Subgroups — #18090535

Order 4864.

702 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926571	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926309	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926303	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926303	C₂	1	1	yes	maximal, characteristic
5	#14563332	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926298	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#427	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	#11926571	—	2	2	no	—
13	#11926571	—	2	2	no	—
14	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
15	#11926309	—	2	2	no	—
16	#11926303	—	2	2	no	—
17	#11926303	—	2	2	no	—
18	#11926299	—	2	2	no	—
19	#11926298	—	2	2	no	—
20	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₁₉×#427	—	2	2	no	—
24	C₁₉×#427	—	2	2	no	—
25	C₂×C₁₉×#107	C₄	1	2	yes	complemented
26	C₂×C₁₉×#106	C₄	1	2	yes	complemented
27	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂³×Dic₁₉	—	2	1	no	—
29	C₂²×C₈×C₁₉	—	2	1	no	—
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₉	D₄	1	2	yes	—
36	C₂²×C₈×C₁₉	Q₈	1	2	yes	—
37	C₁₉×#117	—	2	1	no	—
38	C₁₉×#117	—	2	1	no	—
39	C₁₉×#117	—	2	1	no	—
40	C₁₉×#117	—	2	1	no	—
41	C₁₉×#117	—	2	1	no	—
42	C₁₉×#117	—	2	1	no	—
43	C₁₉×#117	D₄	1	2	yes	—
44	C₁₉×#117	D₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
46	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	—	2	1	no	—
51	C₂×C₄×Dic₁₉	—	2	1	no	—
52	C₂×C₄×Dic₁₉	—	2	1	no	—
53	C₂×C₄×Dic₁₉	—	2	1	no	—
54	C₂×C₄×Dic₁₉	—	2	1	no	—
55	C₂×C₄×Dic₁₉	—	2	1	no	—
56	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
57	C₂×#64520	—	2	1	no	—
58	C₂×#64520	—	2	1	no	—
59	C₂×#64520	—	2	1	no	—
60	C₂×#64520	—	2	1	no	—
61	C₂×#64520	—	2	1	no	—
62	C₂×#64520	—	2	1	no	—
63	C₂×#64520	—	2	1	no	—
64	C₂×#64520	—	2	1	no	—
65	C₂×#64520	—	2	1	no	—
66	C₂×#64520	—	2	1	no	—
67	C₂×#64520	D₄	1	2	yes	—
68	C₂×#64520	Q₈	1	2	yes	—
69	C₂²×C₁₉⋊C₈	—	2	1	no	—
70	C₂²×C₁₉⋊C₈	—	2	1	no	—
71	C₂²×C₁₉⋊C₈	—	2	1	no	—
72	C₂²×C₁₉⋊C₈	—	2	1	no	—
73	C₂²×C₁₉⋊C₈	—	2	1	no	—
74	C₂²×C₁₉⋊C₈	—	2	1	no	—
75	C₂²×C₁₉⋊C₈	—	2	1	no	—
76	C₂²×C₁₉⋊C₈	—	2	1	no	—
77	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
78	C₁₉×#107	—	2	4	no	—
79	C₁₉×#106	—	2	4	no	—
80	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
81	C₂⁴×C₁₉	#41	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×D₄	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	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
98	C₂²×Dic₁₉	—	2	4	no	—
99	C₂²×Dic₁₉	—	2	2	no	—
100	C₂²×Dic₁₉	—	4	2	no	—
101	C₂²×Dic₁₉	—	4	1	no	—
102	C₂²×Dic₁₉	—	4	1	no	—
103	C₂×C₈×C₁₉	—	2	1	no	—
104	C₂×C₈×C₁₉	—	2	1	no	—
105	C₂×C₈×C₁₉	—	2	1	no	—
106	C₂×C₈×C₁₉	—	2	1	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
112	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
113	C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
117	C₂²⋊C₄×C₁₉	—	2	2	no	—
118	C₂²⋊C₄×C₁₉	—	2	2	no	—
119	C₂²⋊C₄×C₁₉	—	4	1	no	—
120	C₂²⋊C₄×C₁₉	—	4	1	no	—
121	C₄²×C₁₉	—	2	2	no	—
122	C₄²×C₁₉	—	2	2	no	—
123	C₄²×C₁₉	—	4	1	no	—
124	C₄²×C₁₉	—	4	1	no	—
125	C₄×Dic₁₉	—	2	2	no	—
126	C₄×Dic₁₉	—	2	2	no	—
127	C₄×Dic₁₉	—	4	1	no	—
128	C₄×Dic₁₉	—	4	1	no	—
129	#64520	—	2	2	no	—
130	#64520	—	2	2	no	—
131	#64520	—	2	2	no	—
132	#64520	—	2	2	no	—
133	#64520	—	4	1	no	—
134	#64520	—	4	1	no	—
135	#64520	—	4	1	no	—
136	#64520	—	4	1	no	—
137	C₂×C₁₉⋊C₈	—	2	2	no	—
138	C₂×C₁₉⋊C₈	—	2	2	no	—
139	C₂×C₁₉⋊C₈	—	2	2	no	—
140	C₂×C₁₉⋊C₈	—	2	2	no	—
141	C₂×C₁₉⋊C₈	—	2	2	no	—
142	C₂×C₁₉⋊C₈	—	4	1	no	—
143	C₂×C₁₉⋊C₈	—	4	1	no	—
144	C₂×C₁₉⋊C₈	—	4	1	no	—
145	C₂×C₁₉⋊C₈	—	4	1	no	—
146	C₂×C₁₉⋊C₈	—	4	1	no	—
147	C₂×C₁₉⋊C₈	—	4	1	no	—
148	C₂×C₁₉⋊C₈	—	4	1	no	—
149	C₂×C₁₉⋊C₈	—	4	1	no	—
150	#11221	—	19	1	no	maximal, Sylow
151	C₂³×C₁₉	—	2	2	no	—
152	C₂³×C₁₉	—	2	2	no	—
153	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
154	C₂³×C₁₉	#121	1	1	yes	characteristic
155	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂³×C₁₉	#123	1	1	yes	characteristic
157	C₂³×C₁₉	#125	1	1	yes	characteristic
158	C₂³×C₁₉	#125	1	1	yes	characteristic
159	C₂³×C₁₉	#126	1	1	yes	characteristic
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₄×Q₈	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	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
194	C₂×Dic₁₉	—	2	4	no	—
195	C₂×Dic₁₉	—	4	4	no	—
196	C₂×Dic₁₉	—	4	4	no	—
197	C₂×Dic₁₉	—	4	2	no	—
198	C₂×Dic₁₉	—	4	2	no	—
199	C₈×C₁₉	—	2	2	no	—
200	C₈×C₁₉	—	2	2	no	—
201	C₁₉⋊C₈	—	4	2	no	—
202	C₁₉⋊C₈	—	4	2	no	—
203	C₁₉⋊C₈	—	4	2	no	—
204	C₂×#427	D₁₉	1	1	yes	characteristic
205	C₂×#424	—	19	1	no	—
206	C₂×#341	—	19	1	no	—
207	C₂×#339	—	19	1	no	—
208	C₂×#339	—	19	1	no	—
209	#1729	—	19	1	no	—
210	C₂×#336	—	19	1	no	—
211	C₂²×C₁₉	—	2	2	no	—
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	2	2	no	—
214	C₂²×C₁₉	—	2	2	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	2	1	no	—
219	C₂²×C₁₉	#386	1	1	yes	characteristic
220	C₂²×C₁₉	#387	1	1	yes	characteristic
221	C₂²×C₁₉	#389	1	1	yes	characteristic
222	C₂²×C₁₉	#396	1	1	yes	characteristic
223	C₂²×C₁₉	#398	1	1	yes	characteristic
224	C₂²×C₁₉	#398	1	1	yes	characteristic
225	C₂²×C₁₉	#400	1	1	yes	characteristic
226	C₂²×C₁₉	#443	1	2	yes	—
227	C₂²×C₁₉	#444	1	2	yes	—
228	C₄×C₁₉	—	4	4	no	—
229	C₄×C₁₉	—	8	2	no	—
230	C₄×C₁₉	#380	1	1	yes	characteristic
231	C₄×C₁₉	#387	1	1	yes	characteristic
232	C₄×C₁₉	#389	1	1	yes	characteristic
233	C₄×C₁₉	#391	1	1	yes	characteristic
234	C₄×C₁₉	#394	1	1	yes	characteristic
235	C₄×C₁₉	#395	1	1	yes	characteristic
236	C₄×C₁₉	#396	1	1	yes	characteristic
237	C₄×C₁₉	#398	1	1	yes	characteristic
238	Dic₁₉	—	4	4	no	—
239	C₂²×M₁₆	—	19	1	no	—
240	C₂²×M₁₆	—	19	1	no	—
241	C₂³×C₈	—	19	1	no	—
242	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
243	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
244	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
245	C₂²×C₄²	—	19	1	no	—
246	#427	—	2	2	no	—
247	#427	—	2	2	no	—
248	C₂×#107	Dic₁₉	1	2	yes	complemented
249	C₂×#106	Dic₁₉	1	2	yes	complemented
250	#424	—	38	2	no	—
251	#424	—	38	2	no	—
252	C₂×C₄⋊C₈	—	38	2	no	—
253	#341	—	38	2	no	—
254	#339	—	38	2	no	—
255	#339	—	38	2	no	—
256	#336	—	38	2	no	—
257	#336	—	38	2	no	—
258	C₂×C₁₉	—	2	1	no	—
259	C₂×C₁₉	—	2	1	no	—
260	C₂×C₁₉	—	2	1	no	—
261	C₂×C₁₉	—	2	1	no	—
262	C₂×C₁₉	#1441	1	1	yes	characteristic
263	C₂×C₁₉	#1876	1	2	yes	—
264	C₂×C₁₉	#1922	1	2	yes	—
265	C₂×C₁₉	#1945	1	1	yes	characteristic
266	C₂×C₁₉	#1946	1	1	yes	characteristic
267	C₂³×C₄	—	38	1	no	—
268	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
269	C₂×M₁₆	—	19	2	no	—
270	C₂×M₁₆	—	19	2	no	—
271	C₂×M₁₆	—	38	1	no	—
272	C₂×M₁₆	—	38	1	no	—
273	C₂×M₁₆	—	38	1	no	—
274	C₂×M₁₆	—	38	1	no	—
275	C₂×M₁₆	—	38	1	no	—
276	C₂×M₁₆	—	38	1	no	—
277	C₂×M₁₆	—	38	1	no	—
278	C₂×M₁₆	—	38	1	no	—
279	C₂×M₁₆	—	38	1	no	—
280	C₂×M₁₆	—	38	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	—	2	1	no	—
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	—	19	2	no	—
286	C₂²×C₈	—	38	1	no	—
287	C₂²×C₈	—	38	1	no	—
288	C₂²×C₈	—	38	1	no	—
289	C₂²×C₈	—	38	1	no	—
290	C₂²×C₈	—	38	1	no	—
291	C₂²×C₈	—	38	1	no	—
292	C₂²×C₈	—	38	1	no	—
293	C₂²×C₈	—	38	1	no	—
294	C₂²×C₈	Dic₃₈	1	2	yes	—
295	C₂²×C₈	D₇₆	1	2	yes	—
296	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
297	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
298	#117	—	2	1	no	—
299	#117	—	2	1	no	—
300	#117	—	2	1	no	—
301	#117	—	2	1	no	—
302	#117	—	2	1	no	—
303	#117	—	2	1	no	—
304	#117	C₂²⋊D₁₉	1	2	yes	—
305	#117	C₂²⋊D₁₉	1	2	yes	—
306	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
307	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	19	2	no	—
313	C₂×C₄²	—	38	1	no	—
314	C₂×C₄²	—	38	1	no	—
315	C₂×C₄²	—	38	1	no	—
316	C₂×C₄²	—	38	1	no	—
317	C₂×C₄²	—	38	1	no	—
318	#107	—	2	4	no	—
319	#106	—	2	4	no	—
320	C₄⋊C₈	—	38	8	no	—
321	C₁₉	#11221	1	1	yes	characteristic, complemented, Sylow
322	C₂⁴	#64543	1	1	yes	characteristic
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	38	4	no	—
326	C₂²×C₄	—	38	2	no	—
327	C₂²×C₄	—	76	2	no	—
328	C₂²×C₄	—	76	1	no	—
329	C₂²×C₄	—	76	1	no	—
330	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
332	C₂²×C₄	#64541	1	1	yes	characteristic
333	C₂²×C₄	#64541	1	1	yes	characteristic
334	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
335	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
336	C₂²×C₄	#64543	1	1	yes	characteristic
337	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
338	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
339	C₂²×C₄	#64545	1	1	yes	characteristic
340	C₂²×C₄	#64545	1	1	yes	characteristic
341	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
344	M₁₆	—	38	2	no	—
345	M₁₆	—	38	2	no	—
346	M₁₆	—	38	2	no	—
347	M₁₆	—	38	2	no	—
348	M₁₆	—	76	1	no	—
349	M₁₆	—	76	1	no	—
350	M₁₆	—	76	1	no	—
351	M₁₆	—	76	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	38	2	no	—
361	C₂×C₈	—	38	2	no	—
362	C₂×C₈	—	38	2	no	—
363	C₂×C₈	—	38	2	no	—
364	C₂×C₈	—	38	2	no	—
365	C₂×C₈	—	76	1	no	—
366	C₂×C₈	—	76	1	no	—
367	C₂×C₈	—	76	1	no	—
368	C₂×C₈	—	76	1	no	—
369	C₂×C₈	—	76	1	no	—
370	C₂×C₈	—	76	1	no	—
371	C₂×C₈	—	76	1	no	—
372	C₂×C₈	—	76	1	no	—
373	C₂×C₈	C₄⋊Dic₁₉	1	2	yes	—
374	C₂×C₈	C₄⋊Dic₁₉	1	2	yes	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	4	1	no	—
382	C₂²⋊C₄	—	4	1	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	4	1	no	—
386	C₄²	—	4	1	no	—
387	C₄²	—	38	2	no	—
388	C₄²	—	38	2	no	—
389	C₄²	—	76	1	no	—
390	C₄²	—	76	1	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	#10597335	1	1	yes	characteristic
394	C₂³	#10597336	1	1	yes	characteristic
395	C₂³	#10597343	1	1	yes	characteristic
396	C₂³	#10597344	1	1	yes	characteristic
397	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
398	C₂³	#10597381	1	1	yes	characteristic
399	C₂³	#10597385	1	1	yes	characteristic
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	38	4	no	—
407	C₂×C₄	—	76	2	no	—
408	C₂×C₄	—	76	4	no	—
409	C₂×C₄	—	76	4	no	—
410	C₂×C₄	—	76	2	no	—
411	C₂×C₄	#10597334	1	1	yes	characteristic
412	C₂×C₄	#10597334	1	1	yes	characteristic
413	C₂×C₄	#10597335	1	1	yes	characteristic
414	C₂×C₄	#10597336	1	1	yes	characteristic
415	C₂×C₄	#10597340	1	1	yes	characteristic
416	C₂×C₄	#10597340	1	1	yes	characteristic
417	C₂×C₄	#10597341	1	1	yes	characteristic
418	C₂×C₄	#10597341	1	1	yes	characteristic
419	C₂×C₄	#10597342	1	1	yes	characteristic
420	C₂×C₄	#10597342	1	1	yes	characteristic
421	C₂×C₄	#10597343	1	1	yes	characteristic
422	C₂×C₄	#10597344	1	1	yes	characteristic
423	C₂×C₄	#10597370	1	1	yes	characteristic
424	C₂×C₄	#10597370	1	1	yes	characteristic
425	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
426	C₂×C₄	#10597372	1	1	yes	characteristic
427	C₂×C₄	#10597376	1	1	yes	characteristic
428	C₂×C₄	#10597376	1	1	yes	characteristic
429	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
430	C₂×C₄	#10597383	1	1	yes	characteristic
431	C₂×C₄	#10597385	1	1	yes	characteristic
432	C₂×C₄	#10597390	1	1	yes	characteristic
433	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
434	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
435	C₂×C₄	#10597392	1	1	yes	characteristic
436	C₂×C₄	#10597392	1	1	yes	characteristic
437	C₂×C₄	#10597393	1	1	yes	characteristic
438	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
439	C₈	—	2	2	no	—
440	C₈	—	2	2	no	—
441	C₈	—	76	2	no	—
442	C₈	—	76	2	no	—
443	C₈	—	76	2	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	#11926424	1	1	yes	characteristic
453	C₂²	#11926430	1	1	yes	characteristic
454	C₂²	#11926443	1	1	yes	characteristic
455	C₂²	#11926466	1	1	yes	characteristic
456	C₂²	#11926474	1	1	yes	characteristic
457	C₂²	#11926477	1	1	yes	characteristic
458	C₂²	#11926483	1	1	yes	characteristic
459	C₂²	#11926661	1	2	yes	—
460	C₂²	#11926666	1	2	yes	—
461	C₄	—	4	4	no	—
462	C₄	—	8	2	no	—
463	C₄	—	76	4	no	—
464	C₄	#11926404	1	1	yes	characteristic
465	C₄	#11926430	1	1	yes	characteristic
466	C₄	#11926443	1	1	yes	characteristic
467	C₄	#11926451	1	1	yes	characteristic
468	C₄	#11926461	1	1	yes	characteristic
469	C₄	#11926464	1	1	yes	characteristic
470	C₄	#11926466	1	1	yes	characteristic
471	C₄	#11926477	1	1	yes	characteristic
472	C₂	—	2	1	no	—
473	C₂	—	2	1	no	—
474	C₂	—	2	1	no	—
475	C₂	—	2	1	no	—
476	C₂	#14561888	1	1	yes	characteristic
477	C₂	#14563964	1	2	yes	—
478	C₂	#14564236	1	2	yes	—
479	C₂	#14564384	1	1	yes	characteristic
480	C₂	#14564389	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#427	C₂
socle	C₂³×C₁₉	C₄×D₄
prime radical	C₂⁴×C₁₉	#41
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#427	D₁₉
hypocenter	C₁₉	#11221
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#427

Complements

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

N	H ≅ G/N	type
25. C₂×C₁₉×#107	C₄	semidirect
26. C₂×C₁₉×#106	C₄	semidirect
248. C₂×#107	Dic₁₉	semidirect
249. C₂×#106	Dic₁₉	semidirect
321. C₁₉	#11221	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926571	2
C₂×#11926309	2
C₂×#11926303	2
#14563332	2
C₂×#11926298	2
C₂×C₁₉×#427	2
#11221	19