Subgroups — #14415278

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91790	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4047	C₂	1	1	yes	maximal, characteristic, complemented
3	#11754581	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748440	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748350	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748342	C₂	1	1	yes	maximal, characteristic, complemented
8	#11747715	C₂	1	4	yes	maximal, complemented
9	C₈×#1202	C₂	1	4	yes	maximal, complemented
10	#10610189	—	3	1	no	maximal, Hall
11	C₂×#6817	C₂²	1	1	yes	characteristic
12	C₂×C₃×#709	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×#6710	C₂²	1	1	yes	characteristic
15	#91790	—	2	4	no	—
16	C₂×#6705	C₂²	1	2	yes	—
17	C₂×C₈×D₁₅	C₂²	1	2	yes	—
18	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
19	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×#681	C₂²	1	1	yes	characteristic
21	C₃×#4047	—	2	4	no	—
22	C₂×C₃×#676	C₂²	1	2	yes	—
23	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
24	#91569	C₄	1	4	yes	—
25	#91458	C₄	1	1	yes	characteristic
26	C₄×#1202	C₂²	1	4	yes	—
27	#91389	C₄	1	1	yes	characteristic
28	#91374	C₄	1	1	yes	characteristic
29	#91364	C₄	1	1	yes	characteristic
30	C₅×C₈×Dic₃	C₂²	1	2	yes	—
31	C₅×C₈×Dic₃	C₂²	1	2	yes	—
32	Dic₃⋊#168	C₂²	1	4	yes	—
33	#90957	C₂²	1	4	yes	—
34	#90955	C₂²	1	4	yes	—
35	#83786	—	5	1	no	maximal, Hall
36	C₂×#4047	—	3	1	no	—
37	C₂×#4047	D₃	1	1	yes	characteristic, complemented
38	#65811	—	3	1	no	—
39	C₂×C₄×C₅×C₈	—	3	1	no	—
40	#65399	—	3	1	no	—
41	#65399	—	3	1	no	—
42	#65213	—	3	1	no	—
43	#64977	—	3	4	no	—
44	C₈×D₂₀	—	3	4	no	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂×#1220	C₂×C₄	1	2	yes	—
47	#6817	—	2	2	no	—
48	#6817	—	2	2	no	—
49	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×D₁₅	C₂³	1	2	yes	—
51	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
53	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
54	C₃×#709	—	2	2	no	—
55	C₃×#709	—	2	2	no	—
56	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
57	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
58	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
59	C₂×#1202	C₂×C₄	1	4	yes	—
60	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
61	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
63	#6710	—	2	2	no	—
64	C₂×C₃⋊#168	C₂³	1	2	yes	—
65	#6705	—	2	4	no	—
66	C₈×D₁₅	—	2	4	no	—
67	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
68	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
69	C₄×C₅×Dic₃	C₂³	1	2	yes	—
70	C₂×C₅×C₃⋊C₈	—	2	2	no	—
71	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
72	C₃×#681	—	2	2	no	—
73	C₂×C₃×#168	C₂³	1	2	yes	—
74	C₃×#676	—	2	4	no	—
75	C₃×C₈×D₅	—	2	4	no	—
76	Dic₃⋊Dic₅	C₂×C₄	1	4	yes	—
77	#6667	C₂×C₄	1	4	yes	—
78	#6665	C₂×C₄	1	4	yes	—
79	C₂×C₃×#131	—	5	1	no	—
80	#5832	—	5	1	no	—
81	C₂×#901	—	5	1	no	—
82	#5234	—	5	1	no	—
83	#5129	—	5	1	no	—
84	#5128	—	5	4	no	—
85	#5118	—	5	1	no	—
86	C₈×#67	—	5	4	no	—
87	C₂×C₈×Dic₃	D₅	1	1	yes	characteristic, complemented
88	C₂×#709	—	3	1	no	—
89	C₂×#709	C₂×D₃	1	1	yes	characteristic
90	C₂²×C₅×C₈	—	3	1	no	—
91	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
92	C₂×C₄²×C₅	—	3	1	no	—
93	#4076	—	3	4	no	—
94	C₂×#681	—	3	1	no	—
95	C₂×#681	C₂×D₃	1	1	yes	characteristic
96	#4047	—	2	4	no	—
97	#4047	—	6	4	no	—
98	C₂×#676	—	3	2	no	—
99	C₂×#676	C₂×D₃	1	2	yes	—
100	C₂×C₈×D₅	—	3	2	no	—
101	C₂×C₈×D₅	C₂×D₃	1	2	yes	—
102	#4021	—	3	1	no	—
103	#4021	—	3	1	no	—
104	#4020	—	3	1	no	—
105	C₄×D₂₀	—	3	4	no	—
106	#4015	—	3	1	no	—
107	C₄×C₅×C₈	—	3	2	no	—
108	C₄×C₅×C₈	—	3	2	no	—
109	#3952	—	3	4	no	—
110	#3952	—	3	4	no	—
111	C₄⋊#168	—	3	4	no	—
112	#2931	—	15	1	no	Sylow
113	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
115	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	#41	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
120	#1220	—	2	4	no	—
121	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
122	D₆₀	—	2	2	no	—
123	C₄×D₁₅	—	2	2	no	—
124	C₄×D₁₅	—	2	2	no	—
125	Dic₃₀	—	2	2	no	—
126	C₂×C₅×Dic₃	—	2	4	no	—
127	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
128	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
129	C₃×C₂²⋊D₅	—	2	4	no	—
130	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
131	C₃×D₂₀	—	2	2	no	—
132	C₃×C₄×D₅	—	2	2	no	—
133	C₃×C₄×D₅	—	2	2	no	—
134	C₃×Dic₁₀	—	2	2	no	—
135	#1202	—	2	8	no	—
136	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
137	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
138	C₃⋊#168	—	2	2	no	—
139	C₃×#168	—	2	2	no	—
140	C₅×C₃⋊C₈	—	2	2	no	—
141	C₂×C₃×#41	—	5	1	no	—
142	C₂×#235	—	5	1	no	—
143	C₃×#131	—	10	4	no	—
144	C₂×C₃×M₁₆	—	5	1	no	—
145	C₂×C₃×M₁₆	—	5	2	no	—
146	C₂²×C₃×C₈	—	5	2	no	—
147	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
148	#947	—	5	1	no	—
149	#944	—	5	1	no	—
150	#940	—	5	1	no	—
151	#939	—	5	4	no	—
152	#936	—	5	1	no	—
153	C₄×#67	—	5	4	no	—
154	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
155	C₂×#208	—	5	1	no	—
156	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
157	#901	—	10	4	no	—
158	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
159	C₂×D₃×C₈	—	5	2	no	—
160	#830	—	5	4	no	—
161	(C₂×D₃)⋊C₈	—	5	4	no	—
162	Dic₃⋊C₈	—	5	4	no	—
163	C₈×Dic₃	C₂×D₅	1	2	yes	—
164	C₈×Dic₃	C₂×D₅	1	2	yes	—
165	C₂²×C₄×C₅	—	3	2	no	—
166	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
167	C₂×C₂²⋊D₅	—	3	2	no	—
168	C₂×C₂²⋊D₅	C₄×D₃	1	2	yes	—
169	#709	—	2	2	no	—
170	#709	—	2	2	no	—
171	#709	—	6	2	no	—
172	#709	—	6	2	no	—
173	C₂×D₂₀	—	3	4	no	—
174	C₂×D₂₀	—	3	1	no	—
175	C₂×D₂₀	C₄×D₃	1	1	yes	characteristic
176	C₂×C₄×D₅	—	3	2	no	—
177	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
178	C₂×Dic₁₀	—	3	1	no	—
179	C₂×Dic₁₀	C₄×D₃	1	1	yes	characteristic
180	C₂×C₅×C₈	—	3	2	no	—
181	C₂×C₅×C₈	—	6	2	no	—
182	C₂×C₅×C₈	#67	1	4	yes	complemented
183	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
184	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
185	C₄²×C₅	—	3	1	no	—
186	C₄²×C₅	—	3	1	no	—
187	C₄²×C₅	—	3	2	no	—
188	#685	—	3	4	no	—
189	#685	—	3	4	no	—
190	C₄⋊Dic₅	—	3	4	no	—
191	#681	—	2	2	no	—
192	#681	—	6	2	no	—
193	C₂×#168	—	3	2	no	—
194	C₂×#168	C₂²×D₃	1	2	yes	—
195	#676	—	2	4	no	—
196	#676	—	6	4	no	—
197	C₈×D₅	—	2	4	no	—
198	C₈×D₅	—	6	4	no	—
199	C₂×#131	—	5	1	no	—
200	C₂×#131	—	15	1	no	—
201	#532	—	15	1	no	—
202	#436	—	15	4	no	—
203	C₈×D₄	—	15	4	no	—
204	#423	—	15	1	no	—
205	#408	—	15	1	no	—
206	#408	—	15	1	no	—
207	C₂×C₄×C₈	—	3	1	no	—
208	C₂²×C₃×C₅	—	2	2	no	—
209	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
210	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
211	C₂×D₁₅	—	2	2	no	—
212	C₂×D₁₅	—	2	4	no	—
213	C₂×C₃×D₅	—	2	2	no	—
214	C₂×C₃×D₅	—	2	4	no	—
215	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
216	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
217	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
218	Dic₁₅	—	2	2	no	—
219	C₃×Dic₅	—	2	2	no	—
220	C₅×Dic₃	—	2	2	no	—
221	C₅×Dic₃	#131	1	4	yes	complemented
222	C₃×#41	—	10	2	no	—
223	C₃×#41	—	10	2	no	—
224	C₂×C₃×Q₈	—	5	1	no	—
225	C₂×C₃×D₄	—	5	2	no	—
226	C₂×C₃×D₄	—	5	1	no	—
227	C₂²×C₃×C₄	—	5	2	no	—
228	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
229	C₂×#67	—	5	2	no	—
230	C₂×#67	—	5	4	no	—
231	C₂²×Dic₃	C₄×D₅	1	2	yes	—
232	#235	—	10	2	no	—
233	#235	—	10	2	no	—
234	C₂×D₁₂	—	5	1	no	—
235	C₂×C₄×D₃	—	5	2	no	—
236	C₂×Dic₆	—	5	1	no	—
237	C₃×M₁₆	—	10	2	no	—
238	C₃×M₁₆	—	10	4	no	—
239	C₂×C₃×C₈	—	5	2	no	—
240	C₂×C₃×C₈	—	10	4	no	—
241	C₂×C₃×C₈	D₂₀	1	4	yes	complemented
242	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
243	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
244	#217	—	5	4	no	—
245	(C₂×D₃)⋊C₄	—	5	4	no	—
246	Dic₃⋊C₄	—	5	4	no	—
247	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
248	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
249	C₄×Dic₃	C₂²×D₅	1	2	yes	—
250	#208	—	10	2	no	—
251	C₂×C₃⋊C₈	—	2	2	no	—
252	C₂×C₃⋊C₈	—	5	2	no	—
253	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
254	ΓL(1,𝔽₂₅)	—	10	4	no	—
255	D₃×C₈	—	10	4	no	—
256	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
257	C₂²×D₅	—	3	2	no	—
258	C₂²×D₅	C₂×C₄×D₃	1	2	yes	—
259	C₂×C₄×C₅	—	3	2	no	—
260	C₂×C₄×C₅	—	3	2	no	—
261	C₂×C₄×C₅	—	6	4	no	—
262	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
263	C₂×C₄×C₅	#235	1	2	yes	—
264	C₂×C₄×C₅	C₂×#67	1	2	yes	—
265	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
266	C₂²⋊D₅	—	2	4	no	—
267	C₂²⋊D₅	—	6	4	no	—
268	C₂×Dic₅	—	3	2	no	—
269	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
270	D₂₀	—	2	2	no	—
271	D₂₀	—	6	8	no	—
272	D₂₀	—	6	2	no	—
273	C₄×D₅	—	2	2	no	—
274	C₄×D₅	—	2	2	no	—
275	C₄×D₅	—	6	2	no	—
276	C₄×D₅	—	6	2	no	—
277	Dic₁₀	—	2	2	no	—
278	Dic₁₀	—	6	2	no	—
279	C₅×C₈	—	6	2	no	—
280	C₅×C₈	C₂×#67	1	2	yes	—
281	C₅×C₈	C₂×#67	1	2	yes	—
282	#168	—	2	2	no	—
283	#168	—	6	2	no	—
284	C₂×#41	—	5	1	no	—
285	C₂×#41	—	15	1	no	—
286	#131	—	10	4	no	—
287	#131	—	30	4	no	—
288	C₂×M₁₆	—	5	1	no	—
289	C₂×M₁₆	—	5	2	no	—
290	C₂×M₁₆	—	15	1	no	—
291	C₂×M₁₆	—	15	2	no	—
292	C₂²×C₈	—	3	1	no	—
293	C₂²×C₈	—	5	2	no	—
294	C₂²×C₈	—	15	2	no	—
295	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
296	C₄⋊Q₈	—	15	1	no	—
297	#127	—	15	1	no	—
298	#124	—	15	1	no	—
299	#124	—	15	1	no	—
300	#121	—	15	4	no	—
301	C₄×D₄	—	15	4	no	—
302	C₂×C₄²	—	3	1	no	—
303	C₄⋊C₈	—	15	4	no	—
304	C₂²⋊C₈	—	15	4	no	—
305	C₂²⋊C₈	—	15	4	no	—
306	C₄×C₈	—	3	2	no	—
307	C₄×C₈	—	3	2	no	—
308	C₂×C₃×C₅	—	2	2	no	—
309	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
310	C₂×C₃×C₅	C₂×#131	1	2	yes	—
311	D₁₅	—	4	2	no	—
312	C₃×D₅	—	4	2	no	—
313	C₂³×C₃	—	5	2	no	—
314	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
315	C₂²×D₃	—	5	2	no	—
316	C₃×Q₈	—	10	2	no	—
317	C₃×D₄	—	10	4	no	—
318	C₃×D₄	—	10	2	no	—
319	C₂×C₃×C₄	—	5	2	no	—
320	C₂×C₃×C₄	—	10	2	no	—
321	C₂×C₃×C₄	—	10	2	no	—
322	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
324	C₂×C₃×C₄	#709	1	2	yes	—
325	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
326	#67	—	10	4	no	—
327	#67	—	10	8	no	—
328	C₂×Dic₃	—	2	4	no	—
329	C₂×Dic₃	—	5	2	no	—
330	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
331	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
332	D₁₂	—	10	2	no	—
333	C₄×D₃	—	10	2	no	—
334	C₄×D₃	—	10	2	no	—
335	Dic₆	—	10	2	no	—
336	C₃×C₈	—	10	2	no	—
337	C₃×C₈	C₂×D₂₀	1	2	yes	—
338	C₃×C₈	C₂×D₂₀	1	2	yes	—
339	C₃⋊C₈	—	2	2	no	—
340	C₃⋊C₈	—	10	2	no	—
341	C₂²×C₅	—	2	2	no	—
342	C₂²×C₅	C₄×#67	1	2	yes	—
343	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
344	C₂×D₅	—	2	4	no	—
345	C₂×D₅	—	2	2	no	—
346	C₂×D₅	—	6	4	no	—
347	C₂×D₅	—	6	2	no	—
348	C₄×C₅	—	3	4	no	—
349	C₄×C₅	—	6	2	no	—
350	C₄×C₅	C₄×#67	1	2	yes	—
351	C₄×C₅	C₂×#235	1	1	yes	characteristic
352	C₄×C₅	C₂²×#67	1	1	yes	characteristic
353	Dic₅	—	2	2	no	—
354	Dic₅	—	6	2	no	—
355	#41	—	10	2	no	—
356	#41	—	10	2	no	—
357	#41	—	30	2	no	—
358	#41	—	30	2	no	—
359	C₂×Q₈	—	5	1	no	—
360	C₂×Q₈	—	15	1	no	—
361	C₂×D₄	—	5	2	no	—
362	C₂×D₄	—	5	1	no	—
363	C₂×D₄	—	15	4	no	—
364	C₂×D₄	—	15	2	no	—
365	C₂×D₄	—	15	1	no	—
366	C₂²×C₄	—	3	2	no	—
367	C₂²×C₄	—	5	2	no	—
368	C₂²×C₄	—	15	2	no	—
369	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
370	M₁₆	—	10	2	no	—
371	M₁₆	—	10	4	no	—
372	M₁₆	—	30	2	no	—
373	M₁₆	—	30	4	no	—
374	C₂×C₈	—	3	2	no	—
375	C₂×C₈	—	5	2	no	—
376	C₂×C₈	—	6	2	no	—
377	C₂×C₈	—	10	4	no	—
378	C₂×C₈	—	15	2	no	—
379	C₂×C₈	—	30	4	no	—
380	C₂×C₈	#1202	1	4	yes	complemented
381	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
382	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
383	C₄⋊C₄	—	15	4	no	—
384	C₂²⋊C₄	—	15	4	no	—
385	C₂²⋊C₄	—	15	4	no	—
386	C₄²	—	3	1	no	—
387	C₄²	—	3	1	no	—
388	C₄²	—	3	2	no	—
389	C₃×C₅	#2931	1	1	yes	characteristic, complemented, Hall
390	C₂²×C₃	—	2	2	no	—
391	C₂²×C₃	—	10	2	no	—
392	C₂²×C₃	—	10	4	no	—
393	C₂²×C₃	C₄×D₂₀	1	2	yes	—
394	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
395	C₂×D₃	—	10	2	no	—
396	C₂×D₃	—	10	4	no	—
397	C₃×C₄	—	10	2	no	—
398	C₃×C₄	C₄×D₂₀	1	2	yes	—
399	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
400	C₃×C₄	C₂×#709	1	1	yes	characteristic
401	Dic₃	—	2	2	no	—
402	Dic₃	—	10	2	no	—
403	Dic₃	#4047	1	4	yes	complemented
404	C₂×C₅	—	2	2	no	—
405	C₂×C₅	D₃×#131	1	2	yes	—
406	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
407	D₅	—	4	2	no	—
408	D₅	—	12	2	no	—
409	C₂³	—	5	2	no	—
410	C₂³	—	15	2	no	—
411	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
412	Q₈	—	10	2	no	—
413	Q₈	—	30	2	no	—
414	D₄	—	10	4	no	—
415	D₄	—	10	2	no	—
416	D₄	—	30	8	no	—
417	D₄	—	30	4	no	—
418	D₄	—	30	2	no	—
419	C₂×C₄	—	3	2	no	—
420	C₂×C₄	—	3	2	no	—
421	C₂×C₄	—	5	2	no	—
422	C₂×C₄	—	6	4	no	—
423	C₂×C₄	—	10	2	no	—
424	C₂×C₄	—	10	2	no	—
425	C₂×C₄	—	15	2	no	—
426	C₂×C₄	—	30	2	no	—
427	C₂×C₄	—	30	2	no	—
428	C₂×C₄	#6771	1	2	yes	—
429	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
430	C₂×C₄	C₂×#1202	1	2	yes	—
431	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
432	C₈	—	6	2	no	—
433	C₈	—	10	2	no	—
434	C₈	—	30	2	no	—
435	C₈	C₂×#1202	1	2	yes	—
436	C₈	C₂×#1202	1	2	yes	—
437	C₂×C₃	—	2	2	no	—
438	C₂×C₃	—	20	2	no	—
439	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
440	C₂×C₃	C₂×#4047	1	2	yes	—
441	D₃	—	20	2	no	—
442	C₅	#83786	1	1	yes	characteristic, complemented, Sylow
443	C₂²	—	2	2	no	—
444	C₂²	—	10	2	no	—
445	C₂²	—	10	4	no	—
446	C₂²	—	30	2	no	—
447	C₂²	—	30	4	no	—
448	C₂²	C₄×#1202	1	2	yes	—
449	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
450	C₄	—	3	4	no	—
451	C₄	—	6	2	no	—
452	C₄	—	10	2	no	—
453	C₄	—	30	2	no	—
454	C₄	C₄×#1202	1	2	yes	—
455	C₄	C₂×#6771	1	1	yes	characteristic
456	C₄	C₂²×#1202	1	1	yes	characteristic
457	C₃	#10610189	1	1	yes	characteristic, complemented, Sylow
458	C₂	—	2	2	no	—
459	C₂	—	20	2	no	—
460	C₂	—	60	2	no	—
461	C₂	D₃×#4047	1	2	yes	—
462	C₂	C₂×C₄×#1202	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂²×C₃×C₅×C₈	C₂²
prime radical	#11754581	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	#2931
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#91790	C₂	semidirect
2. C₂×C₃×#4047	C₂	semidirect
4. C₂×C₅×C₈×Dic₃	C₂	semidirect
5. #11748440	C₂	semidirect
6. #11748350	C₂	semidirect
7. #11748342	C₂	semidirect
8. #11747715	C₂	semidirect
9. C₈×#1202	C₂	semidirect
37. C₂×#4047	D₃	semidirect
60. C₂×C₃×C₅×C₈	D₄	semidirect
87. C₂×C₈×Dic₃	D₅	semidirect
182. C₂×C₅×C₈	#67	semidirect
221. C₅×Dic₃	#131	semidirect
241. C₂×C₃×C₈	D₂₀	semidirect
380. C₂×C₈	#1202	semidirect
389. C₃×C₅	#2931	semidirect
403. Dic₃	#4047	semidirect
442. C₅	#83786	semidirect
457. C₃	#10610189	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91790	2
C₂×C₃×#4047	2
#11754581	2
C₂×C₅×C₈×Dic₃	2
#11748440	2
#11748350	2
#11748342	2
#11747715	2
C₈×#1202	2
#10610189	3
#83786	5