Subgroups — #14297441

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#1200	C₂	1	1	yes	maximal, characteristic
2	C₂×#91104	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#3946	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#90982	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#90957	C₂	1	1	yes	maximal, characteristic
6	C₅×#4550	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745967	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599455	—	3	1	no	maximal, Hall
9	C₂²×C₄×D₁₅	C₂²	1	1	yes	characteristic
10	C₂²×#1200	C₄	1	1	yes	characteristic
11	C₂²×#1200	C₄	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
17	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
18	C₂×Dic₃×Dic₅	C₄	1	1	yes	characteristic
19	C₂×Dic₃×Dic₅	C₄	1	1	yes	characteristic
20	C₄×#1200	—	2	2	no	—
21	C₄×#1200	—	2	2	no	—
22	#91104	—	2	2	no	—
23	C₃×#3946	—	2	2	no	—
24	#90982	—	2	2	no	—
25	#90957	—	2	2	no	—
26	#70475	—	5	1	no	maximal, Hall
27	C₂×C₄²×D₅	—	3	1	no	—
28	C₂×#3952	—	3	1	no	—
29	C₂×#3952	—	3	1	no	—
30	C₂×#3946	—	3	1	no	—
31	C₂×#3946	D₃	1	1	yes	characteristic, complemented
32	C₅×#336	—	3	1	no	—
33	#64744	—	3	1	no	—
34	C₂³×D₁₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×D₁₅	—	2	1	no	—
38	C₂×C₄×D₁₅	—	2	1	no	—
39	C₂×C₄×D₁₅	—	2	1	no	—
40	C₂×C₄×D₁₅	—	2	1	no	—
41	C₂×C₄×D₁₅	D₄	1	2	yes	—
42	C₂×C₄×D₁₅	Q₈	1	2	yes	—
43	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
47	C₂×#1200	—	2	2	no	—
48	C₂×#1200	—	2	2	no	—
49	C₂×#1200	—	2	2	no	—
50	C₂×#1200	—	2	2	no	—
51	C₂×#1200	—	2	2	no	—
52	C₂×#1200	C₈	1	4	yes	complemented
53	C₂×C₃×C₅×C₈	—	2	1	no	—
54	C₂×C₃×C₅×C₈	—	2	1	no	—
55	C₂×C₃×C₅×C₈	—	2	1	no	—
56	C₂×C₃⋊#168	—	2	1	no	—
57	C₂×C₃⋊#168	—	2	1	no	—
58	C₂×C₃⋊#168	—	2	1	no	—
59	C₄×C₅×Dic₃	—	2	1	no	—
60	C₄×C₅×Dic₃	—	2	1	no	—
61	C₂×C₅×C₃⋊C₈	—	2	1	no	—
62	C₂×C₅×C₃⋊C₈	—	2	1	no	—
63	C₂×C₅×C₃⋊C₈	—	2	1	no	—
64	C₃×C₄×Dic₅	D₄	1	2	yes	—
65	C₃×C₄×Dic₅	D₄	1	2	yes	—
66	C₂×C₃×#168	—	2	1	no	—
67	C₂×C₃×#168	—	2	1	no	—
68	C₂×C₃×#168	—	2	1	no	—
69	Dic₃×Dic₅	—	2	2	no	—
70	Dic₃×Dic₅	—	2	2	no	—
71	C₂×C₄²×D₃	—	5	1	no	—
72	C₂×C₃×C₄⋊C₈	—	5	1	no	—
73	C₂×(C₂×D₃)⋊C₈	—	5	1	no	—
74	C₂×(C₂×D₃)⋊C₈	—	5	1	no	—
75	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
76	#4550	—	5	1	no	—
77	#4550	D₅	1	1	yes	characteristic, complemented
78	C₂²×C₄×D₅	—	3	1	no	—
79	C₂²×C₄×D₅	—	3	1	no	—
80	C₂²×C₄×D₅	—	3	1	no	—
81	C₂²×C₅×C₈	—	3	1	no	—
82	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
83	C₂×C₄²×C₅	—	3	1	no	—
84	C₂×C₄×Dic₅	—	3	1	no	—
85	C₂×C₄×Dic₅	—	3	1	no	—
86	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
87	C₂²×#168	—	3	1	no	—
88	C₂²×#168	C₂×D₃	1	1	yes	characteristic
89	C₄²×D₅	—	6	2	no	—
90	C₄²×D₅	—	6	2	no	—
91	#3952	—	6	2	no	—
92	#3952	—	6	2	no	—
93	#3946	—	2	2	no	—
94	#3946	—	6	2	no	—
95	#1797	—	15	1	no	Sylow
96	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×D₁₅	—	2	1	no	—
98	C₂²×D₁₅	—	2	1	no	—
99	C₂²×D₁₅	—	2	1	no	—
100	C₂²×D₁₅	—	2	1	no	—
101	C₂²×D₁₅	C₄⋊C₄	1	2	yes	—
102	C₂²×D₁₅	C₂×C₈	1	2	yes	—
103	C₂²×D₁₅	M₁₆	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
110	C₂×Dic₁₅	—	2	1	no	—
111	C₂×Dic₁₅	—	2	1	no	—
112	C₂×Dic₁₅	C₄⋊C₄	1	2	yes	—
113	C₄×D₁₅	—	2	2	no	—
114	C₄×D₁₅	—	2	2	no	—
115	C₄×D₁₅	—	2	2	no	—
116	C₄×D₁₅	—	2	2	no	—
117	C₂×C₅×Dic₃	—	2	1	no	—
118	C₂×C₅×Dic₃	—	2	1	no	—
119	C₂×C₅×Dic₃	—	2	1	no	—
120	C₂×C₅×Dic₃	—	2	1	no	—
121	C₂×C₅×Dic₃	C₂×C₈	1	2	yes	—
122	C₂×C₅×Dic₃	M₁₆	1	2	yes	—
123	C₂×C₃×Dic₅	—	2	1	no	—
124	C₂×C₃×Dic₅	—	2	1	no	—
125	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
126	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
127	C₂×C₃×Dic₅	C₂×C₈	1	2	yes	—
128	C₂×C₃×Dic₅	M₁₆	1	2	yes	—
129	#1200	—	2	8	no	—
130	#1200	—	2	8	no	—
131	C₃×C₅×C₈	—	4	1	no	—
132	C₃⋊#168	—	4	1	no	—
133	C₃×#168	—	4	1	no	—
134	C₅×C₃⋊C₈	—	4	1	no	—
135	C₂²×C₄×D₃	—	5	1	no	—
136	C₂²×C₄×D₃	—	5	1	no	—
137	C₂²×C₄×D₃	—	5	1	no	—
138	C₂²×C₃×C₈	—	5	1	no	—
139	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
140	C₂×C₃×C₄²	—	5	1	no	—
141	C₂×C₄×Dic₃	—	5	1	no	—
142	C₂×C₄×Dic₃	—	5	1	no	—
143	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
144	C₂²×C₃⋊C₈	—	5	1	no	—
145	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
146	C₄²×D₃	—	10	2	no	—
147	C₄²×D₃	—	10	2	no	—
148	C₃×C₄⋊C₈	—	10	2	no	—
149	(C₂×D₃)⋊C₈	—	10	2	no	—
150	(C₂×D₃)⋊C₈	—	10	2	no	—
151	C₄⋊(C₃⋊C₈)	—	10	2	no	—
152	C₂³×D₅	—	3	1	no	—
153	C₂²×C₄×C₅	—	3	1	no	—
154	C₂²×C₄×C₅	—	3	1	no	—
155	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
156	C₂²×Dic₅	—	3	1	no	—
157	C₂²×Dic₅	C₄×D₃	1	1	yes	characteristic
158	C₂²×Dic₅	C₄×D₃	1	1	yes	characteristic
159	C₂×C₄×D₅	—	3	2	no	—
160	C₂×C₄×D₅	—	3	2	no	—
161	C₂×C₄×D₅	—	3	4	no	—
162	C₂×C₄×D₅	—	6	2	no	—
163	C₂×C₄×D₅	—	6	2	no	—
164	C₂×C₄×D₅	—	6	1	no	—
165	C₂×C₄×D₅	—	6	1	no	—
166	C₂×C₄×D₅	—	6	1	no	—
167	C₂×C₄×D₅	—	6	1	no	—
168	C₂×C₄×D₅	—	6	2	no	—
169	C₂×C₄×D₅	—	6	2	no	—
170	C₂×C₄×D₅	—	6	2	no	—
171	C₂×C₅×C₈	—	2	1	no	—
172	C₂×C₅×C₈	—	2	1	no	—
173	C₂×C₅×C₈	—	2	1	no	—
174	C₂×C₅×C₈	—	6	1	no	—
175	C₂×C₅×C₈	—	6	1	no	—
176	C₂×C₅×C₈	—	6	1	no	—
177	C₄²×C₅	—	6	1	no	—
178	C₄²×C₅	—	6	1	no	—
179	C₄×Dic₅	—	6	2	no	—
180	C₄×Dic₅	—	6	2	no	—
181	C₄×Dic₅	D₁₂	1	2	yes	—
182	C₄×Dic₅	#67	1	2	yes	—
183	C₂×#168	—	2	1	no	—
184	C₂×#168	—	2	1	no	—
185	C₂×#168	—	2	1	no	—
186	C₂×#168	—	6	1	no	—
187	C₂×#168	—	6	1	no	—
188	C₂×#168	—	6	1	no	—
189	C₂²×C₄²	—	15	1	no	—
190	C₂×C₄⋊C₈	—	5	1	no	—
191	C₂×C₄⋊C₈	—	15	1	no	—
192	C₂×C₂²⋊C₈	—	15	1	no	—
193	C₂×C₂²⋊C₈	—	15	1	no	—
194	#336	—	3	1	no	—
195	#336	—	15	1	no	—
196	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂²×C₃×C₅	#117	1	1	yes	characteristic
199	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
200	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
201	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
202	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
203	C₂×D₁₅	—	2	2	no	—
204	C₂×D₁₅	—	2	2	no	—
205	C₂×D₁₅	—	2	2	no	—
206	C₂×D₁₅	—	2	2	no	—
207	C₂×D₁₅	—	2	2	no	—
208	C₂×D₁₅	—	2	2	no	—
209	C₂×D₁₅	C₄⋊C₈	1	4	yes	complemented
210	C₃×C₄×C₅	#121	1	1	yes	characteristic
211	C₃×C₄×C₅	#121	1	1	yes	characteristic
212	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
213	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
214	Dic₁₅	—	2	2	no	—
215	C₃×Dic₅	—	2	2	no	—
216	C₃×Dic₅	C₂²⋊C₈	1	4	yes	complemented
217	C₅×Dic₃	—	2	2	no	—
218	C₅×Dic₃	—	2	2	no	—
219	C₂³×D₃	—	5	1	no	—
220	C₂²×C₃×C₄	—	5	1	no	—
221	C₂²×C₃×C₄	—	5	1	no	—
222	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
223	C₂²×Dic₃	—	5	1	no	—
224	C₂²×Dic₃	C₄×D₅	1	1	yes	characteristic
225	C₂²×Dic₃	C₄×D₅	1	1	yes	characteristic
226	C₂×C₄×D₃	—	5	2	no	—
227	C₂×C₄×D₃	—	5	2	no	—
228	C₂×C₄×D₃	—	5	4	no	—
229	C₂×C₄×D₃	—	10	2	no	—
230	C₂×C₄×D₃	—	10	2	no	—
231	C₂×C₄×D₃	—	10	2	no	—
232	C₂×C₄×D₃	—	10	2	no	—
233	C₂×C₄×D₃	—	10	1	no	—
234	C₂×C₄×D₃	—	10	1	no	—
235	C₂×C₄×D₃	—	10	1	no	—
236	C₂×C₄×D₃	—	10	1	no	—
237	C₂×C₄×D₃	—	10	2	no	—
238	C₂×C₃×C₈	—	2	1	no	—
239	C₂×C₃×C₈	—	2	1	no	—
240	C₂×C₃×C₈	—	2	1	no	—
241	C₂×C₃×C₈	—	10	1	no	—
242	C₂×C₃×C₈	—	10	1	no	—
243	C₂×C₃×C₈	—	10	1	no	—
244	C₃×C₄²	—	5	2	no	—
245	C₃×C₄²	—	5	2	no	—
246	C₄×Dic₃	—	2	1	no	—
247	C₄×Dic₃	—	2	1	no	—
248	C₄×Dic₃	—	10	2	no	—
249	C₄×Dic₃	—	10	2	no	—
250	C₂×C₃⋊C₈	—	2	1	no	—
251	C₂×C₃⋊C₈	—	2	1	no	—
252	C₂×C₃⋊C₈	—	2	1	no	—
253	C₂×C₃⋊C₈	—	10	1	no	—
254	C₂×C₃⋊C₈	—	10	1	no	—
255	C₂×C₃⋊C₈	—	10	1	no	—
256	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
257	C₂²×D₅	—	3	2	no	—
258	C₂²×D₅	—	3	2	no	—
259	C₂²×D₅	—	3	2	no	—
260	C₂²×D₅	—	6	1	no	—
261	C₂²×D₅	—	6	1	no	—
262	C₂²×D₅	—	6	1	no	—
263	C₂²×D₅	—	6	1	no	—
264	C₂×C₄×C₅	—	3	2	no	—
265	C₂×C₄×C₅	—	3	2	no	—
266	C₂×C₄×C₅	—	6	1	no	—
267	C₂×C₄×C₅	—	6	1	no	—
268	C₂×C₄×C₅	—	6	1	no	—
269	C₂×C₄×C₅	—	6	1	no	—
270	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
271	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
272	C₂×C₄×C₅	#237	1	1	yes	characteristic
273	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
274	C₂×C₄×C₅	#239	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
276	C₂×Dic₅	—	2	1	no	—
277	C₂×Dic₅	—	2	1	no	—
278	C₂×Dic₅	—	3	2	no	—
279	C₂×Dic₅	—	6	1	no	—
280	C₂×Dic₅	—	6	1	no	—
281	C₂×Dic₅	D₃×C₈	1	2	yes	—
282	C₂×Dic₅	ΓL(1,𝔽₂₅)	1	2	yes	—
283	C₂×Dic₅	(C₂×D₃)⋊C₄	1	2	yes	—
284	C₂×Dic₅	(C₂×D₃)⋊C₄	1	2	yes	—
285	C₄×D₅	—	6	8	no	—
286	C₄×D₅	—	6	2	no	—
287	C₄×D₅	—	6	2	no	—
288	C₄×D₅	—	6	2	no	—
289	C₄×D₅	—	6	2	no	—
290	C₄×D₅	—	6	8	no	—
291	C₅×C₈	—	4	1	no	—
292	C₅×C₈	—	12	1	no	—
293	#168	—	4	1	no	—
294	#168	—	12	1	no	—
295	C₂³×C₄	—	15	1	no	—
296	C₂³×C₄	—	15	1	no	—
297	C₂³×C₄	—	15	1	no	—
298	C₂²×C₈	—	3	1	no	—
299	C₂²×C₈	—	5	1	no	—
300	C₂²×C₈	—	15	1	no	—
301	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
302	C₂×C₄²	—	3	1	no	—
303	C₂×C₄²	—	5	1	no	—
304	C₂×C₄²	—	15	1	no	—
305	C₂×C₄²	—	15	1	no	—
306	C₂×C₄²	—	30	2	no	—
307	C₂×C₄²	—	30	2	no	—
308	C₄⋊C₈	—	10	2	no	—
309	C₄⋊C₈	—	30	2	no	—
310	C₂²⋊C₈	—	30	2	no	—
311	C₂²⋊C₈	—	30	2	no	—
312	C₂×C₃×C₅	#380	1	1	yes	characteristic
313	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
314	C₂×C₃×C₅	#407	1	1	yes	characteristic
315	C₂×C₃×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
316	C₂×C₃×C₅	#423	1	1	yes	characteristic
317	C₂×C₃×C₅	#431	1	1	yes	characteristic
318	C₂×C₃×C₅	#432	1	1	yes	characteristic
319	D₁₅	—	2	4	no	—
320	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
321	C₂²×D₃	—	5	2	no	—
322	C₂²×D₃	—	5	2	no	—
323	C₂²×D₃	—	5	2	no	—
324	C₂²×D₃	—	10	1	no	—
325	C₂²×D₃	—	10	1	no	—
326	C₂²×D₃	—	10	1	no	—
327	C₂²×D₃	—	10	1	no	—
328	C₂×C₃×C₄	—	5	2	no	—
329	C₂×C₃×C₄	—	5	2	no	—
330	C₂×C₃×C₄	—	5	2	no	—
331	C₂×C₃×C₄	—	5	2	no	—
332	C₂×C₃×C₄	—	10	1	no	—
333	C₂×C₃×C₄	—	10	1	no	—
334	C₂×C₃×C₄	#709	1	1	yes	characteristic
335	C₂×C₃×C₄	#709	1	1	yes	characteristic
336	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
337	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
338	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
339	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
340	C₂×Dic₃	—	2	1	no	—
341	C₂×Dic₃	—	2	1	no	—
342	C₂×Dic₃	—	2	1	no	—
343	C₂×Dic₃	—	2	1	no	—
344	C₂×Dic₃	—	5	2	no	—
345	C₂×Dic₃	—	10	1	no	—
346	C₂×Dic₃	—	10	1	no	—
347	C₂×Dic₃	C₈×D₅	1	2	yes	—
348	C₂×Dic₃	#676	1	2	yes	—
349	C₄×D₃	—	10	8	no	—
350	C₄×D₃	—	10	8	no	—
351	C₄×D₃	—	10	2	no	—
352	C₄×D₃	—	10	2	no	—
353	C₄×D₃	—	10	2	no	—
354	C₄×D₃	—	10	2	no	—
355	C₃×C₈	—	4	1	no	—
356	C₃×C₈	—	20	1	no	—
357	C₃⋊C₈	—	4	1	no	—
358	C₃⋊C₈	—	20	1	no	—
359	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
360	C₂²×C₅	#892	1	1	yes	characteristic
361	C₂²×C₅	C₂×D₃×C₈	1	1	yes	characteristic
362	C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
363	C₂²×C₅	D₃×M₁₆	1	1	yes	characteristic
364	C₂²×C₅	D₃×M₁₆	1	1	yes	characteristic
365	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
366	C₂×D₅	—	3	4	no	—
367	C₂×D₅	—	6	2	no	—
368	C₂×D₅	—	6	2	no	—
369	C₂×D₅	—	6	2	no	—
370	C₂×D₅	—	6	2	no	—
371	C₂×D₅	—	6	2	no	—
372	C₂×D₅	—	6	2	no	—
373	C₄×C₅	—	6	2	no	—
374	C₄×C₅	—	6	2	no	—
375	C₄×C₅	#895	1	1	yes	characteristic
376	C₄×C₅	#897	1	1	yes	characteristic
377	C₄×C₅	#938	1	1	yes	characteristic
378	C₄×C₅	#946	1	1	yes	characteristic
379	Dic₅	—	2	2	no	—
380	Dic₅	—	6	2	no	—
381	Dic₅	(C₂×D₃)⋊C₈	1	4	yes	complemented
382	C₂⁴	—	15	1	no	—
383	C₂²×C₄	—	3	1	no	—
384	C₂²×C₄	—	3	1	no	—
385	C₂²×C₄	—	5	1	no	—
386	C₂²×C₄	—	5	1	no	—
387	C₂²×C₄	—	15	4	no	—
388	C₂²×C₄	—	15	1	no	—
389	C₂²×C₄	—	15	2	no	—
390	C₂²×C₄	—	15	2	no	—
391	C₂²×C₄	—	30	2	no	—
392	C₂²×C₄	—	30	2	no	—
393	C₂²×C₄	—	30	2	no	—
394	C₂²×C₄	—	30	2	no	—
395	C₂²×C₄	—	30	2	no	—
396	C₂²×C₄	—	30	1	no	—
397	C₂²×C₄	—	30	1	no	—
398	C₂²×C₄	—	30	1	no	—
399	C₂²×C₄	—	30	1	no	—
400	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	6	1	no	—
405	C₂×C₈	—	6	1	no	—
406	C₂×C₈	—	6	1	no	—
407	C₂×C₈	—	10	1	no	—
408	C₂×C₈	—	10	1	no	—
409	C₂×C₈	—	10	1	no	—
410	C₂×C₈	—	30	1	no	—
411	C₂×C₈	—	30	1	no	—
412	C₂×C₈	—	30	1	no	—
413	C₄²	—	5	2	no	—
414	C₄²	—	5	2	no	—
415	C₄²	—	6	1	no	—
416	C₄²	—	6	1	no	—
417	C₄²	—	30	2	no	—
418	C₄²	—	30	2	no	—
419	C₃×C₅	#1797	1	1	yes	characteristic, complemented, Hall
420	C₂²×C₃	#4018	1	1	yes	characteristic
421	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
422	C₂²×C₃	D₅×C₄⋊C₄	1	1	yes	characteristic
423	C₂²×C₃	C₂×C₈×D₅	1	1	yes	characteristic
424	C₂²×C₃	C₂×#676	1	1	yes	characteristic
425	C₂²×C₃	D₅×M₁₆	1	1	yes	characteristic
426	C₂²×C₃	D₅×M₁₆	1	1	yes	characteristic
427	C₂×D₃	—	5	4	no	—
428	C₂×D₃	—	10	2	no	—
429	C₂×D₃	—	10	2	no	—
430	C₂×D₃	—	10	2	no	—
431	C₂×D₃	—	10	2	no	—
432	C₂×D₃	—	10	2	no	—
433	C₂×D₃	—	10	2	no	—
434	C₃×C₄	—	5	4	no	—
435	C₃×C₄	—	10	2	no	—
436	C₃×C₄	#4030	1	1	yes	characteristic
437	C₃×C₄	#4030	1	1	yes	characteristic
438	C₃×C₄	#4042	1	1	yes	characteristic
439	C₃×C₄	#4042	1	1	yes	characteristic
440	Dic₃	—	2	2	no	—
441	Dic₃	—	2	2	no	—
442	Dic₃	—	10	2	no	—
443	C₂×C₅	D₃×C₄⋊C₈	1	1	yes	characteristic
444	C₂×C₅	#4833	1	1	yes	characteristic
445	C₂×C₅	#4835	1	1	yes	characteristic
446	C₂×C₅	#4837	1	1	yes	characteristic
447	C₂×C₅	#4987	1	1	yes	characteristic
448	C₂×C₅	C₂×(C₂×D₃)⋊C₈	1	1	yes	characteristic
449	C₂×C₅	#5126	1	1	yes	characteristic
450	D₅	—	6	4	no	—
451	C₂³	—	15	2	no	—
452	C₂³	—	15	2	no	—
453	C₂³	—	15	2	no	—
454	C₂³	—	30	1	no	—
455	C₂³	—	30	1	no	—
456	C₂³	—	30	1	no	—
457	C₂³	—	30	1	no	—
458	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
459	C₂×C₄	—	3	2	no	—
460	C₂×C₄	—	3	2	no	—
461	C₂×C₄	—	5	2	no	—
462	C₂×C₄	—	5	2	no	—
463	C₂×C₄	—	5	2	no	—
464	C₂×C₄	—	5	2	no	—
465	C₂×C₄	—	6	1	no	—
466	C₂×C₄	—	6	1	no	—
467	C₂×C₄	—	6	1	no	—
468	C₂×C₄	—	6	1	no	—
469	C₂×C₄	—	10	1	no	—
470	C₂×C₄	—	10	1	no	—
471	C₂×C₄	—	15	2	no	—
472	C₂×C₄	—	30	8	no	—
473	C₂×C₄	—	30	8	no	—
474	C₂×C₄	—	30	1	no	—
475	C₂×C₄	—	30	1	no	—
476	C₂×C₄	—	30	2	no	—
477	C₂×C₄	—	30	2	no	—
478	C₂×C₄	—	30	2	no	—
479	C₂×C₄	—	30	2	no	—
480	C₂×C₄	#6769	1	1	yes	characteristic
481	C₂×C₄	D₁₅⋊Q₈	1	1	yes	characteristic
482	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
483	C₂×C₄	#6779	1	1	yes	characteristic
484	C₂×C₄	D₅×#67	1	1	yes	characteristic
485	C₂×C₄	#6790	1	1	yes	characteristic
486	C₈	—	4	1	no	—
487	C₈	—	12	1	no	—
488	C₈	—	20	1	no	—
489	C₈	—	60	1	no	—
490	C₂×C₃	#64956	1	1	yes	characteristic
491	C₂×C₃	#64974	1	1	yes	characteristic
492	C₂×C₃	#64994	1	1	yes	characteristic
493	C₂×C₃	D₅×C₂²⋊C₈	1	1	yes	characteristic
494	C₂×C₃	#65015	1	1	yes	characteristic
495	C₂×C₃	D₅×C₄⋊C₈	1	1	yes	characteristic
496	C₂×C₃	#65126	1	1	yes	characteristic
497	D₃	—	10	4	no	—
498	C₅	#70475	1	1	yes	characteristic, complemented, Sylow
499	C₂²	—	15	4	no	—
500	C₂²	—	30	2	no	—
501	C₂²	—	30	2	no	—
502	C₂²	—	30	2	no	—
503	C₂²	—	30	2	no	—
504	C₂²	—	30	2	no	—
505	C₂²	—	30	2	no	—
506	C₂²	D₃×C₈×D₅	1	1	yes	characteristic
507	C₂²	D₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
508	C₂²	D₃×#676	1	1	yes	characteristic
509	C₂²	#91246	1	1	yes	characteristic
510	C₂²	#91403	1	1	yes	characteristic
511	C₂²	#91404	1	1	yes	characteristic
512	C₂²	D₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
513	C₄	—	5	4	no	—
514	C₄	—	6	2	no	—
515	C₄	—	6	2	no	—
516	C₄	—	10	2	no	—
517	C₄	—	30	2	no	—
518	C₄	#91411	1	1	yes	characteristic
519	C₄	#91419	1	1	yes	characteristic
520	C₄	#91420	1	1	yes	characteristic
521	C₄	#91533	1	1	yes	characteristic
522	C₃	#10599455	1	1	yes	characteristic, complemented, Sylow
523	C₂	—	30	4	no	—
524	C₂	#11747584	1	1	yes	characteristic
525	C₂	#11747585	1	1	yes	characteristic
526	C₂	#11747593	1	1	yes	characteristic
527	C₂	#11747594	1	1	yes	characteristic
528	C₂	D₅×(C₂×D₃)⋊C₈	1	1	yes	characteristic
529	C₂	#11748101	1	1	yes	characteristic
530	C₂	#11748876	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×D₃×D₅
commutator	C₂²×C₃×C₅	C₂²×C₈
Fitting	C₂²×C₃×C₅×C₈	C₂²
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×D₁₅	C₂×C₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	#1797
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×#3946	C₂	semidirect
4. C₂×#90982	C₂	semidirect
6. C₅×#4550	C₂	semidirect
7. #11745967	C₂	semidirect
31. C₂×#3946	D₃	semidirect
52. C₂×#1200	C₈	semidirect
77. #4550	D₅	semidirect
209. C₂×D₁₅	C₄⋊C₈	semidirect
216. C₃×Dic₅	C₂²⋊C₈	semidirect
381. Dic₅	(C₂×D₃)⋊C₈	semidirect
419. C₃×C₅	#1797	semidirect
498. C₅	#70475	semidirect
522. C₃	#10599455	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#1200	2
C₂×#91104	2
C₂×C₃×#3946	2
C₂×#90982	2
C₂×#90957	2
C₅×#4550	2
#11745967	2
#10599455	3
#70475	5