Subgroups — #14299795

Order 1920.

572 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	#11756586	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#104	C₂	1	1	yes	maximal, characteristic
3	#11751333	C₂	1	1	yes	maximal, characteristic
4	#11751222	C₂	1	1	yes	maximal, characteristic, complemented
5	#11751037	C₂	1	1	yes	maximal, characteristic, complemented
6	#11746375	C₂	1	1	yes	maximal, characteristic, complemented
7	#11746344	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601157	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	Q₈×Dic₁₅	—	2	1	no	—
13	D₄×Dic₁₅	—	2	1	no	—
14	D₄×Dic₁₅	—	2	2	no	—
15	#91815	—	2	1	no	—
16	#91815	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Dic₁₅	—	2	1	no	—
18	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
20	C₂×#6710	C₂²	1	1	yes	characteristic
21	C₃×C₅×#104	C₄	1	4	yes	complemented
22	#91119	—	2	1	no	—
23	#91116	—	2	1	no	—
24	#91115	—	2	2	no	—
25	#91102	—	2	1	no	—
26	#91101	—	2	1	no	—
27	#70364	—	5	1	no	maximal, Hall
28	#66161	—	3	1	no	—
29	C₂×C₅×#104	D₃	1	1	yes	characteristic
30	#65521	—	3	1	no	—
31	#65410	—	3	1	no	—
32	#65225	—	3	1	no	—
33	#64774	—	3	1	no	—
34	#64743	—	3	1	no	—
35	C₃×C₅×#41	—	2	1	no	—
36	C₃×C₅×#41	—	2	1	no	—
37	C₃×C₅×#41	C₂×C₄	1	2	yes	—
38	C₃×C₅×#41	Q₈	1	2	yes	—
39	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	—	2	1	no	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×Dic₁₅	—	2	2	no	—
46	C₂²×Dic₁₅	—	2	1	no	—
47	C₂²×Dic₁₅	D₄	1	2	yes	—
48	C₃×C₅×M₁₆	—	2	1	no	—
49	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	complemented
50	C₂×C₃×C₅×C₈	—	2	1	no	—
51	C₃×C₄²×C₅	—	2	1	no	—
52	C₃×C₄²×C₅	C₂×C₄	1	2	yes	complemented
53	#6719	—	2	2	no	—
54	#6719	—	2	1	no	—
55	C₄⋊Dic₁₅	—	2	2	no	—
56	C₄⋊Dic₁₅	—	2	1	no	—
57	C₄⋊Dic₁₅	—	2	1	no	—
58	C₄⋊Dic₁₅	—	2	1	no	—
59	C₄⋊Dic₁₅	—	2	1	no	—
60	C₄⋊Dic₁₅	D₄	1	1	yes	characteristic
61	C₄⋊Dic₁₅	D₄	1	1	yes	characteristic
62	C₄×Dic₁₅	—	2	2	no	—
63	C₄×Dic₁₅	—	2	1	no	—
64	#6710	—	2	1	no	—
65	#6710	—	2	1	no	—
66	C₂×C₃⋊#168	—	2	1	no	—
67	#5827	—	5	1	no	—
68	C₂×C₃×#104	D₅	1	1	yes	characteristic
69	#5232	—	5	1	no	—
70	#5121	—	5	1	no	—
71	#4936	—	5	1	no	—
72	#4554	—	5	1	no	—
73	#4523	—	5	1	no	—
74	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
75	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
77	Q₈×Dic₅	—	6	1	no	—
78	D₄×Dic₅	—	6	2	no	—
79	D₄×Dic₅	—	6	1	no	—
80	#4072	—	3	1	no	—
81	#4072	—	6	1	no	—
82	C₂×C₄⋊Dic₅	—	3	1	no	—
83	C₂×C₄⋊Dic₅	—	3	1	no	—
84	C₂×C₄⋊Dic₅	—	6	1	no	—
85	C₂×#681	—	3	1	no	—
86	C₅×#104	Dic₃	1	4	yes	complemented
87	#3967	—	6	1	no	—
88	#3964	—	6	1	no	—
89	#3963	—	6	2	no	—
90	#3950	—	6	1	no	—
91	#3949	—	6	1	no	—
92	#1860	—	15	1	no	Sylow
93	C₂³×C₃×C₅	—	2	1	no	—
94	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
95	C₃×C₅×Q₈	—	2	1	no	—
96	C₃×C₅×Q₈	C₄⋊C₄	1	2	yes	—
97	C₃×C₅×D₄	—	2	2	no	—
98	C₃×C₅×D₄	—	2	2	no	—
99	C₃×C₅×D₄	—	2	1	no	—
100	C₃×C₅×D₄	C₄⋊C₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	—	2	1	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	4	1	no	—
106	C₂×C₃×C₄×C₅	—	4	1	no	—
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
113	C₂×Dic₁₅	—	2	1	no	—
114	C₂×Dic₁₅	—	2	2	no	—
115	C₂×Dic₁₅	—	2	1	no	—
116	C₂×Dic₁₅	—	4	2	no	—
117	C₂×Dic₁₅	—	4	2	no	—
118	C₂×Dic₁₅	—	4	1	no	—
119	C₂×Dic₁₅	—	8	2	no	—
120	C₃×C₅×C₈	—	2	2	no	—
121	C₃⋊#168	—	4	1	no	—
122	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
123	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
124	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
125	Q₈×Dic₃	—	10	1	no	—
126	D₄×Dic₃	—	10	2	no	—
127	D₄×Dic₃	—	10	1	no	—
128	#926	—	5	1	no	—
129	#926	—	10	1	no	—
130	C₂×C₄⋊Dic₃	—	5	1	no	—
131	C₂×C₄⋊Dic₃	—	5	1	no	—
132	C₂×C₄⋊Dic₃	—	10	1	no	—
133	C₂×#208	—	5	1	no	—
134	C₃×#104	Dic₅	1	4	yes	complemented
135	#835	—	10	1	no	—
136	#832	—	10	1	no	—
137	C₃⋊#95	—	10	2	no	—
138	#818	—	10	1	no	—
139	#817	—	10	1	no	—
140	C₅×#41	—	2	1	no	—
141	C₅×#41	—	2	1	no	—
142	C₅×#41	Dic₆	1	2	yes	—
143	C₅×#41	C₂×Dic₃	1	2	yes	—
144	C₂×C₅×Q₈	D₁₂	1	1	yes	characteristic
145	C₂×C₅×D₄	—	2	1	no	—
146	C₂×C₅×D₄	D₁₂	1	1	yes	characteristic
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
150	C₂²×Dic₅	—	3	2	no	—
151	C₂²×Dic₅	—	6	2	no	—
152	C₂²×Dic₅	—	6	1	no	—
153	C₅×M₁₆	—	2	1	no	—
154	C₅×M₁₆	C₂×Dic₃	1	2	yes	complemented
155	C₂×C₅×C₈	—	2	1	no	—
156	C₄²×C₅	—	2	1	no	—
157	C₄²×C₅	C₂×Dic₃	1	2	yes	complemented
158	C₂²⋊Dic₅	—	6	2	no	—
159	C₂²⋊Dic₅	—	6	1	no	—
160	C₄⋊Dic₅	—	3	1	no	—
161	C₄⋊Dic₅	—	3	1	no	—
162	C₄⋊Dic₅	—	6	2	no	—
163	C₄⋊Dic₅	—	6	1	no	—
164	C₄⋊Dic₅	—	6	1	no	—
165	C₄⋊Dic₅	—	6	1	no	—
166	C₄⋊Dic₅	—	6	1	no	—
167	C₄×Dic₅	—	6	2	no	—
168	C₄×Dic₅	—	6	1	no	—
169	#681	—	6	1	no	—
170	#681	—	6	1	no	—
171	C₂×#168	—	6	1	no	—
172	#520	—	15	1	no	—
173	#428	—	15	1	no	—
174	C₂×#104	D₁₅	1	1	yes	characteristic
175	#417	—	15	1	no	—
176	#382	—	15	1	no	—
177	#343	—	15	1	no	—
178	#339	—	15	1	no	—
179	C₂²×C₃×C₅	—	2	1	no	—
180	C₂²×C₃×C₅	—	2	1	no	—
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	—	4	1	no	—
183	C₂²×C₃×C₅	—	4	1	no	—
184	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
185	C₂²×C₃×C₅	#120	1	1	yes	characteristic
186	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
187	C₃×C₄×C₅	—	2	2	no	—
188	C₃×C₄×C₅	—	4	2	no	—
189	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
191	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
192	C₃×C₄×C₅	#123	1	1	yes	characteristic
193	Dic₁₅	—	4	1	no	—
194	Dic₁₅	—	4	2	no	—
195	Dic₁₅	—	4	1	no	—
196	Dic₁₅	—	8	1	no	—
197	C₃×#41	—	2	1	no	—
198	C₃×#41	—	2	1	no	—
199	C₃×#41	Dic₁₀	1	2	yes	—
200	C₃×#41	C₂×Dic₅	1	2	yes	—
201	C₂×C₃×Q₈	D₂₀	1	1	yes	characteristic
202	C₂×C₃×D₄	—	2	1	no	—
203	C₂×C₃×D₄	D₂₀	1	1	yes	characteristic
204	C₂²×C₃×C₄	—	2	1	no	—
205	C₂²×C₃×C₄	—	2	1	no	—
206	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
207	C₂²×Dic₃	—	5	2	no	—
208	C₂²×Dic₃	—	10	2	no	—
209	C₂²×Dic₃	—	10	1	no	—
210	C₃×M₁₆	—	2	1	no	—
211	C₃×M₁₆	C₂×Dic₅	1	2	yes	complemented
212	C₂×C₃×C₈	—	2	1	no	—
213	C₃×C₄²	—	2	1	no	—
214	C₃×C₄²	C₂×Dic₅	1	2	yes	complemented
215	#217	—	10	2	no	—
216	#217	—	10	1	no	—
217	C₄⋊Dic₃	—	5	1	no	—
218	C₄⋊Dic₃	—	5	1	no	—
219	C₄⋊Dic₃	—	10	2	no	—
220	C₄⋊Dic₃	—	10	1	no	—
221	C₄⋊Dic₃	—	10	1	no	—
222	C₄⋊Dic₃	—	10	1	no	—
223	C₄⋊Dic₃	—	10	1	no	—
224	C₄×Dic₃	—	10	2	no	—
225	C₄×Dic₃	—	10	1	no	—
226	#208	—	10	1	no	—
227	#208	—	10	1	no	—
228	C₂×C₃⋊C₈	—	10	1	no	—
229	C₂³×C₅	—	2	1	no	—
230	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
231	C₅×Q₈	—	2	1	no	—
232	C₅×Q₈	C₄⋊Dic₃	1	2	yes	—
233	C₅×D₄	—	2	2	no	—
234	C₅×D₄	—	2	2	no	—
235	C₅×D₄	—	2	1	no	—
236	C₅×D₄	C₄⋊Dic₃	1	2	yes	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	4	1	no	—
243	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
245	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
246	C₂×C₄×C₅	#237	1	1	yes	characteristic
247	C₂×C₄×C₅	#237	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
249	C₂×Dic₅	—	6	1	no	—
250	C₂×Dic₅	—	6	1	no	—
251	C₂×Dic₅	—	6	2	no	—
252	C₂×Dic₅	—	12	2	no	—
253	C₂×Dic₅	—	12	2	no	—
254	C₂×Dic₅	—	12	1	no	—
255	C₂×Dic₅	—	24	2	no	—
256	C₅×C₈	—	2	2	no	—
257	#168	—	12	1	no	—
258	C₂×#41	C₂×D₁₅	1	1	yes	characteristic
259	C₂×M₁₆	—	15	1	no	—
260	C₂×M₁₆	C₂×D₁₅	1	1	yes	characteristic
261	C₄×Q₈	—	30	1	no	—
262	C₄×D₄	—	30	2	no	—
263	C₄×D₄	—	30	1	no	—
264	#117	—	15	1	no	—
265	#117	—	30	1	no	—
266	C₂×C₄⋊C₄	—	15	1	no	—
267	C₂×C₄⋊C₄	—	15	1	no	—
268	C₂×C₄⋊C₄	—	30	1	no	—
269	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
270	#107	—	30	1	no	—
271	#106	—	30	1	no	—
272	#104	Dic₁₅	1	4	yes	complemented
273	#103	—	30	1	no	—
274	#102	—	30	1	no	—
275	#95	—	30	2	no	—
276	C₂×C₃×C₅	—	2	1	no	—
277	C₂×C₃×C₅	—	2	1	no	—
278	C₂×C₃×C₅	—	4	2	no	—
279	C₂×C₃×C₅	#385	1	1	yes	characteristic
280	C₂×C₃×C₅	#454	1	1	yes	characteristic
281	C₂×C₃×C₅	#455	1	1	yes	characteristic
282	C₂³×C₃	—	2	1	no	—
283	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
284	C₃×Q₈	—	2	1	no	—
285	C₃×Q₈	C₄⋊Dic₅	1	2	yes	—
286	C₃×D₄	—	2	2	no	—
287	C₃×D₄	—	2	2	no	—
288	C₃×D₄	—	2	1	no	—
289	C₃×D₄	C₄⋊Dic₅	1	2	yes	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	4	1	no	—
295	C₂×C₃×C₄	—	4	1	no	—
296	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
298	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
299	C₂×C₃×C₄	#711	1	1	yes	characteristic
300	C₂×C₃×C₄	#711	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
302	C₂×Dic₃	—	10	1	no	—
303	C₂×Dic₃	—	10	1	no	—
304	C₂×Dic₃	—	10	2	no	—
305	C₂×Dic₃	—	20	2	no	—
306	C₂×Dic₃	—	20	2	no	—
307	C₂×Dic₃	—	20	1	no	—
308	C₂×Dic₃	—	40	2	no	—
309	C₃×C₈	—	2	2	no	—
310	C₃⋊C₈	—	20	1	no	—
311	C₂²×C₅	—	2	1	no	—
312	C₂²×C₅	—	2	1	no	—
313	C₂²×C₅	—	2	2	no	—
314	C₂²×C₅	—	4	1	no	—
315	C₂²×C₅	—	4	1	no	—
316	C₂²×C₅	#878	1	1	yes	characteristic
317	C₂²×C₅	#882	1	1	yes	characteristic
318	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
319	C₄×C₅	—	2	2	no	—
320	C₄×C₅	—	4	2	no	—
321	C₄×C₅	#878	1	1	yes	characteristic
322	C₄×C₅	#886	1	1	yes	characteristic
323	C₄×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
324	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
325	Dic₅	—	12	2	no	—
326	Dic₅	—	12	1	no	—
327	Dic₅	—	12	1	no	—
328	Dic₅	—	24	1	no	—
329	#41	—	2	1	no	—
330	#41	—	2	1	no	—
331	#41	Dic₃₀	1	2	yes	—
332	#41	C₂×Dic₁₅	1	2	yes	—
333	C₂×Q₈	D₆₀	1	1	yes	characteristic
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	D₆₀	1	1	yes	characteristic
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	15	2	no	—
339	C₂²×C₄	—	30	2	no	—
340	C₂²×C₄	—	30	1	no	—
341	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
342	M₁₆	—	2	1	no	—
343	M₁₆	—	30	1	no	—
344	M₁₆	—	30	1	no	—
345	M₁₆	C₂×Dic₁₅	1	2	yes	complemented
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	30	1	no	—
348	C₄⋊C₄	—	15	1	no	—
349	C₄⋊C₄	—	15	1	no	—
350	C₄⋊C₄	—	30	2	no	—
351	C₄⋊C₄	—	30	1	no	—
352	C₄⋊C₄	—	30	1	no	—
353	C₄⋊C₄	—	30	1	no	—
354	C₄⋊C₄	—	30	1	no	—
355	C₂²⋊C₄	—	30	2	no	—
356	C₂²⋊C₄	—	30	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	30	2	no	—
359	C₄²	—	30	1	no	—
360	C₄²	C₂×Dic₁₅	1	2	yes	complemented
361	C₃×C₅	#1860	1	1	yes	characteristic, complemented, Hall
362	C₂²×C₃	—	2	1	no	—
363	C₂²×C₃	—	2	1	no	—
364	C₂²×C₃	—	2	2	no	—
365	C₂²×C₃	—	4	1	no	—
366	C₂²×C₃	—	4	1	no	—
367	C₂²×C₃	#4024	1	1	yes	characteristic
368	C₂²×C₃	#4028	1	1	yes	characteristic
369	C₂²×C₃	D₄×Dic₅	1	1	yes	characteristic
370	C₃×C₄	—	2	2	no	—
371	C₃×C₄	—	4	2	no	—
372	C₃×C₄	#4024	1	1	yes	characteristic
373	C₃×C₄	#4032	1	1	yes	characteristic
374	C₃×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
375	C₃×C₄	D₄×Dic₅	1	1	yes	characteristic
376	Dic₃	—	20	2	no	—
377	Dic₃	—	20	1	no	—
378	Dic₃	—	20	1	no	—
379	Dic₃	—	40	1	no	—
380	C₂×C₅	—	2	1	no	—
381	C₂×C₅	—	2	1	no	—
382	C₂×C₅	—	4	2	no	—
383	C₂×C₅	#4825	1	1	yes	characteristic
384	C₂×C₅	#4827	1	1	yes	characteristic
385	C₂×C₅	#4950	1	1	yes	characteristic
386	C₂³	—	2	1	no	—
387	C₂³	D₄×D₁₅	1	1	yes	characteristic
388	Q₈	—	2	1	no	—
389	Q₈	C₄⋊Dic₁₅	1	2	yes	—
390	D₄	—	2	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	2	1	no	—
393	D₄	C₄⋊Dic₁₅	1	2	yes	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	30	1	no	—
401	C₂×C₄	—	30	1	no	—
402	C₂×C₄	—	30	2	no	—
403	C₂×C₄	—	60	2	no	—
404	C₂×C₄	—	60	2	no	—
405	C₂×C₄	—	60	1	no	—
406	C₂×C₄	—	120	2	no	—
407	C₂×C₄	C₂×Dic₃₀	1	1	yes	characteristic
408	C₂×C₄	C₂×D₆₀	1	1	yes	characteristic
409	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
410	C₂×C₄	#6819	1	1	yes	characteristic
411	C₂×C₄	#6819	1	1	yes	characteristic
412	C₂×C₄	C₂²×Dic₁₅	1	1	yes	characteristic
413	C₈	—	2	2	no	—
414	C₈	—	60	1	no	—
415	C₂×C₃	—	2	1	no	—
416	C₂×C₃	—	2	1	no	—
417	C₂×C₃	—	4	2	no	—
418	C₂×C₃	#65114	1	1	yes	characteristic
419	C₂×C₃	#65116	1	1	yes	characteristic
420	C₂×C₃	#65239	1	1	yes	characteristic
421	C₅	#70364	1	1	yes	characteristic, complemented, Sylow
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	#91767	1	1	yes	characteristic
428	C₂²	#91771	1	1	yes	characteristic
429	C₂²	D₄×Dic₁₅	1	1	yes	characteristic
430	C₄	—	2	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	60	2	no	—
433	C₄	—	60	1	no	—
434	C₄	—	60	1	no	—
435	C₄	—	120	1	no	—
436	C₄	#91767	1	1	yes	characteristic
437	C₄	#91775	1	1	yes	characteristic
438	C₄	C₂×C₄⋊Dic₁₅	1	1	yes	characteristic
439	C₄	D₄×Dic₁₅	1	1	yes	characteristic
440	C₃	#10601157	1	1	yes	characteristic, complemented, Sylow
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	4	2	no	—
444	C₂	#11750926	1	1	yes	characteristic
445	C₂	#11750928	1	1	yes	characteristic
446	C₂	#11751051	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#91771
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₅
Fitting	C₂×C₃×C₅×#104	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×#104	D₁₅
hypocenter	C₃×C₅	#1860
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#104

Complements

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

N	H ≅ G/N	type
4. #11751222	C₂	semidirect
5. #11751037	C₂	semidirect
6. #11746375	C₂	semidirect
7. #11746344	C₂	semidirect
21. C₃×C₅×#104	C₄	semidirect
49. C₃×C₅×M₁₆	C₂×C₄	semidirect
52. C₃×C₄²×C₅	C₂×C₄	semidirect
86. C₅×#104	Dic₃	semidirect
134. C₃×#104	Dic₅	semidirect
154. C₅×M₁₆	C₂×Dic₃	semidirect
157. C₄²×C₅	C₂×Dic₃	semidirect
211. C₃×M₁₆	C₂×Dic₅	semidirect
214. C₃×C₄²	C₂×Dic₅	semidirect
272. #104	Dic₁₅	semidirect
345. M₁₆	C₂×Dic₁₅	semidirect
360. C₄²	C₂×Dic₁₅	semidirect
361. C₃×C₅	#1860	semidirect
421. C₅	#70364	semidirect
440. C₃	#10601157	semidirect

Maximal subgroups

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

subgroup	index
#11756586	2
C₂×C₃×C₅×#104	2
#11751333	2
#11751222	2
#11751037	2
#11746375	2
#11746344	2
#10601157	3
#70364	5