Subgroups — #14297574

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	#11751025	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65213	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#90959	C₂	1	2	yes	maximal
5	#11745986	C₂	1	2	yes	maximal, complemented
6	#10602410	—	3	1	no	maximal, Hall
7	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₅×D₃	C₄	1	2	yes	—
9	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₂×#6710	C₂²	1	2	yes	—
11	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
12	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
13	C₄×C₅×D₁₂	—	2	1	no	—
14	C₄×C₅×D₁₂	—	2	1	no	—
15	C₄×C₅×D₁₂	—	2	1	no	—
16	C₄×C₅×D₁₂	—	2	1	no	—
17	C₂×C₃×#681	C₂²	1	2	yes	—
18	C₄⋊(C₃⋊#168)	—	2	1	no	—
19	C₄⋊(C₃⋊#168)	—	2	1	no	—
20	C₃×C₄⋊#168	—	2	1	no	—
21	C₃×C₄⋊#168	—	2	1	no	—
22	#90959	—	2	4	no	—
23	#70527	—	5	1	no	maximal, Hall
24	C₂×C₄×C₅×D₄	—	3	1	no	—
25	C₂×#3965	—	3	2	no	—
26	#65213	—	3	1	no	—
27	#65213	D₃	1	1	yes	characteristic, complemented
28	#64750	—	3	2	no	—
29	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
33	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
34	C₂×C₅×D₁₂	—	2	1	no	—
35	C₂×C₅×D₁₂	—	2	1	no	—
36	C₂×C₅×D₁₂	—	2	1	no	—
37	C₂×C₅×D₁₂	—	2	1	no	—
38	C₂×C₅×D₁₂	D₄	1	2	yes	—
39	C₂×C₅×D₁₂	Q₈	1	2	yes	—
40	C₂×C₄×C₅×D₃	—	2	2	no	—
41	C₂×C₄×C₅×D₃	—	2	2	no	—
42	C₂×C₄×C₅×D₃	—	4	4	no	—
43	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
44	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
45	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
46	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
47	#6710	—	2	2	no	—
48	#6710	—	2	2	no	—
49	C₂×C₃⋊#168	—	2	2	no	—
50	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
51	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
52	C₅×C₄⋊Dic₃	—	2	1	no	—
53	C₅×C₄⋊Dic₃	—	2	1	no	—
54	C₃×#681	—	2	2	no	—
55	C₃×#681	—	2	2	no	—
56	C₂×C₃×#168	—	2	2	no	—
57	C₂×C₄×D₁₂	D₅	1	1	yes	characteristic
58	C₃×#423	—	5	1	no	—
59	C₂×#823	—	5	2	no	—
60	#4924	—	5	1	no	—
61	#4554	—	5	2	no	—
62	C₂²×C₅×D₄	—	3	1	no	—
63	C₂³×C₄×C₅	—	3	2	no	—
64	C₄×C₅×D₄	—	6	1	no	—
65	C₄×C₅×D₄	—	6	1	no	—
66	C₄×C₅×D₄	—	6	1	no	—
67	C₄×C₅×D₄	—	6	1	no	—
68	C₂×C₅×C₄⋊C₄	—	3	1	no	—
69	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
70	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
71	C₂×#681	—	3	2	no	—
72	C₂×#681	C₂×D₃	1	2	yes	—
73	#3965	—	6	4	no	—
74	C₄⋊#168	—	2	1	no	—
75	C₄⋊#168	—	2	1	no	—
76	C₄⋊#168	—	6	1	no	—
77	C₄⋊#168	—	6	1	no	—
78	#1800	—	15	1	no	Sylow
79	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₅×D₃	—	2	2	no	—
81	C₂²×C₅×D₃	—	2	2	no	—
82	C₂²×C₅×D₃	—	4	2	no	—
83	C₂²×C₅×D₃	—	4	2	no	—
84	C₂²×C₅×D₃	C₄⋊C₄	1	4	yes	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	4	1	no	—
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
97	C₂×C₅×Dic₃	—	2	2	no	—
98	C₂×C₅×Dic₃	—	4	2	no	—
99	C₅×D₁₂	—	2	2	no	—
100	C₅×D₁₂	—	2	2	no	—
101	C₅×D₁₂	—	2	2	no	—
102	C₅×D₁₂	—	2	2	no	—
103	C₄×C₅×D₃	—	4	4	no	—
104	C₄×C₅×D₃	—	4	4	no	—
105	C₃⋊#168	—	4	2	no	—
106	C₃×#168	—	4	2	no	—
107	C₂²×D₁₂	C₂×D₅	1	1	yes	characteristic
108	C₂²×C₄×D₃	Dic₅	1	2	yes	—
109	C₂×C₃×M₁₆	—	5	2	no	—
110	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
111	C₂×(C₂×D₃)⋊C₄	Dic₅	1	2	yes	—
112	C₂×C₄⋊Dic₃	C₂×D₅	1	1	yes	characteristic
113	C₂×#208	—	5	2	no	—
114	C₄×D₁₂	—	2	1	no	—
115	C₄×D₁₂	—	2	1	no	—
116	C₄×D₁₂	—	2	1	no	—
117	C₄×D₁₂	—	2	1	no	—
118	C₃×C₄⋊C₈	—	10	1	no	—
119	C₃×C₄⋊C₈	—	10	1	no	—
120	#823	—	10	4	no	—
121	C₄⋊(C₃⋊C₈)	—	10	1	no	—
122	C₄⋊(C₃⋊C₈)	—	10	1	no	—
123	C₂⁴×C₅	—	3	2	no	—
124	C₂×C₅×D₄	—	3	2	no	—
125	C₂×C₅×D₄	—	3	2	no	—
126	C₂×C₅×D₄	—	6	1	no	—
127	C₂×C₅×D₄	—	6	1	no	—
128	C₂×C₅×D₄	—	6	1	no	—
129	C₂×C₅×D₄	—	6	1	no	—
130	C₂²×C₄×C₅	—	3	2	no	—
131	C₂²×C₄×C₅	—	6	2	no	—
132	C₂²×C₄×C₅	—	6	2	no	—
133	C₂²×C₄×C₅	—	12	4	no	—
134	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
137	C₅×C₄⋊C₄	—	6	1	no	—
138	C₅×C₄⋊C₄	—	6	1	no	—
139	C₅×C₂²⋊C₄	—	6	2	no	—
140	C₅×C₂²⋊C₄	—	6	2	no	—
141	C₄²×C₅	D₁₂	1	1	yes	characteristic
142	C₄²×C₅	D₁₂	1	1	yes	characteristic
143	C₄²×C₅	#67	1	1	yes	characteristic
144	C₄²×C₅	#67	1	1	yes	characteristic
145	#681	—	2	2	no	—
146	#681	—	2	2	no	—
147	#681	—	6	2	no	—
148	#681	—	6	2	no	—
149	C₂×#168	—	2	2	no	—
150	C₂×#168	—	6	2	no	—
151	C₂×C₄×D₄	—	3	1	no	—
152	#423	—	5	1	no	—
153	#423	—	15	1	no	—
154	C₂×#100	—	15	2	no	—
155	#343	—	15	2	no	—
156	C₂²×C₃×C₅	—	2	1	no	—
157	C₂²×C₃×C₅	—	2	1	no	—
158	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂²×C₃×C₅	#117	1	1	yes	characteristic
161	C₂×C₅×D₃	—	2	4	no	—
162	C₂×C₅×D₃	—	4	4	no	—
163	C₂×C₅×D₃	—	4	2	no	—
164	C₂×C₅×D₃	—	4	2	no	—
165	C₂×C₅×D₃	—	4	4	no	—
166	C₃×C₄×C₅	—	2	1	no	—
167	C₃×C₄×C₅	—	2	1	no	—
168	C₃×C₄×C₅	—	2	1	no	—
169	C₃×C₄×C₅	#100	1	2	yes	complemented
170	C₃×C₄×C₅	#121	1	1	yes	characteristic
171	C₃×C₄×C₅	#121	1	1	yes	characteristic
172	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
173	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
174	C₅×Dic₃	—	4	2	no	—
175	C₂³×D₃	C₂×Dic₅	1	2	yes	—
176	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
179	C₂²×Dic₃	C₂×Dic₅	1	2	yes	—
180	C₂×D₁₂	—	2	1	no	—
181	C₂×D₁₂	—	2	1	no	—
182	C₂×D₁₂	—	2	1	no	—
183	C₂×D₁₂	—	2	1	no	—
184	C₂×D₁₂	Dic₁₀	1	2	yes	—
185	C₂×D₁₂	D₂₀	1	2	yes	—
186	C₂×C₄×D₃	—	2	2	no	—
187	C₂×C₄×D₃	—	2	2	no	—
188	C₂×C₄×D₃	—	4	4	no	—
189	C₃×M₁₆	—	10	2	no	—
190	C₃×M₁₆	—	10	2	no	—
191	C₂×C₃×C₈	—	10	2	no	—
192	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
193	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
194	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
195	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
196	(C₂×D₃)⋊C₄	—	2	2	no	—
197	(C₂×D₃)⋊C₄	—	2	2	no	—
198	C₄⋊Dic₃	—	2	1	no	—
199	C₄⋊Dic₃	—	2	1	no	—
200	#208	—	10	2	no	—
201	#208	—	10	2	no	—
202	C₂×C₃⋊C₈	—	10	2	no	—
203	C₂³×C₅	—	3	4	no	—
204	C₂³×C₅	—	6	2	no	—
205	C₂³×C₅	—	6	2	no	—
206	C₂³×C₅	—	12	2	no	—
207	C₂³×C₅	—	12	2	no	—
208	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
209	C₅×D₄	—	6	2	no	—
210	C₅×D₄	—	6	2	no	—
211	C₅×D₄	—	6	2	no	—
212	C₅×D₄	—	6	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	6	2	no	—
216	C₂×C₄×C₅	—	12	4	no	—
217	C₂×C₄×C₅	—	12	4	no	—
218	C₂×C₄×C₅	—	12	2	no	—
219	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
224	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
225	C₂×C₄×C₅	#237	1	1	yes	characteristic
226	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
227	C₂×C₄×C₅	#239	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
229	#168	—	4	2	no	—
230	#168	—	12	2	no	—
231	C₂²×D₄	—	3	1	no	—
232	C₂³×C₄	—	3	2	no	—
233	C₂×M₁₆	—	5	2	no	—
234	C₂×M₁₆	—	15	2	no	—
235	C₄×D₄	—	6	1	no	—
236	C₄×D₄	—	6	1	no	—
237	C₄×D₄	—	6	1	no	—
238	C₄×D₄	—	6	1	no	—
239	C₂×C₄⋊C₄	—	3	1	no	—
240	C₂×C₂²⋊C₄	—	3	2	no	—
241	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
242	C₄⋊C₈	—	10	1	no	—
243	C₄⋊C₈	—	10	1	no	—
244	C₄⋊C₈	—	30	1	no	—
245	C₄⋊C₈	—	30	1	no	—
246	#100	—	30	4	no	—
247	C₂×C₃×C₅	—	2	1	no	—
248	C₂×C₃×C₅	—	2	1	no	—
249	C₂×C₃×C₅	#380	1	1	yes	characteristic
250	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
251	C₂×C₃×C₅	#413	1	1	yes	characteristic
252	C₅×D₃	—	4	4	no	—
253	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
254	C₂²×D₃	—	2	2	no	—
255	C₂²×D₃	—	2	2	no	—
256	C₂²×D₃	—	4	2	no	—
257	C₂²×D₃	—	4	2	no	—
258	C₂²×D₃	C₄⋊Dic₅	1	4	yes	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	4	1	no	—
261	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
267	C₂×C₃×C₄	#709	1	1	yes	characteristic
268	C₂×C₃×C₄	#709	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
271	C₂×Dic₃	—	2	2	no	—
272	C₂×Dic₃	—	4	2	no	—
273	D₁₂	—	2	2	no	—
274	D₁₂	—	2	2	no	—
275	D₁₂	—	2	2	no	—
276	D₁₂	—	2	2	no	—
277	C₄×D₃	—	4	4	no	—
278	C₄×D₃	—	4	4	no	—
279	C₃×C₈	—	20	2	no	—
280	C₃⋊C₈	—	20	2	no	—
281	C₂²×C₅	—	2	1	no	—
282	C₂²×C₅	—	2	1	no	—
283	C₂²×C₅	—	6	4	no	—
284	C₂²×C₅	—	12	4	no	—
285	C₂²×C₅	—	12	4	no	—
286	C₂²×C₅	—	12	2	no	—
287	C₂²×C₅	—	12	2	no	—
288	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
289	C₂²×C₅	#892	1	1	yes	characteristic
290	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
291	C₄×C₅	—	2	1	no	—
292	C₄×C₅	—	2	1	no	—
293	C₄×C₅	—	2	1	no	—
294	C₄×C₅	—	12	2	no	—
295	C₄×C₅	#823	1	2	yes	complemented
296	C₄×C₅	#895	1	1	yes	characteristic
297	C₄×C₅	#897	1	1	yes	characteristic
298	C₄×C₅	#938	1	1	yes	characteristic
299	C₄×C₅	#946	1	1	yes	characteristic
300	C₂⁴	—	3	2	no	—
301	C₂×D₄	—	3	2	no	—
302	C₂×D₄	—	3	2	no	—
303	C₂×D₄	—	6	1	no	—
304	C₂×D₄	—	6	1	no	—
305	C₂×D₄	—	6	1	no	—
306	C₂×D₄	—	6	1	no	—
307	C₂²×C₄	—	3	2	no	—
308	C₂²×C₄	—	6	2	no	—
309	C₂²×C₄	—	6	2	no	—
310	C₂²×C₄	—	12	4	no	—
311	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
312	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
314	M₁₆	—	10	2	no	—
315	M₁₆	—	10	2	no	—
316	M₁₆	—	30	2	no	—
317	M₁₆	—	30	2	no	—
318	C₂×C₈	—	10	2	no	—
319	C₂×C₈	—	30	2	no	—
320	C₄⋊C₄	—	6	1	no	—
321	C₄⋊C₄	—	6	1	no	—
322	C₂²⋊C₄	—	6	2	no	—
323	C₂²⋊C₄	—	6	2	no	—
324	C₄²	#1201	1	1	yes	characteristic
325	C₄²	#1201	1	1	yes	characteristic
326	C₄²	#1203	1	1	yes	characteristic
327	C₄²	#1203	1	1	yes	characteristic
328	C₃×C₅	#1800	1	1	yes	characteristic, complemented, Hall
329	C₂²×C₃	—	2	1	no	—
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	C₂×C₄⋊Dic₅	1	1	yes	characteristic
332	C₂²×C₃	#4072	1	1	yes	characteristic
333	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
334	C₂×D₃	—	2	4	no	—
335	C₂×D₃	—	4	4	no	—
336	C₂×D₃	—	4	2	no	—
337	C₂×D₃	—	4	2	no	—
338	C₂×D₃	—	4	4	no	—
339	C₃×C₄	—	2	1	no	—
340	C₃×C₄	—	2	1	no	—
341	C₃×C₄	—	2	1	no	—
342	C₃×C₄	#3965	1	2	yes	complemented
343	C₃×C₄	#4070	1	1	yes	characteristic
344	C₃×C₄	#4070	1	1	yes	characteristic
345	C₃×C₄	#4076	1	1	yes	characteristic
346	C₃×C₄	#4076	1	1	yes	characteristic
347	Dic₃	—	4	2	no	—
348	C₂×C₅	—	2	1	no	—
349	C₂×C₅	—	2	1	no	—
350	C₂×C₅	—	12	4	no	—
351	C₂×C₅	#4987	1	1	yes	characteristic
352	C₂×C₅	C₂×#823	1	1	yes	characteristic
353	C₂×C₅	#5132	1	1	yes	characteristic
354	C₂³	—	3	4	no	—
355	C₂³	—	6	2	no	—
356	C₂³	—	6	2	no	—
357	C₂³	—	12	2	no	—
358	C₂³	—	12	2	no	—
359	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
360	D₄	—	6	2	no	—
361	D₄	—	6	2	no	—
362	D₄	—	6	2	no	—
363	D₄	—	6	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	6	2	no	—
367	C₂×C₄	—	12	4	no	—
368	C₂×C₄	—	12	4	no	—
369	C₂×C₄	—	12	2	no	—
370	C₂×C₄	(C₂×D₃)⋊Dic₅	1	1	yes	characteristic
371	C₂×C₄	(C₂×D₃)⋊Dic₅	1	1	yes	characteristic
372	C₂×C₄	(C₂×D₃)⋊Dic₅	1	1	yes	characteristic
373	C₂×C₄	(C₂×D₃)⋊Dic₅	1	1	yes	characteristic
374	C₂×C₄	#6765	1	1	yes	characteristic
375	C₂×C₄	D₃×Dic₁₀	1	1	yes	characteristic
376	C₂×C₄	#6769	1	1	yes	characteristic
377	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
378	C₂×C₄	C₂×#1201	1	1	yes	characteristic
379	C₂×C₄	C₂×#1203	1	1	yes	characteristic
380	C₈	—	20	2	no	—
381	C₈	—	60	2	no	—
382	C₂×C₃	—	2	1	no	—
383	C₂×C₃	—	2	1	no	—
384	C₂×C₃	#65501	1	1	yes	characteristic
385	C₂×C₃	C₂×#3965	1	1	yes	characteristic
386	C₂×C₃	#65526	1	1	yes	characteristic
387	D₃	—	4	4	no	—
388	C₅	#70527	1	1	yes	characteristic, complemented, Sylow
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	6	4	no	—
392	C₂²	—	12	4	no	—
393	C₂²	—	12	4	no	—
394	C₂²	—	12	2	no	—
395	C₂²	—	12	2	no	—
396	C₂²	#91338	1	1	yes	characteristic
397	C₂²	D₃×C₄⋊Dic₅	1	1	yes	characteristic
398	C₂²	C₂×(C₂×D₃)⋊Dic₅	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	12	2	no	—
403	C₄	#90959	1	2	yes	complemented
404	C₄	#91365	1	1	yes	characteristic
405	C₄	#91369	1	1	yes	characteristic
406	C₄	#91456	1	1	yes	characteristic
407	C₄	#91460	1	1	yes	characteristic
408	C₃	#10602410	1	1	yes	characteristic, complemented, Sylow
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	12	4	no	—
412	C₂	C₂×#90959	1	1	yes	characteristic
413	C₂	#11748355	1	1	yes	characteristic
414	C₂	#11748786	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×(C₂×D₃)⋊Dic₅
commutator	C₂³×C₃×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	#1800
LCS	G ▷ C₂³×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #11751025	C₂	semidirect
3. C₃×#65213	C₂	semidirect
5. #11745986	C₂	semidirect
27. #65213	D₃	semidirect
169. C₃×C₄×C₅	#100	semidirect
295. C₄×C₅	#823	semidirect
328. C₃×C₅	#1800	semidirect
342. C₃×C₄	#3965	semidirect
388. C₅	#70527	semidirect
403. C₄	#90959	semidirect
408. C₃	#10602410	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×D₁₂	2
#11751025	2
C₃×#65213	2
C₂×#90959	2
#11745986	2
#10602410	3
#70527	5