Subgroups — #20257859

Order 6016.

1022 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689869	C₂	1	4	yes	maximal, complemented
2	#15689858	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689858	C₂	1	2	yes	maximal, complemented
4	#15689851	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689833	C₂	1	2	yes	maximal, complemented
6	#15689795	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689783	C₂	1	2	yes	maximal, complemented
9	#15689775	C₂	1	2	yes	maximal, complemented
10	#15689747	C₂	1	2	yes	maximal, complemented
11	#15689744	C₂	1	2	yes	maximal, complemented
12	#15689728	C₂	1	2	yes	maximal, complemented
13	#15689721	C₂	1	4	yes	maximal, complemented
14	#15689698	C₂	1	2	yes	maximal, complemented
15	#15689673	C₂	1	1	yes	maximal, characteristic, complemented
16	#15689657	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10625354	C₂²	1	2	yes	—
19	C₂×#10625350	C₂²	1	2	yes	—
20	C₂×Q₈×D₄₇	C₂²	1	2	yes	—
21	#13094024	C₂²	1	2	yes	—
22	#13094024	C₂²	1	1	yes	characteristic
23	#13094022	C₂²	1	2	yes	—
24	#13094021	C₂²	1	2	yes	—
25	#13094021	C₂²	1	1	yes	characteristic
26	#13094019	C₂²	1	4	yes	—
27	#13094018	C₂²	1	2	yes	—
28	#13094016	C₂²	1	2	yes	—
29	#13094016	C₂²	1	1	yes	characteristic
30	#13094014	C₂²	1	4	yes	—
31	#13094013	C₂²	1	4	yes	—
32	#13094013	C₂²	1	2	yes	—
33	#13094012	C₂²	1	2	yes	—
34	#13094012	C₂²	1	2	yes	—
35	#13094012	C₂²	1	1	yes	characteristic
36	#13094010	C₂²	1	4	yes	—
37	#13094009	C₂²	1	4	yes	—
38	#13094009	C₂²	1	4	yes	—
39	#13094009	C₂²	1	4	yes	—
40	#13094009	C₂²	1	4	yes	—
41	#13094009	C₂²	1	4	yes	—
42	#13094007	C₂²	1	2	yes	—
43	#13094006	C₂²	1	4	yes	—
44	#13094004	C₂²	1	2	yes	—
45	#13094004	C₂²	1	4	yes	—
46	#13094003	C₂²	1	1	yes	characteristic
47	#13094002	C₂²	1	4	yes	—
48	#13094002	C₂²	1	4	yes	—
49	#13094002	C₂²	1	4	yes	—
50	#13094000	C₂²	1	4	yes	—
51	#13093999	C₂²	1	2	yes	—
52	#13093999	C₂²	1	4	yes	—
53	#13093998	C₂²	1	1	yes	characteristic
54	#13093998	C₂²	1	2	yes	—
55	#13093998	C₂²	1	2	yes	—
56	#13093997	C₂²	1	4	yes	—
57	#13093997	C₂²	1	4	yes	—
58	C₄×Dic₉₄	C₂²	1	2	yes	—
59	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
60	#13093989	C₂²	1	2	yes	—
61	C₄×D₁₈₈	C₂²	1	2	yes	—
62	C₄×D₁₈₈	C₂²	1	2	yes	—
63	C₄×D₁₈₈	C₂²	1	2	yes	—
64	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
65	C₄×D₁₈₈	C₂²	1	2	yes	—
66	C₄×D₁₈₈	C₂²	1	2	yes	—
67	#13093986	C₂²	1	2	yes	—
68	#13093986	C₂²	1	4	yes	—
69	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
70	#13093981	C₂²	1	2	yes	—
71	C₄⋊C₄×D₄₇	C₂²	1	4	yes	—
72	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
73	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
74	#125×C₄₇	C₂²	1	2	yes	—
75	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
76	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
77	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
78	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
79	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
80	C₄×Q₈×C₄₇	C₂²	1	2	yes	—
81	#117×C₄₇	C₂²	1	2	yes	—
82	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
83	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
86	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
89	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
90	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
91	#10625354	—	4	4	no	—
92	Q₈×D₄₇	—	4	4	no	—
93	#10625350	—	4	4	no	—
94	C₂×D₁₈₈	C₂³	1	2	yes	—
95	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
96	C₂×D₁₈₈	C₂³	1	2	yes	—
97	C₂×D₁₈₈	C₂³	1	4	yes	—
98	C₂×D₁₈₈	C₂³	1	2	yes	—
99	C₂×D₁₈₈	C₂³	1	4	yes	—
100	C₂×C₄×D₄₇	C₂³	1	2	yes	—
101	C₂×C₄×D₄₇	C₂³	1	4	yes	—
102	C₂×C₄×D₄₇	C₂³	1	4	yes	—
103	C₂×C₄×D₄₇	C₂³	1	4	yes	—
104	C₂×C₄×D₄₇	C₂³	1	4	yes	—
105	C₂×Dic₉₄	C₂³	1	2	yes	—
106	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
107	C₂×Dic₉₄	C₂³	1	4	yes	—
108	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
109	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
110	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
111	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
112	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
113	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
114	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
115	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
119	C₄²×C₄₇	C₂³	1	1	yes	characteristic
120	C₄²×C₄₇	C₂³	1	1	yes	characteristic
121	C₄²×C₄₇	C₂³	1	1	yes	characteristic
122	C₄²×C₄₇	C₂³	1	1	yes	characteristic
123	C₄²×C₄₇	C₂³	1	2	yes	—
124	C₄²×C₄₇	C₂³	1	2	yes	—
125	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
126	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
127	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
128	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
129	(C₂×D₄₇)⋊C₄	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	4	yes	—
133	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
134	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
135	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
136	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
137	C₄⋊Dic₄₇	C₂³	1	4	yes	—
138	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₄₇	C₂³	1	2	yes	—
141	C₄⋊Dic₄₇	C₂³	1	2	yes	—
142	Dic₄₇⋊C₄	C₂³	1	2	yes	—
143	Dic₄₇⋊C₄	C₂³	1	4	yes	—
144	Dic₄₇⋊C₄	C₂³	1	2	yes	—
145	Dic₄₇⋊C₄	C₂³	1	2	yes	—
146	Dic₄₇⋊C₄	C₂³	1	4	yes	—
147	Dic₄₇⋊C₄	C₂³	1	4	yes	—
148	Dic₄₇⋊C₄	C₂³	1	2	yes	—
149	C₄×Dic₄₇	C₂³	1	2	yes	—
150	C₄×Dic₄₇	C₂³	1	4	yes	—
151	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
152	C₂²×D₄₇	C₂⁴	1	2	yes	—
153	C₂²×D₄₇	C₂⁴	1	4	yes	—
154	Q₈×C₄₇	—	2	2	no	—
155	Q₈×C₄₇	—	2	2	no	—
156	Q₈×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	4	1	no	—
160	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
161	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
162	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
167	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
168	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
170	C₂²⋊D₄₇	—	4	4	no	—
171	C₂²⋊D₄₇	—	4	2	no	—
172	C₂×Dic₄₇	C₂⁴	1	2	yes	—
173	C₂×Dic₄₇	C₂⁴	1	2	yes	—
174	C₂×Dic₄₇	C₂⁴	1	4	yes	—
175	C₂×Dic₄₇	C₂⁴	1	2	yes	—
176	D₁₈₈	—	2	4	no	—
177	D₁₈₈	—	2	2	no	—
178	D₁₈₈	—	2	4	no	—
179	D₁₈₈	—	4	2	no	—
180	D₁₈₈	—	4	4	no	—
181	D₁₈₈	—	4	4	no	—
182	C₄×D₄₇	—	2	4	no	—
183	C₄×D₄₇	—	4	4	no	—
184	C₄×D₄₇	—	4	4	no	—
185	C₄×D₄₇	—	4	4	no	—
186	C₄×D₄₇	—	4	4	no	—
187	Dic₉₄	—	2	4	no	—
188	Dic₉₄	—	2	2	no	—
189	Dic₉₄	—	4	4	no	—
190	C₂²×C₄₇	—	2	1	no	—
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
194	C₂×D₄₇	—	2	2	no	—
195	C₂×D₄₇	—	2	4	no	—
196	C₂×D₄₇	—	2	2	no	—
197	C₂×D₄₇	—	2	4	no	—
198	C₂×D₄₇	—	2	4	no	—
199	C₂×D₄₇	—	2	2	no	—
200	C₄×C₄₇	—	2	2	no	—
201	C₄×C₄₇	—	2	1	no	—
202	C₄×C₄₇	—	2	2	no	—
203	C₄×C₄₇	—	2	1	no	—
204	C₄×C₄₇	—	2	2	no	—
205	C₄×C₄₇	—	2	1	no	—
206	C₄×C₄₇	—	2	2	no	—
207	C₄×C₄₇	—	2	1	no	—
208	C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
209	C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
210	Dic₄₇	—	2	4	no	—
211	Dic₄₇	—	2	2	no	—
212	Dic₄₇	—	2	2	no	—
213	Dic₄₇	—	2	2	no	—
214	#3554	—	47	1	no	maximal, Sylow
215	C₂×C₄₇	—	4	1	no	—
216	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
217	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
218	C₂×C₄₇	#585	1	1	yes	characteristic
219	D₄₇	—	4	2	no	—
220	D₄₇	—	4	4	no	—
221	#562	—	47	4	no	—
222	#559	—	47	2	no	—
223	#559	—	47	1	no	—
224	#557	—	47	1	no	—
225	#554	—	47	2	no	—
226	#550	—	47	1	no	—
227	D₄×Q₈	—	47	1	no	—
228	#548	—	47	2	no	—
229	#547	—	47	2	no	—
230	#542	—	47	2	no	—
231	#542	—	47	2	no	—
232	#540	—	47	2	no	—
233	#539	—	47	4	no	—
234	#536	—	47	2	no	—
235	#533	D₄₇	1	1	yes	characteristic, complemented
236	#532	—	47	1	no	—
237	#529	—	47	1	no	—
238	C₄₇	#3554	1	1	yes	characteristic, complemented, Sylow
239	C₂×#41	—	47	2	no	—
240	C₂×#41	—	47	2	no	—
241	C₂²×Q₈	—	47	2	no	—
242	C₄⋊Q₈	—	47	2	no	—
243	C₄⋊Q₈	—	47	1	no	—
244	C₄⋊Q₈	—	47	2	no	—
245	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
246	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
247	#127	—	47	1	no	—
248	#127	—	47	2	no	—
249	#126	—	47	4	no	—
250	#126	—	47	2	no	—
251	#125	—	47	4	no	—
252	#125	—	47	1	no	—
253	#125	—	47	2	no	—
254	#125	C₂×D₄₇	1	2	yes	—
255	#124	—	47	2	no	—
256	#124	—	47	4	no	—
257	#124	—	47	4	no	—
258	#124	—	47	1	no	—
259	#124	—	47	2	no	—
260	#124	—	47	2	no	—
261	#123	—	47	2	no	—
262	#123	—	47	4	no	—
263	#123	—	47	4	no	—
264	#123	—	47	4	no	—
265	#123	—	47	4	no	—
266	#123	—	47	4	no	—
267	#123	—	47	4	no	—
268	C₂²⋊Q₈	—	47	4	no	—
269	C₂²⋊Q₈	—	47	1	no	—
270	C₂²⋊Q₈	—	47	4	no	—
271	C₂²⋊Q₈	—	47	4	no	—
272	C₂²⋊Q₈	—	47	4	no	—
273	C₂²⋊Q₈	—	47	4	no	—
274	C₂²⋊Q₈	—	47	2	no	—
275	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
276	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
277	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
278	#121	—	47	1	no	—
279	#121	—	47	2	no	—
280	#121	—	47	2	no	—
281	#121	—	47	4	no	—
282	#121	—	47	2	no	—
283	#121	—	47	4	no	—
284	#121	—	47	4	no	—
285	C₄×Q₈	—	47	2	no	—
286	C₄×Q₈	—	47	1	no	—
287	C₄×Q₈	—	47	2	no	—
288	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
289	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
290	C₄×Q₈	C₂×D₄₇	1	2	yes	—
291	C₄×D₄	—	47	2	no	—
292	C₄×D₄	—	47	4	no	—
293	C₄×D₄	—	47	2	no	—
294	C₄×D₄	—	47	1	no	—
295	C₄×D₄	—	47	2	no	—
296	C₄×D₄	—	47	2	no	—
297	C₄×D₄	—	47	2	no	—
298	C₄×D₄	—	47	2	no	—
299	C₄×D₄	—	47	2	no	—
300	#117	—	47	2	no	—
301	#117	C₂×D₄₇	1	2	yes	—
302	C₂×C₄⋊C₄	—	47	4	no	—
303	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
304	#41	—	188	4	no	—
305	#41	—	188	4	no	—
306	C₂×Q₈	—	47	1	no	—
307	C₂×Q₈	—	47	2	no	—
308	C₂×Q₈	—	47	4	no	—
309	C₂×Q₈	—	188	4	no	—
310	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
311	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
312	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
313	C₂×D₄	—	47	2	no	—
314	C₂×D₄	—	47	4	no	—
315	C₂×D₄	—	47	1	no	—
316	C₂×D₄	—	47	2	no	—
317	C₂×D₄	—	47	2	no	—
318	C₂×D₄	—	47	2	no	—
319	C₂×D₄	—	47	4	no	—
320	C₂×D₄	—	47	4	no	—
321	C₂²×C₄	—	47	2	no	—
322	C₂²×C₄	—	47	4	no	—
323	C₂²×C₄	—	47	4	no	—
324	C₂²×C₄	—	47	4	no	—
325	C₂²×C₄	—	47	4	no	—
326	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
327	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
328	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
329	C₄⋊C₄	—	47	2	no	—
330	C₄⋊C₄	—	47	4	no	—
331	C₄⋊C₄	—	47	2	no	—
332	C₄⋊C₄	—	47	2	no	—
333	C₄⋊C₄	—	47	4	no	—
334	C₄⋊C₄	—	47	4	no	—
335	C₄⋊C₄	—	47	2	no	—
336	C₄⋊C₄	—	47	4	no	—
337	C₄⋊C₄	—	47	1	no	—
338	C₄⋊C₄	—	47	1	no	—
339	C₄⋊C₄	—	47	2	no	—
340	C₄⋊C₄	—	47	2	no	—
341	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
342	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
343	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
344	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
345	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
346	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
347	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
348	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
349	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
350	C₂²⋊C₄	—	47	2	no	—
351	C₂²⋊C₄	—	47	2	no	—
352	C₂²⋊C₄	—	47	2	no	—
353	C₂²⋊C₄	—	47	2	no	—
354	C₂²⋊C₄	—	47	2	no	—
355	C₂²⋊C₄	—	47	4	no	—
356	C₂²⋊C₄	—	47	4	no	—
357	C₂²⋊C₄	—	47	4	no	—
358	C₂²⋊C₄	—	47	4	no	—
359	C₂²⋊C₄	—	47	4	no	—
360	C₂²⋊C₄	—	47	4	no	—
361	C₂²⋊C₄	—	47	4	no	—
362	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
363	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
364	C₄²	—	47	2	no	—
365	C₄²	—	47	4	no	—
366	C₄²	C₂²×D₄₇	1	1	yes	characteristic
367	C₄²	C₂²×D₄₇	1	1	yes	characteristic
368	C₄²	C₂²×D₄₇	1	1	yes	characteristic
369	C₄²	C₂²×D₄₇	1	1	yes	characteristic
370	C₄²	C₂²×D₄₇	1	2	yes	—
371	C₄²	C₂²×D₄₇	1	2	yes	—
372	C₂³	—	47	2	no	—
373	C₂³	—	47	4	no	—
374	C₂³	C₂³×D₄₇	1	1	yes	characteristic
375	Q₈	—	2	2	no	—
376	Q₈	—	2	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	94	4	no	—
379	Q₈	—	94	2	no	—
380	Q₈	—	188	4	no	—
381	D₄	—	94	4	no	—
382	D₄	—	94	2	no	—
383	D₄	—	94	4	no	—
384	D₄	—	188	2	no	—
385	D₄	—	188	4	no	—
386	D₄	—	188	4	no	—
387	D₄	—	188	2	no	—
388	D₄	—	188	4	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	47	2	no	—
393	C₂×C₄	—	47	2	no	—
394	C₂×C₄	—	47	4	no	—
395	C₂×C₄	—	47	2	no	—
396	C₂×C₄	—	94	4	no	—
397	C₂×C₄	—	188	4	no	—
398	C₂×C₄	—	188	4	no	—
399	C₂×C₄	—	188	4	no	—
400	C₂×C₄	—	188	4	no	—
401	C₂×C₄	C₂³×D₄₇	1	2	yes	—
402	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
403	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
404	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
405	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
406	C₂×C₄	C₂³×D₄₇	1	2	yes	—
407	C₂×C₄	C₂³×D₄₇	1	2	yes	—
408	C₂×C₄	C₂³×D₄₇	1	2	yes	—
409	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
410	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	94	2	no	—
415	C₂²	—	94	4	no	—
416	C₂²	—	94	2	no	—
417	C₂²	—	94	4	no	—
418	C₂²	—	94	4	no	—
419	C₂²	—	94	2	no	—
420	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	94	2	no	—
430	C₄	—	94	4	no	—
431	C₄	—	94	2	no	—
432	C₄	—	94	2	no	—
433	C₄	#13094070	1	2	yes	—
434	C₄	#13094072	1	2	yes	—
435	C₂	—	4	1	no	—
436	C₂	—	188	2	no	—
437	C₂	—	188	4	no	—
438	C₂	C₂×#13094070	1	1	yes	characteristic
439	C₂	C₂×#13094072	1	1	yes	characteristic
440	C₂	#15689959	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#533	C₂
hypercenter	#533	D₄₇
hypocenter	C₄₇	#3554
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #533

Complements

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

N	H ≅ G/N	type
1. #15689869	C₂	semidirect
2. #15689858	C₂	semidirect
3. #15689858	C₂	semidirect
4. #15689851	C₂	semidirect
5. #15689833	C₂	semidirect
6. #15689795	C₂	semidirect
7. Q₈×D₁₈₈	C₂	semidirect
8. #15689783	C₂	semidirect
9. #15689775	C₂	semidirect
10. #15689747	C₂	semidirect
11. #15689744	C₂	semidirect
12. #15689728	C₂	semidirect
13. #15689721	C₂	semidirect
14. #15689698	C₂	semidirect
15. #15689673	C₂	semidirect
16. #15689657	C₂	semidirect
17. C₄₇×#533	C₂	semidirect
235. #533	D₄₇	semidirect
238. C₄₇	#3554	semidirect