Subgroups — #18086326

Order 4864.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564442	C₂	1	1	yes	maximal, characteristic, complemented
2	#14564430	C₂	1	1	yes	maximal, characteristic, complemented
3	#14563635	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926296	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926288	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#459	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
10	C₂×#10597289	—	2	1	no	—
11	C₂×#10597289	—	2	1	no	—
12	C₂×#10597289	—	2	1	no	—
13	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
14	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
15	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	#11926414	C₂²	1	1	yes	characteristic
17	#11926306	—	2	1	no	—
18	#11926296	—	2	2	no	—
19	#11926288	—	2	2	no	—
20	C₂²×D₈×C₁₉	—	2	1	no	—
21	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#459	—	2	2	no	—
24	C₁₉×#459	—	2	2	no	—
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#102	—	2	1	no	—
27	C₂²×D₄×C₁₉	—	2	1	no	—
28	C₂²×D₄×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	—	2	1	no	—
32	C₂×D₈×C₁₉	—	2	4	no	—
33	C₂×D₈×C₁₉	—	4	2	no	—
34	C₂×D₈×C₁₉	—	4	2	no	—
35	C₂²×C₈×C₁₉	—	2	1	no	—
36	C₁₉×#127	—	2	1	no	—
37	C₁₉×#127	—	2	1	no	—
38	C₁₉×#127	—	2	1	no	—
39	C₁₉×#127	D₄	1	2	yes	—
40	C₄×D₄×C₁₉	—	2	1	no	—
41	C₄×D₄×C₁₉	—	2	1	no	—
42	C₄×D₄×C₁₉	—	2	1	no	—
43	C₄×D₄×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
47	C₂×C₄⋊Dic₁₉	—	2	1	no	—
48	C₂×C₄⋊Dic₁₉	—	2	1	no	—
49	C₂×C₄⋊Dic₁₉	—	2	1	no	—
50	C₂²×C₁₉⋊C₈	—	2	1	no	—
51	C₂²×C₁₉⋊C₈	—	2	1	no	—
52	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
53	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
54	C₁₉×C₄⋊C₈	—	2	1	no	—
55	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
56	C₁₉×#102	—	2	4	no	—
57	#10597289	—	4	2	no	—
58	#10597289	—	4	2	no	—
59	#10597289	—	4	2	no	—
60	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
61	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
62	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
63	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
64	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₄×C₁₉⋊C₈	—	2	1	no	—
67	C₄×C₁₉⋊C₈	—	2	1	no	—
68	C₂⁴×C₁₉	—	2	1	no	—
69	C₂⁴×C₁₉	—	4	1	no	—
70	C₂×D₄×C₁₉	—	2	1	no	—
71	C₂×D₄×C₁₉	—	2	2	no	—
72	C₂×D₄×C₁₉	—	2	2	no	—
73	C₂×D₄×C₁₉	—	2	1	no	—
74	C₂×D₄×C₁₉	—	2	2	no	—
75	C₂×D₄×C₁₉	—	2	1	no	—
76	C₂×D₄×C₁₉	—	2	1	no	—
77	C₂×D₄×C₁₉	—	2	1	no	—
78	C₂×D₄×C₁₉	—	4	1	no	—
79	C₂×D₄×C₁₉	—	4	1	no	—
80	C₂×D₄×C₁₉	—	4	1	no	—
81	C₂×D₄×C₁₉	—	4	1	no	—
82	C₂×D₄×C₁₉	—	4	1	no	—
83	C₂×D₄×C₁₉	—	4	1	no	—
84	C₂×D₄×C₁₉	—	4	1	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	8	1	no	—
90	C₂×D₄×C₁₉	—	8	1	no	—
91	C₂×D₄×C₁₉	D₈	1	2	yes	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	4	1	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
102	C₂²×Dic₁₉	—	4	1	no	—
103	D₈×C₁₉	—	4	8	no	—
104	C₂×C₈×C₁₉	—	2	2	no	—
105	C₂×C₈×C₁₉	—	4	1	no	—
106	C₂×C₈×C₁₉	—	4	1	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₂²⋊C₄×C₁₉	—	4	1	no	—
110	C₂²⋊C₄×C₁₉	—	4	1	no	—
111	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₁₉	#41	1	1	yes	characteristic
114	C₄²×C₁₉	#41	1	1	yes	characteristic
115	C₄⋊Dic₁₉	—	4	1	no	—
116	C₄⋊Dic₁₉	—	4	1	no	—
117	C₄⋊Dic₁₉	—	4	1	no	—
118	C₄⋊Dic₁₉	—	4	1	no	—
119	C₄⋊Dic₁₉	—	8	1	no	—
120	C₂×C₁₉⋊C₈	—	2	1	no	—
121	C₂×C₁₉⋊C₈	—	2	1	no	—
122	C₂×C₁₉⋊C₈	—	2	1	no	—
123	C₂×C₁₉⋊C₈	—	2	1	no	—
124	C₂×C₁₉⋊C₈	—	2	1	no	—
125	C₂×C₁₉⋊C₈	—	4	1	no	—
126	C₂×C₁₉⋊C₈	—	4	1	no	—
127	C₂×C₁₉⋊C₈	—	4	1	no	—
128	C₂×C₁₉⋊C₈	—	4	1	no	—
129	C₂×C₁₉⋊C₈	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	4	1	no	—
131	C₂×C₁₉⋊C₈	D₈	1	2	yes	complemented
132	#10472	—	19	1	no	maximal, Sylow
133	C₂³×C₁₉	—	2	2	no	—
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	—	4	1	no	—
136	C₂³×C₁₉	—	4	1	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	—	4	1	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	—	8	1	no	—
142	C₂³×C₁₉	—	8	1	no	—
143	C₂³×C₁₉	—	8	1	no	—
144	C₂³×C₁₉	—	8	1	no	—
145	C₂³×C₁₉	—	8	1	no	—
146	C₂³×C₁₉	—	8	1	no	—
147	C₂³×C₁₉	#121	1	1	yes	characteristic
148	D₄×C₁₉	—	2	2	no	—
149	D₄×C₁₉	—	2	2	no	—
150	D₄×C₁₉	—	4	2	no	—
151	D₄×C₁₉	—	4	1	no	—
152	D₄×C₁₉	—	4	2	no	—
153	D₄×C₁₉	—	4	2	no	—
154	D₄×C₁₉	—	4	2	no	—
155	D₄×C₁₉	—	4	1	no	—
156	D₄×C₁₉	—	8	2	no	—
157	D₄×C₁₉	—	8	2	no	—
158	D₄×C₁₉	—	8	1	no	—
159	D₄×C₁₉	—	8	1	no	—
160	D₄×C₁₉	—	8	1	no	—
161	D₄×C₁₉	—	8	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	8	1	no	—
168	C₂×C₄×C₁₉	—	8	1	no	—
169	C₂×C₄×C₁₉	—	8	1	no	—
170	C₂×C₄×C₁₉	—	8	1	no	—
171	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
181	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
185	C₂×Dic₁₉	—	8	1	no	—
186	C₂×Dic₁₉	—	8	1	no	—
187	C₂×Dic₁₉	—	8	1	no	—
188	C₈×C₁₉	—	4	2	no	—
189	C₁₉⋊C₈	—	2	2	no	—
190	C₁₉⋊C₈	—	4	1	no	—
191	C₁₉⋊C₈	—	8	1	no	—
192	C₁₉⋊C₈	—	8	1	no	—
193	C₂×#459	D₁₉	1	1	yes	characteristic
194	#1957	—	19	1	no	—
195	#1954	—	19	1	no	—
196	#1802	—	19	1	no	—
197	C₂×#335	—	19	1	no	—
198	C₂×#331	—	19	1	no	—
199	#1296	—	19	1	no	—
200	C₂²×C₁₉	—	4	2	no	—
201	C₂²×C₁₉	—	4	2	no	—
202	C₂²×C₁₉	—	4	2	no	—
203	C₂²×C₁₉	—	8	1	no	—
204	C₂²×C₁₉	—	8	1	no	—
205	C₂²×C₁₉	—	8	1	no	—
206	C₂²×C₁₉	—	8	1	no	—
207	C₂²×C₁₉	—	8	2	no	—
208	C₂²×C₁₉	—	8	2	no	—
209	C₂²×C₁₉	—	8	2	no	—
210	C₂²×C₁₉	—	16	1	no	—
211	C₂²×C₁₉	—	16	1	no	—
212	C₂²×C₁₉	—	16	1	no	—
213	C₂²×C₁₉	—	16	1	no	—
214	C₂²×C₁₉	#394	1	1	yes	characteristic
215	C₂²×C₁₉	#459	1	1	yes	characteristic
216	C₂²×C₁₉	#463	1	1	yes	characteristic
217	C₂²×C₁₉	#466	1	1	yes	characteristic
218	C₂²×C₁₉	#468	1	1	yes	characteristic
219	C₂²×C₁₉	#471	1	1	yes	characteristic
220	C₂²×C₁₉	#472	1	1	yes	characteristic
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	8	1	no	—
224	C₄×C₁₉	#447	1	1	yes	characteristic
225	C₄×C₁₉	#452	1	1	yes	characteristic
226	C₄×C₁₉	#459	1	1	yes	characteristic
227	C₄×C₁₉	#463	1	1	yes	characteristic
228	C₄×C₁₉	#466	1	1	yes	characteristic
229	C₄×C₁₉	#469	1	1	yes	characteristic
230	C₄×C₁₉	#480	1	1	yes	characteristic
231	C₄×C₁₉	#482	1	1	yes	characteristic
232	Dic₁₉	—	16	1	no	—
233	C₂²×D₈	—	2	1	no	—
234	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
236	#459	—	2	2	no	—
237	#459	—	2	2	no	—
238	C₂×C₄⋊C₈	—	19	1	no	—
239	C₂×C₄⋊C₈	—	19	1	no	—
240	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
241	C₂×#102	—	2	1	no	—
242	C₂×#102	—	38	1	no	—
243	C₂×#102	—	38	1	no	—
244	C₂×#102	—	38	1	no	—
245	C₂×C₂²⋊C₈	—	38	1	no	—
246	C₂×C₂²⋊C₈	—	38	1	no	—
247	C₂×C₄×C₈	—	19	1	no	—
248	#384	—	19	1	no	—
249	#340	—	38	1	no	—
250	#335	—	38	2	no	—
251	#331	—	38	2	no	—
252	C₂×C₁₉	—	8	2	no	—
253	C₂×C₁₉	—	16	2	no	—
254	C₂×C₁₉	#1667	1	1	yes	characteristic
255	C₂×C₁₉	#1681	1	1	yes	characteristic
256	C₂×C₁₉	#1685	1	1	yes	characteristic
257	C₂×C₁₉	#1697	1	1	yes	characteristic
258	C₂×C₁₉	#2033	1	1	yes	characteristic
259	C₂×C₁₉	#2051	1	1	yes	characteristic
260	C₂×C₁₉	#2054	1	1	yes	characteristic
261	C₂²×D₄	—	2	1	no	—
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
265	C₂³×C₄	—	2	1	no	—
266	C₂×D₈	—	2	4	no	—
267	C₂×D₈	—	4	2	no	—
268	C₂×D₈	—	4	2	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	19	1	no	—
271	C₂²×C₈	—	19	1	no	—
272	C₂²×C₈	—	38	1	no	—
273	C₂²×C₈	—	38	1	no	—
274	#127	—	2	1	no	—
275	#127	—	2	1	no	—
276	#127	—	2	1	no	—
277	#127	C₂²⋊D₁₉	1	2	yes	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	38	1	no	—
283	C₂×C₄⋊C₄	—	38	1	no	—
284	C₂×C₄⋊C₄	—	38	1	no	—
285	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	38	1	no	—
290	C₄⋊C₈	—	38	1	no	—
291	C₄⋊C₈	—	38	1	no	—
292	C₄⋊C₈	—	38	1	no	—
293	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
294	#102	—	2	4	no	—
295	#102	—	76	2	no	—
296	#102	—	76	2	no	—
297	#102	—	76	2	no	—
298	C₂²⋊C₈	—	76	2	no	—
299	C₂²⋊C₈	—	76	2	no	—
300	C₄×C₈	—	38	1	no	—
301	C₄×C₈	—	38	1	no	—
302	C₁₉	#10472	1	1	yes	characteristic, complemented, Sylow
303	C₂⁴	—	2	1	no	—
304	C₂⁴	—	4	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	8	1	no	—
325	C₂×D₄	—	8	1	no	—
326	C₂×D₄	#64525	1	2	yes	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	—	76	1	no	—
335	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
336	C₂²×C₄	#64543	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
338	D₈	—	4	8	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	19	2	no	—
343	C₂×C₈	—	38	1	no	—
344	C₂×C₈	—	38	1	no	—
345	C₂×C₈	—	38	1	no	—
346	C₂×C₈	—	38	1	no	—
347	C₂×C₈	—	38	1	no	—
348	C₂×C₈	—	76	1	no	—
349	C₂×C₈	—	76	1	no	—
350	C₂×C₈	—	76	1	no	—
351	C₂×C₈	—	76	1	no	—
352	C₂×C₈	—	76	1	no	—
353	C₂×C₈	—	76	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	76	1	no	—
357	C₄⋊C₄	—	76	1	no	—
358	C₄⋊C₄	—	76	1	no	—
359	C₄⋊C₄	—	76	1	no	—
360	C₄⋊C₄	—	152	1	no	—
361	C₂²⋊C₄	—	4	1	no	—
362	C₂²⋊C₄	—	4	1	no	—
363	C₄²	#64543	1	1	yes	characteristic
364	C₄²	#64543	1	1	yes	characteristic
365	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
366	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
367	C₂³	—	2	2	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	8	1	no	—
376	C₂³	—	8	1	no	—
377	C₂³	—	8	1	no	—
378	C₂³	—	8	1	no	—
379	C₂³	—	8	1	no	—
380	C₂³	—	8	1	no	—
381	C₂³	#10597385	1	1	yes	characteristic
382	D₄	—	2	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	1	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	8	2	no	—
391	D₄	—	8	2	no	—
392	D₄	—	8	1	no	—
393	D₄	—	8	1	no	—
394	D₄	—	8	1	no	—
395	D₄	—	8	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	8	1	no	—
402	C₂×C₄	—	8	1	no	—
403	C₂×C₄	—	8	1	no	—
404	C₂×C₄	—	8	1	no	—
405	C₂×C₄	—	152	1	no	—
406	C₂×C₄	—	152	1	no	—
407	C₂×C₄	—	152	1	no	—
408	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
409	C₂×C₄	#10597357	1	1	yes	characteristic
410	C₂×C₄	#10597357	1	1	yes	characteristic
411	C₂×C₄	#10597358	1	1	yes	characteristic
412	C₂×C₄	C₂×#64525	1	1	yes	characteristic
413	C₂×C₄	#10597378	1	1	yes	characteristic
414	C₂×C₄	#10597381	1	1	yes	characteristic
415	C₂×C₄	#10597381	1	1	yes	characteristic
416	C₂×C₄	#10597382	1	1	yes	characteristic
417	C₂×C₄	#10597384	1	1	yes	characteristic
418	C₂×C₄	#10597385	1	1	yes	characteristic
419	C₂×C₄	#10597396	1	1	yes	characteristic
420	C₂×C₄	#10597397	1	1	yes	characteristic
421	C₂×C₄	#10597399	1	1	yes	characteristic
422	C₈	—	4	2	no	—
423	C₈	—	38	2	no	—
424	C₈	—	76	1	no	—
425	C₈	—	152	1	no	—
426	C₈	—	152	1	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	—	8	1	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	16	1	no	—
438	C₂²	—	16	1	no	—
439	C₂²	—	16	1	no	—
440	C₂²	—	16	1	no	—
441	C₂²	#11926458	1	1	yes	characteristic
442	C₂²	#11926737	1	1	yes	characteristic
443	C₂²	#11926757	1	1	yes	characteristic
444	C₂²	#11926778	1	1	yes	characteristic
445	C₂²	#11926788	1	1	yes	characteristic
446	C₂²	#11926805	1	1	yes	characteristic
447	C₂²	#11926812	1	1	yes	characteristic
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	8	1	no	—
451	C₄	—	304	1	no	—
452	C₄	#11926678	1	1	yes	characteristic
453	C₄	#11926706	1	1	yes	characteristic
454	C₄	#11926737	1	1	yes	characteristic
455	C₄	#11926757	1	1	yes	characteristic
456	C₄	#11926777	1	1	yes	characteristic
457	C₄	#11926794	1	1	yes	characteristic
458	C₄	#11926855	1	1	yes	characteristic
459	C₄	#11926865	1	1	yes	characteristic
460	C₂	—	8	2	no	—
461	C₂	—	16	2	no	—
462	C₂	#14562988	1	1	yes	characteristic
463	C₂	#14563070	1	1	yes	characteristic
464	C₂	#14563098	1	1	yes	characteristic
465	C₂	#14563166	1	1	yes	characteristic
466	C₂	#14564814	1	1	yes	characteristic
467	C₂	#14564924	1	1	yes	characteristic
468	C₂	#14564943	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597385
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₂×C₁₉×#459	C₂
socle	C₂³×C₁₉	#121
hypercenter	C₂×#459	D₁₉
hypocenter	C₁₉	#10472
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#459

Complements

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

N	H ≅ G/N	type
1. #14564442	C₂	semidirect
2. #14564430	C₂	semidirect
3. #14563635	C₂	semidirect
4. C₂×#11926296	C₂	semidirect
5. C₂×#11926288	C₂	semidirect
6. #14561519	C₂	semidirect
131. C₂×C₁₉⋊C₈	D₈	semidirect
302. C₁₉	#10472	semidirect

Maximal subgroups

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

subgroup	index
#14564442	2
#14564430	2
#14563635	2
C₂×#11926296	2
C₂×#11926288	2
#14561519	2
C₂×C₁₉×#459	2
#10472	19