Subgroups — #14419666

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	C₅×#5479	C₂	1	1	yes	maximal, characteristic
2	#11751026	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3935	C₂	1	1	yes	maximal, characteristic, complemented
4	#11748500	C₂	1	2	yes	maximal, complemented
5	#67×#168	C₂	1	2	yes	maximal, complemented
6	#11746987	C₂	1	2	yes	maximal, complemented
7	#11746979	C₂	1	2	yes	maximal, complemented
8	#11746879	C₂	1	2	yes	maximal, complemented
9	#11746850	C₂	1	2	yes	maximal, complemented
10	#10614859	—	3	1	no	maximal, Hall
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₅×#930	C₄	1	1	yes	characteristic
13	C₅×#929	C₄	1	2	yes	—
14	C₄×C₅×#67	C₂²	1	2	yes	—
15	C₅×#924	C₄	1	1	yes	characteristic
16	C₅×#876	C₄	1	2	yes	—
17	C₅×#875	C₄	1	1	yes	characteristic
18	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₅×#872	C₂²	1	2	yes	—
20	C₅×#870	C₄	1	1	yes	characteristic
21	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
22	C₂²×C₃×#168	C₂²	1	2	yes	—
23	C₂×#6650	C₂²	1	2	yes	—
24	C₂×D₃×#168	C₂²	1	2	yes	—
25	#91114	C₂²	1	1	yes	characteristic
26	#91114	C₂²	1	1	yes	characteristic
27	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
28	C₄×C₃⋊#168	C₂²	1	2	yes	—
29	C₃×#3935	C₂²	1	2	yes	—
30	C₃×#3935	C₂²	1	1	yes	characteristic
31	C₃×#3935	C₂²	1	1	yes	characteristic
32	Dic₃⋊#168	C₂²	1	2	yes	—
33	Dic₃⋊#168	C₂²	1	2	yes	—
34	(C₂×D₃)⋊#168	C₂²	1	2	yes	—
35	(C₂×D₃)⋊#168	C₂²	1	2	yes	—
36	#90953	C₂²	1	2	yes	—
37	Dic₃×#168	C₂²	1	2	yes	—
38	#78481	—	5	1	no	maximal, Hall
39	C₅×#529	—	3	1	no	—
40	#65313	—	3	2	no	—
41	#65300	—	3	2	no	—
42	#65300	—	3	2	no	—
43	D₄×#168	—	3	2	no	—
44	#65289	—	3	2	no	—
45	#65286	—	3	2	no	—
46	#65214	—	3	1	no	—
47	C₂×#3935	D₃	1	1	yes	characteristic, complemented
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×C₅×#67	C₂×C₄	1	2	yes	—
52	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
54	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
55	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
56	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
57	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
58	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₃⋊#168	C₂³	1	2	yes	—
60	C₂×C₃⋊#168	C₂³	1	2	yes	—
61	C₅×#217	C₂×C₄	1	2	yes	—
62	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
63	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
64	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
65	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
66	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
67	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
68	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
69	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
70	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
71	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
72	C₄×C₅×Dic₃	C₂³	1	2	yes	—
73	C₂×C₃×#168	—	2	4	no	—
74	C₂×C₃×#168	C₂³	1	2	yes	—
75	C₂×C₃×#168	C₂³	1	2	yes	—
76	#6650	—	2	4	no	—
77	D₃×#168	—	2	4	no	—
78	#5479	D₅	1	1	yes	characteristic
79	C₂×C₃×#97	—	5	1	no	—
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	C₅×#126	—	3	2	no	—
88	C₅×#125	—	3	1	no	—
89	C₅×#124	—	3	1	no	—
90	C₅×#123	—	3	2	no	—
91	C₅×C₂²⋊Q₈	—	3	1	no	—
92	C₅×#121	—	3	1	no	—
93	C₄×C₅×Q₈	—	3	1	no	—
94	C₄×C₅×D₄	—	3	2	no	—
95	C₄×C₅×D₄	—	3	1	no	—
96	C₅×#117	—	3	2	no	—
97	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
98	C₂×#681	—	3	2	no	—
99	C₂²×#168	—	3	2	no	—
100	C₂²×#168	C₂×D₃	1	2	yes	—
101	C₂²⋊#168	—	3	1	no	—
102	C₂²⋊#168	—	3	1	no	—
103	C₂²⋊#168	—	3	2	no	—
104	C₂²⋊#168	—	3	2	no	—
105	C₄⋊#168	—	3	2	no	—
106	C₄⋊#168	—	3	2	no	—
107	C₄⋊#168	—	3	2	no	—
108	#3935	—	3	2	no	—
109	#3935	C₂×D₃	1	1	yes	characteristic
110	#3935	C₂×D₃	1	1	yes	characteristic
111	#3935	C₂×D₃	1	2	yes	—
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×C₅×D₃	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	C₅×#67	—	2	4	no	—
127	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
128	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
129	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
130	C₅×D₁₂	—	4	1	no	—
131	C₄×C₅×D₃	—	2	2	no	—
132	C₄×C₅×D₃	—	2	2	no	—
133	C₅×Dic₆	—	4	1	no	—
134	C₃⋊#168	—	2	2	no	—
135	C₃⋊#168	—	2	2	no	—
136	C₃×#168	—	2	2	no	—
137	C₃×#168	#41	1	4	yes	—
138	C₂²×C₃×C₈	—	5	2	no	—
139	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
140	#930	Dic₅	1	1	yes	characteristic
141	#929	Dic₅	1	2	yes	—
142	C₄×#67	C₂×D₅	1	2	yes	—
143	#924	Dic₅	1	1	yes	characteristic
144	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
145	C₂×D₃×C₈	—	5	2	no	—
146	#876	Dic₅	1	2	yes	—
147	#875	Dic₅	1	1	yes	characteristic
148	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
149	#872	C₂×D₅	1	2	yes	—
150	#870	Dic₅	1	1	yes	characteristic
151	C₄×Dic₆	C₂×D₅	1	1	yes	characteristic
152	C₃×#97	—	5	2	no	—
153	C₃×#97	—	5	1	no	—
154	C₃×#97	—	5	1	no	—
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	C₂×C₅×Q₈	—	3	1	no	—
166	C₂×C₅×D₄	—	3	2	no	—
167	C₂×C₅×D₄	—	3	1	no	—
168	C₂²×C₄×C₅	—	3	2	no	—
169	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
172	C₅×C₄⋊C₄	—	3	2	no	—
173	C₅×C₄⋊C₄	—	3	2	no	—
174	C₅×C₄⋊C₄	—	3	1	no	—
175	C₅×C₄⋊C₄	—	3	2	no	—
176	C₅×C₄⋊C₄	—	3	1	no	—
177	C₅×C₄⋊C₄	—	3	2	no	—
178	C₅×C₂²⋊C₄	—	3	2	no	—
179	C₅×C₂²⋊C₄	—	3	2	no	—
180	C₅×C₂²⋊C₄	—	3	2	no	—
181	C₅×C₂²⋊C₄	—	3	2	no	—
182	C₅×C₂²⋊C₄	—	3	2	no	—
183	C₄²×C₅	—	3	2	no	—
184	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
185	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
186	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
187	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
188	#681	—	6	4	no	—
189	C₂×#168	—	2	4	no	—
190	C₂×#168	—	3	2	no	—
191	C₂×#168	—	3	2	no	—
192	C₂×#168	—	6	4	no	—
193	C₂×#168	C₂²×D₃	1	2	yes	—
194	C₂×#168	C₂²×D₃	1	2	yes	—
195	#529	—	3	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	—	5	1	no	—
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×C₅×D₃	—	2	2	no	—
209	C₂×C₅×D₃	—	2	2	no	—
210	C₂×C₅×D₃	—	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	C₅×Dic₃	—	2	2	no	—
218	C₅×Dic₃	—	2	2	no	—
219	C₅×Dic₃	—	2	2	no	—
220	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
223	C₂×#67	C₂×Dic₅	1	2	yes	—
224	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
225	C₂×C₄×D₃	C₂²×D₅	1	2	yes	—
226	C₂×Dic₆	C₂×Dic₅	1	1	yes	characteristic
227	C₂×C₃×C₈	—	5	2	no	—
228	C₂×C₃×C₈	—	5	2	no	—
229	C₂×C₃×C₈	—	10	4	no	—
230	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
231	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
232	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
233	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
234	#217	C₂×Dic₅	1	2	yes	—
235	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
236	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
237	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
238	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
239	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
240	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
241	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
242	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
243	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
244	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
245	C₄×Dic₃	C₂²×D₅	1	2	yes	—
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	—	3	2	no	—
251	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
252	C₅×Q₈	—	12	1	no	—
253	C₅×D₄	—	6	4	no	—
254	C₅×D₄	—	12	1	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	3	2	no	—
258	C₂×C₄×C₅	—	3	2	no	—
259	C₂×C₄×C₅	—	3	2	no	—
260	C₂×C₄×C₅	—	4	1	no	—
261	C₂×C₄×C₅	—	6	2	no	—
262	C₂×C₄×C₅	—	6	2	no	—
263	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
269	#168	—	2	2	no	—
270	#168	—	6	2	no	—
271	#168	—	6	2	no	—
272	#168	#235	1	4	yes	—
273	C₂×M₁₆	—	15	2	no	—
274	C₂²×C₈	—	5	2	no	—
275	C₂²×C₈	—	15	2	no	—
276	#126	—	3	2	no	—
277	#125	—	3	1	no	—
278	#124	—	3	1	no	—
279	#123	—	3	2	no	—
280	C₂²⋊Q₈	—	3	1	no	—
281	#121	—	3	1	no	—
282	C₄×Q₈	—	3	1	no	—
283	C₄×D₄	—	3	2	no	—
284	C₄×D₄	—	3	1	no	—
285	#117	—	3	2	no	—
286	C₂×C₄²	D₃×D₅	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	2	no	—
291	C₂²⋊C₈	—	15	2	no	—
292	C₂²⋊C₈	—	15	1	no	—
293	C₂²⋊C₈	—	15	1	no	—
294	#97	—	5	1	no	—
295	#97	—	5	1	no	—
296	#97	—	5	2	no	—
297	#97	—	15	2	no	—
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	C₅×D₃	—	4	2	no	—
305	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
306	C₂²×D₃	C₂²×Dic₅	1	2	yes	—
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	C₂²×Dic₅	1	1	yes	characteristic
311	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
312	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
314	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
315	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
316	#67	—	2	4	no	—
317	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
318	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
319	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
320	D₁₂	—	4	1	no	—
321	C₄×D₃	—	2	2	no	—
322	C₄×D₃	—	2	2	no	—
323	Dic₆	—	4	1	no	—
324	C₃×C₈	—	5	4	no	—
325	C₃×C₈	—	10	2	no	—
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	—	6	2	no	—
331	C₂²×C₅	—	6	2	no	—
332	C₂²×C₅	—	6	2	no	—
333	C₂²×C₅	#907	1	2	yes	—
334	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
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	—	6	2	no	—
341	C₄×C₅	—	6	2	no	—
342	C₄×C₅	—	6	2	no	—
343	C₄×C₅	C₂×#235	1	2	yes	—
344	C₂×Q₈	—	3	1	no	—
345	C₂×D₄	—	3	2	no	—
346	C₂×D₄	—	3	1	no	—
347	C₂²×C₄	—	3	2	no	—
348	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
349	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
351	M₁₆	—	30	4	no	—
352	C₂×C₈	—	5	2	no	—
353	C₂×C₈	—	5	2	no	—
354	C₂×C₈	—	10	4	no	—
355	C₂×C₈	—	15	2	no	—
356	C₂×C₈	—	15	2	no	—
357	C₂×C₈	—	30	4	no	—
358	C₄⋊C₄	—	3	2	no	—
359	C₄⋊C₄	—	3	2	no	—
360	C₄⋊C₄	—	3	1	no	—
361	C₄⋊C₄	—	3	2	no	—
362	C₄⋊C₄	—	3	1	no	—
363	C₄⋊C₄	—	3	2	no	—
364	C₂²⋊C₄	—	3	2	no	—
365	C₂²⋊C₄	—	3	2	no	—
366	C₂²⋊C₄	—	3	2	no	—
367	C₂²⋊C₄	—	3	2	no	—
368	C₂²⋊C₄	—	3	2	no	—
369	C₄²	—	3	2	no	—
370	C₄²	D₃×Dic₅	1	1	yes	characteristic
371	C₄²	D₃×Dic₅	1	1	yes	characteristic
372	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
373	C₄²	C₂×D₃×D₅	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	#4094	1	2	yes	—
378	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
379	C₂×D₃	—	2	2	no	—
380	C₂×D₃	—	2	2	no	—
381	C₂×D₃	—	2	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	D₅×#41	1	2	yes	—
388	Dic₃	—	2	2	no	—
389	Dic₃	—	2	2	no	—
390	Dic₃	—	2	2	no	—
391	C₂×C₅	—	2	2	no	—
392	C₂×C₅	—	12	2	no	—
393	C₂×C₅	C₄×#235	1	1	yes	characteristic
394	C₂×C₅	C₂×#907	1	1	yes	characteristic
395	C₂×C₅	#5745	1	1	yes	characteristic
396	C₂³	—	3	2	no	—
397	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
398	Q₈	—	12	1	no	—
399	D₄	—	6	4	no	—
400	D₄	—	12	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	3	2	no	—
404	C₂×C₄	—	3	2	no	—
405	C₂×C₄	—	3	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	6	2	no	—
408	C₂×C₄	—	6	2	no	—
409	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
410	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
411	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
412	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
413	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
415	C₈	—	5	4	no	—
416	C₈	—	10	2	no	—
417	C₈	—	30	2	no	—
418	C₈	—	30	2	no	—
419	C₂×C₃	—	2	2	no	—
420	C₂×C₃	C₂×#4094	1	1	yes	characteristic
421	C₂×C₃	#66153	1	1	yes	characteristic
422	C₂×C₃	#41×Dic₅	1	1	yes	characteristic
423	D₃	—	4	2	no	—
424	C₅	#78481	1	1	yes	characteristic, complemented, Sylow
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	6	2	no	—
428	C₂²	—	6	2	no	—
429	C₂²	—	6	2	no	—
430	C₂²	#91288	1	2	yes	—
431	C₂²	C₂²×D₃×Dic₅	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	—	6	2	no	—
438	C₄	—	6	2	no	—
439	C₄	—	6	2	no	—
440	C₄	D₅×#235	1	2	yes	—
441	C₃	#10614859	1	1	yes	characteristic, complemented, Sylow
442	C₂	—	2	2	no	—
443	C₂	—	12	2	no	—
444	C₂	C₂×#91288	1	1	yes	characteristic
445	C₂	#11754125	1	1	yes	characteristic
446	C₂	Dic₅×#235	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂×C₃×C₄²×C₅	C₂²
prime radical	C₅×#930	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	#2968
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #11751026	C₂	semidirect
3. C₂×C₃×#3935	C₂	semidirect
4. #11748500	C₂	semidirect
5. #67×#168	C₂	semidirect
6. #11746987	C₂	semidirect
7. #11746979	C₂	semidirect
8. #11746879	C₂	semidirect
9. #11746850	C₂	semidirect
47. C₂×#3935	D₃	semidirect
374. C₃×C₅	#2968	semidirect
424. C₅	#78481	semidirect
441. C₃	#10614859	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5479	2
#11751026	2
C₂×C₃×#3935	2
#11748500	2
#67×#168	2
#11746987	2
#11746979	2
#11746879	2
#11746850	2
#10614859	3
#78481	5