116	C₂×C₄×Dic₅	—	3	1	no	—
117	C₂×C₄×Dic₅	—	3	1	no	—
118	C₂×#676	—	3	2	no	—
119	C₂×#676	C₂×D₃	1	2	yes	—
120	C₄²×D₅	—	3	1	no	—
121	C₄²×D₅	—	3	1	no	—
122	C₄²×D₅	—	3	1	no	—
123	C₄²×D₅	—	3	1	no	—
124	C₄²×D₅	—	3	1	no	—
125	C₄²×D₅	—	3	1	no	—
126	C₄²×D₅	—	3	1	no	—
127	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
128	C₅×C₄⋊C₈	—	3	2	no	—
129	C₅×C₂²⋊C₈	—	3	2	no	—
130	C₄×C₅×C₈	—	3	1	no	—
131	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
132	C₂²⋊#168	—	3	2	no	—
133	#3952	—	3	2	no	—
134	#3952	—	3	2	no	—
135	#3947	—	3	2	no	—
136	#3947	C₂×D₃	1	2	yes	complemented
137	#3946	—	3	2	no	—
138	#3946	—	3	2	no	—
139	C₄⋊#168	—	3	2	no	—
140	C₄×#168	—	3	1	no	—
141	C₄×#168	C₂×D₃	1	1	yes	characteristic, complemented
142	#2920	—	15	1	no	Sylow
143	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
146	C₂×D₃×D₅	—	2	2	no	—
147	C₂×D₃×D₅	—	2	2	no	—
148	C₂×D₃×D₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
152	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
153	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
154	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
155	C₄×D₁₅	—	2	2	no	—
156	C₄×D₁₅	—	2	2	no	—
157	C₄×D₁₅	M₁₆	1	4	yes	complemented
158	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
161	C₄×C₅×D₃	—	2	2	no	—
162	C₄×C₅×D₃	—	2	2	no	—
163	C₄×C₅×D₃	M₁₆	1	4	yes	complemented
164	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
167	C₃×C₄×D₅	—	2	2	no	—
168	C₃×C₄×D₅	—	2	2	no	—
169	C₃×C₄×D₅	#41	1	4	yes	—
170	#1200	—	2	2	no	—
171	#1200	—	2	2	no	—
172	#1200	—	2	2	no	—
173	D₃×Dic₅	—	2	2	no	—
174	D₃×Dic₅	—	2	2	no	—
175	D₃×Dic₅	—	2	2	no	—
176	D₅×Dic₃	—	2	2	no	—
177	D₅×Dic₃	—	2	2	no	—
178	D₅×Dic₃	—	2	2	no	—
179	C₃×C₅×C₈	—	2	2	no	—
180	C₃⋊#168	—	2	2	no	—
181	C₃×#168	—	2	2	no	—
182	C₅×C₃⋊C₈	—	2	2	no	—
183	C₂²×C₄×D₃	—	5	1	no	—
184	C₂²×C₄×D₃	—	5	1	no	—
185	C₂²×C₄×D₃	—	5	1	no	—
186	C₂×C₃×M₁₆	—	5	2	no	—
187	C₂×C₃×C₄²	—	5	1	no	—
188	C₂×C₄×Dic₃	—	5	1	no	—
189	C₂×C₄×Dic₃	—	5	1	no	—
190	C₂×C₄×Dic₃	—	5	1	no	—
191	C₂×#208	—	5	2	no	—
192	C₄²×D₃	—	5	1	no	—
193	C₄²×D₃	—	5	1	no	—
194	C₄²×D₃	—	5	1	no	—
195	C₄²×D₃	—	5	1	no	—
196	C₄²×D₃	—	5	1	no	—
197	C₄²×D₃	—	5	1	no	—
198	C₄²×D₃	—	5	1	no	—
199	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
200	C₃×#97	—	5	2	no	—
201	C₃×C₄×C₈	—	5	1	no	—
202	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
203	(C₂×D₃)⋊C₈	—	5	2	no	—
204	(C₂×D₃)⋊C₈	—	5	2	no	—
205	(C₂×D₃)⋊C₈	—	5	2	no	—
206	(C₂×D₃)⋊C₈	C₂×D₅	1	2	yes	—
207	Dic₃⋊C₈	—	5	2	no	—
208	Dic₃⋊C₈	—	5	2	no	—
209	Dic₃⋊C₈	—	5	2	no	—
210	Dic₃⋊C₈	C₂×D₅	1	2	yes	complemented
211	#803	—	5	2	no	—
212	C₄×C₃⋊C₈	—	5	1	no	—
213	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
214	C₂³×D₅	—	3	1	no	—
215	C₂²×C₄×C₅	—	3	1	no	—
216	C₂²×C₄×C₅	—	3	1	no	—
217	C₂²×C₄×C₅	—	3	1	no	—
218	C₂²×Dic₅	—	3	1	no	—
219	C₂²×Dic₅	—	3	1	no	—
220	C₂²×Dic₅	—	3	1	no	—
221	C₂×C₄×D₅	—	3	1	no	—
222	C₂×C₄×D₅	—	3	1	no	—
223	C₂×C₄×D₅	—	3	1	no	—
224	C₂×C₄×D₅	—	3	1	no	—
225	C₂×C₄×D₅	—	3	1	no	—
226	C₂×C₄×D₅	—	3	1	no	—
227	C₂×C₄×D₅	—	3	1	no	—
228	C₂×C₄×D₅	—	3	1	no	—
229	C₂×C₄×D₅	—	3	1	no	—
230	C₂×C₄×D₅	—	6	4	no	—
231	C₂×C₄×D₅	—	6	4	no	—
232	C₂×C₄×D₅	—	6	4	no	—
233	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
234	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
235	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
236	C₂×C₅×C₈	—	3	2	no	—
237	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
238	C₄²×C₅	—	3	1	no	—
239	C₄²×C₅	—	3	1	no	—
240	C₄²×C₅	—	3	1	no	—
241	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
242	C₄×Dic₅	—	3	1	no	—
243	C₄×Dic₅	—	3	1	no	—
244	C₄×Dic₅	—	3	1	no	—
245	C₄×Dic₅	—	3	1	no	—
246	C₄×Dic₅	—	3	1	no	—
247	C₄×Dic₅	—	3	1	no	—
248	C₄×Dic₅	—	3	1	no	—
249	C₄×Dic₅	—	3	1	no	—
250	C₄×Dic₅	—	3	1	no	—
251	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
252	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
253	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
254	C₂×#168	—	3	2	no	—
255	C₂×#168	C₂²×D₃	1	2	yes	—
256	#676	—	2	4	no	—
257	#676	—	6	4	no	—
258	C₂²×C₄²	—	15	1	no	—
259	#432	—	15	2	no	—
260	#432	—	15	2	no	—
261	#431	—	3	1	no	—
262	#431	—	15	1	no	—
263	#431	—	15	1	no	—
264	#431	—	15	1	no	—
265	#423	—	15	2	no	—
266	#407	—	15	2	no	—
267	C₄×M₁₆	—	5	1	no	—
268	C₄×M₁₆	—	15	1	no	—
269	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
270	C₂×D₁₅	—	2	1	no	—
271	C₂×D₁₅	—	2	1	no	—
272	C₂×D₁₅	C₂×M₁₆	1	2	yes	—
273	C₂×C₅×D₃	—	2	1	no	—
274	C₂×C₅×D₃	—	2	1	no	—
275	C₂×C₅×D₃	C₂×M₁₆	1	2	yes	—
276	C₂×C₃×D₅	—	2	1	no	—
277	C₂×C₃×D₅	—	2	1	no	—
278	C₂×C₃×D₅	#117	1	2	yes	—
279	D₃×D₅	—	2	8	no	—
280	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
281	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
282	C₃×C₄×C₅	C₂×#41	1	2	yes	—
283	Dic₁₅	—	2	1	no	—
284	Dic₁₅	—	2	1	no	—
285	Dic₁₅	C₂×M₁₆	1	2	yes	—
286	C₃×Dic₅	—	2	1	no	—
287	C₃×Dic₅	—	2	1	no	—
288	C₃×Dic₅	#117	1	2	yes	—
289	C₅×Dic₃	—	2	1	no	—
290	C₅×Dic₃	—	2	1	no	—
291	C₅×Dic₃	C₂×M₁₆	1	2	yes	—
292	C₂³×D₃	—	5	1	no	—
293	C₂²×C₃×C₄	—	5	1	no	—
294	C₂²×C₃×C₄	—	5	1	no	—
295	C₂²×C₃×C₄	—	5	1	no	—
296	C₂²×Dic₃	—	5	1	no	—
297	C₂²×Dic₃	—	5	1	no	—
298	C₂²×Dic₃	—	5	1	no	—
299	C₂×C₄×D₃	—	5	1	no	—
300	C₂×C₄×D₃	—	5	1	no	—
301	C₂×C₄×D₃	—	5	1	no	—
302	C₂×C₄×D₃	—	5	1	no	—
303	C₂×C₄×D₃	—	5	1	no	—
304	C₂×C₄×D₃	—	5	1	no	—
305	C₂×C₄×D₃	—	5	1	no	—
306	C₂×C₄×D₃	—	5	1	no	—
307	C₂×C₄×D₃	—	5	1	no	—
308	C₂×C₄×D₃	—	10	4	no	—
309	C₂×C₄×D₃	—	10	4	no	—
310	C₂×C₄×D₃	—	10	4	no	—
311	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
312	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
313	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
314	C₃×M₁₆	—	10	4	no	—
315	C₂×C₃×C₈	—	5	2	no	—
316	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
317	C₃×C₄²	—	5	1	no	—
318	C₃×C₄²	—	5	1	no	—
319	C₃×C₄²	—	5	1	no	—
320	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
321	C₄×Dic₃	—	5	1	no	—
322	C₄×Dic₃	—	5	1	no	—
323	C₄×Dic₃	—	5	1	no	—
324	C₄×Dic₃	—	5	1	no	—
325	C₄×Dic₃	—	5	1	no	—
326	C₄×Dic₃	—	5	1	no	—
327	C₄×Dic₃	—	5	1	no	—
328	C₄×Dic₃	—	5	1	no	—
329	C₄×Dic₃	—	5	1	no	—
330	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
331	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
332	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
333	#208	—	10	4	no	—
334	C₂×C₃⋊C₈	—	5	2	no	—
335	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
336	C₂³×C₅	—	3	1	no	—
337	C₂²×D₅	—	3	1	no	—
338	C₂²×D₅	—	6	2	no	—
339	C₂²×D₅	—	6	2	no	—
340	C₂²×D₅	—	6	2	no	—
341	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
342	C₂×C₄×C₅	—	3	1	no	—
343	C₂×C₄×C₅	—	3	4	no	—
344	C₂×C₄×C₅	—	3	1	no	—
345	C₂×C₄×C₅	—	3	1	no	—
346	C₂×C₄×C₅	—	6	2	no	—
347	C₂×C₄×C₅	—	6	2	no	—
348	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
349	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
350	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
351	C₂×Dic₅	—	3	1	no	—
352	C₂×Dic₅	—	3	1	no	—
353	C₂×Dic₅	—	3	1	no	—
354	C₂×Dic₅	—	6	2	no	—
355	C₂×Dic₅	—	6	2	no	—
356	C₂×Dic₅	—	6	2	no	—
357	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
358	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
359	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
360	C₄×D₅	—	2	2	no	—
361	C₄×D₅	—	2	2	no	—
362	C₄×D₅	—	3	4	no	—
363	C₄×D₅	—	6	2	no	—
364	C₄×D₅	—	6	2	no	—
365	C₄×D₅	—	6	2	no	—
366	C₄×D₅	—	6	2	no	—
367	C₄×D₅	—	6	2	no	—
368	C₄×D₅	—	6	2	no	—
369	C₄×D₅	—	6	2	no	—
370	C₄×D₅	—	6	2	no	—
371	C₄×D₅	#235	1	4	yes	—
372	C₅×C₈	—	2	2	no	—
373	C₅×C₈	—	6	2	no	—
374	#168	—	2	2	no	—
375	#168	—	6	2	no	—
376	C₂³×C₄	—	15	1	no	—
377	C₂³×C₄	—	15	1	no	—
378	C₂³×C₄	—	15	1	no	—
379	C₂×M₁₆	—	5	2	no	—
380	C₂×M₁₆	—	15	2	no	—
381	C₂×C₄²	—	3	1	no	—
382	C₂×C₄²	—	5	1	no	—
383	C₂×C₄²	—	15	1	no	—
384	C₂×C₄²	—	15	1	no	—
385	C₂×C₄²	—	15	1	no	—
386	C₂×C₄²	—	15	1	no	—
387	C₂×C₄²	—	15	1	no	—
388	C₂×C₄²	—	15	1	no	—
389	C₂×C₄²	—	15	1	no	—
390	C₂×C₄²	—	15	1	no	—
391	C₂×C₄²	—	15	1	no	—
392	C₂×C₄²	—	15	1	no	—
393	C₄⋊C₈	—	3	2	no	—
394	C₄⋊C₈	—	15	2	no	—
395	C₄⋊C₈	—	15	2	no	—
396	C₄⋊C₈	—	15	2	no	—
397	C₂²⋊C₈	—	3	2	no	—
398	C₂²⋊C₈	—	15	2	no	—
399	C₂²⋊C₈	—	15	2	no	—
400	C₂²⋊C₈	—	15	2	no	—
401	#97	—	5	2	no	—
402	#97	—	15	2	no	—
403	C₄×C₈	—	3	1	no	—
404	C₄×C₈	—	5	1	no	—
405	C₄×C₈	—	15	1	no	—
406	C₄×C₈	D₃×D₅	1	1	yes	characteristic, complemented
407	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
408	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
409	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
410	D₁₅	—	2	2	no	—
411	C₃×D₅	—	2	2	no	—
412	C₅×D₃	—	2	2	no	—
413	C₂³×C₃	—	5	1	no	—
414	C₂²×D₃	—	5	1	no	—
415	C₂²×D₃	—	10	2	no	—
416	C₂²×D₃	—	10	2	no	—
417	C₂²×D₃	—	10	2	no	—
418	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
419	C₂×C₃×C₄	—	5	1	no	—
420	C₂×C₃×C₄	—	5	4	no	—
421	C₂×C₃×C₄	—	5	1	no	—
422	C₂×C₃×C₄	—	5	1	no	—
423	C₂×C₃×C₄	—	10	2	no	—
424	C₂×C₃×C₄	—	10	2	no	—
425	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
426	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
427	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
428	C₂×Dic₃	—	5	1	no	—
429	C₂×Dic₃	—	5	1	no	—
430	C₂×Dic₃	—	5	1	no	—
431	C₂×Dic₃	—	10	2	no	—
432	C₂×Dic₃	—	10	2	no	—
433	C₂×Dic₃	—	10	2	no	—
434	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
435	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
436	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
437	C₄×D₃	—	2	2	no	—
438	C₄×D₃	—	2	2	no	—
439	C₄×D₃	—	5	4	no	—
440	C₄×D₃	—	10	2	no	—
441	C₄×D₃	—	10	2	no	—
442	C₄×D₃	—	10	2	no	—
443	C₄×D₃	—	10	2	no	—
444	C₄×D₃	—	10	2	no	—
445	C₄×D₃	—	10	2	no	—
446	C₄×D₃	—	10	2	no	—
447	C₄×D₃	—	10	2	no	—
448	C₄×D₃	#676	1	4	yes	complemented
449	C₃×C₈	—	2	2	no	—
450	C₃×C₈	—	10	2	no	—
451	C₃⋊C₈	—	2	2	no	—
452	C₃⋊C₈	—	10	2	no	—
453	C₂²×C₅	—	3	2	no	—
454	C₂²×C₅	—	6	1	no	—
455	C₂²×C₅	—	6	1	no	—
456	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
457	C₂×D₅	—	2	1	no	—
458	C₂×D₅	—	2	1	no	—
459	C₂×D₅	—	3	2	no	—
460	C₂×D₅	—	6	8	no	—
461	C₂×D₅	—	6	1	no	—
462	C₂×D₅	—	6	1	no	—
463	C₂×D₅	#872	1	2	yes	—
464	C₄×C₅	—	3	2	no	—
465	C₄×C₅	—	6	1	no	—
466	C₄×C₅	—	6	1	no	—
467	C₄×C₅	D₃×M₁₆	1	2	yes	—
468	C₄×C₅	D₃×M₁₆	1	2	yes	—
469	C₄×C₅	C₂×#235	1	2	yes	—
470	Dic₅	—	2	1	no	—
471	Dic₅	—	2	1	no	—
472	Dic₅	—	3	2	no	—
473	Dic₅	—	6	1	no	—
474	Dic₅	—	6	1	no	—
475	Dic₅	#872	1	2	yes	—
476	C₂⁴	—	15	1	no	—
477	C₂²×C₄	—	3	1	no	—
478	C₂²×C₄	—	3	1	no	—
479	C₂²×C₄	—	3	1	no	—
480	C₂²×C₄	—	5	1	no	—
481	C₂²×C₄	—	5	1	no	—
482	C₂²×C₄	—	5	1	no	—
483	C₂²×C₄	—	15	1	no	—
484	C₂²×C₄	—	15	1	no	—
485	C₂²×C₄	—	15	1	no	—
486	C₂²×C₄	—	15	1	no	—
487	C₂²×C₄	—	15	1	no	—
488	C₂²×C₄	—	15	1	no	—
489	C₂²×C₄	—	15	1	no	—
490	C₂²×C₄	—	15	1	no	—
491	C₂²×C₄	—	15	1	no	—
492	C₂²×C₄	—	15	1	no	—
493	C₂²×C₄	—	15	1	no	—
494	C₂²×C₄	—	15	1	no	—
495	C₂²×C₄	—	30	4	no	—
496	C₂²×C₄	—	30	4	no	—
497	C₂²×C₄	—	30	4	no	—
498	M₁₆	—	10	4	no	—
499	M₁₆	—	30	4	no	—
500	C₂×C₈	—	3	2	no	—
501	C₂×C₈	—	5	2	no	—
502	C₂×C₈	—	15	2	no	—
503	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
504	C₄²	—	3	1	no	—
505	C₄²	—	3	1	no	—
506	C₄²	—	3	1	no	—
507	C₄²	—	5	1	no	—
508	C₄²	—	5	1	no	—
509	C₄²	—	5	1	no	—
510	C₄²	—	15	1	no	—
511	C₄²	—	15	1	no	—
512	C₄²	—	15	1	no	—
513	C₄²	—	15	1	no	—
514	C₄²	—	15	1	no	—
515	C₄²	—	15	1	no	—
516	C₄²	—	15	1	no	—
517	C₄²	—	15	1	no	—
518	C₄²	—	15	1	no	—
519	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
520	C₃×C₅	#2920	1	1	yes	characteristic, complemented, Hall
521	C₂²×C₃	—	5	2	no	—
522	C₂²×C₃	—	10	1	no	—
523	C₂²×C₃	—	10	1	no	—
524	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
525	C₂×D₃	—	2	1	no	—
526	C₂×D₃	—	2	1	no	—
527	C₂×D₃	—	5	2	no	—
528	C₂×D₃	—	10	8	no	—
529	C₂×D₃	—	10	1	no	—
530	C₂×D₃	—	10	1	no	—
531	C₂×D₃	C₂×#676	1	2	yes	—
532	C₃×C₄	—	5	2	no	—
533	C₃×C₄	—	10	1	no	—
534	C₃×C₄	—	10	1	no	—
535	C₃×C₄	C₂×#676	1	2	yes	—
536	C₃×C₄	D₅×M₁₆	1	2	yes	—
537	C₃×C₄	D₅×#41	1	2	yes	—
538	Dic₃	—	2	1	no	—
539	Dic₃	—	2	1	no	—
540	Dic₃	—	5	2	no	—
541	Dic₃	—	10	1	no	—
542	Dic₃	—	10	1	no	—
543	Dic₃	C₂×#676	1	2	yes	—
544	C₂×C₅	—	6	2	no	—
545	C₂×C₅	C₂×#872	1	1	yes	characteristic
546	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
547	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
548	D₅	—	2	2	no	—
549	D₅	—	6	2	no	—
550	C₂³	—	3	1	no	—
551	C₂³	—	5	1	no	—
552	C₂³	—	15	1	no	—
553	C₂³	—	30	2	no	—
554	C₂³	—	30	2	no	—
555	C₂³	—	30	2	no	—
556	C₂×C₄	—	3	1	no	—
557	C₂×C₄	—	3	4	no	—
558	C₂×C₄	—	3	1	no	—
559	C₂×C₄	—	3	1	no	—
560	C₂×C₄	—	5	1	no	—
561	C₂×C₄	—	5	4	no	—
562	C₂×C₄	—	5	1	no	—
563	C₂×C₄	—	5	1	no	—
564	C₂×C₄	—	6	2	no	—
565	C₂×C₄	—	6	2	no	—
566	C₂×C₄	—	10	2	no	—
567	C₂×C₄	—	10	2	no	—
568	C₂×C₄	—	15	1	no	—
569	C₂×C₄	—	15	4	no	—
570	C₂×C₄	—	15	1	no	—
571	C₂×C₄	—	15	1	no	—
572	C₂×C₄	—	30	2	no	—
573	C₂×C₄	—	30	2	no	—
574	C₂×C₄	—	30	2	no	—
575	C₂×C₄	—	30	2	no	—
576	C₂×C₄	—	30	2	no	—
577	C₂×C₄	—	30	2	no	—
578	C₂×C₄	—	30	2	no	—
579	C₂×C₄	—	30	2	no	—
580	C₂×C₄	—	30	2	no	—
581	C₂×C₄	—	30	2	no	—
582	C₂×C₄	—	30	2	no	—
583	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
584	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
585	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
586	C₈	—	2	2	no	—
587	C₈	—	6	2	no	—
588	C₈	—	10	2	no	—
589	C₈	—	30	2	no	—
590	C₂×C₃	—	10	2	no	—
591	C₂×C₃	D₅×#117	1	1	yes	characteristic
592	C₂×C₃	C₂²×#676	1	1	yes	characteristic
593	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
594	D₃	—	2	2	no	—
595	D₃	—	10	2	no	—
596	C₅	#78517	1	1	yes	characteristic, complemented, Sylow
597	C₂²	—	3	2	no	—
598	C₂²	—	5	2	no	—
599	C₂²	—	6	1	no	—
600	C₂²	—	6	1	no	—
601	C₂²	—	10	1	no	—
602	C₂²	—	10	1	no	—
603	C₂²	—	15	2	no	—
604	C₂²	—	30	8	no	—
605	C₂²	—	30	1	no	—
606	C₂²	—	30	1	no	—
607	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
608	C₄	—	3	2	no	—
609	C₄	—	5	2	no	—
610	C₄	—	6	1	no	—
611	C₄	—	6	1	no	—
612	C₄	—	10	1	no	—
613	C₄	—	10	1	no	—
614	C₄	—	15	2	no	—
615	C₄	—	30	1	no	—
616	C₄	—	30	1	no	—
617	C₄	D₃×#676	1	2	yes	—
618	C₄	#91246	1	2	yes	—
619	C₄	D₅×#235	1	2	yes	—
620	C₃	#10611013	1	1	yes	characteristic, complemented, Sylow
621	C₂	—	6	2	no	—
622	C₂	—	10	2	no	—
623	C₂	—	30	2	no	—
624	C₂	D₅×#872	1	1	yes	characteristic
625	C₂	C₂×D₃×#676	1	1	yes	characteristic
626	C₂	C₂×#91246	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂²
prime radical	C₂²×D₃×D₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	#2920
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #11750786	C₂	semidirect
3. C₅×#4685	C₂	semidirect
4. C₃×C₄×#676	C₂	semidirect
6. #11747600	C₂	semidirect
7. #11747598	C₂	semidirect
8. #11747596	C₂	semidirect
9. C₄×#6649	C₂	semidirect
10. #11746937	C₂	semidirect
11. #11746876	C₂	semidirect
30. C₃×C₄×C₅×C₈	C₂²	semidirect
32. #91098	C₂²	semidirect
33. C₄×C₃⋊#168	C₂²	semidirect
35. C₅×Dic₃⋊C₈	C₂²	semidirect
36. C₄×C₅×C₃⋊C₈	C₂²	semidirect
37. C₃×#3947	C₂²	semidirect
38. C₃×C₄×#168	C₂²	semidirect
39. Dic₃⋊#168	C₂²	semidirect
40. #90983	C₂²	semidirect
43. #90952	C₂²	semidirect
53. C₄×#676	D₃	semidirect
110. #4685	D₅	semidirect
131. C₄×C₅×C₈	C₂×D₃	semidirect
136. #3947	C₂×D₃	semidirect
141. C₄×#168	C₂×D₃	semidirect
157. C₄×D₁₅	M₁₆	semidirect
163. C₄×C₅×D₃	M₁₆	semidirect
202. C₃×C₄×C₈	C₂×D₅	semidirect
210. Dic₃⋊C₈	C₂×D₅	semidirect
213. C₄×C₃⋊C₈	C₂×D₅	semidirect
406. C₄×C₈	D₃×D₅	semidirect
448. C₄×D₃	#676	semidirect
520. C₃×C₅	#2920	semidirect
596. C₅	#78517	semidirect
620. C₃	#10611013	semidirect

Maximal subgroups

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

subgroup	index
C₄²×D₃×D₅	2
#11750786	2
C₅×#4685	2
C₃×C₄×#676	2
#11748101	2
#11747600	2
#11747598	2
#11747596	2
C₄×#6649	2
#11746937	2
#11746876	2
#10611013	3
#78517	5