Subgroups — #11756417

Order 960.

496 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	#91826	C₂	1	1	yes	maximal, characteristic
3	D₄×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#6714	C₂	1	1	yes	maximal, characteristic, complemented
5	#91815	C₂	1	1	yes	maximal, characteristic, complemented
6	#91787	C₂	1	1	yes	maximal, characteristic, complemented
7	#91787	C₂	1	1	yes	maximal, characteristic, complemented
8	#91786	C₂	1	1	yes	maximal, characteristic, complemented
9	#91781	C₂	1	1	yes	maximal, characteristic, complemented
10	#91775	C₂	1	1	yes	maximal, characteristic, complemented
11	#91774	C₂	1	1	yes	maximal, characteristic, complemented
12	#91772	C₂	1	1	yes	maximal, characteristic, complemented
13	#91770	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₄×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
15	#91767	C₂	1	1	yes	maximal, characteristic, complemented
16	#65992	—	3	1	no	maximal, Hall
17	C₂³×D₁₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
20	C₂×#1220	C₂²	1	1	yes	characteristic
21	C₂×#1220	C₂²	1	1	yes	characteristic
22	C₂²×Dic₁₅	C₂²	1	1	yes	characteristic
23	C₂²×Dic₁₅	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄×D₁₅	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₁₅	C₂²	1	1	yes	characteristic
26	C₂×Dic₃₀	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	#6719	C₂²	1	1	yes	characteristic
33	#6719	C₂²	1	1	yes	characteristic
34	#6719	C₂²	1	1	yes	characteristic, complemented
35	#6714	C₂²	1	1	yes	characteristic
36	#6714	C₂²	1	1	yes	characteristic
37	#6714	C₂²	1	1	yes	characteristic
38	#6714	C₂²	1	1	yes	characteristic
39	#6714	C₂²	1	1	yes	characteristic
40	#6714	C₂²	1	1	yes	characteristic
41	#6714	C₂²	1	1	yes	characteristic
42	#6714	C₂²	1	1	yes	characteristic
43	C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic, complemented
44	C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic, complemented
45	C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic, complemented
46	C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic, complemented
47	#6712	C₂²	1	1	yes	characteristic, complemented
48	#6712	C₂²	1	1	yes	characteristic, complemented
49	C₄×Dic₁₅	C₂²	1	1	yes	characteristic, complemented
50	C₄×Dic₁₅	C₂²	1	1	yes	characteristic, complemented
51	C₄×Dic₁₅	C₂²	1	1	yes	characteristic, complemented
52	#5658	—	5	1	no	maximal, Hall
53	C₅×#123	D₃	1	1	yes	characteristic, complemented
54	#4083	—	3	1	no	—
55	D₄×Dic₅	—	3	1	no	—
56	C₂×#685	—	3	1	no	—
57	#4072	—	3	1	no	—
58	#4044	—	3	1	no	—
59	#4044	—	3	1	no	—
60	#4043	—	3	1	no	—
61	#4038	—	3	1	no	—
62	#4032	—	3	1	no	—
63	#4031	—	3	1	no	—
64	#4029	—	3	1	no	—
65	#4027	—	3	1	no	—
66	D₅×C₂²⋊C₄	—	3	1	no	—
67	#4024	—	3	1	no	—
68	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
69	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
70	C₂²×D₁₅	—	2	2	no	—
71	C₂²×D₁₅	—	2	2	no	—
72	C₂²×D₁₅	—	4	1	no	—
73	C₂²×D₁₅	C₂³	1	1	yes	characteristic
74	C₂²×D₁₅	C₂³	1	1	yes	characteristic
75	C₃×C₅×D₄	—	2	2	no	—
76	C₂×C₃×C₄×C₅	—	2	2	no	—
77	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	#1220	—	2	2	no	—
83	#1220	—	4	1	no	—
84	C₂×Dic₁₅	—	4	1	no	—
85	C₂×Dic₁₅	—	4	1	no	—
86	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
87	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
88	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
89	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
90	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
91	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
92	C₄×D₁₅	—	2	2	no	—
93	C₄×D₁₅	—	4	1	no	—
94	Dic₃₀	—	4	1	no	—
95	C₃×#123	D₅	1	1	yes	characteristic, complemented
96	#937	—	5	1	no	—
97	D₄×Dic₃	—	5	1	no	—
98	C₂×(C₂×D₃)⋊C₄	—	5	1	no	—
99	#926	—	5	1	no	—
100	#898	—	5	1	no	—
101	#898	—	5	1	no	—
102	#897	—	5	1	no	—
103	#892	—	5	1	no	—
104	#886	—	5	1	no	—
105	#885	—	5	1	no	—
106	#883	—	5	1	no	—
107	#67⋊C₄	—	5	1	no	—
108	D₃×C₂²⋊C₄	—	5	1	no	—
109	#878	—	5	1	no	—
110	C₂³×D₅	—	3	1	no	—
111	C₂×C₅×D₄	C₂×D₃	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic
113	C₂×C₂²⋊D₅	—	3	1	no	—
114	C₂×C₂²⋊D₅	—	3	1	no	—
115	C₂²×Dic₅	—	3	1	no	—
116	C₂²×Dic₅	—	3	1	no	—
117	C₂×C₄×D₅	—	3	1	no	—
118	C₂×C₄×D₅	—	3	1	no	—
119	C₂×Dic₁₀	—	3	1	no	—
120	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
121	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
122	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
123	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
124	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
125	C₂²⋊Dic₅	—	3	1	no	—
126	C₂²⋊Dic₅	—	3	1	no	—
127	C₂²⋊Dic₅	—	3	1	no	—
128	#685	—	3	1	no	—
129	#685	—	3	1	no	—
130	#685	—	3	1	no	—
131	#685	—	3	1	no	—
132	#685	—	3	1	no	—
133	#685	—	3	1	no	—
134	#685	—	3	1	no	—
135	#685	—	3	1	no	—
136	C₄⋊Dic₅	—	3	1	no	—
137	C₄⋊Dic₅	—	3	1	no	—
138	C₄⋊Dic₅	—	3	1	no	—
139	C₄⋊Dic₅	—	3	1	no	—
140	#683	—	3	1	no	—
141	#683	—	3	1	no	—
142	C₄×Dic₅	—	3	1	no	—
143	C₄×Dic₅	—	3	1	no	—
144	C₄×Dic₅	—	3	1	no	—
145	#551	—	15	1	no	Sylow
146	C₂²×C₃×C₅	—	2	1	no	—
147	C₂²×C₃×C₅	—	2	1	no	—
148	C₂²×C₃×C₅	—	2	1	no	—
149	C₂²×C₃×C₅	—	2	1	no	—
150	C₂²×C₃×C₅	—	2	1	no	—
151	C₂²×C₃×C₅	#41	1	2	yes	—
152	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
153	C₂×D₁₅	—	2	1	no	—
154	C₂×D₁₅	—	2	1	no	—
155	C₂×D₁₅	—	2	1	no	—
156	C₂×D₁₅	—	2	1	no	—
157	C₂×D₁₅	—	2	1	no	—
158	C₂×D₁₅	—	4	4	no	—
159	C₂×D₁₅	#41	1	2	yes	—
160	C₃×C₄×C₅	—	2	1	no	—
161	C₃×C₄×C₅	—	2	1	no	—
162	C₃×C₄×C₅	—	2	1	no	—
163	C₃×C₄×C₅	—	2	1	no	—
164	C₃×C₄×C₅	—	2	1	no	—
165	Dic₁₅	—	2	1	no	—
166	Dic₁₅	—	2	1	no	—
167	Dic₁₅	—	2	1	no	—
168	Dic₁₅	—	2	1	no	—
169	Dic₁₅	—	2	1	no	—
170	Dic₁₅	—	2	1	no	—
171	C₂³×D₃	—	5	1	no	—
172	C₂×C₃×D₄	C₂×D₅	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂×D₅	1	1	yes	characteristic
174	C₂×#67	—	5	1	no	—
175	C₂×#67	—	5	1	no	—
176	C₂²×Dic₃	—	5	1	no	—
177	C₂²×Dic₃	—	5	1	no	—
178	C₂×C₄×D₃	—	5	1	no	—
179	C₂×C₄×D₃	—	5	1	no	—
180	C₂×Dic₆	—	5	1	no	—
181	C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
182	C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
183	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
184	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
185	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
186	#217	—	5	1	no	—
187	#217	—	5	1	no	—
188	#217	—	5	1	no	—
189	(C₂×D₃)⋊C₄	—	5	1	no	—
190	(C₂×D₃)⋊C₄	—	5	1	no	—
191	(C₂×D₃)⋊C₄	—	5	1	no	—
192	(C₂×D₃)⋊C₄	—	5	1	no	—
193	(C₂×D₃)⋊C₄	—	5	1	no	—
194	(C₂×D₃)⋊C₄	—	5	1	no	—
195	(C₂×D₃)⋊C₄	—	5	1	no	—
196	(C₂×D₃)⋊C₄	—	5	1	no	—
197	C₄⋊Dic₃	—	5	1	no	—
198	C₄⋊Dic₃	—	5	1	no	—
199	C₄⋊Dic₃	—	5	1	no	—
200	C₄⋊Dic₃	—	5	1	no	—
201	Dic₃⋊C₄	—	5	1	no	—
202	Dic₃⋊C₄	—	5	1	no	—
203	C₄×Dic₃	—	5	1	no	—
204	C₄×Dic₃	—	5	1	no	—
205	C₄×Dic₃	—	5	1	no	—
206	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
207	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
208	C₂²×D₅	—	3	1	no	—
209	C₂²×D₅	—	3	1	no	—
210	C₂²×D₅	—	6	2	no	—
211	C₂²×D₅	—	6	2	no	—
212	C₂²×D₅	—	12	1	no	—
213	C₅×D₄	—	2	2	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
220	C₂²⋊D₅	—	6	2	no	—
221	C₂²⋊D₅	—	12	1	no	—
222	C₂×Dic₅	—	3	1	no	—
223	C₂×Dic₅	—	3	1	no	—
224	C₂×Dic₅	—	3	1	no	—
225	C₂×Dic₅	—	3	1	no	—
226	C₂×Dic₅	—	3	1	no	—
227	C₂×Dic₅	—	3	1	no	—
228	C₂×Dic₅	—	12	1	no	—
229	C₂×Dic₅	—	12	1	no	—
230	C₄×D₅	—	6	2	no	—
231	C₄×D₅	—	12	1	no	—
232	Dic₁₀	—	12	1	no	—
233	#126	—	15	1	no	—
234	#126	—	15	1	no	—
235	#124	—	15	1	no	—
236	#123	—	15	1	no	—
237	#123	—	15	1	no	—
238	#123	D₁₅	1	1	yes	characteristic, complemented
239	C₂²⋊Q₈	—	15	1	no	—
240	C₂²⋊Q₈	—	15	1	no	—
241	#120	—	15	1	no	—
242	C₄×D₄	—	15	1	no	—
243	C₄×D₄	—	15	1	no	—
244	#117	—	15	1	no	—
245	#117	—	15	1	no	—
246	C₂×C₂²⋊C₄	—	15	1	no	—
247	C₂×C₂²⋊C₄	—	15	1	no	—
248	C₂×C₃×C₅	—	2	2	no	—
249	C₂×C₃×C₅	—	4	1	no	—
250	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
251	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
252	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
253	D₁₅	—	2	2	no	—
254	D₁₅	—	4	1	no	—
255	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
256	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
257	C₂²×D₃	—	5	1	no	—
258	C₂²×D₃	—	5	1	no	—
259	C₂²×D₃	—	10	2	no	—
260	C₂²×D₃	—	10	2	no	—
261	C₂²×D₃	—	20	1	no	—
262	C₃×D₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
269	#67	—	10	2	no	—
270	#67	—	20	1	no	—
271	C₂×Dic₃	—	5	1	no	—
272	C₂×Dic₃	—	5	1	no	—
273	C₂×Dic₃	—	5	1	no	—
274	C₂×Dic₃	—	5	1	no	—
275	C₂×Dic₃	—	5	1	no	—
276	C₂×Dic₃	—	5	1	no	—
277	C₂×Dic₃	—	20	1	no	—
278	C₂×Dic₃	—	20	1	no	—
279	C₄×D₃	—	10	2	no	—
280	C₄×D₃	—	20	1	no	—
281	Dic₆	—	20	1	no	—
282	C₂²×C₅	—	2	1	no	—
283	C₂²×C₅	—	2	1	no	—
284	C₂²×C₅	—	2	1	no	—
285	C₂²×C₅	—	2	1	no	—
286	C₂²×C₅	—	2	1	no	—
287	C₂²×C₅	#237	1	2	yes	—
288	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
289	C₂×D₅	—	3	2	no	—
290	C₂×D₅	—	6	1	no	—
291	C₂×D₅	—	6	1	no	—
292	C₂×D₅	—	6	1	no	—
293	C₂×D₅	—	6	1	no	—
294	C₂×D₅	—	6	1	no	—
295	C₂×D₅	—	12	4	no	—
296	C₄×C₅	—	2	1	no	—
297	C₄×C₅	—	2	1	no	—
298	C₄×C₅	—	2	1	no	—
299	C₄×C₅	—	2	1	no	—
300	C₄×C₅	—	2	1	no	—
301	Dic₅	—	6	1	no	—
302	Dic₅	—	6	1	no	—
303	Dic₅	—	6	1	no	—
304	Dic₅	—	6	1	no	—
305	Dic₅	—	6	1	no	—
306	Dic₅	—	6	1	no	—
307	C₂⁴	—	15	1	no	—
308	C₂×Q₈	—	15	1	no	—
309	C₂×D₄	—	15	1	no	—
310	C₂×D₄	—	15	1	no	—
311	C₂×D₄	C₂×D₁₅	1	1	yes	characteristic
312	C₂²×C₄	—	15	1	no	—
313	C₂²×C₄	—	15	1	no	—
314	C₂²×C₄	—	15	1	no	—
315	C₂²×C₄	—	15	1	no	—
316	C₂²×C₄	C₂×D₁₅	1	1	yes	characteristic
317	C₄⋊C₄	—	15	1	no	—
318	C₄⋊C₄	—	15	1	no	—
319	C₄⋊C₄	—	15	1	no	—
320	C₄⋊C₄	—	15	1	no	—
321	C₄⋊C₄	—	15	1	no	—
322	C₄⋊C₄	—	15	1	no	—
323	C₄⋊C₄	C₂×D₁₅	1	1	yes	characteristic, complemented
324	C₄⋊C₄	C₂×D₁₅	1	1	yes	characteristic, complemented
325	C₂²⋊C₄	—	15	1	no	—
326	C₂²⋊C₄	—	15	1	no	—
327	C₂²⋊C₄	—	15	1	no	—
328	C₂²⋊C₄	—	15	1	no	—
329	C₂²⋊C₄	—	15	1	no	—
330	C₂²⋊C₄	—	15	1	no	—
331	C₂²⋊C₄	—	15	1	no	—
332	C₂²⋊C₄	—	15	1	no	—
333	C₂²⋊C₄	—	15	1	no	—
334	C₂²⋊C₄	—	15	1	no	—
335	C₂²⋊C₄	—	15	1	no	—
336	C₂²⋊C₄	C₂×D₁₅	1	1	yes	characteristic
337	C₂²⋊C₄	C₂×D₁₅	1	1	yes	characteristic, complemented
338	C₂²⋊C₄	C₂×D₁₅	1	1	yes	characteristic, complemented
339	C₄²	—	15	1	no	—
340	C₄²	—	15	1	no	—
341	C₄²	—	15	1	no	—
342	C₃×C₅	#551	1	1	yes	characteristic, complemented, Hall
343	C₂²×C₃	—	2	1	no	—
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	2	1	no	—
346	C₂²×C₃	—	2	1	no	—
347	C₂²×C₃	—	2	1	no	—
348	C₂²×C₃	#711	1	2	yes	—
349	C₂²×C₃	C₂³×D₅	1	1	yes	characteristic
350	C₂×D₃	—	5	2	no	—
351	C₂×D₃	—	10	1	no	—
352	C₂×D₃	—	10	1	no	—
353	C₂×D₃	—	10	1	no	—
354	C₂×D₃	—	10	1	no	—
355	C₂×D₃	—	10	1	no	—
356	C₂×D₃	—	20	4	no	—
357	C₃×C₄	—	2	1	no	—
358	C₃×C₄	—	2	1	no	—
359	C₃×C₄	—	2	1	no	—
360	C₃×C₄	—	2	1	no	—
361	C₃×C₄	—	2	1	no	—
362	Dic₃	—	10	1	no	—
363	Dic₃	—	10	1	no	—
364	Dic₃	—	10	1	no	—
365	Dic₃	—	10	1	no	—
366	Dic₃	—	10	1	no	—
367	Dic₃	—	10	1	no	—
368	C₂×C₅	—	2	2	no	—
369	C₂×C₅	—	4	1	no	—
370	C₂×C₅	C₂×#237	1	1	yes	characteristic
371	C₂×C₅	D₃×#41	1	1	yes	characteristic
372	C₂×C₅	#1009	1	1	yes	characteristic
373	D₅	—	6	2	no	—
374	D₅	—	12	1	no	—
375	C₂³	—	15	1	no	—
376	C₂³	—	15	1	no	—
377	C₂³	—	30	2	no	—
378	C₂³	—	30	2	no	—
379	C₂³	—	60	1	no	—
380	C₂³	C₂²×D₁₅	1	1	yes	characteristic
381	C₂³	C₂²×D₁₅	1	1	yes	characteristic
382	Q₈	—	60	1	no	—
383	D₄	—	2	2	no	—
384	D₄	—	30	2	no	—
385	D₄	—	60	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	15	1	no	—
388	C₂×C₄	—	15	1	no	—
389	C₂×C₄	—	15	1	no	—
390	C₂×C₄	—	15	1	no	—
391	C₂×C₄	—	15	1	no	—
392	C₂×C₄	—	15	1	no	—
393	C₂×C₄	—	30	2	no	—
394	C₂×C₄	—	60	1	no	—
395	C₂×C₄	—	60	1	no	—
396	C₂×C₄	—	60	1	no	—
397	C₂×C₄	C₂²×D₁₅	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₁₅	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₁₅	1	1	yes	characteristic
400	C₂×C₄	C₂²×D₁₅	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₁₅	1	1	yes	characteristic
402	C₂×C₃	—	2	2	no	—
403	C₂×C₃	—	4	1	no	—
404	C₂×C₃	C₂×#711	1	1	yes	characteristic
405	C₂×C₃	D₅×#41	1	1	yes	characteristic
406	C₂×C₃	#4149	1	1	yes	characteristic
407	D₃	—	10	2	no	—
408	D₃	—	20	1	no	—
409	C₅	#5658	1	1	yes	characteristic, complemented, Sylow
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	15	2	no	—
416	C₂²	—	30	1	no	—
417	C₂²	—	30	1	no	—
418	C₂²	—	30	1	no	—
419	C₂²	—	30	1	no	—
420	C₂²	—	30	1	no	—
421	C₂²	—	60	4	no	—
422	C₂²	#6819	1	2	yes	—
423	C₂²	C₂³×D₁₅	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	30	1	no	—
430	C₄	—	30	1	no	—
431	C₄	—	30	1	no	—
432	C₄	—	30	1	no	—
433	C₄	—	30	1	no	—
434	C₄	—	30	1	no	—
435	C₃	#65992	1	1	yes	characteristic, complemented, Sylow
436	C₂	—	2	2	no	—
437	C₂	—	4	1	no	—
438	C₂	—	30	2	no	—
439	C₂	—	60	1	no	—
440	C₂	C₂×#6819	1	1	yes	characteristic
441	C₂	#41×D₁₅	1	1	yes	characteristic
442	C₂	#92100	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₅
commutator, socle, cosocle	C₂²×C₃×C₅	C₂⁴
Fitting	C₃×C₅×#123	C₂
prime radical	#91826	C₂
hypercenter	#123	D₁₅
hypocenter	C₃×C₅	#551
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ #123

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#123	C₂	semidirect
3. D₄×Dic₁₅	C₂	semidirect
4. C₂×#6714	C₂	semidirect
5. #91815	C₂	semidirect
6. #91787	C₂	semidirect
7. #91787	C₂	semidirect
8. #91786	C₂	semidirect
9. #91781	C₂	semidirect
10. #91775	C₂	semidirect
11. #91774	C₂	semidirect
12. #91772	C₂	semidirect
13. #91770	C₂	semidirect
14. C₂²⋊C₄×D₁₅	C₂	semidirect
15. #91767	C₂	semidirect
23. C₂²×Dic₁₅	C₂²	semidirect
26. C₂×Dic₃₀	C₂²	semidirect
27. C₃×C₅×C₄⋊C₄	C₂²	semidirect
28. C₃×C₅×C₄⋊C₄	C₂²	semidirect
30. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
31. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
34. #6719	C₂²	semidirect
43. C₄⋊Dic₁₅	C₂²	semidirect
44. C₄⋊Dic₁₅	C₂²	semidirect
45. C₄⋊Dic₁₅	C₂²	semidirect
46. C₄⋊Dic₁₅	C₂²	semidirect
47. #6712	C₂²	semidirect
48. #6712	C₂²	semidirect
49. C₄×Dic₁₅	C₂²	semidirect
50. C₄×Dic₁₅	C₂²	semidirect
51. C₄×Dic₁₅	C₂²	semidirect
53. C₅×#123	D₃	semidirect
95. C₃×#123	D₅	semidirect
120. C₅×C₄⋊C₄	C₂×D₃	semidirect
121. C₅×C₄⋊C₄	C₂×D₃	semidirect
123. C₅×C₂²⋊C₄	C₂×D₃	semidirect
124. C₅×C₂²⋊C₄	C₂×D₃	semidirect
181. C₃×C₄⋊C₄	C₂×D₅	semidirect
182. C₃×C₄⋊C₄	C₂×D₅	semidirect
184. C₃×C₂²⋊C₄	C₂×D₅	semidirect
185. C₃×C₂²⋊C₄	C₂×D₅	semidirect
238. #123	D₁₅	semidirect
323. C₄⋊C₄	C₂×D₁₅	semidirect
324. C₄⋊C₄	C₂×D₁₅	semidirect
337. C₂²⋊C₄	C₂×D₁₅	semidirect
338. C₂²⋊C₄	C₂×D₁₅	semidirect
342. C₃×C₅	#551	semidirect
409. C₅	#5658	semidirect
435. C₃	#65992	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#123	2
#91826	2
D₄×Dic₁₅	2
C₂×#6714	2
#91815	2
#91787	2
#91786	2
#91781	2
#91775	2
#91774	2
#91772	2
#91770	2
C₂²⋊C₄×D₁₅	2
#91767	2
#65992	3
#5658	5