Subgroups — #18075893

Order 4864.

592 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597338	C₂	1	1	yes	maximal, characteristic
2	#14563612	C₂	1	1	yes	maximal, characteristic
3	C₄×(C₂×D₁₉)⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561475	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597338	C₄	1	1	yes	characteristic
9	C₂×#10597338	C₄	1	1	yes	characteristic
10	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
13	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
14	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₄⋊C₄×Dic₁₉	C₄	1	1	yes	characteristic
16	C₄⋊C₄×Dic₁₉	C₄	1	1	yes	characteristic
17	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
18	C₄×(C₂×D₁₉)⋊C₄	—	2	1	no	—
19	#11926391	—	2	1	no	—
20	#11926389	—	2	1	no	—
21	C₄²×Dic₁₉	—	2	1	no	—
22	#11926298	—	2	1	no	—
23	#11926298	—	2	1	no	—
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	—	2	1	no	—
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
37	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
38	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄×Dic₁₉	—	2	1	no	—
41	C₂×C₄×Dic₁₉	—	2	1	no	—
42	C₂×C₄×Dic₁₉	—	2	1	no	—
43	C₂×C₄×Dic₁₉	—	2	1	no	—
44	C₂×C₄×Dic₁₉	—	2	1	no	—
45	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
48	C₂²×C₁₉⋊C₈	—	2	1	no	—
49	C₂²×C₁₉⋊C₈	—	2	1	no	—
50	#10597338	—	2	2	no	—
51	#10597338	—	2	2	no	—
52	#10597338	—	2	2	no	—
53	#10597338	C₈	1	4	yes	complemented
54	C₄²×D₁₉	—	2	1	no	—
55	C₄²×D₁₉	—	2	1	no	—
56	C₄²×D₁₉	—	2	1	no	—
57	C₄²×D₁₉	—	2	1	no	—
58	C₁₉×C₄⋊C₈	—	2	1	no	—
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₄×C₈×C₁₉	—	2	1	no	—
61	C₄×C₈×C₁₉	—	2	1	no	—
62	C₁₉×#95	—	2	1	no	—
63	C₁₉⋊#95	—	2	1	no	—
64	C₁₉⋊#95	—	2	1	no	—
65	C₁₉⋊#95	—	2	1	no	—
66	(C₂×D₁₉)⋊C₈	—	2	4	no	—
67	(C₂×D₁₉)⋊C₈	—	4	2	no	—
68	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
69	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
70	C₄×C₁₉⋊C₈	—	2	1	no	—
71	C₄×C₁₉⋊C₈	—	2	1	no	—
72	C₂³×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂²×Dic₁₉	—	2	1	no	—
79	C₂²×Dic₁₉	—	2	1	no	—
80	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₁₉	—	2	1	no	—
84	C₂×C₄×D₁₉	—	2	1	no	—
85	C₂×C₄×D₁₉	—	2	1	no	—
86	C₂×C₄×D₁₉	—	2	1	no	—
87	C₂×C₄×D₁₉	—	2	1	no	—
88	C₂×C₄×D₁₉	—	2	1	no	—
89	C₂×C₄×D₁₉	—	2	1	no	—
90	C₂×C₄×D₁₉	—	2	1	no	—
91	C₂×C₄×D₁₉	—	2	1	no	—
92	C₂×C₄×D₁₉	—	2	1	no	—
93	C₂×C₄×D₁₉	—	2	1	no	—
94	C₂×C₄×D₁₉	—	2	1	no	—
95	C₂×C₄×D₁₉	—	2	2	no	—
96	C₂×C₄×D₁₉	—	4	1	no	—
97	C₂×C₄×D₁₉	C₂×C₈	1	2	yes	—
98	C₂×C₄×D₁₉	M₁₆	1	2	yes	—
99	C₂×C₈×C₁₉	—	2	2	no	—
100	C₂×C₈×C₁₉	—	4	1	no	—
101	C₂×C₈×C₁₉	—	4	1	no	—
102	C₂×C₈×C₁₉	—	4	1	no	—
103	C₂×C₈×C₁₉	—	4	1	no	—
104	C₂×C₈×C₁₉	—	4	1	no	—
105	C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	C₂×C₈	1	2	yes	—
108	C₄⋊C₄×C₁₉	M₁₆	1	2	yes	—
109	C₄²×C₁₉	—	4	1	no	—
110	C₄²×C₁₉	—	4	1	no	—
111	C₄²×C₁₉	#41	1	1	yes	characteristic
112	C₄²×C₁₉	#41	1	1	yes	characteristic
113	C₄²×C₁₉	#41	1	1	yes	characteristic
114	C₄²×C₁₉	#41	1	1	yes	characteristic
115	(C₂×D₁₉)⋊C₄	—	2	4	no	—
116	(C₂×D₁₉)⋊C₄	—	2	4	no	—
117	C₄⋊Dic₁₉	—	2	1	no	—
118	C₄⋊Dic₁₉	—	2	1	no	—
119	C₄⋊Dic₁₉	C₂×C₈	1	2	yes	—
120	C₄⋊Dic₁₉	M₁₆	1	2	yes	—
121	C₄×Dic₁₉	—	2	4	no	—
122	C₄×Dic₁₉	—	2	1	no	—
123	C₄×Dic₁₉	—	2	1	no	—
124	C₄×Dic₁₉	—	2	1	no	—
125	C₄×Dic₁₉	—	2	1	no	—
126	C₄×Dic₁₉	—	2	1	no	—
127	C₄×Dic₁₉	—	2	1	no	—
128	C₄×Dic₁₉	—	2	4	no	—
129	C₄×Dic₁₉	—	4	2	no	—
130	C₄×Dic₁₉	—	4	1	no	—
131	C₄×Dic₁₉	—	4	1	no	—
132	C₄×Dic₁₉	—	4	2	no	—
133	C₂×C₁₉⋊C₈	—	2	2	no	—
134	C₂×C₁₉⋊C₈	—	4	1	no	—
135	C₂×C₁₉⋊C₈	—	4	1	no	—
136	C₂×C₁₉⋊C₈	—	4	1	no	—
137	C₂×C₁₉⋊C₈	—	4	1	no	—
138	C₂×C₁₉⋊C₈	—	4	1	no	—
139	#8708	—	19	1	no	maximal, Sylow
140	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×D₁₉	—	2	1	no	—
142	C₂²×D₁₉	—	2	1	no	—
143	C₂²×D₁₉	—	2	1	no	—
144	C₂²×D₁₉	—	2	1	no	—
145	C₂²×D₁₉	—	2	1	no	—
146	C₂²×D₁₉	—	2	1	no	—
147	C₂²×D₁₉	C₂²⋊C₈	1	2	yes	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	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	#117	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
161	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂×M₁₆	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	#135	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#135	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×Dic₁₉	—	2	1	no	—
171	C₂×Dic₁₉	—	2	1	no	—
172	C₂×Dic₁₉	—	2	1	no	—
173	C₂×Dic₁₉	—	2	1	no	—
174	C₂×Dic₁₉	—	2	1	no	—
175	C₂×Dic₁₉	—	2	2	no	—
176	C₂×Dic₁₉	—	2	2	no	—
177	C₂×Dic₁₉	—	2	1	no	—
178	C₂×Dic₁₉	—	2	1	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	C₂²⋊C₈	1	2	yes	—
184	C₂×Dic₁₉	#104	1	2	yes	—
185	C₄×D₁₉	—	2	2	no	—
186	C₄×D₁₉	—	2	2	no	—
187	C₄×D₁₉	—	2	2	no	—
188	C₄×D₁₉	—	2	2	no	—
189	C₄×D₁₉	—	4	2	no	—
190	C₄×D₁₉	—	4	2	no	—
191	C₄×D₁₉	—	4	1	no	—
192	C₄×D₁₉	—	4	1	no	—
193	C₄×D₁₉	—	4	1	no	—
194	C₄×D₁₉	—	4	1	no	—
195	C₈×C₁₉	—	4	2	no	—
196	C₈×C₁₉	—	8	1	no	—
197	C₁₉⋊C₈	—	4	2	no	—
198	C₁₉⋊C₈	—	8	1	no	—
199	C₄×#117	—	19	1	no	—
200	#1797	—	19	1	no	—
201	C₄×C₂²⋊C₈	—	19	1	no	—
202	#1279	—	19	1	no	—
203	#1279	—	19	1	no	—
204	#1279	—	19	1	no	—
205	#1279	D₁₉	1	1	yes	characteristic, complemented
206	C₂²×C₁₉	#381	1	1	yes	characteristic
207	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
208	C₂²×C₁₉	#407	1	1	yes	characteristic
209	C₂²×C₁₉	#416	1	1	yes	characteristic
210	C₂²×C₁₉	#417	1	1	yes	characteristic
211	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
212	C₂²×C₁₉	#421	1	1	yes	characteristic
213	C₂×D₁₉	—	2	2	no	—
214	C₂×D₁₉	—	2	2	no	—
215	C₂×D₁₉	—	2	2	no	—
216	C₂×D₁₉	—	4	1	no	—
217	C₂×D₁₉	—	4	1	no	—
218	C₂×D₁₉	—	4	1	no	—
219	C₂×D₁₉	—	4	1	no	—
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	4	2	no	—
223	C₄×C₁₉	—	4	2	no	—
224	C₄×C₁₉	#431	1	1	yes	characteristic
225	C₄×C₁₉	#431	1	1	yes	characteristic
226	C₄×C₁₉	#432	1	1	yes	characteristic
227	C₄×C₁₉	#432	1	1	yes	characteristic
228	C₄×C₁₉	#482	1	1	yes	characteristic
229	C₄×C₁₉	#482	1	1	yes	characteristic
230	C₄×C₁₉	#485	1	1	yes	characteristic
231	C₄×C₁₉	#485	1	1	yes	characteristic
232	Dic₁₉	—	2	2	no	—
233	Dic₁₉	—	2	2	no	—
234	Dic₁₉	—	4	1	no	—
235	Dic₁₉	—	4	2	no	—
236	Dic₁₉	—	4	2	no	—
237	C₂×#117	—	19	1	no	—
238	C₂×#117	—	19	1	no	—
239	C₂²×C₄²	—	19	1	no	—
240	C₂×C₄⋊C₈	—	19	1	no	—
241	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
242	C₂×C₂²⋊C₈	—	38	1	no	—
243	C₂×C₂²⋊C₈	—	38	1	no	—
244	C₂×C₄×C₈	—	19	1	no	—
245	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
246	C₄×C₄⋊C₄	—	19	1	no	—
247	C₄×C₄⋊C₄	—	19	1	no	—
248	C₄×C₄⋊C₄	—	19	1	no	—
249	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
250	C₄×C₂²⋊C₄	—	38	1	no	—
251	C₄×C₂²⋊C₄	—	38	1	no	—
252	#376	—	38	1	no	—
253	C₄³	—	38	1	no	—
254	#336	—	38	1	no	—
255	#336	—	38	1	no	—
256	C₂×C₁₉	#1476	1	1	yes	characteristic
257	C₂×C₁₉	#1477	1	1	yes	characteristic
258	C₂×C₁₉	#1488	1	1	yes	characteristic
259	C₂×C₁₉	#1489	1	1	yes	characteristic
260	C₂×C₁₉	#1817	1	1	yes	characteristic
261	C₂×C₁₉	#1825	1	1	yes	characteristic
262	C₂×C₁₉	#1826	1	1	yes	characteristic
263	D₁₉	—	4	2	no	—
264	C₂³×C₄	—	19	1	no	—
265	C₂³×C₄	—	19	1	no	—
266	C₂³×C₄	—	19	1	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	38	1	no	—
270	C₂²×C₈	—	38	1	no	—
271	#117	—	19	4	no	—
272	#117	—	38	2	no	—
273	#117	—	38	2	no	—
274	#117	—	38	2	no	—
275	C₂×C₄⋊C₄	—	19	1	no	—
276	C₂×C₄⋊C₄	—	19	1	no	—
277	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	—	38	1	no	—
280	C₂×C₂²⋊C₄	—	38	1	no	—
281	C₂×C₄²	—	2	1	no	—
282	C₂×C₄²	—	19	1	no	—
283	C₂×C₄²	—	19	1	no	—
284	C₂×C₄²	—	19	1	no	—
285	C₂×C₄²	—	38	1	no	—
286	C₂×C₄²	—	38	1	no	—
287	C₂×C₄²	—	38	1	no	—
288	C₂×C₄²	—	38	1	no	—
289	C₂×C₄²	—	38	1	no	—
290	C₂×C₄²	—	38	1	no	—
291	C₂×C₄²	—	38	1	no	—
292	C₂×C₄²	—	38	1	no	—
293	C₂×C₄²	—	38	1	no	—
294	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	38	1	no	—
298	C₄⋊C₈	—	38	1	no	—
299	C₂²⋊C₈	—	38	4	no	—
300	C₂²⋊C₈	—	76	2	no	—
301	C₄×C₈	—	2	1	no	—
302	C₄×C₈	—	2	1	no	—
303	C₄×C₈	—	38	1	no	—
304	C₄×C₈	—	38	1	no	—
305	#95	—	2	1	no	—
306	#95	—	38	1	no	—
307	#95	—	38	1	no	—
308	#95	—	38	1	no	—
309	C₁₉	#8708	1	1	yes	characteristic, complemented, Sylow
310	C₂⁴	—	19	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	19	1	no	—
314	C₂²×C₄	—	19	1	no	—
315	C₂²×C₄	—	19	2	no	—
316	C₂²×C₄	—	19	2	no	—
317	C₂²×C₄	—	19	1	no	—
318	C₂²×C₄	—	38	2	no	—
319	C₂²×C₄	—	38	1	no	—
320	C₂²×C₄	—	38	1	no	—
321	C₂²×C₄	—	38	1	no	—
322	C₂²×C₄	—	38	1	no	—
323	C₂²×C₄	—	38	1	no	—
324	C₂²×C₄	—	38	1	no	—
325	C₂²×C₄	—	38	1	no	—
326	C₂²×C₄	—	38	1	no	—
327	C₂²×C₄	—	38	1	no	—
328	C₂²×C₄	—	38	1	no	—
329	C₂²×C₄	—	38	1	no	—
330	C₂²×C₄	—	38	1	no	—
331	C₂²×C₄	—	38	1	no	—
332	C₂²×C₄	—	38	1	no	—
333	C₂²×C₄	—	76	1	no	—
334	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
335	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
336	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	38	2	no	—
344	C₂×C₈	—	76	1	no	—
345	C₂×C₈	—	76	1	no	—
346	C₂×C₈	—	76	1	no	—
347	C₂×C₈	—	76	1	no	—
348	C₂×C₈	—	76	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	19	2	no	—
352	C₄⋊C₄	—	19	2	no	—
353	C₄⋊C₄	—	38	1	no	—
354	C₄⋊C₄	—	38	1	no	—
355	C₄⋊C₄	C₈×D₁₉	1	2	yes	—
356	C₄⋊C₄	#64515	1	2	yes	—
357	C₂²⋊C₄	—	38	4	no	—
358	C₂²⋊C₄	—	38	4	no	—
359	C₄²	—	4	1	no	—
360	C₄²	—	4	1	no	—
361	C₄²	—	38	4	no	—
362	C₄²	—	38	4	no	—
363	C₄²	—	38	1	no	—
364	C₄²	—	38	1	no	—
365	C₄²	—	38	1	no	—
366	C₄²	—	38	1	no	—
367	C₄²	—	38	1	no	—
368	C₄²	—	38	1	no	—
369	C₄²	—	76	2	no	—
370	C₄²	—	76	2	no	—
371	C₄²	—	76	1	no	—
372	C₄²	—	76	1	no	—
373	C₄²	#64541	1	1	yes	characteristic
374	C₄²	#64541	1	1	yes	characteristic
375	C₄²	#64543	1	1	yes	characteristic
376	C₄²	#64545	1	1	yes	characteristic
377	C₂³	—	19	2	no	—
378	C₂³	—	38	1	no	—
379	C₂³	—	38	1	no	—
380	C₂³	—	38	1	no	—
381	C₂³	—	38	1	no	—
382	C₂³	—	38	1	no	—
383	C₂³	—	38	1	no	—
384	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	19	2	no	—
394	C₂×C₄	—	19	2	no	—
395	C₂×C₄	—	38	1	no	—
396	C₂×C₄	—	38	1	no	—
397	C₂×C₄	—	38	1	no	—
398	C₂×C₄	—	38	1	no	—
399	C₂×C₄	—	38	2	no	—
400	C₂×C₄	—	38	2	no	—
401	C₂×C₄	—	38	2	no	—
402	C₂×C₄	—	38	2	no	—
403	C₂×C₄	—	38	1	no	—
404	C₂×C₄	—	38	1	no	—
405	C₂×C₄	—	38	1	no	—
406	C₂×C₄	—	38	2	no	—
407	C₂×C₄	—	38	2	no	—
408	C₂×C₄	—	76	2	no	—
409	C₂×C₄	—	76	2	no	—
410	C₂×C₄	—	76	1	no	—
411	C₂×C₄	—	76	1	no	—
412	C₂×C₄	—	76	1	no	—
413	C₂×C₄	—	76	1	no	—
414	C₂×C₄	—	76	1	no	—
415	C₂×C₄	—	76	1	no	—
416	C₂×C₄	—	76	1	no	—
417	C₂×C₄	—	76	1	no	—
418	C₂×C₄	#10597318	1	1	yes	characteristic
419	C₂×C₄	#10597329	1	1	yes	characteristic
420	C₂×C₄	#10597329	1	1	yes	characteristic
421	C₂×C₄	#10597338	1	1	yes	characteristic
422	C₂×C₄	#10597340	1	1	yes	characteristic
423	C₂×C₄	#10597340	1	1	yes	characteristic
424	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
425	C₂×C₄	C₂×#64515	1	1	yes	characteristic
426	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
427	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
428	C₂×C₄	#10597358	1	1	yes	characteristic
429	C₂×C₄	#10597360	1	1	yes	characteristic
430	C₂×C₄	#10597362	1	1	yes	characteristic
431	C₂×C₄	#10597364	1	1	yes	characteristic
432	C₈	—	4	2	no	—
433	C₈	—	8	1	no	—
434	C₈	—	76	2	no	—
435	C₈	—	152	1	no	—
436	C₂²	—	38	2	no	—
437	C₂²	—	38	2	no	—
438	C₂²	—	38	2	no	—
439	C₂²	—	76	1	no	—
440	C₂²	—	76	1	no	—
441	C₂²	—	76	1	no	—
442	C₂²	—	76	1	no	—
443	C₂²	#11926406	1	1	yes	characteristic
444	C₂²	C₂²⋊C₈×D₁₉	1	1	yes	characteristic
445	C₂²	#11926506	1	1	yes	characteristic
446	C₂²	#11926537	1	1	yes	characteristic
447	C₂²	#11926544	1	1	yes	characteristic
448	C₂²	#104×D₁₉	1	1	yes	characteristic
449	C₂²	#11926559	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	38	2	no	—
455	C₄	—	38	2	no	—
456	C₄	—	76	2	no	—
457	C₄	—	76	1	no	—
458	C₄	—	76	2	no	—
459	C₄	#11926595	1	1	yes	characteristic
460	C₄	#11926596	1	1	yes	characteristic
461	C₄	#11926599	1	1	yes	characteristic
462	C₄	#11926600	1	1	yes	characteristic
463	C₄	#11926866	1	1	yes	characteristic
464	C₄	#11926870	1	1	yes	characteristic
465	C₄	#11926883	1	1	yes	characteristic
466	C₄	#11926887	1	1	yes	characteristic
467	C₂	—	76	2	no	—
468	C₂	#14562014	1	1	yes	characteristic
469	C₂	#14562021	1	1	yes	characteristic
470	C₂	#14562066	1	1	yes	characteristic
471	C₂	#14562073	1	1	yes	characteristic
472	C₂	#14563702	1	1	yes	characteristic
473	C₂	#14563728	1	1	yes	characteristic
474	C₂	#14563733	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1279	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1279	D₁₉
hypocenter	C₁₉	#8708
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
4. #14561476	C₂	semidirect
5. #14561475	C₂	semidirect
6. #14561474	C₂	semidirect
7. C₁₉×#1279	C₂	semidirect
53. #10597338	C₈	semidirect
205. #1279	D₁₉	semidirect
309. C₁₉	#8708	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10597338	2
#14563612	2
C₄×(C₂×D₁₉)⋊C₈	2
#14561476	2
#14561475	2
#14561474	2
C₁₉×#1279	2
#8708	19