Subgroups — #20257094

Order 6016.

1124 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689831	C₂	1	2	yes	maximal, complemented
2	#15689830	C₂	1	2	yes	maximal, complemented
3	#15689825	C₂	1	2	yes	maximal, complemented
4	#15689819	C₂	1	2	yes	maximal, complemented
5	#15689815	C₂	1	2	yes	maximal, complemented
6	#15689813	C₂	1	2	yes	maximal, complemented
7	#15689777	C₂	1	2	yes	maximal, complemented
8	#15689773	C₂	1	2	yes	maximal, complemented
9	#15689751	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689717	C₂	1	4	yes	maximal, complemented
11	#15689701	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689634	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689629	C₂	1	4	yes	maximal, complemented
14	#15689606	C₂	1	1	yes	maximal, characteristic, complemented
15	#15689603	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₇×#525	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10625350	C₂²	1	1	yes	characteristic
19	C₂×#10625352	C₂²	1	4	yes	—
20	C₂³×Dic₄₇	C₂²	1	2	yes	—
21	#13094024	C₂²	1	2	yes	complemented
22	#13094023	C₂²	1	2	yes	complemented
23	#13094019	C₂²	1	4	yes	complemented
24	#13094017	C₂²	1	4	yes	complemented
25	#13094016	C₂²	1	2	yes	complemented
26	#13094015	C₂²	1	2	yes	complemented
27	#13094015	C₂²	1	4	yes	complemented
28	#13094014	C₂²	1	4	yes	complemented
29	#13094008	C₂²	1	4	yes	—
30	#13094008	C₂²	1	4	yes	complemented
31	#13094007	C₂²	1	2	yes	—
32	#13094006	C₂²	1	4	yes	complemented
33	#13094005	C₂²	1	4	yes	—
34	#13094004	C₂²	1	4	yes	complemented
35	#13094003	C₂²	1	1	yes	characteristic
36	#13094003	C₂²	1	1	yes	characteristic
37	#13094003	C₂²	1	2	yes	complemented
38	#13094001	C₂²	1	4	yes	—
39	#13094001	C₂²	1	4	yes	—
40	#13094001	C₂²	1	4	yes	complemented
41	#13094000	C₂²	1	2	yes	complemented
42	#13093998	C₂²	1	1	yes	characteristic
43	#13093998	C₂²	1	1	yes	characteristic
44	#13093998	C₂²	1	2	yes	complemented
45	#13093996	C₂²	1	4	yes	—
46	#13093996	C₂²	1	4	yes	—
47	#13093995	C₂²	1	2	yes	complemented
48	#13093993	C₂²	1	2	yes	—
49	Q₈×Dic₄₇	C₂²	1	2	yes	complemented
50	C₄×Dic₉₄	C₂²	1	2	yes	complemented
51	C₄×D₁₈₈	C₂²	1	2	yes	complemented
52	D₄×Dic₄₇	C₂²	1	4	yes	—
53	D₄×Dic₄₇	C₂²	1	4	yes	—
54	D₄×Dic₄₇	C₂²	1	2	yes	complemented
55	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
56	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
57	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	—
58	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	—
59	#13093983	C₂²	1	1	yes	characteristic
60	#13093983	C₂²	1	2	yes	complemented
61	#13093982	C₂²	1	2	yes	complemented
62	#13093980	C₂²	1	4	yes	—
63	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
65	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
66	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
67	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
68	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
69	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
70	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
71	C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
72	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic
73	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
74	#123×C₄₇	C₂²	1	2	yes	—
75	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
76	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
77	#121×C₄₇	C₂²	1	1	yes	characteristic
78	#121×C₄₇	C₂²	1	1	yes	characteristic
79	#120×C₄₇	C₂²	1	2	yes	—
80	C₄×D₄×C₄₇	C₂²	1	2	yes	—
81	C₄×D₄×C₄₇	C₂²	1	2	yes	—
82	#117×C₄₇	C₂²	1	1	yes	characteristic
83	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
84	#41×C₄₇	—	2	4	no	—
85	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₄₇	C₂³	1	2	yes	—
87	C₂×D₄×C₄₇	C₂³	1	2	yes	—
88	C₂×D₄×C₄₇	C₂³	1	2	yes	—
89	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
98	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
99	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
100	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
101	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
102	C₂²×Dic₄₇	—	4	4	no	—
103	C₂²×Dic₄₇	C₂³	1	4	yes	—
104	C₂²×Dic₄₇	C₂³	1	2	yes	—
105	C₂²×Dic₄₇	C₂³	1	4	yes	—
106	C₂²×Dic₄₇	C₂³	1	2	yes	—
107	C₂²×Dic₄₇	C₂³	1	4	yes	—
108	#10625352	—	4	8	no	—
109	#10625350	—	2	4	no	—
110	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₄₇	C₂³	1	2	yes	—
112	C₂×C₄×D₄₇	C₂³	1	4	yes	—
113	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
114	C₂×Dic₉₄	C₂³	1	4	yes	—
115	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
118	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
119	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
120	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
121	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
122	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
123	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
124	C₄²×C₄₇	C₂³	1	2	yes	—
125	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
126	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
127	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
128	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
129	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
130	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
131	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
132	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
133	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
134	C₄⋊Dic₄₇	C₂³	1	2	yes	—
135	C₄⋊Dic₄₇	C₂³	1	2	yes	—
136	C₄⋊Dic₄₇	C₂³	1	2	yes	—
137	C₄⋊Dic₄₇	C₂³	1	2	yes	—
138	C₄⋊Dic₄₇	C₂³	1	4	yes	—
139	C₄⋊Dic₄₇	C₂³	1	4	yes	—
140	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₄₇	C₂³	1	4	yes	—
142	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₄₇	C₂³	1	4	yes	—
144	Dic₄₇⋊C₄	C₂³	1	4	yes	—
145	Dic₄₇⋊C₄	C₂³	1	4	yes	—
146	Dic₄₇⋊C₄	C₂³	1	4	yes	—
147	Dic₄₇⋊C₄	C₂³	1	4	yes	—
148	Dic₄₇⋊C₄	C₂³	1	2	yes	—
149	Dic₄₇⋊C₄	C₂³	1	2	yes	—
150	C₄×Dic₄₇	C₂³	1	4	yes	—
151	C₄×Dic₄₇	C₂³	1	4	yes	—
152	C₄×Dic₄₇	C₂³	1	2	yes	—
153	C₂³×C₄₇	—	2	2	no	—
154	C₂³×C₄₇	—	2	2	no	—
155	C₂³×C₄₇	—	2	2	no	—
156	C₂³×C₄₇	C₂⁴	1	2	yes	—
157	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
158	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
159	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
160	C₂²×D₄₇	C₂⁴	1	2	yes	—
161	Q₈×C₄₇	—	2	2	no	—
162	D₄×C₄₇	—	2	4	no	—
163	D₄×C₄₇	—	2	4	no	—
164	D₄×C₄₇	—	2	4	no	—
165	D₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	#41	1	4	yes	complemented
173	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
174	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
175	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
176	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
180	C₂²⋊D₄₇	—	2	4	no	—
181	C₂²⋊D₄₇	—	2	4	no	—
182	C₂²⋊D₄₇	—	2	4	no	—
183	C₂²⋊D₄₇	—	4	4	no	—
184	C₂×Dic₄₇	—	2	8	no	—
185	C₂×Dic₄₇	—	4	4	no	—
186	C₂×Dic₄₇	—	4	2	no	—
187	C₂×Dic₄₇	—	4	4	no	—
188	C₂×Dic₄₇	—	4	2	no	—
189	C₂×Dic₄₇	C₂⁴	1	2	yes	—
190	C₂×Dic₄₇	C₂⁴	1	2	yes	—
191	C₂×Dic₄₇	C₂⁴	1	4	yes	—
192	C₂×Dic₄₇	C₂⁴	1	2	yes	—
193	C₂×Dic₄₇	C₂⁴	1	4	yes	—
194	D₁₈₈	—	2	2	no	—
195	C₄×D₄₇	—	2	4	no	—
196	C₄×D₄₇	—	4	4	no	—
197	Dic₉₄	—	2	2	no	—
198	Dic₉₄	—	4	4	no	—
199	C₂²×C₄₇	—	2	8	no	—
200	C₂²×C₄₇	—	2	1	no	—
201	C₂²×C₄₇	—	2	1	no	—
202	C₂²×C₄₇	—	2	1	no	—
203	C₂²×C₄₇	—	2	1	no	—
204	C₂²×C₄₇	—	2	1	no	—
205	C₂²×C₄₇	—	2	1	no	—
206	C₂²×C₄₇	—	2	2	no	—
207	C₂²×C₄₇	—	2	2	no	—
208	C₂²×C₄₇	—	2	2	no	—
209	C₂²×C₄₇	C₂×#41	1	2	yes	—
210	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
211	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
212	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
213	C₂×D₄₇	—	2	2	no	—
214	C₂×D₄₇	—	2	2	no	—
215	C₂×D₄₇	—	2	2	no	—
216	C₄×C₄₇	—	2	1	no	—
217	C₄×C₄₇	—	2	1	no	—
218	C₄×C₄₇	—	2	2	no	—
219	C₄×C₄₇	—	2	2	no	—
220	C₄×C₄₇	—	2	2	no	—
221	C₄×C₄₇	C₂×#41	1	2	yes	—
222	C₄×C₄₇	C₂×#41	1	2	yes	—
223	Dic₄₇	—	2	2	no	—
224	Dic₄₇	—	2	2	no	—
225	Dic₄₇	—	2	4	no	—
226	Dic₄₇	—	2	4	no	—
227	Dic₄₇	—	2	2	no	—
228	#3492	—	47	1	no	maximal, Sylow
229	C₂×C₄₇	—	2	2	no	—
230	C₂×C₄₇	—	2	2	no	—
231	C₂×C₄₇	—	2	2	no	—
232	C₂×C₄₇	—	4	2	no	—
233	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
234	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
236	D₄₇	—	4	2	no	—
237	#554	—	47	2	no	—
238	#554	—	47	2	no	—
239	#553	—	47	2	no	—
240	#553	—	47	2	no	—
241	#552	—	47	2	no	—
242	#552	—	47	2	no	—
243	#547	—	47	2	no	—
244	#547	—	47	2	no	—
245	#544	—	47	1	no	—
246	#539	—	47	4	no	—
247	#537	—	47	1	no	—
248	#525	—	47	1	no	—
249	#525	—	47	4	no	—
250	#525	D₄₇	1	1	yes	characteristic, complemented
251	#520	—	47	1	no	—
252	#520	—	47	1	no	—
253	C₂²×C₄⋊C₄	—	47	1	no	—
254	C₄₇	#3492	1	1	yes	characteristic, complemented, Sylow
255	C₂×#41	—	47	4	no	—
256	C₂×#41	—	47	1	no	—
257	C₂×#41	C₂×D₄₇	1	1	yes	characteristic
258	C₂³×C₄	—	47	2	no	—
259	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
260	C₄⋊Q₈	—	47	2	no	—
261	C₄⋊Q₈	—	47	2	no	—
262	#126	—	47	4	no	—
263	#126	—	47	4	no	—
264	#125	—	47	4	no	—
265	#125	—	47	4	no	—
266	#125	—	47	2	no	—
267	#125	—	47	2	no	—
268	#123	—	47	4	no	—
269	#123	—	47	2	no	—
270	#123	—	47	4	no	—
271	#123	—	47	4	no	—
272	#123	—	47	4	no	—
273	#123	C₂×D₄₇	1	2	yes	—
274	C₂²⋊Q₈	—	47	2	no	—
275	C₂²⋊Q₈	—	47	1	no	—
276	C₂²⋊Q₈	—	47	1	no	—
277	C₂²⋊Q₈	—	47	2	no	—
278	C₂²⋊Q₈	—	47	4	no	—
279	C₂²⋊Q₈	—	47	4	no	—
280	C₂²⋊Q₈	—	47	4	no	—
281	C₂²⋊Q₈	—	47	4	no	—
282	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
283	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
284	#121	—	47	4	no	—
285	#121	—	47	4	no	—
286	#121	—	47	2	no	—
287	#121	—	47	1	no	—
288	#121	—	47	1	no	—
289	#121	—	47	2	no	—
290	#121	C₂×D₄₇	1	1	yes	characteristic
291	#121	C₂×D₄₇	1	1	yes	characteristic
292	#120	—	47	2	no	—
293	#120	C₂×D₄₇	1	2	yes	—
294	C₄×Q₈	—	47	2	no	—
295	C₄×Q₈	—	47	2	no	—
296	C₄×D₄	—	47	4	no	—
297	C₄×D₄	—	47	2	no	—
298	C₄×D₄	—	47	4	no	—
299	C₄×D₄	—	47	2	no	—
300	C₄×D₄	—	47	2	no	—
301	C₄×D₄	—	47	4	no	—
302	C₄×D₄	—	47	4	no	—
303	C₄×D₄	—	47	2	no	—
304	C₄×D₄	C₂×D₄₇	1	2	yes	—
305	C₄×D₄	C₂×D₄₇	1	2	yes	—
306	#117	—	47	1	no	—
307	#117	—	47	2	no	—
308	#117	—	47	2	no	—
309	#117	—	47	4	no	—
310	#117	C₂×D₄₇	1	1	yes	characteristic
311	C₂×C₄⋊C₄	—	47	1	no	—
312	C₂×C₄⋊C₄	—	47	1	no	—
313	C₂×C₄⋊C₄	—	47	2	no	—
314	C₂×C₄⋊C₄	—	47	2	no	—
315	C₂×C₄⋊C₄	—	47	2	no	—
316	C₂×C₄⋊C₄	—	47	2	no	—
317	C₂×C₄⋊C₄	—	47	2	no	—
318	C₂×C₄⋊C₄	—	47	2	no	—
319	C₂×C₄⋊C₄	—	47	2	no	—
320	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
321	#41	—	2	4	no	—
322	#41	—	94	4	no	—
323	#41	—	188	8	no	—
324	C₂×Q₈	—	47	1	no	—
325	C₂×Q₈	—	47	4	no	—
326	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
327	C₂×D₄	—	47	2	no	—
328	C₂×D₄	—	47	2	no	—
329	C₂×D₄	—	47	2	no	—
330	C₂×D₄	—	47	4	no	—
331	C₂×D₄	—	47	1	no	—
332	C₂×D₄	C₂²×D₄₇	1	2	yes	—
333	C₂×D₄	C₂²×D₄₇	1	2	yes	—
334	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
335	C₂×D₄	C₂²×D₄₇	1	2	yes	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	47	4	no	—
338	C₂²×C₄	—	47	2	no	—
339	C₂²×C₄	—	47	4	no	—
340	C₂²×C₄	—	47	2	no	—
341	C₂²×C₄	—	47	4	no	—
342	C₂²×C₄	—	47	2	no	—
343	C₂²×C₄	—	47	4	no	—
344	C₂²×C₄	—	188	4	no	—
345	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
346	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
347	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
348	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
349	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
350	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
351	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
352	C₄⋊C₄	—	47	4	no	—
353	C₄⋊C₄	—	47	4	no	—
354	C₄⋊C₄	—	47	4	no	—
355	C₄⋊C₄	—	47	2	no	—
356	C₄⋊C₄	—	47	4	no	—
357	C₄⋊C₄	—	47	2	no	—
358	C₄⋊C₄	—	47	2	no	—
359	C₄⋊C₄	—	47	2	no	—
360	C₄⋊C₄	—	47	2	no	—
361	C₄⋊C₄	—	47	2	no	—
362	C₄⋊C₄	—	47	4	no	—
363	C₄⋊C₄	—	47	4	no	—
364	C₄⋊C₄	—	47	1	no	—
365	C₄⋊C₄	—	47	4	no	—
366	C₄⋊C₄	—	47	1	no	—
367	C₄⋊C₄	—	47	4	no	—
368	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
369	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
370	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
371	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
372	C₂²⋊C₄	—	47	2	no	—
373	C₂²⋊C₄	—	47	2	no	—
374	C₂²⋊C₄	—	47	4	no	—
375	C₂²⋊C₄	—	47	2	no	—
376	C₂²⋊C₄	—	47	4	no	—
377	C₂²⋊C₄	—	47	4	no	—
378	C₂²⋊C₄	—	47	4	no	—
379	C₂²⋊C₄	—	47	2	no	—
380	C₂²⋊C₄	—	47	2	no	—
381	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
382	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
383	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
384	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
385	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
386	C₄²	—	47	4	no	—
387	C₄²	—	47	4	no	—
388	C₄²	—	47	2	no	—
389	C₄²	C₂²×D₄₇	1	2	yes	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	47	2	no	—
394	C₂³	C₂³×D₄₇	1	2	yes	—
395	C₂³	C₂³×D₄₇	1	1	yes	characteristic
396	C₂³	C₂³×D₄₇	1	1	yes	characteristic
397	C₂³	C₂³×D₄₇	1	1	yes	characteristic
398	Q₈	—	2	2	no	—
399	Q₈	—	94	2	no	—
400	Q₈	—	188	4	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	4	no	—
403	D₄	—	2	4	no	—
404	D₄	—	2	2	no	—
405	D₄	—	94	4	no	—
406	D₄	—	94	4	no	—
407	D₄	—	94	4	no	—
408	D₄	—	94	2	no	—
409	D₄	—	188	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	47	2	no	—
417	C₂×C₄	—	47	2	no	—
418	C₂×C₄	—	47	4	no	—
419	C₂×C₄	—	47	2	no	—
420	C₂×C₄	—	47	4	no	—
421	C₂×C₄	—	94	8	no	—
422	C₂×C₄	—	94	4	no	—
423	C₂×C₄	—	188	4	no	—
424	C₂×C₄	—	188	2	no	—
425	C₂×C₄	—	188	4	no	—
426	C₂×C₄	—	188	2	no	—
427	C₂×C₄	—	188	4	no	—
428	C₂×C₄	#10625352	1	4	yes	complemented
429	C₂×C₄	C₂³×D₄₇	1	2	yes	—
430	C₂×C₄	C₂³×D₄₇	1	2	yes	—
431	C₂×C₄	C₂³×D₄₇	1	2	yes	—
432	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
433	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
434	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
435	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
436	C₂²	—	2	8	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	94	2	no	—
447	C₂²	—	94	2	no	—
448	C₂²	—	94	2	no	—
449	C₂²	C₂×#10625352	1	2	yes	—
450	C₂²	#13094070	1	2	yes	—
451	C₂²	#13094071	1	2	yes	—
452	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	94	2	no	—
459	C₄	—	94	4	no	—
460	C₄	—	94	4	no	—
461	C₄	—	94	2	no	—
462	C₄	—	94	2	no	—
463	C₄	C₂×#10625352	1	2	yes	—
464	C₄	C₂×#10625352	1	2	yes	—
465	C₂	—	2	2	no	—
466	C₂	—	2	2	no	—
467	C₂	—	2	2	no	—
468	C₂	—	4	2	no	—
469	C₂	—	188	2	no	—
470	C₂	C₂²×#10625352	1	1	yes	characteristic
471	C₂	C₂×#13094070	1	1	yes	characteristic
472	C₂	C₂×#13094071	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#525	C₂
hypercenter	#525	D₄₇
hypocenter	C₄₇	#3492
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. #15689831	C₂	semidirect
2. #15689830	C₂	semidirect
3. #15689825	C₂	semidirect
4. #15689819	C₂	semidirect
5. #15689815	C₂	semidirect
6. #15689813	C₂	semidirect
7. #15689777	C₂	semidirect
8. #15689773	C₂	semidirect
9. #15689751	C₂	semidirect
10. #15689717	C₂	semidirect
11. #15689701	C₂	semidirect
12. #15689634	C₂	semidirect
13. #15689629	C₂	semidirect
14. #15689606	C₂	semidirect
15. #15689603	C₂	semidirect
16. C₂²×C₄⋊Dic₄₇	C₂	semidirect
17. C₄₇×#525	C₂	semidirect
21. #13094024	C₂²	semidirect
22. #13094023	C₂²	semidirect
23. #13094019	C₂²	semidirect
24. #13094017	C₂²	semidirect
25. #13094016	C₂²	semidirect
26. #13094015	C₂²	semidirect
27. #13094015	C₂²	semidirect
28. #13094014	C₂²	semidirect
30. #13094008	C₂²	semidirect
32. #13094006	C₂²	semidirect
34. #13094004	C₂²	semidirect
37. #13094003	C₂²	semidirect
40. #13094001	C₂²	semidirect
41. #13094000	C₂²	semidirect
44. #13093998	C₂²	semidirect
47. #13093995	C₂²	semidirect
49. Q₈×Dic₄₇	C₂²	semidirect
50. C₄×Dic₉₄	C₂²	semidirect
51. C₄×D₁₈₈	C₂²	semidirect
54. D₄×Dic₄₇	C₂²	semidirect
60. #13093983	C₂²	semidirect
61. #13093982	C₂²	semidirect
70. C₂×C₄⋊Dic₄₇	C₂²	semidirect
71. C₄⋊C₄×D₄₇	C₂²	semidirect
172. C₂×C₄×C₄₇	#41	semidirect
250. #525	D₄₇	semidirect
254. C₄₇	#3492	semidirect
428. C₂×C₄	#10625352	semidirect