Subgroups — #11753293

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	#91770	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#883	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#4031	C₂	1	1	yes	maximal, characteristic, complemented
4	#91577	C₂	1	1	yes	maximal, characteristic
5	#91562	C₂	1	1	yes	maximal, characteristic, complemented
6	#67⋊Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
7	#91537	C₂	1	1	yes	maximal, characteristic, complemented
8	#91473	C₂	1	1	yes	maximal, characteristic, complemented
9	D₃×#685	C₂	1	1	yes	maximal, characteristic, complemented
10	#91410	C₂	1	1	yes	maximal, characteristic, complemented
11	#91402	C₂	1	1	yes	maximal, characteristic, complemented
12	#91390	C₂	1	1	yes	maximal, characteristic, complemented
13	#91371	C₂	1	1	yes	maximal, characteristic, complemented
14	#91366	C₂	1	1	yes	maximal, characteristic, complemented
15	#91361	C₂	1	1	yes	maximal, characteristic, complemented
16	#65992	—	3	1	no	maximal, Hall
17	C₂²×D₃×D₅	C₂²	1	1	yes	characteristic
18	C₂×#1220	C₂²	1	1	yes	characteristic
19	C₂²×Dic₁₅	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₄×D₁₅	C₂²	1	1	yes	characteristic
21	C₂×C₅×#67	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
24	C₂×C₃×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
25	C₂×#1200	C₂²	1	1	yes	characteristic
26	C₂×D₃×Dic₅	C₂²	1	1	yes	characteristic
27	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
28	#6714	C₂²	1	1	yes	characteristic
29	#6712	C₂²	1	1	yes	characteristic, complemented
30	C₄×Dic₁₅	C₂²	1	1	yes	characteristic, complemented
31	C₅×#217	C₂²	1	1	yes	characteristic, complemented
32	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
33	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
34	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
36	C₃×#685	C₂²	1	1	yes	characteristic
37	C₃×#685	C₂²	1	1	yes	characteristic
38	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
39	Dic₃⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
40	Dic₃⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
41	Dic₃⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
42	Dic₃⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
43	#6668	C₂²	1	1	yes	characteristic, complemented
44	#6667	C₂²	1	1	yes	characteristic
45	#6667	C₂²	1	1	yes	characteristic
46	(C₂×D₃)⋊Dic₅	C₂²	1	1	yes	characteristic
47	(C₂×D₃)⋊Dic₅	C₂²	1	1	yes	characteristic
48	#6665	C₂²	1	1	yes	characteristic
49	#6665	C₂²	1	1	yes	characteristic
50	#6665	C₂²	1	1	yes	characteristic
51	Dic₃×Dic₅	C₂²	1	1	yes	characteristic, complemented
52	#5679	—	5	1	no	maximal, Hall
53	C₅×#123	—	3	1	no	—
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	D₃	1	1	yes	characteristic, complemented
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	C₂²×D₁₅	C₂³	1	1	yes	characteristic
70	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
71	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
72	C₂×D₃×D₅	—	2	2	no	—
73	C₂×D₃×D₅	—	2	2	no	—
74	C₂×D₃×D₅	—	4	1	no	—
75	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	#1220	—	2	2	no	—
78	C₂×Dic₁₅	—	4	1	no	—
79	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
80	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
81	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
82	C₄×D₁₅	—	4	1	no	—
83	C₅×#67	—	2	2	no	—
84	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
85	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
86	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
87	C₄×C₅×D₃	—	2	2	no	—
88	C₃×C₂²⋊D₅	—	4	1	no	—
89	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
90	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
91	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
92	C₃×Dic₁₀	—	4	1	no	—
93	#1200	—	2	2	no	—
94	D₃×Dic₅	—	4	1	no	—
95	C₃×#124	—	5	1	no	—
96	#946	—	5	1	no	—
97	#946	—	5	1	no	—
98	#937	—	5	1	no	—
99	#935	—	5	1	no	—
100	#883	—	5	1	no	—
101	#883	D₅	1	1	yes	characteristic, complemented
102	#67⋊C₄	—	5	1	no	—
103	#67⋊C₄	—	5	1	no	—
104	D₃×C₂²⋊C₄	—	5	1	no	—
105	D₃×C₂²⋊C₄	—	5	1	no	—
106	#879	—	5	1	no	—
107	#879	—	5	1	no	—
108	#872	—	5	1	no	—
109	#872	—	5	1	no	—
110	C₂³×D₅	—	3	1	no	—
111	C₂×C₅×D₄	—	3	1	no	—
112	C₂²×C₄×C₅	—	3	1	no	—
113	C₂×C₂²⋊D₅	—	3	1	no	—
114	C₂×C₂²⋊D₅	C₂×D₃	1	1	yes	characteristic
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	C₂×D₃	1	1	yes	characteristic, complemented
120	C₅×C₄⋊C₄	—	3	1	no	—
121	C₅×C₄⋊C₄	—	3	1	no	—
122	C₅×C₂²⋊C₄	—	3	1	no	—
123	C₅×C₂²⋊C₄	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic, complemented
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	C₂×D₃	1	1	yes	characteristic
135	#685	C₂×D₃	1	1	yes	characteristic
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	C₂×D₃	1	1	yes	characteristic, complemented
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	C₂⁴	1	1	yes	characteristic
150	C₂×D₁₅	—	2	1	no	—
151	C₂×D₁₅	—	2	1	no	—
152	C₂×D₁₅	#41	1	2	yes	—
153	C₂×C₅×D₃	—	2	1	no	—
154	C₂×C₅×D₃	—	2	1	no	—
155	C₂×C₅×D₃	#41	1	2	yes	—
156	C₂×C₃×D₅	—	2	1	no	—
157	C₂×C₃×D₅	—	2	1	no	—
158	C₂×C₃×D₅	—	2	1	no	—
159	D₃×D₅	—	4	4	no	—
160	C₃×C₄×C₅	—	2	1	no	—
161	C₃×C₄×C₅	—	2	1	no	—
162	Dic₁₅	—	2	1	no	—
163	Dic₁₅	—	2	1	no	—
164	Dic₁₅	—	2	1	no	—
165	C₃×Dic₅	—	2	1	no	—
166	C₃×Dic₅	—	2	1	no	—
167	C₃×Dic₅	—	2	1	no	—
168	C₅×Dic₃	—	2	1	no	—
169	C₅×Dic₃	—	2	1	no	—
170	C₅×Dic₃	—	2	1	no	—
171	C₂³×D₃	—	5	1	no	—
172	C₂×C₃×Q₈	—	5	1	no	—
173	C₂×C₃×D₄	—	5	1	no	—
174	C₂×#67	—	5	1	no	—
175	C₂×#67	C₂×D₅	1	1	yes	characteristic
176	C₂²×Dic₃	—	5	1	no	—
177	C₂×C₄×D₃	—	5	1	no	—
178	C₂×C₄×D₃	—	5	1	no	—
179	C₂×C₄×D₃	—	5	1	no	—
180	C₂×C₄×D₃	C₂×D₅	1	1	yes	characteristic
181	C₃×C₂²⋊C₄	—	5	1	no	—
182	C₃×C₂²⋊C₄	—	5	1	no	—
183	C₃×C₂²⋊C₄	—	5	1	no	—
184	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
185	C₃×C₄²	—	5	1	no	—
186	#217	—	5	1	no	—
187	#217	—	5	1	no	—
188	#217	—	5	1	no	—
189	#217	C₂×D₅	1	1	yes	characteristic, complemented
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	C₂×D₅	1	1	yes	characteristic
196	C₄⋊Dic₃	—	5	1	no	—
197	C₄⋊Dic₃	C₂×D₅	1	1	yes	characteristic, complemented
198	Dic₃⋊C₄	—	5	1	no	—
199	Dic₃⋊C₄	—	5	1	no	—
200	Dic₃⋊C₄	—	5	1	no	—
201	Dic₃⋊C₄	—	5	1	no	—
202	Dic₃⋊C₄	—	5	1	no	—
203	Dic₃⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
204	C₄×Dic₃	—	5	1	no	—
205	C₄×Dic₃	—	5	1	no	—
206	C₂³×C₅	—	3	1	no	—
207	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
208	C₂²×D₅	—	3	1	no	—
209	C₂²×D₅	—	6	2	no	—
210	C₂²×D₅	—	6	2	no	—
211	C₂²×D₅	—	12	1	no	—
212	C₂²×D₅	C₂²×D₃	1	1	yes	characteristic
213	C₅×D₄	—	6	2	no	—
214	C₂×C₄×C₅	—	3	1	no	—
215	C₂×C₄×C₅	—	3	1	no	—
216	C₂×C₄×C₅	—	3	1	no	—
217	C₂×C₄×C₅	—	6	2	no	—
218	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
220	C₂²⋊D₅	—	4	1	no	—
221	C₂²⋊D₅	—	6	2	no	—
222	C₂×Dic₅	—	3	1	no	—
223	C₂×Dic₅	—	3	1	no	—
224	C₂×Dic₅	—	3	1	no	—
225	C₂×Dic₅	—	12	1	no	—
226	C₂×Dic₅	—	12	1	no	—
227	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
228	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
229	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
230	C₄×D₅	—	6	2	no	—
231	C₄×D₅	—	12	1	no	—
232	Dic₁₀	—	4	1	no	—
233	#126	—	15	1	no	—
234	#126	—	15	1	no	—
235	#124	—	5	1	no	—
236	#123	—	3	1	no	—
237	#123	—	15	1	no	—
238	#123	—	15	1	no	—
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	—	4	1	no	—
249	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
250	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
251	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
252	D₁₅	—	2	2	no	—
253	C₃×D₅	—	4	1	no	—
254	C₅×D₃	—	2	2	no	—
255	C₂³×C₃	—	5	1	no	—
256	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
257	C₂²×D₃	—	5	1	no	—
258	C₂²×D₃	—	10	2	no	—
259	C₂²×D₃	—	10	2	no	—
260	C₂²×D₃	—	20	1	no	—
261	C₂²×D₃	C₂²×D₅	1	1	yes	characteristic
262	C₃×Q₈	—	20	1	no	—
263	C₃×D₄	—	20	1	no	—
264	C₂×C₃×C₄	—	5	1	no	—
265	C₂×C₃×C₄	—	5	1	no	—
266	C₂×C₃×C₄	—	5	1	no	—
267	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
269	#67	—	2	2	no	—
270	#67	—	10	2	no	—
271	C₂×Dic₃	—	5	1	no	—
272	C₂×Dic₃	—	5	1	no	—
273	C₂×Dic₃	—	5	1	no	—
274	C₂×Dic₃	—	20	1	no	—
275	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
276	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
277	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
278	C₄×D₃	—	2	2	no	—
279	C₄×D₃	—	10	2	no	—
280	C₄×D₃	—	20	1	no	—
281	C₄×D₃	—	20	1	no	—
282	C₂²×C₅	—	2	1	no	—
283	C₂²×C₅	—	2	1	no	—
284	C₂²×C₅	—	2	1	no	—
285	C₂²×C₅	—	3	2	no	—
286	C₂²×C₅	—	6	1	no	—
287	C₂²×C₅	—	6	1	no	—
288	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
289	C₂×D₅	—	2	1	no	—
290	C₂×D₅	—	2	1	no	—
291	C₂×D₅	—	2	1	no	—
292	C₂×D₅	—	3	2	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	—	6	1	no	—
299	C₄×C₅	—	6	1	no	—
300	C₄×C₅	—	6	1	no	—
301	Dic₅	—	2	1	no	—
302	Dic₅	—	2	1	no	—
303	Dic₅	—	2	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	—	5	1	no	—
309	C₂×D₄	—	3	1	no	—
310	C₂×D₄	—	5	1	no	—
311	C₂×D₄	—	15	1	no	—
312	C₂²×C₄	—	3	1	no	—
313	C₂²×C₄	—	15	1	no	—
314	C₂²×C₄	—	15	1	no	—
315	C₂²×C₄	—	15	1	no	—
316	C₂²×C₄	—	15	1	no	—
317	C₄⋊C₄	—	3	1	no	—
318	C₄⋊C₄	—	3	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	—	15	1	no	—
324	C₄⋊C₄	—	15	1	no	—
325	C₂²⋊C₄	—	3	1	no	—
326	C₂²⋊C₄	—	3	1	no	—
327	C₂²⋊C₄	—	5	1	no	—
328	C₂²⋊C₄	—	5	1	no	—
329	C₂²⋊C₄	—	5	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	—	15	1	no	—
337	C₂²⋊C₄	—	15	1	no	—
338	C₂²⋊C₄	D₃×D₅	1	1	yes	characteristic, complemented
339	C₄²	—	5	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	—	10	1	no	—
347	C₂²×C₃	—	10	1	no	—
348	C₂²×C₃	—	10	1	no	—
349	C₂²×C₃	C₂³×D₅	1	1	yes	characteristic
350	C₂×D₃	—	2	1	no	—
351	C₂×D₃	—	2	1	no	—
352	C₂×D₃	—	5	2	no	—
353	C₂×D₃	—	10	1	no	—
354	C₂×D₃	—	10	1	no	—
355	C₂×D₃	—	20	4	no	—
356	C₂×D₃	#711	1	2	yes	—
357	C₃×C₄	—	2	1	no	—
358	C₃×C₄	—	2	1	no	—
359	C₃×C₄	—	10	1	no	—
360	C₃×C₄	—	10	1	no	—
361	C₃×C₄	—	10	1	no	—
362	Dic₃	—	2	1	no	—
363	Dic₃	—	2	1	no	—
364	Dic₃	—	2	1	no	—
365	Dic₃	—	10	1	no	—
366	Dic₃	—	10	1	no	—
367	Dic₃	—	10	1	no	—
368	C₂×C₅	—	4	1	no	—
369	C₂×C₅	—	6	2	no	—
370	C₂×C₅	#1004	1	1	yes	characteristic
371	C₂×C₅	D₃×#41	1	1	yes	characteristic
372	C₂×C₅	D₃×#41	1	1	yes	characteristic
373	D₅	—	4	1	no	—
374	D₅	—	6	2	no	—
375	C₂³	—	3	1	no	—
376	C₂³	—	5	1	no	—
377	C₂³	—	15	1	no	—
378	C₂³	—	30	2	no	—
379	C₂³	—	30	2	no	—
380	C₂³	—	60	1	no	—
381	C₂³	C₂×D₃×D₅	1	1	yes	characteristic
382	Q₈	—	20	1	no	—
383	D₄	—	6	2	no	—
384	D₄	—	20	1	no	—
385	D₄	—	30	2	no	—
386	C₂×C₄	—	3	1	no	—
387	C₂×C₄	—	3	1	no	—
388	C₂×C₄	—	3	1	no	—
389	C₂×C₄	—	5	1	no	—
390	C₂×C₄	—	5	1	no	—
391	C₂×C₄	—	5	1	no	—
392	C₂×C₄	—	6	2	no	—
393	C₂×C₄	—	15	1	no	—
394	C₂×C₄	—	15	1	no	—
395	C₂×C₄	—	15	1	no	—
396	C₂×C₄	—	30	2	no	—
397	C₂×C₄	—	60	1	no	—
398	C₂×C₄	—	60	1	no	—
399	C₂×C₄	—	60	1	no	—
400	C₂×C₄	C₂×D₃×D₅	1	1	yes	characteristic
401	C₂×C₄	C₂×D₃×D₅	1	1	yes	characteristic
402	C₂×C₃	—	4	1	no	—
403	C₂×C₃	—	20	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	—	2	2	no	—
408	D₃	—	10	2	no	—
409	C₅	#5679	1	1	yes	characteristic, complemented, Sylow
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	3	2	no	—
414	C₂²	—	6	1	no	—
415	C₂²	—	6	1	no	—
416	C₂²	—	10	1	no	—
417	C₂²	—	10	1	no	—
418	C₂²	—	10	1	no	—
419	C₂²	—	15	2	no	—
420	C₂²	—	30	1	no	—
421	C₂²	—	30	1	no	—
422	C₂²	—	60	4	no	—
423	C₂²	C₂²×D₃×D₅	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	6	1	no	—
427	C₄	—	6	1	no	—
428	C₄	—	6	1	no	—
429	C₄	—	10	1	no	—
430	C₄	—	10	1	no	—
431	C₄	—	10	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	—	4	1	no	—
437	C₂	—	6	2	no	—
438	C₂	—	20	1	no	—
439	C₂	—	30	2	no	—
440	C₂	#92016	1	1	yes	characteristic
441	C₂	D₃×#711	1	1	yes	characteristic
442	C₂	#92026	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃×D₅
commutator, socle, cosocle	C₂²×C₃×C₅	C₂⁴
Fitting	C₃×C₅×C₂²⋊C₄	C₂²
prime radical	#91577	C₂
hypercenter	C₂²⋊C₄	D₃×D₅
hypocenter	C₃×C₅	#551
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. #91770	C₂	semidirect
2. C₅×#883	C₂	semidirect
3. C₃×#4031	C₂	semidirect
5. #91562	C₂	semidirect
6. #67⋊Dic₅	C₂	semidirect
7. #91537	C₂	semidirect
8. #91473	C₂	semidirect
9. D₃×#685	C₂	semidirect
10. #91410	C₂	semidirect
11. #91402	C₂	semidirect
12. #91390	C₂	semidirect
13. #91371	C₂	semidirect
14. #91366	C₂	semidirect
15. #91361	C₂	semidirect
19. C₂²×Dic₁₅	C₂²	semidirect
24. C₂×C₃×Dic₁₀	C₂²	semidirect
27. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
29. #6712	C₂²	semidirect
30. C₄×Dic₁₅	C₂²	semidirect
31. C₅×#217	C₂²	semidirect
33. C₅×C₄⋊Dic₃	C₂²	semidirect
34. C₅×Dic₃⋊C₄	C₂²	semidirect
35. C₃×C₂²⋊Dic₅	C₂²	semidirect
38. C₃×C₄×Dic₅	C₂²	semidirect
39. Dic₃⋊Dic₅	C₂²	semidirect
40. Dic₃⋊Dic₅	C₂²	semidirect
41. Dic₃⋊Dic₅	C₂²	semidirect
42. Dic₃⋊Dic₅	C₂²	semidirect
43. #6668	C₂²	semidirect
51. Dic₃×Dic₅	C₂²	semidirect
63. #4031	D₃	semidirect
101. #883	D₅	semidirect
119. C₂×Dic₁₀	C₂×D₃	semidirect
124. C₅×C₂²⋊C₄	C₂×D₃	semidirect
127. C₂²⋊Dic₅	C₂×D₃	semidirect
144. C₄×Dic₅	C₂×D₃	semidirect
184. C₃×C₂²⋊C₄	C₂×D₅	semidirect
189. #217	C₂×D₅	semidirect
197. C₄⋊Dic₃	C₂×D₅	semidirect
203. Dic₃⋊C₄	C₂×D₅	semidirect
338. C₂²⋊C₄	D₃×D₅	semidirect
342. C₃×C₅	#551	semidirect
409. C₅	#5679	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
#91770	2
C₅×#883	2
C₃×#4031	2
#91577	2
#91562	2
#67⋊Dic₅	2
#91537	2
#91473	2
D₃×#685	2
#91410	2
#91402	2
#91390	2
#91371	2
#91366	2
#91361	2
#65992	3
#5679	5