Subgroups — #18086743

Order 4864.

622 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926920	C₂	1	1	yes	maximal, characteristic
2	#14564563	C₂	1	1	yes	maximal, characteristic, complemented
3	#14564561	C₂	1	1	yes	maximal, characteristic, complemented
4	#14564351	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926287	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#331	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64525	—	2	1	no	—
9	C₂²×#64525	—	2	1	no	—
10	C₂×#10597320	C₂²	1	1	yes	characteristic
11	#11926920	—	2	2	no	—
12	#11926920	—	2	2	no	—
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×Dic₁₉⋊C₈	—	2	1	no	—
15	C₂×#10597278	—	2	1	no	—
16	C₂×#10597278	—	2	1	no	—
17	C₂×#10597289	—	2	1	no	—
18	C₂×#10597289	—	2	1	no	—
19	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
21	#11926298	—	2	1	no	—
22	#11926287	—	2	2	no	—
23	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₁₉×#331	—	2	2	no	—
27	C₂²×D₄×C₁₉	—	2	1	no	—
28	C₂²×D₄×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	—	2	1	no	—
30	C₂²×D₇₆	—	2	1	no	—
31	C₂²×D₇₆	—	2	1	no	—
32	C₂²×D₇₆	—	2	1	no	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₂²×C₈×C₁₉	—	2	1	no	—
35	C₁₉×#127	—	2	1	no	—
36	C₁₉×#127	—	2	1	no	—
37	C₁₉×#127	—	2	1	no	—
38	C₁₉×#127	D₄	1	2	yes	—
39	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×#64525	—	2	4	no	—
41	C₂×#64525	—	2	4	no	—
42	C₂×#64525	—	4	2	no	—
43	C₂×#64525	—	4	2	no	—
44	C₂×#64525	—	4	2	no	—
45	C₂×#64525	—	4	2	no	—
46	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
47	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄×Dic₁₉	—	2	1	no	—
49	C₂²×C₁₉⋊C₈	—	2	1	no	—
50	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
51	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
52	#10597320	—	2	1	no	—
53	#10597320	—	2	1	no	—
54	#10597320	—	2	1	no	—
55	#10597320	D₄	1	2	yes	—
56	C₁₉×C₄⋊C₈	—	2	1	no	—
57	C₁₉×C₄⋊C₈	—	2	1	no	—
58	C₁₉×C₄⋊C₈	—	2	1	no	—
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	#10597289	—	4	2	no	—
61	#10597289	—	4	2	no	—
62	C₁₉⋊#95	—	2	1	no	—
63	#10597278	—	4	2	no	—
64	#10597278	—	4	2	no	—
65	Dic₁₉⋊C₈	—	4	2	no	—
66	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
67	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
68	C₄×C₁₉⋊C₈	—	2	1	no	—
69	C₄×C₁₉⋊C₈	—	2	1	no	—
70	C₂⁴×C₁₉	—	4	1	no	—
71	C₂³×D₁₉	—	4	1	no	—
72	C₂×D₄×C₁₉	—	2	2	no	—
73	C₂×D₄×C₁₉	—	2	2	no	—
74	C₂×D₄×C₁₉	—	2	2	no	—
75	C₂×D₄×C₁₉	—	4	1	no	—
76	C₂×D₄×C₁₉	—	4	1	no	—
77	C₂×D₄×C₁₉	—	4	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	—	8	1	no	—
87	C₂×D₄×C₁₉	—	8	1	no	—
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
91	C₂²×Dic₁₉	—	2	1	no	—
92	C₂²×Dic₁₉	—	2	1	no	—
93	C₂×D₇₆	—	2	2	no	—
94	C₂×D₇₆	—	2	2	no	—
95	C₂×D₇₆	—	2	2	no	—
96	C₂×D₇₆	—	4	1	no	—
97	C₂×D₇₆	—	4	1	no	—
98	C₂×D₇₆	—	4	1	no	—
99	C₂×D₇₆	—	4	1	no	—
100	C₂×D₇₆	—	4	1	no	—
101	C₂×D₇₆	—	4	1	no	—
102	C₂×D₇₆	—	4	1	no	—
103	C₂×D₇₆	—	4	1	no	—
104	C₂×D₇₆	—	4	1	no	—
105	C₂×D₇₆	—	4	1	no	—
106	C₂×D₇₆	—	4	1	no	—
107	C₂×D₇₆	—	8	1	no	—
108	C₂×D₇₆	—	8	1	no	—
109	C₂×C₈×C₁₉	—	4	1	no	—
110	C₂×C₈×C₁₉	—	4	1	no	—
111	C₂×C₈×C₁₉	—	4	1	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₁₉	#41	1	1	yes	characteristic
118	C₄²×C₁₉	#41	1	1	yes	characteristic
119	#64525	—	4	8	no	—
120	#64525	—	4	8	no	—
121	C₄⋊Dic₁₉	—	2	1	no	—
122	C₄⋊Dic₁₉	—	2	1	no	—
123	C₄⋊Dic₁₉	—	2	1	no	—
124	C₄⋊Dic₁₉	D₈	1	2	yes	complemented
125	C₄×Dic₁₉	—	4	1	no	—
126	C₄×Dic₁₉	—	4	1	no	—
127	C₂×C₁₉⋊C₈	—	2	1	no	—
128	C₂×C₁₉⋊C₈	—	2	1	no	—
129	C₂×C₁₉⋊C₈	—	2	1	no	—
130	C₂×C₁₉⋊C₈	—	2	1	no	—
131	C₂×C₁₉⋊C₈	—	4	1	no	—
132	C₂×C₁₉⋊C₈	—	4	1	no	—
133	C₂×C₁₉⋊C₈	—	4	1	no	—
134	C₂×C₁₉⋊C₈	D₈	1	2	yes	—
135	C₂×C₁₉⋊C₈	SD₁₆	1	2	yes	—
136	#10536	—	19	1	no	maximal, Sylow
137	C₂³×C₁₉	—	4	2	no	—
138	C₂³×C₁₉	—	8	1	no	—
139	C₂³×C₁₉	—	8	1	no	—
140	C₂³×C₁₉	—	8	1	no	—
141	C₂³×C₁₉	—	8	1	no	—
142	C₂³×C₁₉	—	8	1	no	—
143	C₂³×C₁₉	—	8	1	no	—
144	C₂³×C₁₉	#121	1	1	yes	characteristic
145	C₂²×D₁₉	—	4	2	no	—
146	C₂²×D₁₉	—	8	1	no	—
147	C₂²×D₁₉	—	8	1	no	—
148	C₂²×D₁₉	—	8	1	no	—
149	C₂²×D₁₉	—	8	1	no	—
150	C₂²×D₁₉	—	8	1	no	—
151	C₂²×D₁₉	—	8	1	no	—
152	D₄×C₁₉	—	4	2	no	—
153	D₄×C₁₉	—	4	2	no	—
154	D₄×C₁₉	—	4	2	no	—
155	D₄×C₁₉	—	4	2	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	#120	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
174	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
176	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
178	C₂×Dic₁₉	—	2	2	no	—
179	C₂×Dic₁₉	—	4	1	no	—
180	C₂×Dic₁₉	—	4	1	no	—
181	C₂×Dic₁₉	—	4	1	no	—
182	C₂×Dic₁₉	—	4	1	no	—
183	C₂×Dic₁₉	—	4	1	no	—
184	D₇₆	—	4	2	no	—
185	D₇₆	—	4	2	no	—
186	D₇₆	—	4	2	no	—
187	D₇₆	—	4	2	no	—
188	D₇₆	—	8	2	no	—
189	D₇₆	—	8	2	no	—
190	D₇₆	—	8	1	no	—
191	D₇₆	—	8	1	no	—
192	D₇₆	—	8	1	no	—
193	D₇₆	—	8	1	no	—
194	C₈×C₁₉	—	8	1	no	—
195	C₈×C₁₉	—	8	1	no	—
196	C₁₉⋊C₈	—	2	2	no	—
197	C₁₉⋊C₈	—	2	2	no	—
198	C₁₉⋊C₈	—	8	1	no	—
199	C₂×#493	—	19	1	no	—
200	#1982	—	19	1	no	—
201	#1982	—	19	1	no	—
202	#1939	—	19	1	no	—
203	C₂×#331	—	19	1	no	—
204	C₂×#331	D₁₉	1	1	yes	characteristic, complemented
205	#1277	—	19	1	no	—
206	C₂²×C₁₉	—	8	2	no	—
207	C₂²×C₁₉	—	8	2	no	—
208	C₂²×C₁₉	—	8	2	no	—
209	C₂²×C₁₉	—	16	1	no	—
210	C₂²×C₁₉	—	16	1	no	—
211	C₂²×C₁₉	—	16	1	no	—
212	C₂²×C₁₉	—	16	1	no	—
213	C₂²×C₁₉	#394	1	1	yes	characteristic
214	C₂²×C₁₉	#459	1	1	yes	characteristic
215	C₂²×C₁₉	#460	1	1	yes	characteristic
216	C₂²×C₁₉	#466	1	1	yes	characteristic
217	C₂²×C₁₉	#469	1	1	yes	characteristic
218	C₂²×C₁₉	#472	1	1	yes	characteristic
219	C₂²×C₁₉	#472	1	1	yes	characteristic
220	C₂×D₁₉	—	8	2	no	—
221	C₂×D₁₉	—	8	2	no	—
222	C₂×D₁₉	—	8	2	no	—
223	C₂×D₁₉	—	16	1	no	—
224	C₂×D₁₉	—	16	1	no	—
225	C₂×D₁₉	—	16	1	no	—
226	C₂×D₁₉	—	16	1	no	—
227	C₄×C₁₉	—	2	1	no	—
228	C₄×C₁₉	—	2	1	no	—
229	C₄×C₁₉	#447	1	1	yes	characteristic
230	C₄×C₁₉	#450	1	1	yes	characteristic
231	C₄×C₁₉	#459	1	1	yes	characteristic
232	C₄×C₁₉	#459	1	1	yes	characteristic
233	C₄×C₁₉	#463	1	1	yes	characteristic
234	C₄×C₁₉	#463	1	1	yes	characteristic
235	C₄×C₁₉	#486	1	1	yes	characteristic
236	C₄×C₁₉	#490	1	1	yes	characteristic
237	Dic₁₉	—	4	2	no	—
238	Dic₁₉	—	8	1	no	—
239	C₂²×D₈	—	38	1	no	—
240	C₂²×D₈	—	38	1	no	—
241	C₂×#127	—	19	1	no	—
242	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
243	#493	—	38	2	no	—
244	#493	—	38	2	no	—
245	C₂×C₄⋊C₈	—	19	1	no	—
246	C₂×C₄⋊C₈	—	38	1	no	—
247	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
248	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
249	C₂×#102	—	38	1	no	—
250	C₂×#102	—	38	1	no	—
251	C₂×#102	—	38	1	no	—
252	C₂×#102	—	38	1	no	—
253	C₂×C₄×C₈	—	19	1	no	—
254	C₄×C₄⋊C₄	—	19	1	no	—
255	#336	—	38	1	no	—
256	#331	—	2	2	no	—
257	#331	—	38	2	no	—
258	C₂×C₁₉	—	16	2	no	—
259	C₂×C₁₉	#1667	1	1	yes	characteristic
260	C₂×C₁₉	#1668	1	1	yes	characteristic
261	C₂×C₁₉	#1687	1	1	yes	characteristic
262	C₂×C₁₉	#1688	1	1	yes	characteristic
263	C₂×C₁₉	#2041	1	1	yes	characteristic
264	C₂×C₁₉	#2045	1	1	yes	characteristic
265	C₂×C₁₉	#2054	1	1	yes	characteristic
266	D₁₉	—	16	2	no	—
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	—	38	1	no	—
271	C₂²×D₄	—	38	1	no	—
272	C₂²×D₄	—	38	1	no	—
273	C₂×D₈	—	38	4	no	—
274	C₂×D₈	—	38	4	no	—
275	C₂×D₈	—	76	2	no	—
276	C₂×D₈	—	76	2	no	—
277	C₂×D₈	—	76	2	no	—
278	C₂×D₈	—	76	2	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	19	1	no	—
282	C₂²×C₈	—	19	1	no	—
283	C₂²×C₈	—	38	1	no	—
284	#127	—	2	1	no	—
285	#127	—	2	1	no	—
286	#127	—	2	1	no	—
287	#127	—	19	2	no	—
288	#127	—	38	1	no	—
289	#127	—	38	1	no	—
290	#127	—	38	1	no	—
291	#127	C₂²⋊D₁₉	1	2	yes	—
292	C₂×C₄⋊C₄	—	19	1	no	—
293	C₂×C₄⋊C₄	—	19	1	no	—
294	C₂×C₄²	—	38	1	no	—
295	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	—	38	1	no	—
301	C₄⋊C₈	—	38	1	no	—
302	C₄⋊C₈	—	76	2	no	—
303	#102	—	76	2	no	—
304	#102	—	76	2	no	—
305	#102	—	76	2	no	—
306	#102	—	76	2	no	—
307	C₄×C₈	—	38	1	no	—
308	C₄×C₈	—	38	1	no	—
309	#95	—	38	1	no	—
310	C₁₉	#10536	1	1	yes	characteristic, complemented, Sylow
311	C₂⁴	—	4	1	no	—
312	C₂⁴	—	76	1	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	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	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	8	1	no	—
328	C₂×D₄	—	8	1	no	—
329	C₂×D₄	—	38	2	no	—
330	C₂×D₄	—	38	2	no	—
331	C₂×D₄	—	38	2	no	—
332	C₂×D₄	—	76	1	no	—
333	C₂×D₄	—	76	1	no	—
334	C₂×D₄	—	76	1	no	—
335	C₂×D₄	—	76	1	no	—
336	C₂×D₄	—	76	1	no	—
337	C₂×D₄	—	76	1	no	—
338	C₂×D₄	—	76	1	no	—
339	C₂×D₄	—	76	1	no	—
340	C₂×D₄	—	76	1	no	—
341	C₂×D₄	—	76	1	no	—
342	C₂×D₄	—	76	1	no	—
343	C₂×D₄	—	152	1	no	—
344	C₂×D₄	—	152	1	no	—
345	C₂²×C₄	—	38	1	no	—
346	C₂²×C₄	—	38	1	no	—
347	C₂²×C₄	#64541	1	1	yes	characteristic
348	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
349	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
350	D₈	—	76	8	no	—
351	D₈	—	76	8	no	—
352	C₂×C₈	—	4	1	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	19	2	no	—
359	C₂×C₈	—	19	2	no	—
360	C₂×C₈	—	38	1	no	—
361	C₂×C₈	—	38	1	no	—
362	C₂×C₈	—	38	1	no	—
363	C₂×C₈	—	38	1	no	—
364	C₂×C₈	—	76	1	no	—
365	C₂×C₈	—	76	1	no	—
366	C₂×C₈	—	76	1	no	—
367	C₄⋊C₄	—	19	2	no	—
368	C₄⋊C₄	—	38	1	no	—
369	C₄⋊C₄	—	38	1	no	—
370	C₄⋊C₄	—	38	1	no	—
371	C₄²	—	76	1	no	—
372	C₄²	—	76	1	no	—
373	C₄²	#64541	1	1	yes	characteristic
374	C₄²	D₄×D₁₉	1	1	yes	characteristic
375	C₄²	#64543	1	1	yes	characteristic
376	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
377	C₂³	—	4	2	no	—
378	C₂³	—	8	1	no	—
379	C₂³	—	8	1	no	—
380	C₂³	—	8	1	no	—
381	C₂³	—	8	1	no	—
382	C₂³	—	8	1	no	—
383	C₂³	—	8	1	no	—
384	C₂³	—	76	2	no	—
385	C₂³	—	152	1	no	—
386	C₂³	—	152	1	no	—
387	C₂³	—	152	1	no	—
388	C₂³	—	152	1	no	—
389	C₂³	—	152	1	no	—
390	C₂³	—	152	1	no	—
391	C₂³	#10597330	1	1	yes	characteristic
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	8	2	no	—
397	D₄	—	8	2	no	—
398	D₄	—	8	1	no	—
399	D₄	—	8	1	no	—
400	D₄	—	8	1	no	—
401	D₄	—	8	1	no	—
402	D₄	—	76	2	no	—
403	D₄	—	76	2	no	—
404	D₄	—	76	2	no	—
405	D₄	—	76	2	no	—
406	D₄	—	152	2	no	—
407	D₄	—	152	2	no	—
408	D₄	—	152	1	no	—
409	D₄	—	152	1	no	—
410	D₄	—	152	1	no	—
411	D₄	—	152	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	38	2	no	—
415	C₂×C₄	—	76	1	no	—
416	C₂×C₄	—	76	1	no	—
417	C₂×C₄	—	76	1	no	—
418	C₂×C₄	—	76	1	no	—
419	C₂×C₄	—	76	1	no	—
420	C₂×C₄	#10597329	1	1	yes	characteristic
421	C₂×C₄	#10597330	1	1	yes	characteristic
422	C₂×C₄	#10597331	1	1	yes	characteristic
423	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
424	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
425	C₂×C₄	#10597357	1	1	yes	characteristic
426	C₂×C₄	#10597357	1	1	yes	characteristic
427	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
428	C₂×C₄	#10597360	1	1	yes	characteristic
429	C₂×C₄	#10597360	1	1	yes	characteristic
430	C₂×C₄	#10597362	1	1	yes	characteristic
431	C₂×C₄	#10597375	1	1	yes	characteristic
432	C₂×C₄	#10597383	1	1	yes	characteristic
433	C₂×C₄	#10597385	1	1	yes	characteristic
434	C₈	—	8	1	no	—
435	C₈	—	8	1	no	—
436	C₈	—	38	2	no	—
437	C₈	—	38	2	no	—
438	C₈	—	152	1	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	8	2	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	16	1	no	—
443	C₂²	—	16	1	no	—
444	C₂²	—	16	1	no	—
445	C₂²	—	16	1	no	—
446	C₂²	—	304	1	no	—
447	C₂²	—	304	1	no	—
448	C₂²	—	304	1	no	—
449	C₂²	—	304	1	no	—
450	C₂²	—	152	2	no	—
451	C₂²	—	152	2	no	—
452	C₂²	—	152	2	no	—
453	C₂²	#11926459	1	1	yes	characteristic
454	C₂²	#11926738	1	1	yes	characteristic
455	C₂²	#11926743	1	1	yes	characteristic
456	C₂²	#11926779	1	1	yes	characteristic
457	C₂²	#11926796	1	1	yes	characteristic
458	C₂²	#11926813	1	1	yes	characteristic
459	C₂²	#11926813	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	76	2	no	—
463	C₄	—	152	1	no	—
464	C₄	#11926676	1	1	yes	characteristic
465	C₄	#11926693	1	1	yes	characteristic
466	C₄	#11926737	1	1	yes	characteristic
467	C₄	#11926738	1	1	yes	characteristic
468	C₄	#11926758	1	1	yes	characteristic
469	C₄	#11926761	1	1	yes	characteristic
470	C₄	#11926889	1	1	yes	characteristic
471	C₄	#11926907	1	1	yes	characteristic
472	C₂	—	16	2	no	—
473	C₂	—	304	2	no	—
474	C₂	#14562989	1	1	yes	characteristic
475	C₂	#14562994	1	1	yes	characteristic
476	C₂	#14563113	1	1	yes	characteristic
477	C₂	#14563118	1	1	yes	characteristic
478	C₂	#14564867	1	1	yes	characteristic
479	C₂	#14564889	1	1	yes	characteristic
480	C₂	#14564944	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597330
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#331	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂×#11926920	C₂
hypercenter	C₂×#331	D₁₉
hypocenter	C₁₉	#10536
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#331

Complements

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

N	H ≅ G/N	type
2. #14564563	C₂	semidirect
3. #14564561	C₂	semidirect
4. #14564351	C₂	semidirect
5. C₂×#11926287	C₂	semidirect
6. #14561469	C₂	semidirect
7. C₂×C₁₉×#331	C₂	semidirect
124. C₄⋊Dic₁₉	D₈	semidirect
204. C₂×#331	D₁₉	semidirect
310. C₁₉	#10536	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926920	2
#14564563	2
#14564561	2
#14564351	2
C₂×#11926287	2
#14561469	2
C₂×C₁₉×#331	2
#10536	19