Subgroups — #14419588

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11756238	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
3	#11751212	C₂	1	2	yes	maximal, complemented
4	C₈×#1220	C₂	1	2	yes	maximal, complemented
5	#11751026	C₂	1	1	yes	maximal, characteristic, complemented
6	#11750810	C₂	1	2	yes	maximal, complemented
7	#11750809	C₂	1	2	yes	maximal, complemented
8	#11750807	C₂	1	2	yes	maximal, complemented
9	#11750802	C₂	1	2	yes	maximal, complemented
10	#10610212	—	3	1	no	maximal, Hall
11	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	#91819	C₄	1	1	yes	characteristic
14	#91818	C₄	1	2	yes	—
15	C₄×#1220	C₂²	1	2	yes	—
16	#91813	C₄	1	1	yes	characteristic
17	C₂×#6705	C₂²	1	2	yes	—
18	C₂×C₈×D₁₅	C₂²	1	2	yes	—
19	#91765	C₄	1	2	yes	—
20	#91764	C₄	1	1	yes	characteristic
21	C₄×D₆₀	C₂²	1	1	yes	characteristic
22	#91761	C₂²	1	2	yes	—
23	#91759	C₄	1	1	yes	characteristic
24	C₄×Dic₃₀	C₂²	1	1	yes	characteristic
25	C₃×C₅×#97	C₂²	1	2	yes	—
26	C₃×C₅×#97	C₂²	1	1	yes	characteristic
27	C₃×C₅×#97	C₂²	1	1	yes	characteristic
28	#91114	C₂²	1	1	yes	characteristic
29	#91114	C₂²	1	1	yes	characteristic
30	#91104	C₂²	1	2	yes	—
31	#91104	C₂²	1	2	yes	—
32	#91099	C₂²	1	2	yes	—
33	#91098	C₂²	1	2	yes	—
34	#91098	C₂²	1	2	yes	—
35	C₈×Dic₁₅	C₂²	1	2	yes	—
36	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
37	C₄×C₃⋊#168	C₂²	1	2	yes	—
38	#78481	—	5	1	no	maximal, Hall
39	#65813	—	3	1	no	—
40	C₂×C₅×#97	D₃	1	1	yes	characteristic, complemented
41	#65400	—	3	2	no	—
42	C₈×C₂²⋊D₅	—	3	2	no	—
43	#65214	—	3	1	no	—
44	#64998	—	3	2	no	—
45	#64997	—	3	2	no	—
46	#64995	—	3	2	no	—
47	#64990	—	3	2	no	—
48	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×#1220	C₂×C₄	1	2	yes	—
52	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×D₁₅	C₂³	1	2	yes	—
54	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
55	C₂×C₃×C₅×C₈	—	2	4	no	—
56	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
57	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
58	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
59	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
60	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
61	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
62	#6719	C₂×C₄	1	2	yes	—
63	#6714	C₂×C₄	1	2	yes	—
64	#6714	C₂×C₄	1	2	yes	—
65	#6714	C₂×C₄	1	2	yes	—
66	#6714	C₂×C₄	1	2	yes	—
67	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
68	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
69	#6712	C₂×C₄	1	2	yes	—
70	#6712	C₂×C₄	1	2	yes	—
71	#6712	C₂×C₄	1	2	yes	—
72	#6712	C₂×C₄	1	2	yes	—
73	C₄×Dic₁₅	C₂³	1	2	yes	—
74	C₂×C₃⋊#168	C₂³	1	2	yes	—
75	C₂×C₃⋊#168	C₂³	1	2	yes	—
76	#6705	—	2	4	no	—
77	C₈×D₁₅	—	2	4	no	—
78	#5479	—	5	1	no	—
79	C₂×C₃×#97	D₅	1	1	yes	characteristic, complemented
80	#5111	—	5	2	no	—
81	C₈×#67	—	5	2	no	—
82	#4925	—	5	1	no	—
83	#4709	—	5	2	no	—
84	#4708	—	5	2	no	—
85	#4706	—	5	2	no	—
86	#4701	—	5	2	no	—
87	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
88	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
89	#4076	—	3	1	no	—
90	#4075	—	3	2	no	—
91	C₄×C₂²⋊D₅	—	3	2	no	—
92	#4070	—	3	1	no	—
93	C₂×#676	—	3	2	no	—
94	C₂×C₈×D₅	—	3	2	no	—
95	#4022	—	3	2	no	—
96	#4021	—	3	1	no	—
97	C₄×D₂₀	—	3	1	no	—
98	#4018	—	3	2	no	—
99	#4016	—	3	1	no	—
100	C₄×Dic₁₀	—	3	1	no	—
101	C₅×#97	C₂×D₃	1	2	yes	—
102	C₅×#97	C₂×D₃	1	1	yes	characteristic
103	C₅×#97	C₂×D₃	1	1	yes	characteristic
104	C₂²⋊#168	—	3	1	no	—
105	C₂²⋊#168	—	3	1	no	—
106	#3952	—	3	2	no	—
107	#3952	—	3	2	no	—
108	#3947	—	3	2	no	—
109	#3946	—	3	2	no	—
110	#3946	—	3	2	no	—
111	C₈×Dic₅	—	3	2	no	—
112	C₄⋊#168	—	3	2	no	—
113	C₄×#168	—	3	2	no	—
114	#2968	—	15	1	no	Sylow
115	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	4	1	no	—
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
126	#1220	—	2	4	no	—
127	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
128	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
129	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
130	D₆₀	—	4	1	no	—
131	C₄×D₁₅	—	2	2	no	—
132	C₄×D₁₅	—	2	2	no	—
133	Dic₃₀	—	4	1	no	—
134	C₃×C₅×C₈	—	2	2	no	—
135	C₃×C₅×C₈	#41	1	4	yes	—
136	C₃⋊#168	—	2	2	no	—
137	C₃⋊#168	—	2	2	no	—
138	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
139	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
140	#930	—	5	1	no	—
141	#929	—	5	2	no	—
142	C₄×#67	—	5	2	no	—
143	#924	—	5	1	no	—
144	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
145	C₂×D₃×C₈	—	5	2	no	—
146	#876	—	5	2	no	—
147	#875	—	5	1	no	—
148	C₄×D₁₂	—	5	1	no	—
149	#872	—	5	2	no	—
150	#870	—	5	1	no	—
151	C₄×Dic₆	—	5	1	no	—
152	C₃×#97	C₂×D₅	1	2	yes	—
153	C₃×#97	C₂×D₅	1	1	yes	characteristic
154	C₃×#97	C₂×D₅	1	1	yes	characteristic
155	#830	—	5	1	no	—
156	#830	—	5	1	no	—
157	(C₂×D₃)⋊C₈	—	5	2	no	—
158	(C₂×D₃)⋊C₈	—	5	2	no	—
159	#815	—	5	2	no	—
160	Dic₃⋊C₈	—	5	2	no	—
161	Dic₃⋊C₈	—	5	2	no	—
162	C₈×Dic₃	—	5	2	no	—
163	C₄⋊(C₃⋊C₈)	—	5	2	no	—
164	C₄×C₃⋊C₈	—	5	2	no	—
165	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
168	C₂×C₂²⋊D₅	—	3	2	no	—
169	C₂×D₂₀	—	3	1	no	—
170	C₂×C₄×D₅	—	3	2	no	—
171	C₂×Dic₁₀	—	3	1	no	—
172	C₂×C₅×C₈	—	2	4	no	—
173	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
174	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
175	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
176	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
177	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
178	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
179	C₂²⋊Dic₅	—	3	2	no	—
180	#685	—	3	2	no	—
181	#685	—	3	2	no	—
182	#685	—	3	2	no	—
183	#685	—	3	2	no	—
184	C₄⋊Dic₅	—	3	1	no	—
185	C₄⋊Dic₅	—	3	1	no	—
186	#683	—	3	2	no	—
187	#683	—	3	2	no	—
188	#683	—	3	2	no	—
189	#683	—	3	2	no	—
190	C₄×Dic₅	—	3	2	no	—
191	C₂×#168	—	3	2	no	—
192	C₂×#168	—	3	2	no	—
193	#676	—	6	4	no	—
194	C₈×D₅	—	6	4	no	—
195	#529	—	15	1	no	—
196	#446	—	15	2	no	—
197	#435	—	15	2	no	—
198	#435	—	15	2	no	—
199	C₈×D₄	—	15	2	no	—
200	#433	—	15	2	no	—
201	#431	—	15	1	no	—
202	#405	—	15	2	no	—
203	C₂×#97	D₁₅	1	1	yes	characteristic, complemented
204	C₂²×C₃×C₅	—	2	1	no	—
205	C₂²×C₃×C₅	—	2	1	no	—
206	C₂²×C₃×C₅	#131	1	2	yes	—
207	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
208	C₂×D₁₅	—	2	2	no	—
209	C₂×D₁₅	—	2	2	no	—
210	C₂×D₁₅	—	2	2	no	—
211	C₃×C₄×C₅	—	2	1	no	—
212	C₃×C₄×C₅	—	2	1	no	—
213	C₃×C₄×C₅	—	2	1	no	—
214	C₃×C₄×C₅	—	2	1	no	—
215	C₃×C₄×C₅	—	2	1	no	—
216	C₃×C₄×C₅	C₂×#41	1	2	yes	—
217	Dic₁₅	—	2	2	no	—
218	Dic₁₅	—	2	2	no	—
219	Dic₁₅	—	2	2	no	—
220	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
223	C₂×#67	—	5	2	no	—
224	C₂×D₁₂	—	5	1	no	—
225	C₂×C₄×D₃	—	5	2	no	—
226	C₂×Dic₆	—	5	1	no	—
227	C₂×C₃×C₈	—	2	4	no	—
228	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
229	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
230	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
231	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
232	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
233	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
234	#217	—	5	2	no	—
235	(C₂×D₃)⋊C₄	—	5	2	no	—
236	(C₂×D₃)⋊C₄	—	5	2	no	—
237	(C₂×D₃)⋊C₄	—	5	2	no	—
238	(C₂×D₃)⋊C₄	—	5	2	no	—
239	C₄⋊Dic₃	—	5	1	no	—
240	C₄⋊Dic₃	—	5	1	no	—
241	Dic₃⋊C₄	—	5	2	no	—
242	Dic₃⋊C₄	—	5	2	no	—
243	Dic₃⋊C₄	—	5	2	no	—
244	Dic₃⋊C₄	—	5	2	no	—
245	C₄×Dic₃	—	5	2	no	—
246	C₂×C₃⋊C₈	—	5	2	no	—
247	C₂×C₃⋊C₈	—	5	2	no	—
248	ΓL(1,𝔽₂₅)	—	10	4	no	—
249	D₃×C₈	—	10	4	no	—
250	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
251	C₂²×D₅	—	3	2	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	4	1	no	—
255	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
261	C₂²⋊D₅	—	6	4	no	—
262	C₂×Dic₅	—	3	2	no	—
263	C₂×Dic₅	—	3	2	no	—
264	C₂×Dic₅	—	3	2	no	—
265	D₂₀	—	12	1	no	—
266	C₄×D₅	—	6	2	no	—
267	C₄×D₅	—	6	2	no	—
268	Dic₁₀	—	12	1	no	—
269	C₅×C₈	—	2	2	no	—
270	C₅×C₈	#235	1	4	yes	—
271	#168	—	6	2	no	—
272	#168	—	6	2	no	—
273	C₂×M₁₆	—	15	2	no	—
274	C₂²×C₈	—	15	2	no	—
275	C₂²×C₈	C₂×D₁₅	1	2	yes	—
276	#126	—	15	2	no	—
277	#125	—	15	1	no	—
278	#124	—	15	1	no	—
279	#123	—	15	2	no	—
280	C₂²⋊Q₈	—	15	1	no	—
281	#121	—	15	1	no	—
282	C₄×Q₈	—	15	1	no	—
283	C₄×D₄	—	15	2	no	—
284	C₄×D₄	—	15	1	no	—
285	#117	—	15	2	no	—
286	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
287	C₄⋊C₈	—	15	2	no	—
288	C₄⋊C₈	—	15	2	no	—
289	C₄⋊C₈	—	15	2	no	—
290	C₂²⋊C₈	—	15	1	no	—
291	C₂²⋊C₈	—	15	1	no	—
292	C₂²⋊C₈	—	15	2	no	—
293	C₂²⋊C₈	—	15	2	no	—
294	#97	—	15	2	no	—
295	#97	C₂×D₁₅	1	1	yes	characteristic
296	#97	C₂×D₁₅	1	1	yes	characteristic
297	#97	C₂×D₁₅	1	2	yes	—
298	C₄×C₈	—	15	2	no	—
299	C₄×C₈	—	15	2	no	—
300	C₂×C₃×C₅	—	2	2	no	—
301	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
303	C₂×C₃×C₅	#568	1	1	yes	characteristic
304	D₁₅	—	4	2	no	—
305	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
306	C₂²×D₃	—	5	2	no	—
307	C₂×C₃×C₄	—	2	2	no	—
308	C₂×C₃×C₄	—	2	2	no	—
309	C₂×C₃×C₄	—	4	1	no	—
310	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
311	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
312	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
314	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
315	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
316	#67	—	10	4	no	—
317	C₂×Dic₃	—	5	2	no	—
318	C₂×Dic₃	—	5	2	no	—
319	C₂×Dic₃	—	5	2	no	—
320	D₁₂	—	20	1	no	—
321	C₄×D₃	—	10	2	no	—
322	C₄×D₃	—	10	2	no	—
323	Dic₆	—	20	1	no	—
324	C₃×C₈	—	2	2	no	—
325	C₃×C₈	#709	1	4	yes	—
326	C₃⋊C₈	—	10	2	no	—
327	C₃⋊C₈	—	10	2	no	—
328	C₂²×C₅	—	2	1	no	—
329	C₂²×C₅	—	2	1	no	—
330	C₂²×C₅	#907	1	2	yes	—
331	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
332	C₂×D₅	—	6	2	no	—
333	C₂×D₅	—	6	2	no	—
334	C₂×D₅	—	6	2	no	—
335	C₄×C₅	—	2	1	no	—
336	C₄×C₅	—	2	1	no	—
337	C₄×C₅	—	2	1	no	—
338	C₄×C₅	—	2	1	no	—
339	C₄×C₅	—	2	1	no	—
340	C₄×C₅	C₂×#235	1	2	yes	—
341	Dic₅	—	6	2	no	—
342	Dic₅	—	6	2	no	—
343	Dic₅	—	6	2	no	—
344	C₂×Q₈	—	15	1	no	—
345	C₂×D₄	—	15	2	no	—
346	C₂×D₄	—	15	1	no	—
347	C₂²×C₄	—	15	2	no	—
348	C₂²×C₄	C₄×D₁₅	1	1	yes	characteristic
349	C₂²×C₄	C₄×D₁₅	1	1	yes	characteristic
350	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
351	M₁₆	—	30	4	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	15	2	no	—
354	C₂×C₈	—	15	2	no	—
355	C₂×C₈	—	30	4	no	—
356	C₂×C₈	C₂²×D₁₅	1	2	yes	—
357	C₂×C₈	C₂²×D₁₅	1	2	yes	—
358	C₄⋊C₄	—	15	2	no	—
359	C₄⋊C₄	—	15	2	no	—
360	C₄⋊C₄	—	15	1	no	—
361	C₄⋊C₄	—	15	2	no	—
362	C₄⋊C₄	—	15	1	no	—
363	C₄⋊C₄	—	15	2	no	—
364	C₂²⋊C₄	—	15	2	no	—
365	C₂²⋊C₄	—	15	2	no	—
366	C₂²⋊C₄	—	15	2	no	—
367	C₂²⋊C₄	—	15	2	no	—
368	C₂²⋊C₄	—	15	2	no	—
369	C₄²	—	15	2	no	—
370	C₄²	C₄×D₁₅	1	1	yes	characteristic
371	C₄²	C₄×D₁₅	1	1	yes	characteristic
372	C₄²	C₂²×D₁₅	1	1	yes	characteristic
373	C₄²	C₂²×D₁₅	1	1	yes	characteristic
374	C₃×C₅	#2968	1	1	yes	characteristic, complemented, Hall
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	2	1	no	—
377	C₂²×C₃	#4053	1	2	yes	—
378	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
379	C₂×D₃	—	10	2	no	—
380	C₂×D₃	—	10	2	no	—
381	C₂×D₃	—	10	2	no	—
382	C₃×C₄	—	2	1	no	—
383	C₃×C₄	—	2	1	no	—
384	C₃×C₄	—	2	1	no	—
385	C₃×C₄	—	2	1	no	—
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	C₂×#709	1	2	yes	—
388	Dic₃	—	10	2	no	—
389	Dic₃	—	10	2	no	—
390	Dic₃	—	10	2	no	—
391	C₂×C₅	—	2	2	no	—
392	C₂×C₅	C₄×#235	1	1	yes	characteristic
393	C₂×C₅	C₂×#907	1	1	yes	characteristic
394	C₂×C₅	#5745	1	1	yes	characteristic
395	D₅	—	12	2	no	—
396	C₂³	—	15	2	no	—
397	C₂³	C₂×C₄×D₁₅	1	1	yes	characteristic
398	Q₈	—	60	1	no	—
399	D₄	—	30	4	no	—
400	D₄	—	60	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	15	2	no	—
405	C₂×C₄	—	15	2	no	—
406	C₂×C₄	—	15	2	no	—
407	C₂×C₄	—	30	2	no	—
408	C₂×C₄	—	30	2	no	—
409	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
410	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
411	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
412	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
413	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
414	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	30	2	no	—
417	C₈	—	30	2	no	—
418	C₈	#6817	1	4	yes	—
419	C₂×C₃	—	2	2	no	—
420	C₂×C₃	C₄×#709	1	1	yes	characteristic
421	C₂×C₃	C₂×#4053	1	1	yes	characteristic
422	C₂×C₃	#66079	1	1	yes	characteristic
423	D₃	—	20	2	no	—
424	C₅	#78481	1	1	yes	characteristic, complemented, Sylow
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	30	2	no	—
428	C₂²	—	30	2	no	—
429	C₂²	—	30	2	no	—
430	C₂²	#91796	1	2	yes	—
431	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	30	2	no	—
438	C₄	—	30	2	no	—
439	C₄	—	30	2	no	—
440	C₄	C₂×#6817	1	2	yes	—
441	C₃	#10610212	1	1	yes	characteristic, complemented, Sylow
442	C₂	—	2	2	no	—
443	C₂	—	60	2	no	—
444	C₂	C₄×#6817	1	1	yes	characteristic
445	C₂	C₂×#91796	1	1	yes	characteristic
446	C₂	#11756504	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂×C₃×C₅×#97	C₂
prime radical	#91819	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×#97	D₁₅
hypocenter	C₃×C₅	#2968
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#97	C₂	semidirect
3. #11751212	C₂	semidirect
4. C₈×#1220	C₂	semidirect
5. #11751026	C₂	semidirect
6. #11750810	C₂	semidirect
7. #11750809	C₂	semidirect
8. #11750807	C₂	semidirect
9. #11750802	C₂	semidirect
40. C₂×C₅×#97	D₃	semidirect
79. C₂×C₃×#97	D₅	semidirect
203. C₂×#97	D₁₅	semidirect
374. C₃×C₅	#2968	semidirect
424. C₅	#78481	semidirect
441. C₃	#10610212	semidirect

Maximal subgroups

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

subgroup	index
#11756238	2
C₂×C₃×C₅×#97	2
#11751212	2
C₈×#1220	2
#11751026	2
#11750810	2
#11750809	2
#11750807	2
#11750802	2
#10610212	3
#78481	5