Subgroups — #14411545

Order 1920.

1112 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	C₂×#91790	C₂	1	1	yes	maximal, characteristic
2	#11754414	C₂	1	1	yes	maximal, characteristic
3	C₂×#91290	C₂	1	1	yes	maximal, characteristic
4	C₅×#5101	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3947	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748323	C₂	1	1	yes	maximal, characteristic, complemented
7	Dic₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
8	#11748054	C₂	1	2	yes	maximal, complemented
9	#11747668	C₂	1	2	yes	maximal, complemented
10	#11747603	C₂	1	2	yes	maximal, complemented
11	#11747599	C₂	1	2	yes	maximal, complemented
12	#10610281	—	3	1	no	maximal, Hall
13	C₂×#6817	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×#6710	C₂²	1	1	yes	characteristic
16	#91790	C₄	1	8	yes	complemented
17	C₂×#6705	C₂²	1	2	yes	—
18	C₂×C₈×D₁₅	C₂²	1	2	yes	—
19	C₅×#926	C₂²	1	1	yes	characteristic
20	C₂×C₅×#208	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
22	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
23	#91552	C₄	1	4	yes	—
24	#91418	C₄	1	2	yes	—
25	C₄×#1200	C₂²	1	2	yes	—
26	#91386	C₂²	1	2	yes	—
27	#91333	C₄	1	2	yes	—
28	C₂×#6651	C₂²	1	2	yes	—
29	#91290	C₄	1	8	yes	complemented
30	C₂×#6648	C₂²	1	2	yes	—
31	C₅×#815	C₂²	1	2	yes	—
32	C₅×C₈×Dic₃	C₂²	1	2	yes	—
33	C₃×#3947	C₂²	1	1	yes	characteristic
34	C₃×#3947	C₂²	1	1	yes	characteristic
35	C₃×#3947	C₂²	1	1	yes	characteristic
36	C₃×#3947	C₂²	1	1	yes	characteristic
37	#90953	C₂²	1	2	yes	—
38	#90952	C₂²	1	2	yes	—
39	Dic₃×#168	C₂²	1	2	yes	—
40	Dic₅×C₃⋊C₈	C₂²	1	2	yes	—
41	#78486	—	5	1	no	maximal, Hall
42	C₂×#4053	—	3	1	no	—
43	C₂×#4047	—	3	1	no	—
44	#65856	—	3	1	no	—
45	C₅×#405	—	3	1	no	—
46	M₁₆×Dic₅	—	3	1	no	—
47	C₂×#3947	D₃	1	1	yes	characteristic, complemented
48	#65286	—	3	1	no	—
49	#64997	—	3	2	no	—
50	D₅×#97	—	3	2	no	—
51	#64978	—	3	2	no	—
52	C₄×#676	—	3	2	no	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂×#1220	C₂×C₄	1	2	yes	—
55	#6817	C₂×C₄	1	4	yes	—
56	#6817	C₂×C₄	1	4	yes	—
57	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×D₁₅	C₂³	1	2	yes	—
59	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
61	C₂×#1200	C₂×C₄	1	4	yes	—
62	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
63	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	#6710	C₂×C₄	1	4	yes	complemented
66	C₂×C₃⋊#168	C₂³	1	2	yes	—
67	#6705	C₂×C₄	1	8	yes	complemented
68	C₈×D₁₅	C₂×C₄	1	8	yes	complemented
69	C₅×#217	C₂×C₄	1	2	yes	—
70	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
71	C₄×C₅×Dic₃	C₂³	1	2	yes	—
72	C₅×#208	C₂×C₄	1	4	yes	complemented
73	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
74	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
75	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
76	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
77	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
78	C₂×C₃×#168	C₂³	1	1	yes	characteristic
79	C₂×C₃×#168	C₂³	1	1	yes	characteristic
80	#6669	C₂×C₄	1	4	yes	—
81	#6667	C₂×C₄	1	4	yes	—
82	Dic₃×Dic₅	C₂×C₄	1	4	yes	—
83	#6651	C₂×C₄	1	8	yes	complemented
84	#6648	C₂×C₄	1	8	yes	complemented
85	C₂×#901	—	5	1	no	—
86	C₂×#901	—	5	1	no	—
87	C₄×#235	—	5	1	no	—
88	C₂×C₃×#97	—	5	1	no	—
89	#5101	—	5	1	no	—
90	#5101	D₅	1	1	yes	characteristic, complemented
91	C₄×#208	—	5	1	no	—
92	#4708	—	5	2	no	—
93	#4708	—	5	2	no	—
94	#4707	—	5	2	no	—
95	D₃×#97	—	5	2	no	—
96	C₂×#709	—	3	1	no	—
97	C₂×C₅×M₁₆	—	3	1	no	—
98	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
99	C₅×#117	—	3	1	no	—
100	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
101	C₂×#681	—	3	1	no	—
102	C₂²×#168	C₂×D₃	1	1	yes	characteristic
103	#4053	—	3	8	no	—
104	#4047	—	3	8	no	—
105	C₂×#676	—	3	2	no	—
106	C₂×#676	—	3	2	no	—
107	C₂×C₈×D₅	—	3	2	no	—
108	C₂×C₈×D₅	—	3	2	no	—
109	#4039	—	3	2	no	—
110	#4033	—	3	2	no	—
111	#4027	—	3	4	no	—
112	#4018	—	3	2	no	—
113	C₄²×D₅	—	3	2	no	—
114	C₅×#97	—	3	2	no	—
115	C₄×C₅×C₈	—	3	2	no	—
116	#3947	—	3	2	no	—
117	#3947	C₂×D₃	1	1	yes	characteristic
118	#3947	C₂×D₃	1	1	yes	characteristic
119	#3947	C₂×D₃	1	1	yes	characteristic
120	#3947	C₂×D₃	1	1	yes	characteristic
121	C₈×Dic₅	—	3	2	no	—
122	#3935	—	3	2	no	—
123	C₄×#168	—	3	2	no	—
124	#2875	—	15	1	no	Sylow
125	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
131	#1220	C₄²	1	8	yes	—
132	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
133	D₆₀	C₄²	1	4	yes	—
134	C₄×D₁₅	C₂²×C₄	1	4	yes	—
135	C₄×D₁₅	C₂²×C₄	1	4	yes	—
136	Dic₃₀	C₄²	1	4	yes	—
137	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
138	C₂×C₃×Dic₅	—	4	2	no	—
139	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
140	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
141	#1200	—	4	4	no	—
142	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
143	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
144	C₃⋊#168	C₂²×C₄	1	4	yes	—
145	C₃×#168	C₂²×C₄	1	2	yes	—
146	C₃×#168	C₂²×C₄	1	2	yes	—
147	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	—
148	C₂×#235	—	5	1	no	—
149	C₂²×C₃×C₈	—	5	1	no	—
150	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
151	C₂×C₃×C₄²	—	5	1	no	—
152	C₄×#67	—	5	4	no	—
153	#926	C₂×D₅	1	1	yes	characteristic
154	C₂×#208	—	5	1	no	—
155	C₂×#208	C₂×D₅	1	1	yes	characteristic
156	#901	—	5	8	no	—
157	#901	—	5	8	no	—
158	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
159	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
160	C₂×D₃×C₈	—	5	2	no	—
161	C₂×D₃×C₈	—	5	2	no	—
162	C₄×D₁₂	—	5	2	no	—
163	#872	—	5	2	no	—
164	C₄²×D₃	—	5	2	no	—
165	C₄×Dic₆	—	5	2	no	—
166	C₃×#97	—	5	1	no	—
167	C₃×#97	—	5	1	no	—
168	C₃×#97	—	5	1	no	—
169	C₃×#97	—	5	1	no	—
170	#815	—	5	2	no	—
171	#815	C₂×D₅	1	2	yes	—
172	C₈×Dic₃	—	5	2	no	—
173	C₈×Dic₃	C₂×D₅	1	2	yes	—
174	#803	—	5	2	no	—
175	C₄×C₃⋊C₈	—	5	2	no	—
176	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
177	C₂×C₂²⋊D₅	—	3	2	no	—
178	C₂²×Dic₅	C₄×D₃	1	2	yes	—
179	#709	—	3	4	no	—
180	#709	—	3	4	no	—
181	C₂×D₂₀	—	3	1	no	—
182	C₂×C₄×D₅	—	3	2	no	—
183	C₂×C₄×D₅	—	3	4	no	—
184	C₂×Dic₁₀	—	3	1	no	—
185	C₅×M₁₆	—	3	4	no	—
186	C₂×C₅×C₈	—	3	2	no	—
187	C₂×C₅×C₈	C₄×D₃	1	4	yes	complemented
188	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
189	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
190	C₅×C₄⋊C₄	—	3	2	no	—
191	C₅×C₂²⋊C₄	—	3	2	no	—
192	C₄²×C₅	—	3	2	no	—
193	#685	—	3	4	no	—
194	#683	—	3	4	no	—
195	C₄×Dic₅	—	3	4	no	—
196	C₄×Dic₅	C₄×D₃	1	2	yes	—
197	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
198	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
199	#681	—	3	4	no	—
200	C₂×#168	—	3	2	no	—
201	C₂×#168	C₄×D₃	1	4	yes	complemented
202	C₂×#168	C₂²×D₃	1	1	yes	characteristic
203	C₂×#168	C₂²×D₃	1	1	yes	characteristic
204	#676	—	3	8	no	—
205	#676	—	3	8	no	—
206	C₈×D₅	—	3	8	no	—
207	C₈×D₅	—	3	8	no	—
208	C₂×#131	—	15	1	no	—
209	C₂×#131	—	15	1	no	—
210	C₄×#41	—	15	1	no	—
211	#405	—	3	1	no	—
212	#405	—	15	2	no	—
213	#405	—	15	2	no	—
214	#405	—	15	1	no	—
215	C₄×M₁₆	—	15	2	no	—
216	C₄×M₁₆	—	15	1	no	—
217	C₂×#97	—	5	1	no	—
218	C₂×#97	—	15	2	no	—
219	C₂²×C₃×C₅	—	2	2	no	—
220	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
221	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
222	C₂×D₁₅	—	2	4	no	—
223	C₂×D₁₅	C₂×C₄²	1	4	yes	—
224	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
225	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
226	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
227	Dic₁₅	C₂×C₄²	1	4	yes	—
228	C₃×Dic₅	—	2	2	no	—
229	C₃×Dic₅	—	2	2	no	—
230	C₅×Dic₃	—	2	4	no	—
231	C₂²×C₃×C₄	—	5	2	no	—
232	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
233	C₂×#67	—	5	2	no	—
234	#235	—	5	4	no	—
235	#235	—	5	4	no	—
236	C₂×D₁₂	—	5	1	no	—
237	C₂×C₄×D₃	—	5	2	no	—
238	C₂×C₄×D₃	—	5	4	no	—
239	C₂×Dic₆	—	5	1	no	—
240	C₂×C₃×C₈	—	5	4	no	—
241	C₂×C₃×C₈	—	5	1	no	—
242	C₂×C₃×C₈	—	5	1	no	—
243	C₂×C₃×C₈	C₄×D₅	1	4	yes	complemented
244	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
245	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
246	C₃×C₄²	—	5	2	no	—
247	C₃×C₄²	—	5	1	no	—
248	C₃×C₄²	—	5	1	no	—
249	#217	C₄×D₅	1	2	yes	—
250	(C₂×D₃)⋊C₄	—	5	4	no	—
251	C₄⋊Dic₃	C₄×D₅	1	2	yes	—
252	Dic₃⋊C₄	—	5	4	no	—
253	C₄×Dic₃	—	5	4	no	—
254	C₄×Dic₃	C₂²×D₅	1	2	yes	—
255	#208	—	5	4	no	—
256	#208	C₄×D₅	1	4	yes	complemented
257	C₂×C₃⋊C₈	—	5	2	no	—
258	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
259	ΓL(1,𝔽₂₅)	—	5	8	no	—
260	ΓL(1,𝔽₂₅)	—	5	8	no	—
261	D₃×C₈	—	5	8	no	—
262	D₃×C₈	—	5	8	no	—
263	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
264	C₂²×D₅	—	3	2	no	—
265	C₂×C₄×C₅	—	3	4	no	—
266	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
268	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
269	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
270	C₂²⋊D₅	—	3	8	no	—
271	C₂×Dic₅	—	3	2	no	—
272	C₂×Dic₅	—	4	2	no	—
273	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
274	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
275	D₂₀	—	3	4	no	—
276	C₄×D₅	—	3	4	no	—
277	C₄×D₅	—	3	4	no	—
278	C₄×D₅	—	12	4	no	—
279	Dic₁₀	—	3	4	no	—
280	C₅×C₈	—	3	4	no	—
281	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
282	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
283	#168	—	3	4	no	—
284	#168	C₂×C₄×D₃	1	2	yes	—
285	#168	C₂×C₄×D₃	1	2	yes	—
286	C₂×#41	—	15	1	no	—
287	#131	—	15	8	no	—
288	#131	—	15	8	no	—
289	C₂×M₁₆	—	3	1	no	—
290	C₂×M₁₆	—	15	2	no	—
291	C₂×M₁₆	—	15	1	no	—
292	C₂×M₁₆	—	15	2	no	—
293	C₂²×C₈	—	5	1	no	—
294	C₂²×C₈	—	15	2	no	—
295	C₂²×C₈	—	15	2	no	—
296	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
297	C₄×Q₈	—	15	2	no	—
298	C₄×D₄	—	15	2	no	—
299	C₄×D₄	—	15	4	no	—
300	#117	—	3	1	no	—
301	#117	—	15	2	no	—
302	C₂×C₄²	—	5	1	no	—
303	C₂×C₄²	—	15	2	no	—
304	#97	—	3	2	no	—
305	#97	—	5	1	no	—
306	#97	—	5	1	no	—
307	#97	—	5	1	no	—
308	#97	—	5	1	no	—
309	#97	—	15	2	no	—
310	#97	—	15	2	no	—
311	C₄×C₈	—	3	2	no	—
312	C₄×C₈	—	15	2	no	—
313	C₄×C₈	—	15	2	no	—
314	C₂×C₃×C₅	—	2	2	no	—
315	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
316	C₂×C₃×C₅	#568	1	2	yes	—
317	D₁₅	—	2	4	no	—
318	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
319	C₂²×D₃	—	5	2	no	—
320	C₂×C₃×C₄	—	5	2	no	—
321	C₂×C₃×C₄	—	5	2	no	—
322	C₂×C₃×C₄	—	20	2	no	—
323	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
324	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
326	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
327	#67	—	5	8	no	—
328	C₂×Dic₃	—	5	2	no	—
329	C₂×Dic₃	C₂×C₄×D₅	1	4	yes	—
330	D₁₂	—	5	4	no	—
331	C₄×D₃	—	5	4	no	—
332	C₄×D₃	—	5	4	no	—
333	C₄×D₃	—	20	4	no	—
334	Dic₆	—	5	4	no	—
335	C₃×C₈	—	5	2	no	—
336	C₃×C₈	—	5	2	no	—
337	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
338	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
339	C₃⋊C₈	—	5	4	no	—
340	C₃⋊C₈	C₂×C₄×D₅	1	4	yes	—
341	C₂²×C₅	—	2	2	no	—
342	C₂²×C₅	C₄²×D₃	1	2	yes	—
343	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
344	C₂×D₅	—	3	4	no	—
345	C₂×D₅	—	6	4	no	—
346	C₄×C₅	—	6	4	no	—
347	C₄×C₅	C₄²×D₃	1	2	yes	—
348	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
349	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
350	Dic₅	—	2	2	no	—
351	Dic₅	—	2	2	no	—
352	Dic₅	—	3	4	no	—
353	#41	—	15	4	no	—
354	#41	—	15	4	no	—
355	C₂×Q₈	—	15	1	no	—
356	C₂×D₄	—	15	2	no	—
357	C₂×D₄	—	15	1	no	—
358	C₂²×C₄	—	5	2	no	—
359	C₂²×C₄	—	15	4	no	—
360	C₂²×C₄	—	15	2	no	—
361	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
362	M₁₆	—	3	4	no	—
363	M₁₆	—	15	8	no	—
364	M₁₆	—	15	4	no	—
365	M₁₆	—	15	8	no	—
366	C₂×C₈	—	3	2	no	—
367	C₂×C₈	—	5	4	no	—
368	C₂×C₈	—	5	1	no	—
369	C₂×C₈	—	5	1	no	—
370	C₂×C₈	—	15	8	no	—
371	C₂×C₈	—	15	2	no	—
372	C₂×C₈	—	15	8	no	—
373	C₂×C₈	#1200	1	4	yes	complemented
374	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
375	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
376	C₄⋊C₄	—	3	2	no	—
377	C₄⋊C₄	—	15	4	no	—
378	C₂²⋊C₄	—	3	2	no	—
379	C₂²⋊C₄	—	15	4	no	—
380	C₄²	—	3	2	no	—
381	C₄²	—	5	2	no	—
382	C₄²	—	5	1	no	—
383	C₄²	—	5	1	no	—
384	C₄²	—	15	4	no	—
385	C₃×C₅	#2875	1	1	yes	characteristic, complemented, Hall
386	C₂²×C₃	—	2	2	no	—
387	C₂²×C₃	C₄²×D₅	1	2	yes	—
388	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
389	C₂×D₃	—	5	4	no	—
390	C₂×D₃	—	10	4	no	—
391	C₃×C₄	—	10	2	no	—
392	C₃×C₄	—	10	2	no	—
393	C₃×C₄	C₄²×D₅	1	2	yes	—
394	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
395	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
396	Dic₃	—	2	4	no	—
397	Dic₃	—	5	4	no	—
398	C₂×C₅	—	2	2	no	—
399	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
400	C₂×C₅	#5745	1	2	yes	—
401	D₅	—	6	4	no	—
402	C₂³	—	15	2	no	—
403	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
404	Q₈	—	15	4	no	—
405	D₄	—	15	8	no	—
406	D₄	—	15	4	no	—
407	C₂×C₄	—	3	4	no	—
408	C₂×C₄	—	5	2	no	—
409	C₂×C₄	—	5	2	no	—
410	C₂×C₄	—	15	2	no	—
411	C₂×C₄	—	15	4	no	—
412	C₂×C₄	—	15	4	no	—
413	C₂×C₄	—	20	2	no	—
414	C₂×C₄	—	60	4	no	—
415	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
416	C₂×C₄	C₄×D₃×D₅	1	2	yes	—
417	C₂×C₄	C₂×#1200	1	2	yes	—
418	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
419	C₈	—	3	4	no	—
420	C₈	—	5	2	no	—
421	C₈	—	5	2	no	—
422	C₈	—	15	4	no	—
423	C₈	C₂×#1200	1	2	yes	—
424	C₈	C₂×#1200	1	2	yes	—
425	C₂×C₃	—	2	2	no	—
426	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
427	C₂×C₃	#66084	1	2	yes	—
428	D₃	—	10	4	no	—
429	C₅	#78486	1	1	yes	characteristic, complemented, Sylow
430	C₂²	—	2	2	no	—
431	C₂²	—	15	4	no	—
432	C₂²	—	30	4	no	—
433	C₂²	C₄×#1200	1	2	yes	—
434	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
435	C₄	—	6	4	no	—
436	C₄	—	10	2	no	—
437	C₄	—	10	2	no	—
438	C₄	—	15	4	no	—
439	C₄	C₄×#1200	1	2	yes	—
440	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
441	C₄	C₂²×#1200	1	1	yes	characteristic
442	C₃	#10610281	1	1	yes	characteristic, complemented, Sylow
443	C₂	—	2	2	no	—
444	C₂	—	30	4	no	—
445	C₂	#11753949	1	2	yes	—
446	C₂	C₂×C₄×#1200	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator	C₂×C₃×C₅	C₂²×C₄²
Fitting	C₂²×C₃×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×#6817	C₂²
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	#2875
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. C₅×#5101	C₂	semidirect
5. C₂×C₃×#3947	C₂	semidirect
6. #11748323	C₂	semidirect
7. Dic₅×#208	C₂	semidirect
8. #11748054	C₂	semidirect
9. #11747668	C₂	semidirect
10. #11747603	C₂	semidirect
11. #11747599	C₂	semidirect
16. #91790	C₄	semidirect
29. #91290	C₄	semidirect
47. C₂×#3947	D₃	semidirect
62. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
65. #6710	C₂×C₄	semidirect
67. #6705	C₂×C₄	semidirect
68. C₈×D₁₅	C₂×C₄	semidirect
72. C₅×#208	C₂×C₄	semidirect
77. C₂×C₃×#168	C₂×C₄	semidirect
83. #6651	C₂×C₄	semidirect
84. #6648	C₂×C₄	semidirect
90. #5101	D₅	semidirect
187. C₂×C₅×C₈	C₄×D₃	semidirect
201. C₂×#168	C₄×D₃	semidirect
243. C₂×C₃×C₈	C₄×D₅	semidirect
256. #208	C₄×D₅	semidirect
373. C₂×C₈	#1200	semidirect
385. C₃×C₅	#2875	semidirect
429. C₅	#78486	semidirect
442. C₃	#10610281	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
#11754414	2
C₂×#91290	2
C₅×#5101	2
C₂×C₃×#3947	2
#11748323	2
Dic₅×#208	2
#11748054	2
#11747668	2
#11747603	2
#11747599	2
#10610281	3
#78486	5