Subgroups — #18088015

Order 4864.

1230 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	C₂×#11926545	C₂	1	2	yes	maximal
2	C₂×#11926312	C₂	1	2	yes	maximal, complemented
3	C₂×#11926309	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926307	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₉×#131	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64520	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₁₉	C₂²	1	2	yes	—
8	#11926545	—	2	4	no	—
9	#11926545	C₄	1	8	yes	complemented
10	C₂×#10597292	—	2	2	no	—
11	C₂×#10597289	—	2	2	no	—
12	#11926312	—	2	4	no	—
13	#11926309	—	2	2	no	—
14	#11926307	—	2	1	no	—
15	#11926307	—	2	1	no	—
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#131	—	2	4	no	—
18	C₂×C₁₉×#131	—	2	4	no	—
19	C₂×C₁₉×#131	—	2	2	no	—
20	C₂×C₁₉×#131	C₄	1	4	yes	complemented
21	C₂²×M₁₆×C₁₉	—	2	1	no	—
22	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₁₉	—	2	1	no	—
24	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×#41×C₁₉	—	2	1	no	—
26	C₂×#41×C₁₉	—	2	2	no	—
27	C₂×#41×C₁₉	—	2	2	no	—
28	C₂×#41×C₁₉	—	2	1	no	—
29	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
30	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×#41×C₁₉	D₄	1	4	yes	—
32	C₂×#41×C₁₉	Q₈	1	2	yes	—
33	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	—	2	1	no	—
37	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂³×Dic₁₉	—	2	2	no	—
39	C₁₉×#131	—	2	16	no	—
40	C₁₉×#131	—	2	8	no	—
41	C₁₉×#131	—	2	8	no	—
42	C₂×M₁₆×C₁₉	—	2	8	no	—
43	C₂×M₁₆×C₁₉	—	2	1	no	—
44	C₂×M₁₆×C₁₉	—	2	2	no	—
45	C₂×M₁₆×C₁₉	—	2	4	no	—
46	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
47	C₂×M₁₆×C₁₉	D₄	1	4	yes	—
48	C₂²×C₈×C₁₉	—	2	8	no	—
49	C₂²×C₈×C₁₉	—	2	1	no	—
50	C₂²×C₈×C₁₉	—	2	2	no	—
51	C₂²×C₈×C₁₉	—	2	2	no	—
52	C₂²×C₈×C₁₉	—	2	4	no	—
53	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₉	D₄	1	2	yes	—
57	C₂×C₄⋊Dic₁₉	—	2	2	no	—
58	C₂×C₄⋊Dic₁₉	—	2	2	no	—
59	C₂×C₄⋊Dic₁₉	—	2	2	no	—
60	C₂×C₄⋊Dic₁₉	—	2	2	no	—
61	C₂×C₄⋊Dic₁₉	—	2	2	no	—
62	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
63	C₂×#64520	—	2	2	no	—
64	C₂×#64520	—	2	2	no	—
65	C₂×#64520	—	2	2	no	—
66	C₂×#64520	—	2	2	no	—
67	C₂×#64520	—	2	2	no	—
68	C₂×#64520	C₂×C₄	1	4	yes	—
69	C₂²×C₁₉⋊C₈	—	2	2	no	—
70	#10597292	—	2	8	no	—
71	#10597289	—	2	8	no	—
72	C₂⁴×C₁₉	—	2	1	no	—
73	C₂⁴×C₁₉	#41	1	1	yes	characteristic
74	#41×C₁₉	—	2	2	no	—
75	#41×C₁₉	—	2	2	no	—
76	#41×C₁₉	—	2	4	no	—
77	#41×C₁₉	—	2	4	no	—
78	#41×C₁₉	—	2	4	no	—
79	#41×C₁₉	—	2	4	no	—
80	#41×C₁₉	—	2	4	no	—
81	#41×C₁₉	C₄²	1	4	yes	—
82	#41×C₁₉	C₂²⋊C₄	1	4	yes	—
83	#41×C₁₉	C₄⋊C₄	1	8	yes	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
87	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
88	C₂×D₄×C₁₉	—	2	2	no	—
89	C₂×D₄×C₁₉	—	2	4	no	—
90	C₂×D₄×C₁₉	—	2	2	no	—
91	C₂×D₄×C₁₉	—	2	4	no	—
92	C₂×D₄×C₁₉	—	2	2	no	—
93	C₂×D₄×C₁₉	—	2	1	no	—
94	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
95	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	4	no	—
99	C₂²×C₄×C₁₉	—	2	4	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	#41	1	2	yes	—
110	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
111	C₂²×Dic₁₉	—	2	4	no	—
112	C₂²×Dic₁₉	—	4	2	no	—
113	C₂²×Dic₁₉	—	4	2	no	—
114	C₂²×Dic₁₉	—	8	2	no	—
115	C₂²×Dic₁₉	—	8	2	no	—
116	M₁₆×C₁₉	—	2	16	no	—
117	M₁₆×C₁₉	—	2	2	no	—
118	M₁₆×C₁₉	—	2	4	no	—
119	M₁₆×C₁₉	C₂²⋊C₄	1	4	yes	—
120	C₂×C₈×C₁₉	—	2	16	no	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	4	no	—
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₂×C₈×C₁₉	—	2	4	no	—
128	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
129	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
130	C₄⋊Dic₁₉	—	2	4	no	—
131	C₄⋊Dic₁₉	—	2	4	no	—
132	C₄⋊Dic₁₉	—	4	2	no	—
133	C₄⋊Dic₁₉	—	4	2	no	—
134	#64520	—	2	4	no	—
135	#64520	—	2	4	no	—
136	#64520	—	4	2	no	—
137	#64520	—	4	2	no	—
138	C₂×C₁₉⋊C₈	—	2	4	no	—
139	C₂×C₁₉⋊C₈	—	4	2	no	—
140	C₂×C₁₉⋊C₈	—	4	2	no	—
141	#10774	—	19	1	no	maximal, Sylow
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	2	1	no	—
144	C₂³×C₁₉	—	2	1	no	—
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	—	2	4	no	—
147	C₂³×C₁₉	—	4	2	no	—
148	C₂³×C₁₉	—	4	1	no	—
149	C₂³×C₁₉	—	4	1	no	—
150	C₂³×C₁₉	#117	1	1	yes	characteristic
151	C₂³×C₁₉	C₄×D₄	1	2	yes	—
152	C₂³×C₁₉	#121	1	1	yes	characteristic
153	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂³×C₁₉	#123	1	2	yes	—
155	Q₈×C₁₉	—	2	2	no	—
156	Q₈×C₁₉	—	2	4	no	—
157	Q₈×C₁₉	#95	1	4	yes	—
158	D₄×C₁₉	—	2	4	no	—
159	D₄×C₁₉	—	2	4	no	—
160	D₄×C₁₉	—	2	8	no	—
161	D₄×C₁₉	—	2	2	no	—
162	D₄×C₁₉	—	2	4	no	—
163	D₄×C₁₉	#95	1	4	yes	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	8	no	—
169	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
175	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
180	C₂×C₄×C₁₉	#120	1	2	yes	—
181	C₂×C₄×C₁₉	#120	1	2	yes	—
182	C₂×C₄×C₁₉	#121	1	2	yes	—
183	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
185	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#123	1	2	yes	—
187	C₂×Dic₁₉	—	4	4	no	—
188	C₂×Dic₁₉	—	8	4	no	—
189	C₂×Dic₁₉	—	8	2	no	—
190	C₂×Dic₁₉	—	8	2	no	—
191	C₂×Dic₁₉	—	8	4	no	—
192	C₈×C₁₉	—	2	2	no	—
193	C₈×C₁₉	—	2	4	no	—
194	C₈×C₁₉	—	2	2	no	—
195	C₁₉⋊C₈	—	4	4	no	—
196	C₂²×#131	D₁₉	1	1	yes	characteristic
197	C₂×#417	—	19	2	no	—
198	C₂×#343	—	19	2	no	—
199	C₂×#341	—	19	1	no	—
200	C₂×#340	—	19	1	no	—
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	2	1	no	—
203	C₂²×C₁₉	—	2	1	no	—
204	C₂²×C₁₉	—	2	1	no	—
205	C₂²×C₁₉	—	2	2	no	—
206	C₂²×C₁₉	—	2	2	no	—
207	C₂²×C₁₉	—	2	2	no	—
208	C₂²×C₁₉	—	2	2	no	—
209	C₂²×C₁₉	—	2	4	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	—	4	2	no	—
212	C₂²×C₁₉	—	4	4	no	—
213	C₂²×C₁₉	—	4	4	no	—
214	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
215	C₂²×C₁₉	#380	1	1	yes	characteristic
216	C₂²×C₁₉	#381	1	1	yes	characteristic
217	C₂²×C₁₉	#385	1	2	yes	—
218	C₂²×C₁₉	#386	1	2	yes	—
219	C₂²×C₁₉	#471	1	2	yes	—
220	C₂²×C₁₉	#472	1	1	yes	characteristic
221	C₂²×C₁₉	#473	1	1	yes	characteristic
222	C₄×C₁₉	—	2	4	no	—
223	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
224	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
225	C₄×C₁₉	#379	1	1	yes	characteristic
226	C₄×C₁₉	#380	1	1	yes	characteristic
227	C₄×C₁₉	#385	1	2	yes	—
228	C₄×C₁₉	#386	1	2	yes	—
229	Dic₁₉	—	8	4	no	—
230	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
231	C₂×#131	—	2	4	no	—
232	C₂×#131	—	2	4	no	—
233	C₂×#131	—	2	2	no	—
234	C₂×#131	Dic₁₉	1	4	yes	complemented
235	C₂²×M₁₆	—	2	1	no	—
236	C₂²×M₁₆	—	19	2	no	—
237	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
238	C₂³×C₈	—	2	1	no	—
239	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	—	19	2	no	—
241	#417	—	19	8	no	—
242	#417	—	38	4	no	—
243	C₂×#103	—	38	2	no	—
244	C₂×#102	—	38	2	no	—
245	#343	—	38	4	no	—
246	#341	—	38	2	no	—
247	#340	—	38	1	no	—
248	#340	—	38	1	no	—
249	C₂×C₁₉	—	2	1	no	—
250	C₂×C₁₉	—	2	1	no	—
251	C₂×C₁₉	—	2	2	no	—
252	C₂×C₁₉	—	4	4	no	—
253	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
254	C₂×C₁₉	#1815	1	1	yes	characteristic
255	C₂×C₁₉	#1816	1	1	yes	characteristic
256	C₂×C₁₉	#1907	1	2	yes	—
257	C₂×C₁₉	#1908	1	2	yes	—
258	C₂×#41	—	2	1	no	—
259	C₂×#41	—	2	2	no	—
260	C₂×#41	—	2	1	no	—
261	C₂×#41	—	2	2	no	—
262	C₂×#41	Dic₃₈	1	2	yes	—
263	C₂×#41	C₄×D₁₉	1	4	yes	—
264	C₂×#41	C₂×Dic₁₉	1	2	yes	—
265	C₂×#41	C₂²⋊D₁₉	1	4	yes	—
266	C₂²×Q₈	D₇₆	1	1	yes	characteristic
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	D₇₆	1	1	yes	characteristic
269	C₂³×C₄	—	2	1	no	—
270	C₂³×C₄	—	38	2	no	—
271	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
272	#131	—	2	16	no	—
273	#131	—	2	8	no	—
274	#131	—	2	8	no	—
275	C₂×M₁₆	—	2	8	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	—	2	4	no	—
279	C₂×M₁₆	—	19	4	no	—
280	C₂×M₁₆	—	38	2	no	—
281	C₂×M₁₆	—	38	2	no	—
282	C₂×M₁₆	—	38	2	no	—
283	C₂×M₁₆	—	38	2	no	—
284	C₂×M₁₆	—	38	2	no	—
285	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
286	C₂×M₁₆	C₂²⋊D₁₉	1	4	yes	—
287	C₂²×C₈	—	2	8	no	—
288	C₂²×C₈	—	2	1	no	—
289	C₂²×C₈	—	2	2	no	—
290	C₂²×C₈	—	2	2	no	—
291	C₂²×C₈	—	2	4	no	—
292	C₂²×C₈	—	38	2	no	—
293	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
294	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
295	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
296	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
297	C₂×C₄⋊C₄	—	19	4	no	—
298	C₂×C₄⋊C₄	—	38	2	no	—
299	C₂×C₄⋊C₄	—	38	2	no	—
300	C₂×C₄⋊C₄	—	38	2	no	—
301	C₂×C₄⋊C₄	—	38	2	no	—
302	C₂×C₄⋊C₄	—	38	2	no	—
303	#103	—	38	8	no	—
304	#102	—	38	8	no	—
305	C₁₉	#10774	1	1	yes	characteristic, complemented, Sylow
306	C₂⁴	—	2	1	no	—
307	C₂⁴	#64541	1	1	yes	characteristic
308	#41	—	2	2	no	—
309	#41	—	2	4	no	—
310	#41	—	2	4	no	—
311	#41	—	2	2	no	—
312	#41	—	2	4	no	—
313	#41	—	2	4	no	—
314	#41	—	2	4	no	—
315	#41	C₄×Dic₁₉	1	4	yes	—
316	#41	Dic₁₉⋊C₄	1	8	yes	—
317	#41	C₂²⋊Dic₁₉	1	4	yes	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	C₄⋊Dic₁₉	1	2	yes	—
321	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	C₄⋊Dic₁₉	1	2	yes	—
329	C₂×D₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	38	4	no	—
336	C₂²×C₄	—	76	2	no	—
337	C₂²×C₄	—	76	2	no	—
338	C₂²×C₄	—	152	2	no	—
339	C₂²×C₄	—	152	2	no	—
340	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
341	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
342	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
343	C₂²×C₄	#64541	1	2	yes	—
344	C₂²×C₄	#64541	1	1	yes	characteristic
345	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
347	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
349	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
350	M₁₆	—	2	16	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	4	no	—
353	M₁₆	—	38	4	no	—
354	M₁₆	—	38	4	no	—
355	M₁₆	—	76	2	no	—
356	M₁₆	—	76	2	no	—
357	M₁₆	C₂²⋊Dic₁₉	1	4	yes	—
358	C₂×C₈	—	2	16	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	4	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	4	no	—
366	C₂×C₈	—	38	4	no	—
367	C₂×C₈	—	76	2	no	—
368	C₂×C₈	—	76	2	no	—
369	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
370	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
371	C₄⋊C₄	—	38	4	no	—
372	C₄⋊C₄	—	38	4	no	—
373	C₄⋊C₄	—	76	2	no	—
374	C₄⋊C₄	—	76	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	#10597370	1	1	yes	characteristic
384	C₂³	#10597372	1	1	yes	characteristic
385	C₂³	C₄×C₂²⋊D₁₉	1	2	yes	—
386	C₂³	#10597375	1	2	yes	—
387	C₂³	#10597376	1	1	yes	characteristic
388	Q₈	—	2	2	no	—
389	Q₈	—	2	4	no	—
390	Q₈	C₁₉⋊#95	1	4	yes	—
391	D₄	—	2	4	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	8	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	4	no	—
396	D₄	C₁₉⋊#95	1	4	yes	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	76	4	no	—
403	C₂×C₄	—	152	4	no	—
404	C₂×C₄	—	152	2	no	—
405	C₂×C₄	—	152	2	no	—
406	C₂×C₄	—	152	4	no	—
407	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
408	C₂×C₄	C₂×Dic₁₉⋊C₄	1	2	yes	—
409	C₂×C₄	#10597370	1	2	yes	—
410	C₂×C₄	#10597370	1	1	yes	characteristic
411	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
412	C₂×C₄	#10597372	1	1	yes	characteristic
413	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	2	yes	—
414	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
415	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
416	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
417	C₂×C₄	#10597375	1	2	yes	—
418	C₂×C₄	#10597376	1	2	yes	—
419	C₂×C₄	#10597376	1	1	yes	characteristic
420	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
421	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
422	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
423	C₂×C₄	#10597399	1	2	yes	—
424	C₂×C₄	#10597399	1	2	yes	—
425	C₈	—	2	2	no	—
426	C₈	—	2	4	no	—
427	C₈	—	2	2	no	—
428	C₈	—	76	4	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
443	C₂²	#11926404	1	1	yes	characteristic
444	C₂²	#11926407	1	1	yes	characteristic
445	C₂²	#11926417	1	2	yes	—
446	C₂²	#11926423	1	2	yes	—
447	C₂²	#11926807	1	2	yes	—
448	C₂²	#11926814	1	1	yes	characteristic
449	C₂²	#11926819	1	1	yes	characteristic
450	C₄	—	2	4	no	—
451	C₄	—	152	4	no	—
452	C₄	C₂×C₁₉⋊#95	1	1	yes	characteristic
453	C₄	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
454	C₄	#11926400	1	1	yes	characteristic
455	C₄	#11926404	1	1	yes	characteristic
456	C₄	#11926417	1	2	yes	—
457	C₄	#11926423	1	2	yes	—
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	2	2	no	—
461	C₂	—	4	4	no	—
462	C₂	#14561858	1	1	yes	characteristic
463	C₂	#14563694	1	1	yes	characteristic
464	C₂	#14563699	1	1	yes	characteristic
465	C₂	#14564143	1	2	yes	—
466	C₂	#14564150	1	2	yes	—

	subgroup	G/H
center	C₂³	#10597376
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₁₉×#131	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂²×#41×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×#131	D₁₉
hypocenter	C₁₉	#10774
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂²×#131

Complements

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

N	H ≅ G/N	type
2. C₂×#11926312	C₂	semidirect
3. C₂×#11926309	C₂	semidirect
4. C₂×#11926307	C₂	semidirect
9. #11926545	C₄	semidirect
20. C₂×C₁₉×#131	C₄	semidirect
234. C₂×#131	Dic₁₉	semidirect
305. C₁₉	#10774	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926545	2
C₂×#11926312	2
C₂×#11926309	2
C₂×#11926307	2
C₂²×C₁₉×#131	2
#10774	19