Subgroups — #18075272

Order 4864.

698 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563615	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11926278	C₂	1	2	yes	maximal
3	#14561862	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561513	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₉×#121	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
7	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₁₉⋊#95	—	2	1	no	—
9	C₂×C₁₉⋊#95	—	2	1	no	—
10	C₂×C₁₉⋊#95	C₂²	1	2	yes	—
11	#11926299	—	2	1	no	—
12	#11926278	—	2	4	no	—
13	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₉	—	2	1	no	—
15	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic, complemented
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#390	C₄	1	1	yes	characteristic, complemented
18	C₁₉×#389	C₄	1	1	yes	characteristic, complemented
19	C₁₉×#388	—	2	1	no	—
20	C₁₉×#386	—	2	1	no	—
21	C₁₉×#380	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
23	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
24	C₂²×D₄×C₁₉	—	2	1	no	—
25	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	—	2	1	no	—
27	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂³×Dic₁₉	—	2	2	no	—
31	C₁₉×#121	—	2	1	no	—
32	C₁₉×#121	—	2	1	no	—
33	C₁₉×#121	D₄	1	2	yes	—
34	C₁₉×#121	Q₈	1	2	yes	—
35	C₄×D₄×C₁₉	—	4	2	no	—
36	C₄×D₄×C₁₉	—	4	4	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄²×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	—	4	2	no	—
48	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
52	C₂²×C₁₉⋊C₈	—	2	2	no	—
53	C₁₉×#95	—	2	1	no	—
54	C₁₉×#95	—	2	1	no	—
55	C₁₉×#95	—	2	1	no	—
56	C₁₉⋊#95	—	2	4	no	—
57	C₁₉⋊#95	—	2	2	no	—
58	C₁₉⋊#95	—	2	2	no	—
59	C₁₉⋊#95	—	4	2	no	—
60	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
61	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
62	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
63	C₂⁴×C₁₉	—	2	1	no	—
64	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂×D₄×C₁₉	—	2	2	no	—
66	C₂×D₄×C₁₉	—	2	2	no	—
67	C₂×D₄×C₁₉	—	2	1	no	—
68	C₂×D₄×C₁₉	—	4	1	no	—
69	C₂×D₄×C₁₉	—	4	1	no	—
70	C₂×D₄×C₁₉	—	4	2	no	—
71	C₂×D₄×C₁₉	—	4	2	no	—
72	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	2	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	4	1	no	—
81	C₂²×C₄×C₁₉	—	4	1	no	—
82	C₂²×C₄×C₁₉	—	4	1	no	—
83	C₂²×C₄×C₁₉	—	4	1	no	—
84	C₂²×C₄×C₁₉	—	4	2	no	—
85	C₂²×C₄×C₁₉	—	4	2	no	—
86	C₂²×C₄×C₁₉	—	4	2	no	—
87	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
97	C₂²×Dic₁₉	—	2	4	no	—
98	C₂²×Dic₁₉	—	4	2	no	—
99	C₂²×Dic₁₉	—	4	2	no	—
100	C₂²×Dic₁₉	—	4	2	no	—
101	C₂²×Dic₁₉	—	4	2	no	—
102	C₂²×Dic₁₉	—	4	2	no	—
103	C₂²×Dic₁₉	—	4	2	no	—
104	C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₄⋊C₄×C₁₉	—	4	1	no	—
106	C₄⋊C₄×C₁₉	—	4	1	no	—
107	C₄⋊C₄×C₁₉	—	4	2	no	—
108	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
109	C₂²⋊C₄×C₁₉	—	2	2	no	—
110	C₂²⋊C₄×C₁₉	—	2	2	no	—
111	C₂²⋊C₄×C₁₉	—	4	2	no	—
112	C₂²⋊C₄×C₁₉	—	4	2	no	—
113	C₂²⋊C₄×C₁₉	—	4	2	no	—
114	C₂²⋊C₄×C₁₉	—	4	2	no	—
115	C₄²×C₁₉	—	2	2	no	—
116	C₄²×C₁₉	—	2	2	no	—
117	C₄²×C₁₉	—	4	1	no	—
118	C₄²×C₁₉	—	4	1	no	—
119	C₄²×C₁₉	—	4	2	no	—
120	C₂×C₁₉⋊C₈	—	4	2	no	—
121	C₂×C₁₉⋊C₈	—	4	2	no	—
122	C₂×C₁₉⋊C₈	—	4	2	no	—
123	#8573	—	19	1	no	maximal, Sylow
124	C₂³×C₁₉	—	2	1	no	—
125	C₂³×C₁₉	—	2	1	no	—
126	C₂³×C₁₉	—	2	1	no	—
127	C₂³×C₁₉	—	2	1	no	—
128	C₂³×C₁₉	—	2	2	no	—
129	C₂³×C₁₉	—	4	1	no	—
130	C₂³×C₁₉	—	4	1	no	—
131	C₂³×C₁₉	—	4	1	no	—
132	C₂³×C₁₉	—	4	1	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂³×C₁₉	#121	1	1	yes	characteristic
137	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
138	C₂³×C₁₉	#135	1	2	yes	—
139	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
140	D₄×C₁₉	—	4	2	no	—
141	D₄×C₁₉	—	4	2	no	—
142	D₄×C₁₉	—	4	4	no	—
143	D₄×C₁₉	—	4	4	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	4	no	—
164	C₂×C₄×C₁₉	—	4	4	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	8	4	no	—
174	C₂×C₄×C₁₉	#99	1	2	yes	—
175	C₂×C₄×C₁₉	#104	1	2	yes	—
176	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
180	C₂×Dic₁₉	—	4	4	no	—
181	C₂×Dic₁₉	—	4	4	no	—
182	C₂×Dic₁₉	—	4	4	no	—
183	C₂×Dic₁₉	—	8	2	no	—
184	C₂×Dic₁₉	—	8	2	no	—
185	C₂×Dic₁₉	—	8	2	no	—
186	C₂×Dic₁₉	—	8	2	no	—
187	C₁₉⋊C₈	—	8	2	no	—
188	C₄×#121	D₁₉	1	1	yes	characteristic
189	#1797	—	19	1	no	—
190	C₂×#327	—	19	2	no	—
191	#1434	—	19	1	no	—
192	#1294	—	19	2	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	2	1	no	—
197	C₂²×C₁₉	—	2	2	no	—
198	C₂²×C₁₉	—	2	2	no	—
199	C₂²×C₁₉	—	2	2	no	—
200	C₂²×C₁₉	—	2	2	no	—
201	C₂²×C₁₉	—	4	2	no	—
202	C₂²×C₁₉	—	4	2	no	—
203	C₂²×C₁₉	—	4	2	no	—
204	C₂²×C₁₉	—	8	1	no	—
205	C₂²×C₁₉	—	8	1	no	—
206	C₂²×C₁₉	—	8	1	no	—
207	C₂²×C₁₉	—	8	1	no	—
208	C₂²×C₁₉	#380	1	1	yes	characteristic
209	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
210	C₂²×C₁₉	#410	1	1	yes	characteristic
211	C₂²×C₁₉	#416	1	1	yes	characteristic
212	C₂²×C₁₉	#418	1	1	yes	characteristic
213	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
214	C₂²×C₁₉	#421	1	1	yes	characteristic
215	C₂²×C₁₉	#463	1	2	yes	—
216	C₂²×C₁₉	#478	1	2	yes	—
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	—	2	1	no	—
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	2	no	—
222	C₄×C₁₉	—	2	2	no	—
223	C₄×C₁₉	—	4	2	no	—
224	C₄×C₁₉	—	4	1	no	—
225	C₄×C₁₉	—	4	1	no	—
226	C₄×C₁₉	—	8	1	no	—
227	C₄×C₁₉	—	8	1	no	—
228	Dic₁₉	—	8	4	no	—
229	C₂×#121	C₂×D₁₉	1	1	yes	characteristic
230	C₂×C₄×D₄	—	2	1	no	—
231	C₂×C₄×D₄	Dic₁₉	1	1	yes	characteristic, complemented
232	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
233	C₂×C₄⋊C₈	—	38	1	no	—
234	C₂×C₂²⋊C₈	—	19	2	no	—
235	#390	Dic₁₉	1	1	yes	characteristic, complemented
236	#389	Dic₁₉	1	1	yes	characteristic, complemented
237	#388	—	2	1	no	—
238	#386	—	2	1	no	—
239	#380	C₂×D₁₉	1	1	yes	characteristic
240	C₄×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic, complemented
241	C₄×C₂²⋊C₄	—	2	1	no	—
242	C₂×#95	—	19	2	no	—
243	C₂×#95	—	38	1	no	—
244	C₂×#95	—	38	1	no	—
245	#336	—	38	1	no	—
246	#327	—	38	4	no	—
247	C₂×C₁₉	—	2	2	no	—
248	C₂×C₁₉	—	2	2	no	—
249	C₂×C₁₉	—	8	2	no	—
250	C₂×C₁₉	#1500	1	1	yes	characteristic
251	C₂×C₁₉	#1507	1	1	yes	characteristic
252	C₂×C₁₉	#1514	1	1	yes	characteristic
253	C₂×C₁₉	#1516	1	1	yes	characteristic
254	C₂×C₁₉	#1799	1	1	yes	characteristic
255	C₂×C₁₉	#1804	1	1	yes	characteristic
256	C₂×C₁₉	#1806	1	1	yes	characteristic
257	C₂²×D₄	—	2	1	no	—
258	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
259	C₂³×C₄	—	2	1	no	—
260	C₂³×C₄	—	38	2	no	—
261	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
262	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
263	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
264	C₂²×C₈	—	38	2	no	—
265	#121	—	2	1	no	—
266	#121	—	2	1	no	—
267	#121	Dic₃₈	1	2	yes	—
268	#121	D₇₆	1	2	yes	—
269	C₄×D₄	—	4	2	no	—
270	C₄×D₄	—	4	4	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₄²	—	2	1	no	—
281	C₂×C₄²	—	4	2	no	—
282	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
283	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
284	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
285	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
286	C₄⋊C₈	—	76	2	no	—
287	C₂²⋊C₈	—	38	2	no	—
288	C₂²⋊C₈	—	38	2	no	—
289	#95	—	2	1	no	—
290	#95	—	2	1	no	—
291	#95	—	2	1	no	—
292	#95	—	38	4	no	—
293	#95	—	38	2	no	—
294	#95	—	38	2	no	—
295	#95	—	76	2	no	—
296	C₁₉	#8573	1	1	yes	characteristic, complemented, Sylow
297	C₂⁴	—	2	1	no	—
298	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	C₄⋊Dic₁₉	1	2	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	38	4	no	—
322	C₂²×C₄	—	76	2	no	—
323	C₂²×C₄	—	76	2	no	—
324	C₂²×C₄	—	76	2	no	—
325	C₂²×C₄	—	76	2	no	—
326	C₂²×C₄	—	76	2	no	—
327	C₂²×C₄	—	76	2	no	—
328	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
329	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
330	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
331	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
334	C₂²×C₄	#64541	1	1	yes	characteristic
335	C₂²×C₄	#64541	1	1	yes	characteristic
336	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
338	C₂×C₈	—	76	2	no	—
339	C₂×C₈	—	76	2	no	—
340	C₂×C₈	—	76	2	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	C₄⋊Dic₁₉	1	2	yes	—
346	C₂²⋊C₄	—	2	2	no	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	4	1	no	—
355	C₄²	—	4	1	no	—
356	C₄²	—	4	2	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	#10597370	1	1	yes	characteristic
369	C₂³	#10597376	1	1	yes	characteristic
370	C₂³	#10597378	1	2	yes	—
371	C₂³	#10597396	1	2	yes	—
372	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	4	no	—
376	D₄	—	4	4	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	8	4	no	—
407	C₂×C₄	—	76	4	no	—
408	C₂×C₄	—	76	4	no	—
409	C₂×C₄	—	76	4	no	—
410	C₂×C₄	—	152	2	no	—
411	C₂×C₄	—	152	2	no	—
412	C₂×C₄	—	152	2	no	—
413	C₂×C₄	—	152	2	no	—
414	C₂×C₄	#10597291	1	2	yes	—
415	C₂×C₄	#10597294	1	2	yes	—
416	C₂×C₄	#10597370	1	1	yes	characteristic
417	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
418	C₂×C₄	#10597372	1	1	yes	characteristic
419	C₂×C₄	#10597376	1	1	yes	characteristic
420	C₈	—	152	2	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	8	1	no	—
433	C₂²	—	8	1	no	—
434	C₂²	—	8	1	no	—
435	C₂²	—	8	1	no	—
436	C₂²	#11926404	1	1	yes	characteristic
437	C₂²	C₂×#10597291	1	1	yes	characteristic
438	C₂²	#11926518	1	1	yes	characteristic
439	C₂²	#11926540	1	1	yes	characteristic
440	C₂²	#11926549	1	1	yes	characteristic
441	C₂²	C₂×#10597294	1	1	yes	characteristic
442	C₂²	#11926561	1	1	yes	characteristic
443	C₂²	#11926759	1	2	yes	—
444	C₂²	#11926844	1	2	yes	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	8	1	no	—
455	C₄	—	8	1	no	—
456	C₄	—	152	4	no	—
457	C₂	—	2	2	no	—
458	C₂	—	2	2	no	—
459	C₂	—	8	2	no	—
460	C₂	#14562121	1	1	yes	characteristic
461	C₂	#14562151	1	1	yes	characteristic
462	C₂	#14562182	1	1	yes	characteristic
463	C₂	#14562191	1	1	yes	characteristic
464	C₂	#14563623	1	1	yes	characteristic
465	C₂	#14563645	1	1	yes	characteristic
466	C₂	#14563655	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₄×C₁₉×#121	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂×C₁₉×#121	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₄×#121	D₁₉
hypocenter	C₁₉	#8573
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₄×#121

Complements

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

N	H ≅ G/N	type
1. #14563615	C₂	semidirect
3. #14561862	C₂	semidirect
4. #14561513	C₂	semidirect
15. C₂×C₄×D₄×C₁₉	C₄	semidirect
17. C₁₉×#390	C₄	semidirect
18. C₁₉×#389	C₄	semidirect
22. C₄×C₄⋊C₄×C₁₉	C₄	semidirect
231. C₂×C₄×D₄	Dic₁₉	semidirect
235. #390	Dic₁₉	semidirect
236. #389	Dic₁₉	semidirect
240. C₄×C₄⋊C₄	Dic₁₉	semidirect
296. C₁₉	#8573	semidirect

Maximal subgroups

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

subgroup	index
#14563615	2
C₂×#11926278	2
#14561862	2
#14561513	2
C₄×C₁₉×#121	2
#8573	19