Subgroups — #18075380

Order 4864.

546 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#64520	C₂	1	1	yes	maximal, characteristic
2	#14563615	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926296	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926294	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561469	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₄	1	1	yes	characteristic
9	C₂²×#64520	C₄	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
13	C₄×#64520	—	2	2	no	—
14	C₄×#64520	—	2	2	no	—
15	C₂×#10597260	C₄	1	1	yes	characteristic
16	C₂×#10597260	C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	#11926299	—	2	1	no	—
20	#11926296	—	2	2	no	—
21	#11926294	—	2	2	no	—
22	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
26	C₁₉×#336	—	2	1	no	—
27	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	Q₈	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂×C₄²×C₁₉	—	2	1	no	—
33	C₂×C₄²×C₁₉	—	2	1	no	—
34	C₂×C₄²×C₁₉	—	2	1	no	—
35	C₂×C₄²×C₁₉	—	2	1	no	—
36	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×#64520	—	2	2	no	—
41	C₂×#64520	—	2	2	no	—
42	C₂×#64520	—	2	2	no	—
43	C₂×#64520	—	2	2	no	—
44	C₂×#64520	—	2	2	no	—
45	C₂×#64520	C₈	1	4	yes	complemented
46	C₂²×C₁₉⋊C₈	—	2	1	no	—
47	C₂²×C₁₉⋊C₈	—	2	1	no	—
48	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
52	C₁₉×C₄⋊C₈	—	2	1	no	—
53	C₁₉×C₄⋊C₈	—	2	1	no	—
54	C₁₉×C₄⋊C₈	—	2	1	no	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₁₉×C₂²⋊C₈	—	4	2	no	—
57	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
59	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
60	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
61	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
62	#10597260	—	2	2	no	—
63	#10597260	—	2	2	no	—
64	C₄×C₁₉⋊C₈	—	2	1	no	—
65	C₄×C₁₉⋊C₈	—	2	1	no	—
66	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
67	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
68	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	1	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	4	1	no	—
82	C₂²×C₄×C₁₉	—	4	1	no	—
83	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
87	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
88	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
91	C₂×C₈×C₁₉	—	4	1	no	—
92	C₂×C₈×C₁₉	—	4	1	no	—
93	C₂×C₈×C₁₉	—	4	1	no	—
94	C₂×C₈×C₁₉	—	4	1	no	—
95	C₂×C₈×C₁₉	—	4	1	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₄²×C₁₉	—	2	1	no	—
98	C₄²×C₁₉	—	2	1	no	—
99	C₄²×C₁₉	—	2	1	no	—
100	C₄²×C₁₉	—	2	1	no	—
101	C₄²×C₁₉	—	2	1	no	—
102	C₄²×C₁₉	—	2	1	no	—
103	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₉	#41	1	1	yes	characteristic
106	C₄²×C₁₉	#41	1	1	yes	characteristic
107	#64520	—	2	8	no	—
108	#64520	—	2	8	no	—
109	C₂×C₁₉⋊C₈	—	2	1	no	—
110	C₂×C₁₉⋊C₈	—	2	1	no	—
111	C₂×C₁₉⋊C₈	—	2	1	no	—
112	C₂×C₁₉⋊C₈	—	2	1	no	—
113	C₂×C₁₉⋊C₈	—	2	1	no	—
114	C₂×C₁₉⋊C₈	—	2	1	no	—
115	C₂×C₁₉⋊C₈	—	4	1	no	—
116	C₂×C₁₉⋊C₈	—	4	1	no	—
117	C₂×C₁₉⋊C₈	—	4	1	no	—
118	C₂×C₁₉⋊C₈	—	4	1	no	—
119	C₂×C₁₉⋊C₈	—	4	1	no	—
120	C₂×C₁₉⋊C₈	—	4	1	no	—
121	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
122	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
123	C₂×C₁₉⋊C₈	C₂×C₈	1	2	yes	—
124	C₂×C₁₉⋊C₈	C₂×C₈	1	2	yes	—
125	C₂×C₁₉⋊C₈	M₁₆	1	2	yes	—
126	C₂×C₁₉⋊C₈	M₁₆	1	2	yes	—
127	#8597	—	19	1	no	maximal, Sylow
128	C₂³×C₁₉	—	2	1	no	—
129	C₂³×C₁₉	—	2	1	no	—
130	C₂³×C₁₉	—	2	1	no	—
131	C₂³×C₁₉	—	2	1	no	—
132	C₂³×C₁₉	—	2	1	no	—
133	C₂³×C₁₉	—	2	1	no	—
134	C₂³×C₁₉	C₄⋊C₈	1	2	yes	—
135	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	2	2	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	—	4	2	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
157	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
167	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
168	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
171	C₈×C₁₉	—	8	1	no	—
172	C₈×C₁₉	—	8	1	no	—
173	C₁₉⋊C₈	—	2	2	no	—
174	C₁₉⋊C₈	—	2	2	no	—
175	C₁₉⋊C₈	—	2	2	no	—
176	C₁₉⋊C₈	—	8	1	no	—
177	C₁₉⋊C₈	—	8	1	no	—
178	C₁₉⋊C₈	C₂²⋊C₈	1	4	yes	complemented
179	C₂×C₄×M₁₆	—	19	1	no	—
180	#1797	—	19	1	no	—
181	#1797	D₁₉	1	1	yes	characteristic
182	C₂×#335	—	19	1	no	—
183	C₂×#334	—	19	1	no	—
184	#1277	—	19	1	no	—
185	#1277	—	19	1	no	—
186	C₂²×C₁₉	—	2	2	no	—
187	C₂²×C₁₉	—	2	2	no	—
188	C₂²×C₁₉	—	2	2	no	—
189	C₂²×C₁₉	—	4	1	no	—
190	C₂²×C₁₉	—	4	1	no	—
191	C₂²×C₁₉	—	4	1	no	—
192	C₂²×C₁₉	—	4	1	no	—
193	C₂²×C₁₉	#380	1	1	yes	characteristic
194	C₂²×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
195	C₂²×C₁₉	#423	1	1	yes	characteristic
196	C₂²×C₁₉	#428	1	1	yes	characteristic
197	C₂²×C₁₉	#428	1	1	yes	characteristic
198	C₂²×C₁₉	#430	1	1	yes	characteristic
199	C₂²×C₁₉	#430	1	1	yes	characteristic
200	C₄×C₁₉	—	2	2	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	4	1	no	—
204	C₄×C₁₉	—	4	1	no	—
205	C₄×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
206	C₄×C₁₉	#407	1	1	yes	characteristic
207	C₄×C₁₉	#431	1	1	yes	characteristic
208	C₄×C₁₉	#432	1	1	yes	characteristic
209	C₄×C₁₉	#468	1	1	yes	characteristic
210	C₄×C₁₉	#468	1	1	yes	characteristic
211	C₄×C₁₉	#469	1	1	yes	characteristic
212	C₄×C₁₉	#470	1	1	yes	characteristic
213	C₂²×M₁₆	—	19	1	no	—
214	C₂²×M₁₆	—	19	1	no	—
215	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
216	C₂×C₄⋊C₈	—	19	1	no	—
217	C₂×C₄⋊C₈	—	19	1	no	—
218	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
220	C₂×C₂²⋊C₈	—	2	1	no	—
221	C₂×C₂²⋊C₈	—	38	1	no	—
222	C₄×M₁₆	—	38	2	no	—
223	C₄×M₁₆	—	38	2	no	—
224	C₂×#97	—	19	1	no	—
225	C₂×#97	—	19	1	no	—
226	C₂×C₄×C₈	—	19	1	no	—
227	C₂×C₄×C₈	—	19	1	no	—
228	#336	—	2	1	no	—
229	#336	—	38	1	no	—
230	#335	—	38	2	no	—
231	#334	—	38	2	no	—
232	C₂×C₁₉	—	4	2	no	—
233	C₂×C₁₉	#1565	1	1	yes	characteristic
234	C₂×C₁₉	#1565	1	1	yes	characteristic
235	C₂×C₁₉	#1569	1	1	yes	characteristic
236	C₂×C₁₉	#1569	1	1	yes	characteristic
237	C₂×C₁₉	#1797	1	1	yes	characteristic
238	C₂×C₁₉	#1809	1	1	yes	characteristic
239	C₂×C₁₉	#1811	1	1	yes	characteristic
240	C₂³×C₄	Dic₃₈	1	1	yes	characteristic
241	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
242	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
243	C₂×M₁₆	—	19	4	no	—
244	C₂×M₁₆	—	38	2	no	—
245	C₂×M₁₆	—	38	2	no	—
246	C₂×M₁₆	—	38	2	no	—
247	C₂×M₁₆	—	38	2	no	—
248	C₂×M₁₆	—	38	2	no	—
249	C₂²×C₈	—	2	1	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	19	1	no	—
252	C₂²×C₈	—	19	1	no	—
253	C₂²×C₈	—	19	1	no	—
254	C₂²×C₈	—	19	1	no	—
255	C₂²×C₈	—	38	1	no	—
256	C₂²×C₈	—	38	1	no	—
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	—	2	1	no	—
260	C₂×C₄²	—	2	1	no	—
261	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
262	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
263	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
264	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	—	38	1	no	—
270	C₄⋊C₈	—	38	1	no	—
271	C₄⋊C₈	—	38	1	no	—
272	C₄⋊C₈	—	38	1	no	—
273	C₂²⋊C₈	—	4	2	no	—
274	C₂²⋊C₈	—	76	2	no	—
275	#97	—	38	2	no	—
276	#97	—	38	2	no	—
277	C₄×C₈	—	19	2	no	—
278	C₄×C₈	—	19	2	no	—
279	C₄×C₈	—	38	1	no	—
280	C₄×C₈	—	38	1	no	—
281	C₁₉	#8597	1	1	yes	characteristic, complemented, Sylow
282	C₂⁴	Dic₁₉⋊C₄	1	1	yes	characteristic
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	C₈×D₁₉	1	2	yes	—
298	C₂²×C₄	#64515	1	2	yes	—
299	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
300	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
301	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
302	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
305	M₁₆	—	38	8	no	—
306	M₁₆	—	38	8	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	—	4	1	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	19	2	no	—
314	C₂×C₈	—	19	2	no	—
315	C₂×C₈	—	19	2	no	—
316	C₂×C₈	—	19	2	no	—
317	C₂×C₈	—	19	2	no	—
318	C₂×C₈	—	19	2	no	—
319	C₂×C₈	—	38	1	no	—
320	C₂×C₈	—	38	1	no	—
321	C₂×C₈	—	38	1	no	—
322	C₂×C₈	—	38	1	no	—
323	C₂×C₈	—	38	1	no	—
324	C₂×C₈	—	38	1	no	—
325	C₂×C₈	—	76	1	no	—
326	C₂×C₈	—	76	1	no	—
327	C₂×C₈	—	76	1	no	—
328	C₂×C₈	—	76	1	no	—
329	C₂×C₈	—	76	1	no	—
330	C₂×C₈	—	76	1	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	2	1	no	—
337	C₄²	D₄×D₁₉	1	1	yes	characteristic
338	C₄²	D₄×D₁₉	1	1	yes	characteristic
339	C₄²	#64543	1	1	yes	characteristic
340	C₄²	#64543	1	1	yes	characteristic
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	1	no	—
347	C₂³	Dic₁₉⋊C₈	1	2	yes	—
348	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	Dic₁₉⋊C₈	1	2	yes	—
370	C₂×C₄	#10597323	1	1	yes	characteristic
371	C₂×C₄	#10597324	1	1	yes	characteristic
372	C₂×C₄	#10597324	1	1	yes	characteristic
373	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
374	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
375	C₂×C₄	C₂×#64515	1	1	yes	characteristic
376	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
377	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
378	C₂×C₄	#10597378	1	1	yes	characteristic
379	C₂×C₄	#10597385	1	1	yes	characteristic
380	C₂×C₄	#10597385	1	1	yes	characteristic
381	C₂×C₄	#10597388	1	1	yes	characteristic
382	C₂×C₄	#10597395	1	1	yes	characteristic
383	C₂×C₄	#10597397	1	1	yes	characteristic
384	C₈	—	8	1	no	—
385	C₈	—	8	1	no	—
386	C₈	—	19	4	no	—
387	C₈	—	38	2	no	—
388	C₈	—	38	2	no	—
389	C₈	—	38	2	no	—
390	C₈	—	152	1	no	—
391	C₈	—	152	1	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	#11926402	1	1	yes	characteristic
400	C₂²	C₂×Dic₁₉⋊C₈	1	1	yes	characteristic
401	C₂²	#11926567	1	1	yes	characteristic
402	C₂²	#11926584	1	1	yes	characteristic
403	C₂²	#11926587	1	1	yes	characteristic
404	C₂²	#11926592	1	1	yes	characteristic
405	C₂²	#11926592	1	1	yes	characteristic
406	C₄	—	2	2	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	C₂²⋊C₈×D₁₉	1	1	yes	characteristic
412	C₄	#11926506	1	1	yes	characteristic
413	C₄	#11926594	1	1	yes	characteristic
414	C₄	#11926598	1	1	yes	characteristic
415	C₄	#11926788	1	1	yes	characteristic
416	C₄	#11926792	1	1	yes	characteristic
417	C₄	#11926795	1	1	yes	characteristic
418	C₄	#11926800	1	1	yes	characteristic
419	C₂	—	4	2	no	—
420	C₂	#14562385	1	1	yes	characteristic
421	C₂	#14562388	1	1	yes	characteristic
422	C₂	#14562400	1	1	yes	characteristic
423	C₂	#14562403	1	1	yes	characteristic
424	C₂	#14563613	1	1	yes	characteristic
425	C₂	#14563666	1	1	yes	characteristic
426	C₂	#14563675	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1797	C₂
socle	C₂³×C₁₉	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1797	D₁₉
hypocenter	C₁₉	#8597
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ #1797

Complements

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

N	H ≅ G/N	type
3. C₂×#11926296	C₂	semidirect
4. C₂×#11926294	C₂	semidirect
5. #14561469	C₂	semidirect
6. #14561469	C₂	semidirect
45. C₂×#64520	C₈	semidirect
178. C₁₉⋊C₈	C₂²⋊C₈	semidirect
281. C₁₉	#8597	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#64520	2
#14563615	2
C₂×#11926296	2
C₂×#11926294	2
#14561469	2
C₁₉×#1797	2
#8597	19