Subgroups — #18077140

Order 4864.

636 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#64525	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926622	C₂	1	1	yes	maximal, characteristic, complemented
3	#14564428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926273	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561469	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64525	C₄	1	1	yes	characteristic
9	C₂²×#64520	—	2	1	no	—
10	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
11	C₄×#64525	—	2	2	no	—
12	C₄×#64525	—	2	2	no	—
13	#11926622	—	2	2	no	—
14	#11926622	—	2	2	no	—
15	C₂×#10597264	C₄	1	1	yes	characteristic
16	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#10597289	C₄	1	1	yes	characteristic
18	C₂×#10597266	C₄	1	1	yes	characteristic
19	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
20	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
21	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
22	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
24	#11926273	—	2	2	no	—
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×D₄⋊C₈	—	2	2	no	—
29	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂²×D₇₆	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄×D₁₉	—	2	1	no	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₂²×C₈×C₁₉	—	2	1	no	—
35	C₄×D₄×C₁₉	—	2	1	no	—
36	C₄×D₄×C₁₉	—	2	1	no	—
37	C₄×D₄×C₁₉	D₄	1	2	yes	—
38	C₄×D₄×C₁₉	D₄	1	2	yes	—
39	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
42	C₂×#64525	—	2	2	no	—
43	C₂×#64525	—	2	2	no	—
44	C₂×#64525	—	2	2	no	—
45	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
46	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
47	C₂×#64520	—	2	4	no	—
48	C₂×#64520	—	4	2	no	—
49	C₂×#64520	—	4	2	no	—
50	C₂²×C₁₉⋊C₈	—	2	1	no	—
51	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
54	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
55	C₄×D₇₆	—	2	1	no	—
56	C₄×D₇₆	—	2	1	no	—
57	C₄×D₇₆	—	2	1	no	—
58	C₄×D₇₆	—	2	1	no	—
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₁₉×C₄⋊C₈	—	2	1	no	—
61	C₄×C₈×C₁₉	—	2	1	no	—
62	C₄×C₈×C₁₉	—	2	1	no	—
63	#10597289	—	2	2	no	—
64	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
65	(C₂×D₁₉)⋊C₈	—	4	2	no	—
66	(C₂×D₁₉)⋊C₈	—	4	2	no	—
67	#10597266	—	2	2	no	—
68	#10597264	—	2	2	no	—
69	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
70	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
71	C₄×C₁₉⋊C₈	—	2	1	no	—
72	C₄×C₁₉⋊C₈	—	2	1	no	—
73	C₄×C₁₉⋊C₈	—	2	1	no	—
74	C₄×C₁₉⋊C₈	—	2	1	no	—
75	C₂⁴×C₁₉	—	2	1	no	—
76	C₂³×D₁₉	—	2	1	no	—
77	C₂×D₄×C₁₉	—	2	1	no	—
78	C₂×D₄×C₁₉	—	2	1	no	—
79	C₂×D₄×C₁₉	—	2	1	no	—
80	C₂×D₄×C₁₉	—	2	1	no	—
81	C₂×D₄×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
93	C₂²×Dic₁₉	—	2	1	no	—
94	C₂×D₇₆	—	2	1	no	—
95	C₂×D₇₆	—	2	1	no	—
96	C₂×D₇₆	—	2	1	no	—
97	C₂×D₇₆	—	2	1	no	—
98	C₂×D₇₆	—	2	1	no	—
99	C₂×D₇₆	M₁₆	1	2	yes	complemented
100	C₂×C₄×D₁₉	—	4	1	no	—
101	C₂×C₄×D₁₉	—	4	1	no	—
102	C₂×C₄×D₁₉	—	4	1	no	—
103	C₂×C₄×D₁₉	—	4	1	no	—
104	C₂×C₄×D₁₉	—	4	1	no	—
105	C₂×C₄×D₁₉	—	4	1	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	4	1	no	—
108	C₂×C₈×C₁₉	—	4	1	no	—
109	C₂×C₈×C₁₉	—	4	1	no	—
110	C₂×C₈×C₁₉	—	4	1	no	—
111	C₂×C₈×C₁₉	—	4	1	no	—
112	C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
114	C₂²⋊C₄×C₁₉	—	2	2	no	—
115	C₂²⋊C₄×C₁₉	—	2	2	no	—
116	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₁₉	#41	1	1	yes	characteristic
120	#64525	—	2	8	no	—
121	(C₂×D₁₉)⋊C₄	—	4	1	no	—
122	(C₂×D₁₉)⋊C₄	—	4	1	no	—
123	C₄⋊Dic₁₉	—	2	1	no	—
124	C₄⋊Dic₁₉	—	2	1	no	—
125	#64520	—	4	8	no	—
126	C₂×C₁₉⋊C₈	—	2	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	—	2	1	no	—
132	C₂×C₁₉⋊C₈	—	2	2	no	—
133	C₂×C₁₉⋊C₈	—	2	1	no	—
134	C₂×C₁₉⋊C₈	—	2	1	no	—
135	C₂×C₁₉⋊C₈	—	2	1	no	—
136	C₂×C₁₉⋊C₈	—	2	1	no	—
137	C₂×C₁₉⋊C₈	—	4	1	no	—
138	C₂×C₁₉⋊C₈	—	4	1	no	—
139	C₂×C₁₉⋊C₈	M₁₆	1	2	yes	complemented
140	C₂×C₁₉⋊C₈	D₈	1	2	yes	complemented
141	#8951	—	19	1	no	maximal, Sylow
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	—	4	1	no	—
147	C₂³×C₁₉	—	4	1	no	—
148	C₂³×C₁₉	—	4	1	no	—
149	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
150	C₂²×D₁₉	—	2	2	no	—
151	C₂²×D₁₉	—	4	1	no	—
152	C₂²×D₁₉	—	4	1	no	—
153	C₂²×D₁₉	—	4	1	no	—
154	C₂²×D₁₉	—	4	1	no	—
155	C₂²×D₁₉	—	4	1	no	—
156	C₂²×D₁₉	—	4	1	no	—
157	D₄×C₁₉	—	2	2	no	—
158	D₄×C₁₉	—	2	2	no	—
159	D₄×C₁₉	—	4	1	no	—
160	D₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#135	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×Dic₁₉	—	4	1	no	—
185	C₂×Dic₁₉	—	4	1	no	—
186	C₂×Dic₁₉	—	4	1	no	—
187	D₇₆	—	2	2	no	—
188	D₇₆	—	2	2	no	—
189	D₇₆	—	4	1	no	—
190	D₇₆	—	4	1	no	—
191	C₄×D₁₉	—	8	1	no	—
192	C₄×D₁₉	—	8	1	no	—
193	C₄×D₁₉	—	8	1	no	—
194	C₄×D₁₉	—	8	1	no	—
195	C₈×C₁₉	—	4	2	no	—
196	C₈×C₁₉	—	8	1	no	—
197	C₁₉⋊C₈	—	2	2	no	—
198	C₁₉⋊C₈	—	2	2	no	—
199	C₁₉⋊C₈	—	4	1	no	—
200	C₁₉⋊C₈	—	4	2	no	—
201	C₁₉⋊C₈	—	4	1	no	—
202	C₂×C₄×D₈	—	19	1	no	—
203	C₂×#436	—	19	1	no	—
204	#1954	—	19	1	no	—
205	C₂×D₄⋊C₈	—	19	1	no	—
206	C₂×D₄⋊C₈	D₁₉	1	1	yes	characteristic, complemented
207	#1277	—	19	1	no	—
208	#1273	—	19	1	no	—
209	C₂²×C₁₉	—	4	2	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	—	4	2	no	—
212	C₂²×C₁₉	—	8	1	no	—
213	C₂²×C₁₉	—	8	1	no	—
214	C₂²×C₁₉	—	8	1	no	—
215	C₂²×C₁₉	—	8	1	no	—
216	C₂²×C₁₉	#386	1	1	yes	characteristic
217	C₂²×C₁₉	#435	1	1	yes	characteristic
218	C₂²×C₁₉	#436	1	1	yes	characteristic
219	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
220	C₂²×C₁₉	#442	1	1	yes	characteristic
221	C₂²×C₁₉	#443	1	1	yes	characteristic
222	C₂²×C₁₉	#444	1	1	yes	characteristic
223	C₂×D₁₉	—	4	2	no	—
224	C₂×D₁₉	—	4	2	no	—
225	C₂×D₁₉	—	4	2	no	—
226	C₂×D₁₉	—	8	1	no	—
227	C₂×D₁₉	—	8	1	no	—
228	C₂×D₁₉	—	8	1	no	—
229	C₂×D₁₉	—	8	1	no	—
230	C₄×C₁₉	—	2	1	no	—
231	C₄×C₁₉	—	2	1	no	—
232	C₄×C₁₉	—	4	2	no	—
233	C₄×C₁₉	#407	1	1	yes	characteristic
234	C₄×C₁₉	#408	1	1	yes	characteristic
235	C₄×C₁₉	#435	1	1	yes	characteristic
236	C₄×C₁₉	#436	1	1	yes	characteristic
237	C₄×C₁₉	#447	1	1	yes	characteristic
238	C₄×C₁₉	#449	1	1	yes	characteristic
239	C₄×C₁₉	#459	1	1	yes	characteristic
240	C₄×C₁₉	#463	1	1	yes	characteristic
241	Dic₁₉	—	8	1	no	—
242	C₂²×D₈	—	19	1	no	—
243	C₂²×M₁₆	—	38	1	no	—
244	C₂×C₄×D₄	—	19	1	no	—
245	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
246	C₄×D₈	—	38	2	no	—
247	C₄×D₈	—	38	2	no	—
248	#436	—	38	2	no	—
249	#436	—	38	2	no	—
250	C₂×#107	—	19	1	no	—
251	C₂×C₄⋊C₈	—	19	1	no	—
252	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
253	C₂×#102	—	19	1	no	—
254	C₂×#102	—	19	1	no	—
255	C₂×C₂²⋊C₈	—	38	1	no	—
256	C₂×C₂²⋊C₈	—	38	1	no	—
257	C₂×C₂²⋊C₈	—	38	1	no	—
258	C₂×C₄×C₈	—	19	1	no	—
259	C₂×C₄×C₈	—	19	1	no	—
260	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
261	D₄⋊C₈	—	2	2	no	—
262	D₄⋊C₈	—	38	2	no	—
263	C₂×C₁₉	—	8	2	no	—
264	C₂×C₁₉	#1581	1	1	yes	characteristic
265	C₂×C₁₉	#1586	1	1	yes	characteristic
266	C₂×C₁₉	#1589	1	1	yes	characteristic
267	C₂×C₁₉	#1594	1	1	yes	characteristic
268	C₂×C₁₉	#1870	1	1	yes	characteristic
269	C₂×C₁₉	#1876	1	1	yes	characteristic
270	C₂×C₁₉	#1879	1	1	yes	characteristic
271	D₁₉	—	8	2	no	—
272	C₂²×D₄	—	19	1	no	—
273	C₂²×D₄	C₄×D₁₉	1	1	yes	characteristic
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	—	38	1	no	—
276	C₂×D₈	—	38	2	no	—
277	C₂×D₈	—	38	2	no	—
278	C₂×D₈	—	38	2	no	—
279	C₂×M₁₆	—	38	4	no	—
280	C₂×M₁₆	—	76	2	no	—
281	C₂×M₁₆	—	76	2	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	—	2	1	no	—
284	C₂²×C₈	—	19	1	no	—
285	C₂²×C₈	—	19	1	no	—
286	C₂²×C₈	—	19	1	no	—
287	C₂²×C₈	—	19	1	no	—
288	C₂²×C₈	—	38	1	no	—
289	C₄×D₄	—	2	1	no	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	38	1	no	—
292	C₄×D₄	—	38	1	no	—
293	C₄×D₄	—	38	1	no	—
294	C₄×D₄	—	38	1	no	—
295	C₄×D₄	D₇₆	1	2	yes	—
296	C₄×D₄	C₂²⋊D₁₉	1	2	yes	—
297	C₂×C₄⋊C₄	—	19	1	no	—
298	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	38	1	no	—
301	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
302	#107	—	38	2	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	—	2	1	no	—
305	C₄⋊C₈	—	19	2	no	—
306	C₄⋊C₈	—	38	1	no	—
307	#102	—	38	2	no	—
308	#102	—	38	2	no	—
309	C₂²⋊C₈	—	38	4	no	—
310	C₂²⋊C₈	—	76	2	no	—
311	C₂²⋊C₈	—	76	2	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	—	2	1	no	—
314	C₄×C₈	—	38	1	no	—
315	C₄×C₈	—	38	1	no	—
316	C₄×C₈	—	38	1	no	—
317	C₄×C₈	—	38	1	no	—
318	C₁₉	#8951	1	1	yes	characteristic, complemented, Sylow
319	C₂⁴	—	2	1	no	—
320	C₂⁴	—	38	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	19	2	no	—
327	C₂×D₄	—	38	1	no	—
328	C₂×D₄	—	38	1	no	—
329	C₂×D₄	—	38	1	no	—
330	C₂×D₄	—	38	1	no	—
331	C₂×D₄	—	38	1	no	—
332	C₂×D₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	1	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	38	1	no	—
341	C₂²×C₄	—	76	1	no	—
342	C₂²×C₄	—	76	1	no	—
343	C₂²×C₄	—	76	1	no	—
344	C₂²×C₄	—	76	1	no	—
345	C₂²×C₄	—	76	1	no	—
346	C₂²×C₄	—	76	1	no	—
347	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
348	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
349	C₂²×C₄	#64543	1	1	yes	characteristic
350	D₈	—	38	8	no	—
351	M₁₆	—	76	8	no	—
352	C₂×C₈	—	2	2	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	—	38	1	no	—
365	C₂×C₈	—	38	2	no	—
366	C₂×C₈	—	38	1	no	—
367	C₂×C₈	—	38	1	no	—
368	C₂×C₈	—	38	1	no	—
369	C₂×C₈	—	38	1	no	—
370	C₂×C₈	—	38	1	no	—
371	C₂×C₈	—	76	1	no	—
372	C₂×C₈	—	76	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	38	1	no	—
375	C₄⋊C₄	—	38	1	no	—
376	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	76	1	no	—
380	C₂²⋊C₄	—	76	1	no	—
381	C₄²	C₂×D₇₆	1	1	yes	characteristic
382	C₄²	D₄×D₁₉	1	1	yes	characteristic
383	C₄²	#64543	1	1	yes	characteristic
384	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
385	C₂³	—	2	2	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	38	2	no	—
393	C₂³	—	76	1	no	—
394	C₂³	—	76	1	no	—
395	C₂³	—	76	1	no	—
396	C₂³	—	76	1	no	—
397	C₂³	—	76	1	no	—
398	C₂³	—	76	1	no	—
399	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
400	D₄	—	2	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	4	1	no	—
403	D₄	—	4	1	no	—
404	D₄	—	38	2	no	—
405	D₄	—	38	2	no	—
406	D₄	—	76	1	no	—
407	D₄	—	76	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	76	1	no	—
418	C₂×C₄	—	76	1	no	—
419	C₂×C₄	—	76	1	no	—
420	C₂×C₄	—	152	1	no	—
421	C₂×C₄	—	152	1	no	—
422	C₂×C₄	—	152	1	no	—
423	C₂×C₄	—	152	1	no	—
424	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
425	C₂×C₄	#10597328	1	1	yes	characteristic
426	C₂×C₄	#10597332	1	1	yes	characteristic
427	C₂×C₄	#10597347	1	1	yes	characteristic
428	C₂×C₄	#10597347	1	1	yes	characteristic
429	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
430	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
431	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
432	C₂×C₄	#10597357	1	1	yes	characteristic
433	C₂×C₄	#10597360	1	1	yes	characteristic
434	C₂×C₄	#10597362	1	1	yes	characteristic
435	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
436	C₂×C₄	#10597385	1	1	yes	characteristic
437	C₂×C₄	#10597385	1	1	yes	characteristic
438	C₈	—	4	2	no	—
439	C₈	—	8	1	no	—
440	C₈	—	38	2	no	—
441	C₈	—	38	2	no	—
442	C₈	—	76	2	no	—
443	C₈	—	76	1	no	—
444	C₈	—	76	1	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	1	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	76	2	no	—
453	C₂²	—	76	2	no	—
454	C₂²	—	76	2	no	—
455	C₂²	—	152	1	no	—
456	C₂²	—	152	1	no	—
457	C₂²	—	152	1	no	—
458	C₂²	—	152	1	no	—
459	C₂²	#11926421	1	1	yes	characteristic
460	C₂²	#11926618	1	1	yes	characteristic
461	C₂²	#11926619	1	1	yes	characteristic
462	C₂²	#11926624	1	1	yes	characteristic
463	C₂²	#11926653	1	1	yes	characteristic
464	C₂²	#11926658	1	1	yes	characteristic
465	C₂²	#11926663	1	1	yes	characteristic
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	4	2	no	—
469	C₄	—	152	1	no	—
470	C₄	#11926507	1	1	yes	characteristic
471	C₄	#11926510	1	1	yes	characteristic
472	C₄	#11926618	1	1	yes	characteristic
473	C₄	#11926619	1	1	yes	characteristic
474	C₄	#11926679	1	1	yes	characteristic
475	C₄	#11926690	1	1	yes	characteristic
476	C₄	#11926737	1	1	yes	characteristic
477	C₄	#11926761	1	1	yes	characteristic
478	C₂	—	8	2	no	—
479	C₂	—	152	2	no	—
480	C₂	#14562467	1	1	yes	characteristic
481	C₂	#14562502	1	1	yes	characteristic
482	C₂	#14562517	1	1	yes	characteristic
483	C₂	#14562546	1	1	yes	characteristic
484	C₂	#14563930	1	1	yes	characteristic
485	C₂	#14563960	1	1	yes	characteristic
486	C₂	#14563981	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×D₄⋊C₈	C₂
socle	C₂³×C₁₉	C₄×D₄
prime radical	C₂²×#64525	C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×D₄⋊C₈	D₁₉
hypocenter	C₁₉	#8951
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×D₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#11926622	C₂	semidirect
3. #14564428	C₂	semidirect
4. C₂×#11926273	C₂	semidirect
5. #14561469	C₂	semidirect
6. C₁₉⋊#1273	C₂	semidirect
7. C₂×C₁₉×D₄⋊C₈	C₂	semidirect
99. C₂×D₇₆	M₁₆	semidirect
139. C₂×C₁₉⋊C₈	M₁₆	semidirect
140. C₂×C₁₉⋊C₈	D₈	semidirect
206. C₂×D₄⋊C₈	D₁₉	semidirect
318. C₁₉	#8951	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#64525	2
C₂×#11926622	2
#14564428	2
C₂×#11926273	2
#14561469	2
C₁₉⋊#1273	2
C₂×C₁₉×D₄⋊C₈	2
#8951	19