Subgroups — #13088985

Order 1440.

696 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624235	C₂	1	1	yes	maximal, characteristic, complemented
2	#67×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	#10624207	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3804	C₂	1	1	yes	maximal, characteristic, complemented
5	#10624165	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#1200	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#6782	C₂	1	1	yes	maximal, characteristic, complemented
8	#10624054	C₂	1	1	yes	maximal, characteristic, complemented
9	#10624053	C₂	1	1	yes	maximal, characteristic, complemented
10	#10624052	C₂	1	1	yes	maximal, characteristic, complemented
11	#10624049	C₂	1	1	yes	maximal, characteristic, complemented
12	#10624038	C₂	1	1	yes	maximal, characteristic, complemented
13	#10624033	C₂	1	1	yes	maximal, characteristic, complemented
14	#10624022	C₂	1	1	yes	maximal, characteristic, complemented
15	D₃×#1200	C₂	1	1	yes	maximal, characteristic, complemented
16	#92024	—	3	1	no	maximal
17	D₅×#235	—	3	1	no	maximal
18	C₂²×C₃×D₁₅	C₂²	1	1	yes	characteristic
19	C₂×(C₃⋊D₃)⋊D₅	C₂²	1	1	yes	characteristic
20	C₂×D₃×D₁₅	C₂²	1	1	yes	characteristic
21	#67184	C₂²	1	1	yes	characteristic, complemented
22	C₅×#638	C₂²	1	1	yes	characteristic, complemented
23	C₃×#1220	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₅×#67	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃²×Dic₅	C₂²	1	1	yes	characteristic, complemented
27	#67157	C₂²	1	1	yes	characteristic, complemented
28	#67156	C₂²	1	1	yes	characteristic, complemented
29	#67154	C₂²	1	1	yes	characteristic
30	#67153	C₂²	1	1	yes	characteristic, complemented
31	#67151	C₂²	1	1	yes	characteristic, complemented
32	#67151	C₂²	1	1	yes	characteristic, complemented
33	#67150	C₂²	1	1	yes	characteristic, complemented
34	#67149	C₂²	1	1	yes	characteristic, complemented
35	Dic₃×D₁₅	C₂²	1	1	yes	characteristic
36	Dic₃×D₁₅	C₂²	1	1	yes	characteristic, complemented
37	C₅×#627	C₂²	1	1	yes	characteristic, complemented
38	C₅×#626	C₂²	1	1	yes	characteristic, complemented
39	C₅×#624	C₂²	1	1	yes	characteristic, complemented
40	C₅×D₃×Dic₃	C₂²	1	1	yes	characteristic, complemented
41	#67141	C₂²	1	1	yes	characteristic, complemented
42	#67140	C₂²	1	1	yes	characteristic, complemented
43	#67137	C₂²	1	1	yes	characteristic, complemented
44	C₃⋊D₃×Dic₅	C₂²	1	1	yes	characteristic, complemented
45	C₃×#1204	C₂²	1	1	yes	characteristic, complemented
46	C₃×#1203	C₂²	1	1	yes	characteristic, complemented
47	C₃×#1200	C₂²	1	1	yes	characteristic
48	C₃×#1200	C₂²	1	1	yes	characteristic
49	C₃×#1200	C₂²	1	1	yes	characteristic, complemented
50	C₃×#1200	C₂²	1	1	yes	characteristic, complemented
51	C₃×#1200	C₂²	1	1	yes	characteristic, complemented
52	C₃×D₃×Dic₅	C₂²	1	1	yes	characteristic, complemented
53	D₃×#235	—	5	1	no	maximal, Hall
54	D₄×D₁₅	—	3	1	no	—
55	#6817	—	3	1	no	—
56	C₅×#237	—	3	1	no	—
57	C₅×#235	—	3	1	no	—
58	C₃×#711	—	3	1	no	—
59	C₂×C₃×C₄×D₅	—	3	1	no	—
60	#6790	—	3	1	no	—
61	#6790	—	3	1	no	—
62	D₅×#67	—	3	1	no	—
63	D₅×#67	—	3	1	no	—
64	C₂×#1200	—	3	1	no	—
65	C₂×#1200	D₃	1	1	yes	characteristic, complemented
66	#6782	—	3	1	no	—
67	#6782	—	3	1	no	—
68	#6782	—	3	1	no	—
69	#6782	—	6	1	no	—
70	#6782	D₃	1	1	yes	characteristic, complemented
71	#6779	—	3	1	no	—
72	#6779	—	3	1	no	—
73	D₅×D₁₂	—	3	1	no	—
74	C₄×D₃×D₅	—	3	1	no	—
75	C₄×D₃×D₅	—	3	1	no	—
76	C₄×D₃×D₅	—	3	1	no	—
77	#6773	—	3	1	no	—
78	#6773	—	3	1	no	—
79	#6772	—	3	1	no	—
80	#6771	—	3	1	no	—
81	#6771	—	3	1	no	—
82	D₁₅⋊Q₈	—	3	1	no	—
83	#6769	—	3	1	no	—
84	D₅×Dic₆	—	3	1	no	—
85	C₂²×C₃²×C₅	C₂³	1	1	yes	characteristic
86	C₂×C₃⋊D₁₅	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₃⋊D₃	C₂³	1	1	yes	characteristic
88	C₂×C₃×D₁₅	—	2	2	no	—
89	C₂×C₃×D₁₅	C₂³	1	1	yes	characteristic
90	C₂×C₃×D₁₅	C₂³	1	1	yes	characteristic
91	C₂×C₃×D₁₅	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₅×D₃	C₂³	1	1	yes	characteristic
93	(C₃⋊D₃)⋊D₅	—	2	2	no	—
94	D₃×D₁₅	—	2	2	no	—
95	C₃⋊Dic₁₅	C₂³	1	1	yes	characteristic
96	C₅×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
97	C₃×Dic₁₅	C₂³	1	1	yes	characteristic
98	C₃×C₅×Dic₃	C₂³	1	1	yes	characteristic
99	C₃×C₅×Dic₃	C₂³	1	1	yes	characteristic
100	C₃×C₅×Dic₃	C₂³	1	1	yes	characteristic
101	C₃²×Dic₅	C₂³	1	1	yes	characteristic
102	C₃²×Dic₅	C₂³	1	1	yes	characteristic
103	D₅×#41	—	9	1	no	Hall
104	#3828	—	5	1	no	—
105	C₃×#235	—	5	1	no	—
106	C₂×C₃×C₄×D₃	—	5	1	no	—
107	D₃×#67	—	5	1	no	—
108	D₃×#67	—	5	1	no	—
109	#3804	—	5	1	no	—
110	#3804	D₅	1	1	yes	characteristic, complemented
111	D₃×D₁₂	—	5	1	no	—
112	C₄×D₃²	—	5	1	no	—
113	C₄×D₃²	—	5	1	no	—
114	#3799	—	5	1	no	—
115	#3798	—	5	1	no	—
116	#3798	—	5	1	no	—
117	#3795	—	5	1	no	—
118	D₃×Dic₆	—	5	1	no	—
119	C₂²×D₁₅	—	3	1	no	—
120	C₂²×D₁₅	C₂×D₃	1	1	yes	characteristic
121	C₂²×C₃×D₅	—	3	1	no	—
122	C₂×D₃×D₅	—	3	1	no	—
123	C₂×D₃×D₅	—	3	1	no	—
124	C₂×D₃×D₅	—	3	1	no	—
125	C₃×C₅×D₄	—	3	1	no	—
126	C₂×C₃×C₄×C₅	—	3	1	no	—
127	#1220	—	3	1	no	—
128	#1220	—	3	1	no	—
129	#1220	—	3	1	no	—
130	#1220	—	6	1	no	—
131	#1220	C₂×D₃	1	1	yes	characteristic, complemented
132	D₆₀	—	3	1	no	—
133	D₆₀	—	3	1	no	—
134	C₄×D₁₅	—	3	1	no	—
135	C₄×D₁₅	—	3	1	no	—
136	C₄×D₁₅	—	3	1	no	—
137	Dic₃₀	—	3	1	no	—
138	C₅×#67	—	3	1	no	—
139	C₅×#67	—	3	1	no	—
140	C₅×#67	—	3	1	no	—
141	C₅×#67	—	6	1	no	—
142	C₅×#67	C₂×D₃	1	1	yes	characteristic, complemented
143	C₂×C₅×Dic₃	—	3	1	no	—
144	C₂×C₅×Dic₃	C₂×D₃	1	1	yes	characteristic, complemented
145	C₅×D₁₂	—	3	1	no	—
146	C₄×C₅×D₃	—	3	1	no	—
147	C₄×C₅×D₃	—	3	1	no	—
148	C₄×C₅×D₃	—	3	1	no	—
149	C₅×Dic₆	—	3	1	no	—
150	C₅×Dic₆	—	3	1	no	—
151	C₃×C₂²⋊D₅	—	3	1	no	—
152	C₃×C₂²⋊D₅	—	3	1	no	—
153	C₂×C₃×Dic₅	—	2	1	no	—
154	C₂×C₃×Dic₅	—	3	1	no	—
155	C₂×C₃×Dic₅	C₂×D₃	1	1	yes	characteristic, complemented
156	C₂×C₃×Dic₅	C₂×D₃	1	1	yes	characteristic, complemented
157	C₃×C₄×D₅	—	3	1	no	—
158	C₃×C₄×D₅	—	3	1	no	—
159	C₃×C₄×D₅	—	3	1	no	—
160	C₃×C₄×D₅	—	3	1	no	—
161	C₃×C₄×D₅	—	3	1	no	—
162	C₃×Dic₁₀	—	3	1	no	—
163	#1204	—	3	1	no	—
164	#1204	—	3	1	no	—
165	#1204	—	3	1	no	—
166	#1204	—	6	1	no	—
167	#1204	C₂×D₃	1	1	yes	characteristic, complemented
168	#1203	—	3	1	no	—
169	#1203	—	3	1	no	—
170	#1203	—	3	1	no	—
171	#1203	—	6	1	no	—
172	#1203	C₂×D₃	1	1	yes	characteristic, complemented
173	#1202	—	3	1	no	—
174	#1202	—	3	1	no	—
175	#1202	—	3	1	no	—
176	#1202	—	3	1	no	—
177	#1201	—	3	1	no	—
178	#1201	—	3	1	no	—
179	#1200	—	3	1	no	—
180	#1200	—	3	1	no	—
181	#1200	—	3	1	no	—
182	#1200	—	3	1	no	—
183	#1200	—	6	1	no	—
184	#1200	C₂×D₃	1	1	yes	characteristic
185	#1200	C₂×D₃	1	1	yes	characteristic
186	#1200	C₂×D₃	1	1	yes	characteristic, complemented
187	#1200	C₂×D₃	1	1	yes	characteristic, complemented
188	#1200	C₂×D₃	1	1	yes	characteristic, complemented
189	D₃×Dic₅	—	3	1	no	—
190	D₃×Dic₅	—	3	1	no	—
191	D₃×Dic₅	—	6	1	no	—
192	D₃×Dic₅	C₂×D₃	1	1	yes	characteristic, complemented
193	D₅×Dic₃	—	3	1	no	—
194	D₅×Dic₃	—	3	1	no	—
195	D₅×Dic₃	—	3	1	no	—
196	D₃×#41	—	15	1	no	—
197	C₂×#235	—	15	1	no	—
198	C₂×C₃²×C₅	—	2	1	no	—
199	C₂×C₃²×C₅	C₂⁴	1	1	yes	characteristic
200	C₃⋊D₁₅	—	2	1	no	—
201	C₅×C₃⋊D₃	—	2	1	no	—
202	C₃×D₁₅	—	2	1	no	—
203	C₃×D₁₅	—	2	1	no	—
204	C₃×D₁₅	#41	1	2	yes	complemented
205	C₃×C₅×D₃	—	2	1	no	—
206	C₅×#41	—	9	1	no	—
207	#713	—	9	1	no	—
208	Q₈×D₅	—	9	1	no	—
209	#711	—	3	1	no	—
210	#711	—	9	1	no	—
211	#711	—	9	1	no	—
212	D₄×D₅	—	9	1	no	—
213	D₄×D₅	—	9	1	no	—
214	D₄×D₅	—	9	1	no	—
215	#709	—	9	1	no	—
216	#709	—	9	1	no	—
217	#709	—	9	1	no	—
218	C₂×C₄×D₅	—	3	1	no	—
219	C₂×C₄×D₅	—	9	1	no	—
220	C₂×C₄×D₅	—	9	1	no	—
221	C₂²×C₃×D₃	—	5	1	no	—
222	C₂×D₃²	—	5	1	no	—
223	C₂×D₃²	—	5	1	no	—
224	C₂×C₃²×C₄	—	5	1	no	—
225	#638	—	5	1	no	—
226	#638	C₂×D₅	1	1	yes	characteristic, complemented
227	C₄⋊(C₃⋊D₃)	—	5	1	no	—
228	C₄×C₃⋊D₃	—	5	1	no	—
229	C₄×C₃⋊D₃	—	5	1	no	—
230	#634	—	5	1	no	—
231	C₃×#67	—	5	1	no	—
232	C₃×#67	C₂×D₅	1	1	yes	characteristic, complemented
233	C₂×C₃×Dic₃	C₂×D₅	1	1	yes	characteristic, complemented
234	C₃×D₁₂	—	5	1	no	—
235	C₃×C₄×D₃	—	5	1	no	—
236	C₃×C₄×D₃	—	5	1	no	—
237	C₃×C₄×D₃	—	5	1	no	—
238	C₃×C₄×D₃	—	5	1	no	—
239	C₃×C₄×D₃	—	5	1	no	—
240	C₃×C₄×D₃	—	5	1	no	—
241	C₃×Dic₆	—	5	1	no	—
242	#627	—	5	1	no	—
243	#627	C₂×D₅	1	1	yes	characteristic, complemented
244	#626	—	5	1	no	—
245	#626	—	5	1	no	—
246	#626	—	5	1	no	—
247	#626	C₂×D₅	1	1	yes	characteristic, complemented
248	#625	—	5	1	no	—
249	#625	—	5	1	no	—
250	#624	—	5	1	no	—
251	#624	C₂×D₅	1	1	yes	characteristic, complemented
252	D₃×Dic₃	—	5	1	no	—
253	D₃×Dic₃	—	5	1	no	—
254	D₃×Dic₃	—	5	1	no	—
255	D₃×Dic₃	C₂×D₅	1	1	yes	characteristic, complemented
256	C₂²×C₃×C₅	—	2	1	no	—
257	C₂²×C₃×C₅	—	3	1	no	—
258	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
259	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
260	C₂×D₁₅	—	2	2	no	—
261	C₂×D₁₅	—	3	1	no	—
262	C₂×D₁₅	—	3	1	no	—
263	C₂×D₁₅	—	6	1	no	—
264	C₂×D₁₅	—	6	2	no	—
265	C₂×D₁₅	C₂²×D₃	1	1	yes	characteristic
266	C₂×D₁₅	C₂²×D₃	1	1	yes	characteristic
267	C₂×D₁₅	C₂²×D₃	1	1	yes	characteristic
268	C₂×C₅×D₃	—	3	1	no	—
269	C₂×C₅×D₃	—	3	1	no	—
270	C₂×C₅×D₃	—	6	1	no	—
271	C₂×C₅×D₃	C₂²×D₃	1	1	yes	characteristic
272	C₂×C₃×D₅	—	3	1	no	—
273	C₂×C₃×D₅	—	3	1	no	—
274	C₂×C₃×D₅	—	3	1	no	—
275	C₂×C₃×D₅	—	6	2	no	—
276	D₃×D₅	—	6	2	no	—
277	D₃×D₅	—	6	2	no	—
278	D₃×D₅	—	6	2	no	—
279	C₃×C₄×C₅	—	3	1	no	—
280	C₃×C₄×C₅	—	3	1	no	—
281	C₃×C₄×C₅	—	3	1	no	—
282	Dic₁₅	—	3	1	no	—
283	Dic₁₅	—	3	1	no	—
284	Dic₁₅	—	6	1	no	—
285	Dic₁₅	C₂²×D₃	1	1	yes	characteristic
286	C₃×Dic₅	—	2	1	no	—
287	C₃×Dic₅	—	2	1	no	—
288	C₃×Dic₅	—	3	1	no	—
289	C₃×Dic₅	C₂²×D₃	1	1	yes	characteristic
290	C₃×Dic₅	C₂²×D₃	1	1	yes	characteristic
291	C₃×Dic₅	C₂²×D₃	1	1	yes	characteristic
292	C₃×Dic₅	C₂²×D₃	1	1	yes	characteristic
293	C₅×Dic₃	—	3	1	no	—
294	C₅×Dic₃	—	3	1	no	—
295	C₅×Dic₃	—	6	1	no	—
296	C₅×Dic₃	C₂²×D₃	1	1	yes	characteristic
297	C₅×Dic₃	C₂²×D₃	1	1	yes	characteristic
298	C₅×Dic₃	C₂²×D₃	1	1	yes	characteristic
299	C₃×#41	—	15	1	no	—
300	C₂²×C₃×C₄	—	15	1	no	—
301	C₂×#67	—	15	1	no	—
302	C₂×#67	—	15	1	no	—
303	#239	—	15	1	no	—
304	D₃×Q₈	—	15	1	no	—
305	#237	—	3	1	no	—
306	#237	—	15	1	no	—
307	#237	—	15	1	no	—
308	D₃×D₄	—	15	1	no	—
309	D₃×D₄	—	15	1	no	—
310	D₃×D₄	—	15	1	no	—
311	#235	—	3	1	no	—
312	#235	—	5	1	no	—
313	#235	—	15	1	no	—
314	#235	—	15	1	no	—
315	#235	—	15	1	no	—
316	#235	—	15	1	no	—
317	#235	—	15	1	no	—
318	#235	—	15	1	no	—
319	#235	—	15	1	no	—
320	#235	—	15	1	no	—
321	#235	—	15	1	no	—
322	#235	—	30	1	no	—
323	C₂×D₁₂	—	15	1	no	—
324	C₂×C₄×D₃	—	5	1	no	—
325	C₂×C₄×D₃	—	15	1	no	—
326	C₂×C₄×D₃	—	15	1	no	—
327	C₂×C₄×D₃	—	15	1	no	—
328	C₂×C₄×D₃	—	15	1	no	—
329	C₂×Dic₆	—	15	1	no	—
330	C₃²×C₅	C₂×#41	1	1	yes	characteristic, complemented, Hall
331	C₂²×D₅	—	3	1	no	—
332	C₂²×D₅	—	9	1	no	—
333	C₂²×D₅	—	9	1	no	—
334	C₅×Q₈	—	9	1	no	—
335	C₅×D₄	—	3	1	no	—
336	C₅×D₄	—	9	1	no	—
337	C₅×D₄	—	9	1	no	—
338	C₂×C₄×C₅	—	3	1	no	—
339	C₂×C₄×C₅	—	9	1	no	—
340	C₂×C₄×C₅	—	9	1	no	—
341	C₂²⋊D₅	—	3	1	no	—
342	C₂²⋊D₅	—	3	1	no	—
343	C₂²⋊D₅	—	9	1	no	—
344	C₂²⋊D₅	—	9	1	no	—
345	C₂²⋊D₅	—	9	1	no	—
346	C₂²⋊D₅	—	9	1	no	—
347	C₂×Dic₅	—	3	1	no	—
348	C₂×Dic₅	—	9	1	no	—
349	C₂×Dic₅	D₃²	1	1	yes	characteristic, complemented
350	D₂₀	—	9	1	no	—
351	D₂₀	—	9	1	no	—
352	D₂₀	—	9	1	no	—
353	C₄×D₅	—	3	1	no	—
354	C₄×D₅	—	3	1	no	—
355	C₄×D₅	—	3	1	no	—
356	C₄×D₅	—	3	1	no	—
357	C₄×D₅	—	3	1	no	—
358	C₄×D₅	—	9	1	no	—
359	C₄×D₅	—	9	1	no	—
360	C₄×D₅	—	9	1	no	—
361	C₄×D₅	—	9	1	no	—
362	C₄×D₅	—	9	1	no	—
363	Dic₁₀	—	3	1	no	—
364	Dic₁₀	—	9	1	no	—
365	Dic₁₀	—	9	1	no	—
366	C₂²×C₃²	C₂²×D₅	1	1	yes	characteristic
367	C₂×C₃⋊D₃	—	5	1	no	—
368	C₂×C₃⋊D₃	C₂²×D₅	1	1	yes	characteristic
369	C₂×C₃×D₃	—	5	1	no	—
370	C₂×C₃×D₃	—	5	1	no	—
371	C₂×C₃×D₃	—	5	1	no	—
372	C₂×C₃×D₃	—	10	2	no	—
373	C₂×C₃×D₃	C₂²×D₅	1	1	yes	characteristic
374	D₃²	—	10	2	no	—
375	D₃²	—	10	2	no	—
376	C₃²×C₄	—	5	1	no	—
377	C₃²×C₄	—	5	1	no	—
378	C₃⋊Dic₃	—	5	1	no	—
379	C₃⋊Dic₃	C₂²×D₅	1	1	yes	characteristic
380	C₃×Dic₃	—	5	1	no	—
381	C₃×Dic₃	C₂²×D₅	1	1	yes	characteristic
382	C₃×Dic₃	C₂²×D₅	1	1	yes	characteristic
383	C₃×Dic₃	C₂²×D₅	1	1	yes	characteristic
384	C₂×#41	—	45	1	no	Sylow
385	C₂×C₃×C₅	—	2	1	no	—
386	C₂×C₃×C₅	—	2	1	no	—
387	C₂×C₃×C₅	—	2	1	no	—
388	C₂×C₃×C₅	—	4	1	no	—
389	C₂×C₃×C₅	—	6	1	no	—
390	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
391	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
392	D₁₅	—	2	1	no	—
393	D₁₅	—	2	1	no	—
394	D₁₅	—	6	1	no	—
395	D₁₅	—	6	1	no	—
396	D₁₅	—	12	1	no	—
397	D₁₅	#235	1	2	yes	complemented
398	C₃×D₅	—	3	2	no	—
399	C₃×D₅	—	6	1	no	—
400	C₃×D₅	—	6	1	no	—
401	C₅×D₃	—	2	1	no	—
402	C₅×D₃	—	6	1	no	—
403	C₅×D₃	—	6	1	no	—
404	C₅×D₃	—	12	1	no	—
405	C₂³×C₃	—	15	1	no	—
406	C₂²×D₃	—	5	1	no	—
407	C₂²×D₃	—	15	1	no	—
408	C₂²×D₃	—	15	1	no	—
409	C₂²×D₃	—	15	1	no	—
410	C₂²×D₃	—	15	1	no	—
411	C₃×Q₈	—	15	1	no	—
412	C₃×D₄	—	3	1	no	—
413	C₃×D₄	—	15	1	no	—
414	C₃×D₄	—	15	1	no	—
415	C₂×C₃×C₄	—	3	1	no	—
416	C₂×C₃×C₄	—	5	1	no	—
417	C₂×C₃×C₄	—	5	1	no	—
418	C₂×C₃×C₄	—	10	1	no	—
419	C₂×C₃×C₄	—	15	1	no	—
420	C₂×C₃×C₄	—	15	1	no	—
421	C₂×C₃×C₄	—	15	1	no	—
422	C₂×C₃×C₄	—	15	1	no	—
423	C₂×C₃×C₄	—	15	1	no	—
424	C₂×C₃×C₄	—	15	1	no	—
425	#67	—	3	1	no	—
426	#67	—	3	1	no	—
427	#67	—	3	1	no	—
428	#67	—	5	1	no	—
429	#67	—	6	1	no	—
430	#67	—	15	1	no	—
431	#67	—	15	1	no	—
432	#67	—	15	1	no	—
433	#67	—	15	1	no	—
434	#67	—	15	1	no	—
435	#67	—	15	1	no	—
436	#67	—	15	1	no	—
437	#67	—	15	1	no	—
438	#67	—	15	1	no	—
439	#67	—	30	1	no	—
440	#67	D₃×D₅	1	1	yes	characteristic, complemented
441	C₂×Dic₃	—	3	1	no	—
442	C₂×Dic₃	—	15	1	no	—
443	C₂×Dic₃	—	15	1	no	—
444	C₂×Dic₃	—	15	1	no	—
445	C₂×Dic₃	D₃×D₅	1	1	yes	characteristic, complemented
446	D₁₂	—	3	1	no	—
447	D₁₂	—	5	1	no	—
448	D₁₂	—	15	1	no	—
449	D₁₂	—	15	1	no	—
450	D₁₂	—	15	1	no	—
451	D₁₂	—	15	1	no	—
452	D₁₂	—	15	1	no	—
453	D₁₂	—	30	1	no	—
454	C₄×D₃	—	3	1	no	—
455	C₄×D₃	—	3	1	no	—
456	C₄×D₃	—	3	1	no	—
457	C₄×D₃	—	5	1	no	—
458	C₄×D₃	—	5	1	no	—
459	C₄×D₃	—	5	1	no	—
460	C₄×D₃	—	5	1	no	—
461	C₄×D₃	—	5	1	no	—
462	C₄×D₃	—	5	1	no	—
463	C₄×D₃	—	15	1	no	—
464	C₄×D₃	—	15	1	no	—
465	C₄×D₃	—	15	1	no	—
466	C₄×D₃	—	15	1	no	—
467	C₄×D₃	—	15	1	no	—
468	C₄×D₃	—	15	1	no	—
469	C₄×D₃	—	15	1	no	—
470	C₄×D₃	—	15	1	no	—
471	C₄×D₃	—	15	1	no	—
472	C₄×D₃	—	30	1	no	—
473	C₄×D₃	—	30	1	no	—
474	Dic₆	—	3	1	no	—
475	Dic₆	—	3	1	no	—
476	Dic₆	—	5	1	no	—
477	Dic₆	—	15	1	no	—
478	Dic₆	—	15	1	no	—
479	Dic₆	—	15	1	no	—
480	Dic₆	—	15	1	no	—
481	Dic₆	—	30	1	no	—
482	C₂²×C₅	—	3	1	no	—
483	C₂²×C₅	—	9	1	no	—
484	C₂²×C₅	C₂×D₃²	1	1	yes	characteristic
485	C₂×D₅	—	3	1	no	—
486	C₂×D₅	—	3	1	no	—
487	C₂×D₅	—	3	1	no	—
488	C₂×D₅	—	6	2	no	—
489	C₂×D₅	—	9	1	no	—
490	C₂×D₅	—	18	2	no	—
491	C₂×D₅	—	18	2	no	—
492	C₄×C₅	—	3	1	no	—
493	C₄×C₅	—	3	1	no	—
494	C₄×C₅	—	3	1	no	—
495	C₄×C₅	—	9	1	no	—
496	Dic₅	—	3	1	no	—
497	Dic₅	—	9	1	no	—
498	Dic₅	C₂×D₃²	1	1	yes	characteristic
499	Dic₅	C₂×D₃²	1	1	yes	characteristic
500	C₂×C₃²	—	2	1	no	—
501	C₂×C₃²	C₂³×D₅	1	1	yes	characteristic
502	C₃⋊D₃	—	2	1	no	—
503	C₃⋊D₃	—	10	1	no	—
504	C₃×D₃	—	2	1	no	—
505	C₃×D₃	—	5	2	no	—
506	C₃×D₃	—	10	1	no	—
507	C₃×D₃	—	10	1	no	—
508	#41	—	9	1	no	—
509	#41	—	15	1	no	—
510	#41	—	45	1	no	—
511	#41	—	45	1	no	—
512	#41	—	45	1	no	—
513	#41	—	45	1	no	—
514	#41	—	45	1	no	—
515	#41	—	45	1	no	—
516	C₂×Q₈	—	45	1	no	—
517	C₂×D₄	—	45	1	no	—
518	C₂×D₄	—	45	1	no	—
519	C₂×D₄	—	45	1	no	—
520	C₂²×C₄	—	15	1	no	—
521	C₂²×C₄	—	45	1	no	—
522	C₂²×C₄	—	45	1	no	—
523	C₃×C₅	—	2	1	no	—
524	C₃×C₅	C₂×#235	1	1	yes	characteristic, complemented
525	C₃×C₅	D₃×#41	1	1	yes	characteristic, complemented
526	C₂²×C₃	—	2	1	no	—
527	C₂²×C₃	—	3	1	no	—
528	C₂²×C₃	—	15	1	no	—
529	C₂²×C₃	—	15	1	no	—
530	C₂²×C₃	—	15	1	no	—
531	C₂²×C₃	—	30	2	no	—
532	C₂²×C₃	C₂×D₃×D₅	1	1	yes	characteristic
533	C₂²×C₃	C₂×D₃×D₅	1	1	yes	characteristic
534	C₂×D₃	—	3	1	no	—
535	C₂×D₃	—	3	1	no	—
536	C₂×D₃	—	5	1	no	—
537	C₂×D₃	—	5	1	no	—
538	C₂×D₃	—	5	1	no	—
539	C₂×D₃	—	6	1	no	—
540	C₂×D₃	—	10	2	no	—
541	C₂×D₃	—	15	1	no	—
542	C₂×D₃	—	15	1	no	—
543	C₂×D₃	—	30	1	no	—
544	C₂×D₃	—	30	2	no	—
545	C₂×D₃	—	30	2	no	—
546	C₂×D₃	—	30	2	no	—
547	C₂×D₃	—	30	2	no	—
548	C₂×D₃	C₂×D₃×D₅	1	1	yes	characteristic
549	C₃×C₄	—	3	1	no	—
550	C₃×C₄	—	3	1	no	—
551	C₃×C₄	—	3	1	no	—
552	C₃×C₄	—	5	1	no	—
553	C₃×C₄	—	5	1	no	—
554	C₃×C₄	—	5	1	no	—
555	C₃×C₄	—	5	1	no	—
556	C₃×C₄	—	10	1	no	—
557	C₃×C₄	—	10	1	no	—
558	C₃×C₄	—	15	1	no	—
559	Dic₃	—	3	1	no	—
560	Dic₃	—	3	1	no	—
561	Dic₃	—	5	1	no	—
562	Dic₃	—	6	1	no	—
563	Dic₃	—	15	1	no	—
564	Dic₃	—	15	1	no	—
565	Dic₃	—	30	1	no	—
566	Dic₃	C₂×D₃×D₅	1	1	yes	characteristic
567	Dic₃	C₂×D₃×D₅	1	1	yes	characteristic
568	Dic₃	C₂×D₃×D₅	1	1	yes	characteristic
569	C₂×C₅	—	2	1	no	—
570	C₂×C₅	—	6	1	no	—
571	C₂×C₅	—	18	1	no	—
572	C₂×C₅	C₂²×D₃²	1	1	yes	characteristic
573	D₅	—	3	2	no	—
574	D₅	—	6	1	no	—
575	D₅	—	6	1	no	—
576	D₅	—	18	1	no	—
577	C₃²	D₅×#41	1	1	yes	characteristic, complemented, Sylow
578	C₂³	—	15	1	no	—
579	C₂³	—	45	1	no	—
580	C₂³	—	45	1	no	—
581	Q₈	—	9	1	no	—
582	Q₈	—	15	1	no	—
583	Q₈	—	45	1	no	—
584	Q₈	—	45	1	no	—
585	D₄	—	3	1	no	—
586	D₄	—	9	1	no	—
587	D₄	—	9	1	no	—
588	D₄	—	15	1	no	—
589	D₄	—	15	1	no	—
590	D₄	—	45	1	no	—
591	D₄	—	45	1	no	—
592	D₄	—	45	1	no	—
593	D₄	—	45	1	no	—
594	D₄	—	45	1	no	—
595	D₄	—	45	1	no	—
596	D₄	—	45	1	no	—
597	C₂×C₄	—	3	1	no	—
598	C₂×C₄	—	5	1	no	—
599	C₂×C₄	—	9	1	no	—
600	C₂×C₄	—	9	1	no	—
601	C₂×C₄	—	15	1	no	—
602	C₂×C₄	—	15	1	no	—
603	C₂×C₄	—	15	1	no	—
604	C₂×C₄	—	15	1	no	—
605	C₂×C₄	—	15	1	no	—
606	C₂×C₄	—	15	1	no	—
607	C₂×C₄	—	45	1	no	—
608	C₂×C₄	—	45	1	no	—
609	C₂×C₄	—	45	1	no	—
610	C₂×C₄	—	45	1	no	—
611	C₂×C₄	—	45	1	no	—
612	C₂×C₄	—	45	1	no	—
613	C₂×C₃	—	2	1	no	—
614	C₂×C₃	—	2	1	no	—
615	C₂×C₃	—	2	1	no	—
616	C₂×C₃	—	4	1	no	—
617	C₂×C₃	—	6	1	no	—
618	C₂×C₃	—	15	2	no	—
619	C₂×C₃	—	30	1	no	—
620	C₂×C₃	—	30	1	no	—
621	C₂×C₃	C₂²×D₃×D₅	1	1	yes	characteristic
622	C₂×C₃	C₂²×D₃×D₅	1	1	yes	characteristic
623	D₃	—	2	1	no	—
624	D₃	—	5	2	no	—
625	D₃	—	6	1	no	—
626	D₃	—	6	1	no	—
627	D₃	—	10	1	no	—
628	D₃	—	10	1	no	—
629	D₃	—	12	1	no	—
630	D₃	—	30	1	no	—
631	D₃	—	30	1	no	—
632	D₃	—	60	1	no	—
633	C₅	D₃×#235	1	1	yes	characteristic, complemented, Sylow
634	C₂²	—	3	1	no	—
635	C₂²	—	9	1	no	—
636	C₂²	—	15	1	no	—
637	C₂²	—	15	1	no	—
638	C₂²	—	15	1	no	—
639	C₂²	—	30	2	no	—
640	C₂²	—	45	1	no	—
641	C₂²	—	90	2	no	—
642	C₂²	—	90	2	no	—
643	C₂²	D₃²×D₅	1	1	yes	characteristic
644	C₄	—	3	1	no	—
645	C₄	—	3	1	no	—
646	C₄	—	3	1	no	—
647	C₄	—	5	1	no	—
648	C₄	—	5	1	no	—
649	C₄	—	9	1	no	—
650	C₄	—	15	1	no	—
651	C₄	—	45	1	no	—
652	C₃	—	2	1	no	—
653	C₃	D₅×#235	1	1	yes	characteristic, complemented
654	C₃	#92024	1	1	yes	characteristic, complemented
655	C₂	—	2	1	no	—
656	C₂	—	6	1	no	—
657	C₂	—	15	2	no	—
658	C₂	—	18	1	no	—
659	C₂	—	30	1	no	—
660	C₂	—	30	1	no	—
661	C₂	—	90	1	no	—
662	C₂	C₂×D₃²×D₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₃²×D₅
commutator, socle, cosocle	C₂×C₃²×C₅	C₂⁴
Fitting	C₂²×C₃²×C₅	C₂³
hypercenter	C₂²	D₃²×D₅
hypocenter	C₃²×C₅	C₂×#41
LCS	G ▷ C₂×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₂ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. #10624235	C₂	semidirect
2. #67×D₁₅	C₂	semidirect
3. #10624207	C₂	semidirect
4. C₅×#3804	C₂	semidirect
5. #10624165	C₂	semidirect
6. C₂×C₃×#1200	C₂	semidirect
7. C₃×#6782	C₂	semidirect
8. #10624054	C₂	semidirect
9. #10624053	C₂	semidirect
10. #10624052	C₂	semidirect
11. #10624049	C₂	semidirect
12. #10624038	C₂	semidirect
13. #10624033	C₂	semidirect
14. #10624022	C₂	semidirect
15. D₃×#1200	C₂	semidirect
21. #67184	C₂²	semidirect
22. C₅×#638	C₂²	semidirect
23. C₃×#1220	C₂²	semidirect
24. C₃×C₅×#67	C₂²	semidirect
25. C₂×C₃×C₅×Dic₃	C₂²	semidirect
26. C₂×C₃²×Dic₅	C₂²	semidirect
27. #67157	C₂²	semidirect
28. #67156	C₂²	semidirect
30. #67153	C₂²	semidirect
31. #67151	C₂²	semidirect
32. #67151	C₂²	semidirect
33. #67150	C₂²	semidirect
34. #67149	C₂²	semidirect
36. Dic₃×D₁₅	C₂²	semidirect
37. C₅×#627	C₂²	semidirect
38. C₅×#626	C₂²	semidirect
39. C₅×#624	C₂²	semidirect
40. C₅×D₃×Dic₃	C₂²	semidirect
41. #67141	C₂²	semidirect
42. #67140	C₂²	semidirect
43. #67137	C₂²	semidirect
44. C₃⋊D₃×Dic₅	C₂²	semidirect
45. C₃×#1204	C₂²	semidirect
46. C₃×#1203	C₂²	semidirect
49. C₃×#1200	C₂²	semidirect
50. C₃×#1200	C₂²	semidirect
51. C₃×#1200	C₂²	semidirect
52. C₃×D₃×Dic₅	C₂²	semidirect
65. C₂×#1200	D₃	semidirect
70. #6782	D₃	semidirect
110. #3804	D₅	semidirect
131. #1220	C₂×D₃	semidirect
142. C₅×#67	C₂×D₃	semidirect
144. C₂×C₅×Dic₃	C₂×D₃	semidirect
155. C₂×C₃×Dic₅	C₂×D₃	semidirect
156. C₂×C₃×Dic₅	C₂×D₃	semidirect
167. #1204	C₂×D₃	semidirect
172. #1203	C₂×D₃	semidirect
186. #1200	C₂×D₃	semidirect
187. #1200	C₂×D₃	semidirect
188. #1200	C₂×D₃	semidirect
192. D₃×Dic₅	C₂×D₃	semidirect
204. C₃×D₁₅	#41	semidirect
226. #638	C₂×D₅	semidirect
232. C₃×#67	C₂×D₅	semidirect
233. C₂×C₃×Dic₃	C₂×D₅	semidirect
243. #627	C₂×D₅	semidirect
247. #626	C₂×D₅	semidirect
251. #624	C₂×D₅	semidirect
255. D₃×Dic₃	C₂×D₅	semidirect
330. C₃²×C₅	C₂×#41	semidirect
349. C₂×Dic₅	D₃²	semidirect
397. D₁₅	#235	semidirect
440. #67	D₃×D₅	semidirect
445. C₂×Dic₃	D₃×D₅	semidirect
524. C₃×C₅	C₂×#235	semidirect
525. C₃×C₅	D₃×#41	semidirect
577. C₃²	D₅×#41	semidirect
633. C₅	D₃×#235	semidirect
653. C₃	D₅×#235	semidirect
654. C₃	#92024	semidirect

Maximal subgroups

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

subgroup	index
#10624235	2
#67×D₁₅	2
#10624207	2
C₅×#3804	2
#10624165	2
C₂×C₃×#1200	2
C₃×#6782	2
#10624054	2
#10624053	2
#10624052	2
#10624049	2
#10624038	2
#10624033	2
#10624022	2
D₃×#1200	2
#92024	3
D₅×#235	3
D₃×#235	5