Subgroups — D₄×#6705 #14415668

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6705	C₂	1	2	yes	maximal, complemented
2	C₄×D₄×D₁₅	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751212	C₂	1	2	yes	maximal, complemented
5	D₄×C₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
6	#11750939	C₂	1	1	yes	maximal, characteristic, complemented
7	#11750938	C₂	1	1	yes	maximal, characteristic, complemented
8	#11750831	C₂	1	2	yes	maximal, complemented
9	#11750827	C₂	1	2	yes	maximal, complemented
10	#11750789	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#6705	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×#676	—	3	1	no	maximal, Hall
13	C₂×D₄×D₁₅	C₄	1	1	yes	characteristic
14	C₂²×C₄×D₁₅	C₂²	1	2	yes	—
15	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
16	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	D₄×Dic₁₅	C₄	1	1	yes	characteristic
18	C₄×#1220	C₂²	1	2	yes	—
19	C₂²×C₃⋊#168	C₂²	1	2	yes	complemented
20	C₂×#6705	—	2	8	no	—
21	C₂×#6705	C₂²	1	2	yes	—
22	C₂×#6705	C₂²	1	1	yes	characteristic
23	C₂×#6705	C₂²	1	1	yes	characteristic
24	C₂×#6705	C₂²	1	2	yes	complemented
25	C₂×#6705	C₂²	1	2	yes	complemented
26	#91782	C₄	1	1	yes	characteristic
27	C₄⋊C₄×D₁₅	C₄	1	1	yes	characteristic
28	#91770	C₄	1	2	yes	—
29	C₂²⋊C₄×D₁₅	C₄	1	2	yes	—
30	C₄×D₆₀	C₂²	1	1	yes	characteristic
31	C₄²×D₁₅	C₂²	1	1	yes	characteristic
32	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
34	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
35	#91114	C₂²	1	2	yes	complemented
36	#91104	C₂²	1	2	yes	complemented
37	#91104	C₂²	1	2	yes	complemented
38	#91099	C₂²	1	1	yes	characteristic, complemented
39	#91099	C₂²	1	1	yes	characteristic, complemented
40	#91098	C₂²	1	2	yes	complemented
41	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic, complemented
43	D₄×ΓL(1,𝔽₂₅)	—	5	1	no	maximal, Hall
44	C₂²×#676	—	3	2	no	—
45	C₄×D₄×D₅	—	3	1	no	—
46	C₅×C₈×D₄	D₃	1	1	yes	characteristic, complemented
47	#65400	—	3	2	no	—
48	D₄×#168	—	3	1	no	—
49	#65127	—	3	1	no	—
50	#65126	—	3	1	no	—
51	#65019	—	3	2	no	—
52	#65015	—	3	2	no	—
53	#64977	—	3	1	no	—
54	C₄×#676	—	3	1	no	—
55	C₂³×D₁₅	C₂×C₄	1	2	yes	—
56	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂×#1220	C₂×C₄	1	2	yes	—
59	C₂²×Dic₁₅	C₂×C₄	1	2	yes	—
60	D₄×D₁₅	—	2	4	no	—
61	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×D₁₅	—	2	4	no	—
63	C₂×C₄×D₁₅	—	2	4	no	—
64	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
66	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
67	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×D₁₅	C₂³	1	2	yes	—
69	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₅×C₈	—	2	4	no	—
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
76	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
77	#6719	C₂×C₄	1	2	yes	—
78	#6714	C₂×C₄	1	2	yes	—
79	#6714	C₂×C₄	1	2	yes	—
80	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
81	#6712	C₂×C₄	1	2	yes	—
82	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
83	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
84	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
85	C₂×C₃⋊#168	—	2	4	no	—
86	C₂×C₃⋊#168	C₂³	1	2	yes	—
87	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
88	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
89	#6705	—	2	4	no	—
90	#6705	—	2	2	no	—
91	#6705	—	2	4	no	—
92	#6705	—	2	4	no	—
93	#6705	D₄	1	4	yes	direct product factor
94	C₂²×ΓL(1,𝔽₂₅)	—	5	2	no	—
95	C₄×D₃×D₄	—	5	1	no	—
96	C₃×C₈×D₄	D₅	1	1	yes	characteristic, complemented
97	#5111	—	5	2	no	—
98	D₄×C₃⋊C₈	—	5	1	no	—
99	#4838	—	5	1	no	—
100	#4837	—	5	1	no	—
101	#4730	—	5	2	no	—
102	#4726	—	5	2	no	—
103	#4688	—	5	1	no	—
104	C₄×ΓL(1,𝔽₂₅)	—	5	1	no	—
105	C₂×D₄×D₅	—	3	1	no	—
106	C₂²×C₄×D₅	—	3	2	no	—
107	C₂²×C₅×C₈	C₂×D₃	1	2	yes	complemented
108	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
109	D₄×Dic₅	—	3	1	no	—
110	C₄×C₂²⋊D₅	—	3	2	no	—
111	C₂²×#168	—	3	2	no	—
112	C₂×#676	—	3	1	no	—
113	C₂×#676	—	3	2	no	—
114	C₂×#676	—	3	2	no	—
115	C₂×#676	—	3	2	no	—
116	C₂×#676	—	3	1	no	—
117	C₂×#676	—	6	8	no	—
118	#4039	—	3	1	no	—
119	D₅×C₄⋊C₄	—	3	1	no	—
120	#4027	—	3	2	no	—
121	D₅×C₂²⋊C₄	—	3	2	no	—
122	C₄×D₂₀	—	3	1	no	—
123	C₄²×D₅	—	3	1	no	—
124	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
125	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	complemented
126	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
127	C₂²⋊#168	—	3	2	no	—
128	#3952	—	3	2	no	—
129	#3952	—	3	2	no	—
130	#3947	—	3	1	no	—
131	#3947	—	3	1	no	—
132	#3946	—	3	2	no	—
133	C₄⋊#168	—	3	1	no	—
134	C₄×#168	—	3	1	no	—
135	D₄×M₁₆	—	15	1	no	Sylow
136	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
137	C₂²×D₁₅	—	2	4	no	—
138	C₂²×D₁₅	—	2	4	no	—
139	C₂²×D₁₅	—	4	2	no	—
140	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
141	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
142	C₃×C₅×D₄	M₁₆	1	4	yes	complemented
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	#1220	—	2	4	no	—
150	C₂×Dic₁₅	—	2	4	no	—
151	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
152	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
153	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
154	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
155	D₆₀	—	2	2	no	—
156	C₄×D₁₅	—	2	4	no	—
157	C₄×D₁₅	—	2	2	no	—
158	C₄×D₁₅	—	2	2	no	—
159	C₄×D₁₅	—	2	2	no	—
160	C₄×D₁₅	—	2	4	no	—
161	C₄×D₁₅	—	4	1	no	—
162	C₄×D₁₅	C₂×D₄	1	2	yes	—
163	C₄×D₁₅	#41	1	2	yes	—
164	C₃×C₅×C₈	—	2	2	no	—
165	C₃×C₅×C₈	—	2	1	no	—
166	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
167	C₃⋊#168	—	2	2	no	—
168	C₃⋊#168	—	2	1	no	—
169	C₃⋊#168	C₂×D₄	1	2	yes	complemented
170	C₂×D₃×D₄	—	5	1	no	—
171	C₂²×C₄×D₃	—	5	2	no	—
172	C₂²×C₃×C₈	C₂×D₅	1	2	yes	complemented
173	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
174	D₄×Dic₃	—	5	1	no	—
175	C₄×#67	—	5	2	no	—
176	C₂²×C₃⋊C₈	—	5	2	no	—
177	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
178	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
179	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
180	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
181	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
182	C₂×ΓL(1,𝔽₂₅)	—	10	8	no	—
183	#893	—	5	1	no	—
184	D₃×C₄⋊C₄	—	5	1	no	—
185	#67⋊C₄	—	5	2	no	—
186	D₃×C₂²⋊C₄	—	5	2	no	—
187	C₄×D₁₂	—	5	1	no	—
188	C₄²×D₃	—	5	1	no	—
189	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
190	C₃×C₂²⋊C₈	C₂×D₅	1	2	yes	complemented
191	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
192	#830	—	5	2	no	—
193	(C₂×D₃)⋊C₈	—	5	2	no	—
194	(C₂×D₃)⋊C₈	—	5	2	no	—
195	#815	—	5	1	no	—
196	#815	—	5	1	no	—
197	Dic₃⋊C₈	—	5	2	no	—
198	C₄⋊(C₃⋊C₈)	—	5	1	no	—
199	C₄×C₃⋊C₈	—	5	1	no	—
200	C₂³×D₅	—	3	2	no	—
201	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
203	C₂×C₂²⋊D₅	—	3	2	no	—
204	C₂²×Dic₅	—	3	2	no	—
205	D₄×D₅	—	6	4	no	—
206	C₂×D₂₀	—	3	1	no	—
207	C₂×C₄×D₅	—	3	1	no	—
208	C₂×C₄×D₅	—	3	2	no	—
209	C₂×C₄×D₅	—	3	2	no	—
210	C₂×C₄×D₅	—	3	1	no	—
211	C₂×C₄×D₅	—	3	2	no	—
212	C₂×C₄×D₅	—	3	1	no	—
213	C₂×C₄×D₅	—	6	4	no	—
214	C₂×C₄×D₅	—	6	4	no	—
215	C₂×C₅×C₈	—	2	4	no	—
216	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
217	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
218	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
219	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
220	C₅×C₂²⋊C₄	C₄×D₃	1	2	yes	—
221	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
222	C₂²⋊Dic₅	—	3	2	no	—
223	#685	—	3	2	no	—
224	#685	—	3	2	no	—
225	C₄⋊Dic₅	—	3	1	no	—
226	#683	—	3	2	no	—
227	C₄×Dic₅	—	3	1	no	—
228	C₄×Dic₅	—	3	1	no	—
229	C₄×Dic₅	—	3	1	no	—
230	C₂×#168	—	3	1	no	—
231	C₂×#168	—	3	1	no	—
232	C₂×#168	—	3	2	no	—
233	C₂×#168	—	6	4	no	—
234	#676	—	3	4	no	—
235	#676	—	6	4	no	—
236	#676	—	6	2	no	—
237	#676	—	6	4	no	—
238	#676	—	6	4	no	—
239	C₂²×M₁₆	—	15	2	no	—
240	C₂×C₄×D₄	—	15	1	no	—
241	#436	—	15	1	no	—
242	#436	—	15	1	no	—
243	#435	—	15	2	no	—
244	#435	—	15	2	no	—
245	C₈×D₄	—	15	1	no	—
246	C₈×D₄	D₁₅	1	1	yes	characteristic, complemented
247	#423	—	15	1	no	—
248	#407	—	15	2	no	—
249	C₄×M₁₆	—	15	1	no	—
250	C₂²×C₃×C₅	—	2	2	no	—
251	C₂²×C₃×C₅	—	2	2	no	—
252	C₂²×C₃×C₅	C₂×M₁₆	1	4	yes	complemented
253	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
254	C₂×D₁₅	—	2	1	no	—
255	C₂×D₁₅	—	2	1	no	—
256	C₂×D₁₅	—	2	2	no	—
257	C₂×D₁₅	—	2	2	no	—
258	C₂×D₁₅	—	2	2	no	—
259	C₂×D₁₅	—	4	8	no	—
260	C₂×D₁₅	C₄×D₄	1	2	yes	—
261	C₃×C₄×C₅	—	2	2	no	—
262	C₃×C₄×C₅	—	2	1	no	—
263	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	complemented
264	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
265	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
266	Dic₁₅	—	2	2	no	—
267	Dic₁₅	—	2	1	no	—
268	Dic₁₅	—	2	1	no	—
269	Dic₁₅	C₄×D₄	1	2	yes	—
270	C₂³×D₃	—	5	2	no	—
271	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
272	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
273	C₂×#67	—	5	2	no	—
274	C₂²×Dic₃	—	5	2	no	—
275	D₃×D₄	—	10	4	no	—
276	C₂×D₁₂	—	5	1	no	—
277	C₂×C₄×D₃	—	5	1	no	—
278	C₂×C₄×D₃	—	5	1	no	—
279	C₂×C₄×D₃	—	5	2	no	—
280	C₂×C₄×D₃	—	5	2	no	—
281	C₂×C₄×D₃	—	5	2	no	—
282	C₂×C₄×D₃	—	5	1	no	—
283	C₂×C₄×D₃	—	10	4	no	—
284	C₂×C₄×D₃	—	10	4	no	—
285	C₂×C₃×C₈	—	2	4	no	—
286	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
287	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
288	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
289	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
290	C₃×C₂²⋊C₄	C₄×D₅	1	2	yes	—
291	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
292	#217	—	5	2	no	—
293	(C₂×D₃)⋊C₄	—	5	2	no	—
294	(C₂×D₃)⋊C₄	—	5	2	no	—
295	C₄⋊Dic₃	—	5	1	no	—
296	Dic₃⋊C₄	—	5	2	no	—
297	C₄×Dic₃	—	5	1	no	—
298	C₄×Dic₃	—	5	1	no	—
299	C₄×Dic₃	—	5	1	no	—
300	C₂×C₃⋊C₈	—	5	1	no	—
301	C₂×C₃⋊C₈	—	5	1	no	—
302	C₂×C₃⋊C₈	—	5	2	no	—
303	C₂×C₃⋊C₈	—	10	4	no	—
304	ΓL(1,𝔽₂₅)	—	5	4	no	—
305	ΓL(1,𝔽₂₅)	—	10	4	no	—
306	ΓL(1,𝔽₂₅)	—	10	2	no	—
307	ΓL(1,𝔽₂₅)	—	10	4	no	—
308	ΓL(1,𝔽₂₅)	—	10	4	no	—
309	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
310	C₂²×D₅	—	3	1	no	—
311	C₂²×D₅	—	3	2	no	—
312	C₂²×D₅	—	6	4	no	—
313	C₂²×D₅	—	6	4	no	—
314	C₂²×D₅	—	12	2	no	—
315	C₅×D₄	ΓL(1,𝔽₂₅)	1	4	yes	complemented
316	C₂×C₄×C₅	—	2	2	no	—
317	C₂×C₄×C₅	—	2	2	no	—
318	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
319	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
320	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
321	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
322	C₂²⋊D₅	—	6	4	no	—
323	C₂×Dic₅	—	3	1	no	—
324	C₂×Dic₅	—	3	1	no	—
325	C₂×Dic₅	—	3	1	no	—
326	C₂×Dic₅	—	3	2	no	—
327	C₂×Dic₅	—	6	4	no	—
328	D₂₀	—	6	2	no	—
329	C₄×D₅	—	3	2	no	—
330	C₄×D₅	—	3	2	no	—
331	C₄×D₅	—	6	4	no	—
332	C₄×D₅	—	6	4	no	—
333	C₄×D₅	—	6	2	no	—
334	C₄×D₅	—	6	2	no	—
335	C₄×D₅	—	6	2	no	—
336	C₄×D₅	—	12	1	no	—
337	C₅×C₈	—	2	2	no	—
338	C₅×C₈	—	2	1	no	—
339	C₅×C₈	D₃×D₄	1	2	yes	complemented
340	#168	—	3	2	no	—
341	#168	—	6	2	no	—
342	#168	—	6	1	no	—
343	C₂²×D₄	—	15	1	no	—
344	C₂³×C₄	—	15	2	no	—
345	C₂×M₁₆	—	15	1	no	—
346	C₂×M₁₆	—	15	2	no	—
347	C₂×M₁₆	—	15	2	no	—
348	C₂×M₁₆	—	15	2	no	—
349	C₂×M₁₆	—	15	1	no	—
350	C₂×M₁₆	—	30	8	no	—
351	C₂²×C₈	—	15	2	no	—
352	C₂²×C₈	C₂×D₁₅	1	2	yes	complemented
353	C₄×D₄	—	15	1	no	—
354	C₄×D₄	—	15	2	no	—
355	C₄×D₄	—	15	1	no	—
356	C₄×D₄	—	15	2	no	—
357	C₄×D₄	—	15	1	no	—
358	C₄×D₄	C₂×D₁₅	1	1	yes	characteristic
359	C₂×C₄⋊C₄	—	15	1	no	—
360	C₂×C₂²⋊C₄	—	15	2	no	—
361	C₂×C₄²	—	15	1	no	—
362	C₄⋊C₈	—	15	2	no	—
363	C₄⋊C₈	—	15	1	no	—
364	C₄⋊C₈	C₂×D₁₅	1	1	yes	characteristic, complemented
365	C₂²⋊C₈	—	15	2	no	—
366	C₂²⋊C₈	—	15	2	no	—
367	C₂²⋊C₈	—	15	2	no	—
368	C₂²⋊C₈	C₂×D₁₅	1	2	yes	complemented
369	#97	—	15	1	no	—
370	#97	—	15	1	no	—
371	C₄×C₈	—	15	1	no	—
372	C₄×C₈	C₂×D₁₅	1	1	yes	characteristic, complemented
373	C₂×C₃×C₅	—	2	4	no	—
374	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
375	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
376	C₂×C₃×C₅	#568	1	1	yes	characteristic
377	D₁₅	—	2	2	no	—
378	D₁₅	—	4	2	no	—
379	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
380	C₂²×D₃	—	5	1	no	—
381	C₂²×D₃	—	5	2	no	—
382	C₂²×D₃	—	10	4	no	—
383	C₂²×D₃	—	10	4	no	—
384	C₂²×D₃	—	20	2	no	—
385	C₃×D₄	#676	1	4	yes	complemented
386	C₂×C₃×C₄	—	2	2	no	—
387	C₂×C₃×C₄	—	2	2	no	—
388	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
390	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
392	#67	—	10	4	no	—
393	C₂×Dic₃	—	5	1	no	—
394	C₂×Dic₃	—	5	1	no	—
395	C₂×Dic₃	—	5	1	no	—
396	C₂×Dic₃	—	5	2	no	—
397	C₂×Dic₃	—	10	4	no	—
398	D₁₂	—	10	2	no	—
399	C₄×D₃	—	5	2	no	—
400	C₄×D₃	—	5	2	no	—
401	C₄×D₃	—	10	4	no	—
402	C₄×D₃	—	10	4	no	—
403	C₄×D₃	—	10	2	no	—
404	C₄×D₃	—	10	2	no	—
405	C₄×D₃	—	10	2	no	—
406	C₄×D₃	—	20	1	no	—
407	C₃×C₈	—	2	2	no	—
408	C₃×C₈	—	2	1	no	—
409	C₃×C₈	D₄×D₅	1	2	yes	complemented
410	C₃⋊C₈	—	5	2	no	—
411	C₃⋊C₈	—	10	2	no	—
412	C₃⋊C₈	—	10	1	no	—
413	C₂²×C₅	—	2	2	no	—
414	C₂²×C₅	—	2	2	no	—
415	C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	1	4	yes	complemented
416	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
417	C₂×D₅	—	3	2	no	—
418	C₂×D₅	—	6	1	no	—
419	C₂×D₅	—	6	1	no	—
420	C₂×D₅	—	6	2	no	—
421	C₂×D₅	—	6	2	no	—
422	C₂×D₅	—	6	2	no	—
423	C₂×D₅	—	12	8	no	—
424	C₄×C₅	—	2	1	no	—
425	C₄×C₅	—	2	2	no	—
426	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	complemented
427	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
428	C₄×C₅	D₃×#41	1	1	yes	characteristic
429	Dic₅	—	3	2	no	—
430	Dic₅	—	6	1	no	—
431	Dic₅	—	6	1	no	—
432	Dic₅	—	6	2	no	—
433	C₂⁴	—	15	2	no	—
434	C₂×D₄	—	15	2	no	—
435	C₂×D₄	—	15	1	no	—
436	C₂×D₄	—	30	4	no	—
437	C₂×D₄	C₄×D₁₅	1	1	yes	characteristic
438	C₂²×C₄	—	15	1	no	—
439	C₂²×C₄	—	15	2	no	—
440	C₂²×C₄	—	15	1	no	—
441	C₂²×C₄	—	15	2	no	—
442	C₂²×C₄	—	15	2	no	—
443	C₂²×C₄	—	15	2	no	—
444	C₂²×C₄	—	15	1	no	—
445	C₂²×C₄	—	30	4	no	—
446	C₂²×C₄	—	30	4	no	—
447	C₂²×C₄	C₂²×D₁₅	1	2	yes	—
448	M₁₆	—	15	4	no	—
449	M₁₆	—	30	4	no	—
450	M₁₆	—	30	4	no	—
451	M₁₆	—	30	2	no	—
452	M₁₆	—	30	4	no	—
453	C₂×C₈	—	2	4	no	—
454	C₂×C₈	—	15	1	no	—
455	C₂×C₈	—	15	1	no	—
456	C₂×C₈	—	15	2	no	—
457	C₂×C₈	—	30	4	no	—
458	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
459	C₂×C₈	C₂²×D₁₅	1	2	yes	—
460	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
461	C₄⋊C₄	—	15	2	no	—
462	C₄⋊C₄	—	15	1	no	—
463	C₄⋊C₄	C₄×D₁₅	1	1	yes	characteristic
464	C₂²⋊C₄	—	15	2	no	—
465	C₂²⋊C₄	—	15	2	no	—
466	C₂²⋊C₄	—	15	2	no	—
467	C₂²⋊C₄	C₄×D₁₅	1	2	yes	—
468	C₄²	—	15	1	no	—
469	C₄²	—	15	1	no	—
470	C₄²	—	15	1	no	—
471	C₄²	C₂²×D₁₅	1	1	yes	characteristic
472	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
473	C₂²×C₃	—	2	2	no	—
474	C₂²×C₃	—	2	2	no	—
475	C₂²×C₃	C₂×#676	1	4	yes	complemented
476	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
477	C₂×D₃	—	5	2	no	—
478	C₂×D₃	—	10	1	no	—
479	C₂×D₃	—	10	1	no	—
480	C₂×D₃	—	10	2	no	—
481	C₂×D₃	—	10	2	no	—
482	C₂×D₃	—	10	2	no	—
483	C₂×D₃	—	20	8	no	—
484	C₃×C₄	—	2	1	no	—
485	C₃×C₄	—	2	2	no	—
486	C₃×C₄	C₂×#676	1	2	yes	complemented
487	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
488	C₃×C₄	D₅×#41	1	1	yes	characteristic
489	Dic₃	—	5	2	no	—
490	Dic₃	—	10	1	no	—
491	Dic₃	—	10	1	no	—
492	Dic₃	—	10	2	no	—
493	C₂×C₅	—	2	4	no	—
494	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
495	C₂×C₅	C₂²×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
496	C₂×C₅	#5750	1	1	yes	characteristic
497	D₅	—	6	2	no	—
498	D₅	—	12	2	no	—
499	C₂³	—	15	1	no	—
500	C₂³	—	15	2	no	—
501	C₂³	—	30	4	no	—
502	C₂³	—	30	4	no	—
503	C₂³	—	60	2	no	—
504	C₂³	C₂×C₄×D₁₅	1	2	yes	—
505	D₄	—	30	4	no	—
506	D₄	—	30	2	no	—
507	D₄	#6705	1	4	yes	direct product factor
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	15	1	no	—
511	C₂×C₄	—	15	2	no	—
512	C₂×C₄	—	15	2	no	—
513	C₂×C₄	—	15	1	no	—
514	C₂×C₄	—	15	1	no	—
515	C₂×C₄	—	15	2	no	—
516	C₂×C₄	—	30	4	no	—
517	C₂×C₄	—	30	4	no	—
518	C₂×C₄	—	30	4	no	—
519	C₂×C₄	—	30	2	no	—
520	C₂×C₄	—	30	2	no	—
521	C₂×C₄	—	30	2	no	—
522	C₂×C₄	—	60	1	no	—
523	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
524	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
525	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
526	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
527	C₈	—	2	2	no	—
528	C₈	—	2	1	no	—
529	C₈	—	15	2	no	—
530	C₈	—	30	2	no	—
531	C₈	—	30	1	no	—
532	C₈	D₄×D₁₅	1	2	yes	complemented
533	C₂×C₃	—	2	4	no	—
534	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
535	C₂×C₃	C₂²×#676	1	1	yes	characteristic
536	C₂×C₃	#66084	1	1	yes	characteristic
537	D₃	—	10	2	no	—
538	D₃	—	20	2	no	—
539	C₅	D₄×ΓL(1,𝔽₂₅)	1	1	yes	characteristic, complemented, Sylow
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	15	2	no	—
543	C₂²	—	30	1	no	—
544	C₂²	—	30	1	no	—
545	C₂²	—	30	2	no	—
546	C₂²	—	30	2	no	—
547	C₂²	—	30	2	no	—
548	C₂²	—	60	8	no	—
549	C₂²	C₂×#6705	1	4	yes	complemented
550	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
551	C₄	—	2	2	no	—
552	C₄	—	2	1	no	—
553	C₄	—	15	2	no	—
554	C₄	—	30	2	no	—
555	C₄	—	30	1	no	—
556	C₄	—	30	1	no	—
557	C₄	C₂×#6705	1	2	yes	complemented
558	C₄	C₂×D₄×D₁₅	1	1	yes	characteristic
559	C₄	#41×D₁₅	1	1	yes	characteristic
560	C₃	D₄×#676	1	1	yes	characteristic, complemented, Sylow
561	C₂	—	2	4	no	—
562	C₂	—	30	2	no	—
563	C₂	—	60	2	no	—
564	C₂	C₄×D₄×D₁₅	1	1	yes	characteristic
565	C₂	C₂²×#6705	1	1	yes	characteristic
566	C₂	#11756509	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₅×C₈×D₄	C₂
prime radical	C₂×D₄×D₁₅	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₈×D₄	D₁₅
hypocenter	C₃×C₅	D₄×M₁₆
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#6705	C₂	semidirect
3. C₃×C₅×C₈×D₄	C₂	semidirect
4. #11751212	C₂	semidirect
5. D₄×C₃⋊#168	C₂	semidirect
6. #11750939	C₂	semidirect
7. #11750938	C₂	semidirect
8. #11750831	C₂	semidirect
9. #11750827	C₂	semidirect
10. #11750789	C₂	semidirect
11. C₄×#6705	C₂	semidirect
15. C₂²×C₃×C₅×C₈	C₂²	semidirect
19. C₂²×C₃⋊#168	C₂²	semidirect
24. C₂×#6705	C₂²	semidirect
25. C₂×#6705	C₂²	semidirect
32. C₃×C₅×C₄⋊C₈	C₂²	semidirect
33. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
34. C₃×C₄×C₅×C₈	C₂²	semidirect
35. #91114	C₂²	semidirect
36. #91104	C₂²	semidirect
37. #91104	C₂²	semidirect
38. #91099	C₂²	semidirect
39. #91099	C₂²	semidirect
40. #91098	C₂²	semidirect
41. C₄⋊(C₃⋊#168)	C₂²	semidirect
42. C₄×C₃⋊#168	C₂²	semidirect
46. C₅×C₈×D₄	D₃	semidirect
93. #6705	D₄	direct (N × H)
96. C₃×C₈×D₄	D₅	semidirect
107. C₂²×C₅×C₈	C₂×D₃	semidirect
124. C₅×C₄⋊C₈	C₂×D₃	semidirect
125. C₅×C₂²⋊C₈	C₂×D₃	semidirect
126. C₄×C₅×C₈	C₂×D₃	semidirect
142. C₃×C₅×D₄	M₁₆	semidirect
166. C₃×C₅×C₈	C₂×D₄	semidirect
169. C₃⋊#168	C₂×D₄	semidirect
172. C₂²×C₃×C₈	C₂×D₅	semidirect
189. C₃×C₄⋊C₈	C₂×D₅	semidirect
190. C₃×C₂²⋊C₈	C₂×D₅	semidirect
191. C₃×C₄×C₈	C₂×D₅	semidirect
246. C₈×D₄	D₁₅	semidirect
252. C₂²×C₃×C₅	C₂×M₁₆	semidirect
263. C₃×C₄×C₅	C₂×M₁₆	semidirect
315. C₅×D₄	ΓL(1,𝔽₂₅)	semidirect
339. C₅×C₈	D₃×D₄	semidirect
352. C₂²×C₈	C₂×D₁₅	semidirect
364. C₄⋊C₈	C₂×D₁₅	semidirect
368. C₂²⋊C₈	C₂×D₁₅	semidirect
372. C₄×C₈	C₂×D₁₅	semidirect
385. C₃×D₄	#676	semidirect
409. C₃×C₈	D₄×D₅	semidirect
415. C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	semidirect
426. C₄×C₅	C₂×ΓL(1,𝔽₂₅)	semidirect
472. C₃×C₅	D₄×M₁₆	semidirect
475. C₂²×C₃	C₂×#676	semidirect
486. C₃×C₄	C₂×#676	semidirect
507. D₄	#6705	direct (N × H)
532. C₈	D₄×D₁₅	semidirect
539. C₅	D₄×ΓL(1,𝔽₂₅)	semidirect
549. C₂²	C₂×#6705	semidirect
557. C₄	C₂×#6705	semidirect
560. C₃	D₄×#676	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#6705	2
C₄×D₄×D₁₅	2
C₃×C₅×C₈×D₄	2
#11751212	2
D₄×C₃⋊#168	2
#11750939	2
#11750938	2
#11750831	2
#11750827	2
#11750789	2
C₄×#6705	2
D₄×#676	3
D₄×ΓL(1,𝔽₂₅)	5

Subgroups — D4×#6705 #14415668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#6705 #14415668