Subgroups — #18090947

Order 4864.

658 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	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	C₁₉×#1735	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×#340	C₄	1	2	yes	complemented
24	C₁₉×#340	C₄	1	2	yes	complemented
25	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂³×Dic₁₉	—	2	1	no	—
27	C₂²×C₈×C₁₉	—	2	1	no	—
28	C₂²×C₈×C₁₉	—	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	2	yes	—
34	C₁₉×#117	—	2	1	no	—
35	C₁₉×#117	—	2	1	no	—
36	C₁₉×#117	—	2	1	no	—
37	C₁₉×#117	—	2	1	no	—
38	C₁₉×#117	—	2	1	no	—
39	C₁₉×#117	—	2	1	no	—
40	C₁₉×#117	D₄	1	2	yes	—
41	C₁₉×#117	Q₈	1	2	yes	—
42	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	—	2	1	no	—
48	C₂×C₄²×C₁₉	—	2	1	no	—
49	C₂×C₄×Dic₁₉	—	2	1	no	—
50	C₂×C₄×Dic₁₉	—	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	D₄	1	2	yes	—
55	C₂×#64520	—	2	1	no	—
56	C₂×#64520	—	2	1	no	—
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	D₄	1	2	yes	—
66	C₂×#64520	Q₈	1	2	yes	—
67	C₂²×C₁₉⋊C₈	—	2	1	no	—
68	C₂²×C₁₉⋊C₈	—	2	1	no	—
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	D₄	1	2	yes	—
76	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
77	C₂⁴×C₁₉	#41	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
95	C₂²×Dic₁₉	—	2	4	no	—
96	C₂²×Dic₁₉	—	2	2	no	—
97	C₂²×Dic₁₉	—	4	2	no	—
98	C₂²×Dic₁₉	—	4	1	no	—
99	C₂²×Dic₁₉	—	4	1	no	—
100	C₂×C₈×C₁₉	—	2	2	no	—
101	C₂×C₈×C₁₉	—	2	2	no	—
102	C₂×C₈×C₁₉	—	2	2	no	—
103	C₂×C₈×C₁₉	—	4	1	no	—
104	C₂×C₈×C₁₉	—	4	1	no	—
105	C₂×C₈×C₁₉	—	4	1	no	—
106	C₂×C₈×C₁₉	—	4	1	no	—
107	C₄⋊C₄×C₁₉	—	2	2	no	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₄⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	—
113	C₂²⋊C₄×C₁₉	—	2	2	no	—
114	C₂²⋊C₄×C₁₉	—	2	2	no	—
115	C₂²⋊C₄×C₁₉	—	4	1	no	—
116	C₂²⋊C₄×C₁₉	—	4	1	no	—
117	C₄²×C₁₉	—	2	2	no	—
118	C₄²×C₁₉	—	2	2	no	—
119	C₄²×C₁₉	—	4	1	no	—
120	C₄²×C₁₉	—	4	1	no	—
121	C₄×Dic₁₉	—	2	2	no	—
122	C₄×Dic₁₉	—	2	2	no	—
123	C₄×Dic₁₉	—	4	1	no	—
124	C₄×Dic₁₉	—	4	1	no	—
125	#64520	—	2	2	no	—
126	#64520	—	2	2	no	—
127	#64520	—	2	2	no	—
128	#64520	—	2	2	no	—
129	#64520	—	4	1	no	—
130	#64520	—	4	1	no	—
131	#64520	—	4	1	no	—
132	#64520	—	4	1	no	—
133	C₂×C₁₉⋊C₈	—	2	2	no	—
134	C₂×C₁₉⋊C₈	—	2	2	no	—
135	C₂×C₁₉⋊C₈	—	2	2	no	—
136	C₂×C₁₉⋊C₈	—	2	2	no	—
137	C₂×C₁₉⋊C₈	—	2	2	no	—
138	C₂×C₁₉⋊C₈	—	4	1	no	—
139	C₂×C₁₉⋊C₈	—	4	1	no	—
140	C₂×C₁₉⋊C₈	—	4	1	no	—
141	C₂×C₁₉⋊C₈	—	4	1	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	#11291	—	19	1	no	maximal, Sylow
147	C₂³×C₁₉	—	2	2	no	—
148	C₂³×C₁₉	—	2	2	no	—
149	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
150	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂³×C₁₉	#123	1	1	yes	characteristic
152	C₂³×C₁₉	#123	1	1	yes	characteristic
153	C₂³×C₁₉	#125	1	1	yes	characteristic
154	C₂³×C₁₉	#126	1	1	yes	characteristic
155	C₂³×C₁₉	#126	1	1	yes	characteristic
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
191	C₂×Dic₁₉	—	2	4	no	—
192	C₂×Dic₁₉	—	4	4	no	—
193	C₂×Dic₁₉	—	4	4	no	—
194	C₂×Dic₁₉	—	4	2	no	—
195	C₂×Dic₁₉	—	4	2	no	—
196	C₈×C₁₉	—	4	2	no	—
197	C₁₉⋊C₈	—	4	2	no	—
198	C₁₉⋊C₈	—	4	2	no	—
199	C₁₉⋊C₈	—	4	2	no	—
200	C₂×#424	—	19	1	no	—
201	C₂×#341	—	19	1	no	—
202	#1735	D₁₉	1	1	yes	characteristic
203	C₂×#339	—	19	1	no	—
204	C₂×#339	—	19	1	no	—
205	#1729	—	19	1	no	—
206	C₂×#336	—	19	1	no	—
207	C₂²×C₁₉	—	2	2	no	—
208	C₂²×C₁₉	—	2	2	no	—
209	C₂²×C₁₉	—	2	2	no	—
210	C₂²×C₁₉	—	2	2	no	—
211	C₂²×C₁₉	—	2	1	no	—
212	C₂²×C₁₉	—	2	1	no	—
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	#385	1	1	yes	characteristic
216	C₂²×C₁₉	#387	1	1	yes	characteristic
217	C₂²×C₁₉	#388	1	1	yes	characteristic
218	C₂²×C₁₉	#397	1	1	yes	characteristic
219	C₂²×C₁₉	#398	1	1	yes	characteristic
220	C₂²×C₁₉	#400	1	1	yes	characteristic
221	C₂²×C₁₉	#400	1	1	yes	characteristic
222	C₂²×C₁₉	#443	1	2	yes	—
223	C₂²×C₁₉	#444	1	2	yes	—
224	C₄×C₁₉	—	4	4	no	—
225	C₄×C₁₉	—	8	1	no	—
226	C₄×C₁₉	—	8	1	no	—
227	C₄×C₁₉	#382	1	1	yes	characteristic
228	C₄×C₁₉	#387	1	1	yes	characteristic
229	C₄×C₁₉	#388	1	1	yes	characteristic
230	C₄×C₁₉	#389	1	1	yes	characteristic
231	C₄×C₁₉	#393	1	1	yes	characteristic
232	C₄×C₁₉	#394	1	1	yes	characteristic
233	C₄×C₁₉	#398	1	1	yes	characteristic
234	C₄×C₁₉	#400	1	1	yes	characteristic
235	Dic₁₉	—	4	4	no	—
236	C₂²×M₁₆	—	19	1	no	—
237	C₂²×M₁₆	—	19	1	no	—
238	C₂³×C₈	—	19	1	no	—
239	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
240	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
241	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
242	C₂²×C₄²	—	19	1	no	—
243	#424	—	38	2	no	—
244	#424	—	38	2	no	—
245	C₂×C₄⋊C₈	—	38	2	no	—
246	#341	—	38	2	no	—
247	#340	Dic₁₉	1	2	yes	complemented
248	#340	Dic₁₉	1	2	yes	complemented
249	#339	—	38	2	no	—
250	#339	—	38	2	no	—
251	#336	—	38	2	no	—
252	#336	—	38	2	no	—
253	C₂×C₁₉	—	2	1	no	—
254	C₂×C₁₉	—	2	1	no	—
255	C₂×C₁₉	—	2	1	no	—
256	C₂×C₁₉	—	2	1	no	—
257	C₂×C₁₉	#1442	1	1	yes	characteristic
258	C₂×C₁₉	#1866	1	2	yes	—
259	C₂×C₁₉	#1922	1	2	yes	—
260	C₂×C₁₉	#1937	1	1	yes	characteristic
261	C₂×C₁₉	#1938	1	1	yes	characteristic
262	C₂³×C₄	—	38	1	no	—
263	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
264	C₂×M₁₆	—	19	2	no	—
265	C₂×M₁₆	—	19	2	no	—
266	C₂×M₁₆	—	38	1	no	—
267	C₂×M₁₆	—	38	1	no	—
268	C₂×M₁₆	—	38	1	no	—
269	C₂×M₁₆	—	38	1	no	—
270	C₂×M₁₆	—	38	1	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	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	19	2	no	—
283	C₂²×C₈	—	38	1	no	—
284	C₂²×C₈	—	38	1	no	—
285	C₂²×C₈	—	38	1	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	C₂×Dic₁₉	1	2	yes	—
292	#117	—	2	1	no	—
293	#117	—	2	1	no	—
294	#117	—	2	1	no	—
295	#117	—	2	1	no	—
296	#117	—	2	1	no	—
297	#117	—	2	1	no	—
298	#117	Dic₃₈	1	2	yes	—
299	#117	D₇₆	1	2	yes	—
300	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	—	19	2	no	—
308	C₂×C₄²	—	38	1	no	—
309	C₂×C₄²	—	38	1	no	—
310	C₂×C₄²	—	38	1	no	—
311	C₂×C₄²	—	38	1	no	—
312	C₂×C₄²	—	38	1	no	—
313	C₄⋊C₈	—	38	8	no	—
314	C₁₉	#11291	1	1	yes	characteristic, complemented, Sylow
315	C₂⁴	#64543	1	1	yes	characteristic
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	38	4	no	—
320	C₂²×C₄	—	38	2	no	—
321	C₂²×C₄	—	76	2	no	—
322	C₂²×C₄	—	76	1	no	—
323	C₂²×C₄	—	76	1	no	—
324	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
326	C₂²×C₄	#64541	1	1	yes	characteristic
327	C₂²×C₄	#64541	1	1	yes	characteristic
328	C₂²×C₄	#64541	1	1	yes	characteristic
329	C₂²×C₄	#64541	1	1	yes	characteristic
330	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
331	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
332	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
333	C₂²×C₄	#64543	1	1	yes	characteristic
334	C₂²×C₄	#64543	1	1	yes	characteristic
335	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
336	C₂²×C₄	#64545	1	1	yes	characteristic
337	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
338	M₁₆	—	38	2	no	—
339	M₁₆	—	38	2	no	—
340	M₁₆	—	38	2	no	—
341	M₁₆	—	38	2	no	—
342	M₁₆	—	76	1	no	—
343	M₁₆	—	76	1	no	—
344	M₁₆	—	76	1	no	—
345	M₁₆	—	76	1	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	4	1	no	—
353	C₂×C₈	—	38	2	no	—
354	C₂×C₈	—	38	2	no	—
355	C₂×C₈	—	38	2	no	—
356	C₂×C₈	—	38	2	no	—
357	C₂×C₈	—	38	2	no	—
358	C₂×C₈	—	76	1	no	—
359	C₂×C₈	—	76	1	no	—
360	C₂×C₈	—	76	1	no	—
361	C₂×C₈	—	76	1	no	—
362	C₂×C₈	—	76	1	no	—
363	C₂×C₈	—	76	1	no	—
364	C₂×C₈	—	76	1	no	—
365	C₂×C₈	—	76	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	C₄⋊Dic₁₉	1	4	yes	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	4	1	no	—
375	C₂²⋊C₄	—	4	1	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	4	1	no	—
379	C₄²	—	4	1	no	—
380	C₄²	—	38	2	no	—
381	C₄²	—	38	2	no	—
382	C₄²	—	76	1	no	—
383	C₄²	—	76	1	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	#10597324	1	1	yes	characteristic
387	C₂³	#10597325	1	1	yes	characteristic
388	C₂³	#10597329	1	1	yes	characteristic
389	C₂³	#10597332	1	1	yes	characteristic
390	C₂³	#10597335	1	1	yes	characteristic
391	C₂³	#10597344	1	1	yes	characteristic
392	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	38	4	no	—
401	C₂×C₄	—	76	4	no	—
402	C₂×C₄	—	76	4	no	—
403	C₂×C₄	—	76	2	no	—
404	C₂×C₄	—	76	2	no	—
405	C₂×C₄	#10597316	1	1	yes	characteristic
406	C₂×C₄	#10597316	1	1	yes	characteristic
407	C₂×C₄	#10597321	1	1	yes	characteristic
408	C₂×C₄	#10597321	1	1	yes	characteristic
409	C₂×C₄	#10597324	1	1	yes	characteristic
410	C₂×C₄	#10597325	1	1	yes	characteristic
411	C₂×C₄	#10597328	1	1	yes	characteristic
412	C₂×C₄	#10597329	1	1	yes	characteristic
413	C₂×C₄	#10597330	1	1	yes	characteristic
414	C₂×C₄	#10597330	1	1	yes	characteristic
415	C₂×C₄	#10597331	1	1	yes	characteristic
416	C₂×C₄	#10597331	1	1	yes	characteristic
417	C₂×C₄	#10597334	1	1	yes	characteristic
418	C₂×C₄	#10597335	1	1	yes	characteristic
419	C₂×C₄	#10597336	1	1	yes	characteristic
420	C₂×C₄	#10597340	1	1	yes	characteristic
421	C₂×C₄	#10597340	1	1	yes	characteristic
422	C₂×C₄	#10597341	1	1	yes	characteristic
423	C₂×C₄	#10597342	1	1	yes	characteristic
424	C₂×C₄	#10597342	1	1	yes	characteristic
425	C₂×C₄	#10597343	1	1	yes	characteristic
426	C₂×C₄	#10597344	1	1	yes	characteristic
427	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
428	C₂×C₄	#10597372	1	1	yes	characteristic
429	C₂×C₄	#10597372	1	1	yes	characteristic
430	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
431	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
432	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
433	C₈	—	4	2	no	—
434	C₈	—	76	2	no	—
435	C₈	—	76	2	no	—
436	C₈	—	76	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	#11926419	1	1	yes	characteristic
446	C₂²	#11926430	1	1	yes	characteristic
447	C₂²	#11926437	1	1	yes	characteristic
448	C₂²	#11926471	1	1	yes	characteristic
449	C₂²	#11926478	1	1	yes	characteristic
450	C₂²	#11926484	1	1	yes	characteristic
451	C₂²	#11926486	1	1	yes	characteristic
452	C₂²	#11926661	1	2	yes	—
453	C₂²	#11926666	1	2	yes	—
454	C₄	—	4	4	no	—
455	C₄	—	8	1	no	—
456	C₄	—	8	1	no	—
457	C₄	—	76	4	no	—
458	C₄	#11926410	1	1	yes	characteristic
459	C₄	#11926430	1	1	yes	characteristic
460	C₄	#11926437	1	1	yes	characteristic
461	C₄	#11926443	1	1	yes	characteristic
462	C₄	#11926457	1	1	yes	characteristic
463	C₄	#11926462	1	1	yes	characteristic
464	C₄	#11926478	1	1	yes	characteristic
465	C₄	#11926486	1	1	yes	characteristic
466	C₂	—	2	1	no	—
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	—	2	1	no	—
470	C₂	#14561892	1	1	yes	characteristic
471	C₂	#14563912	1	2	yes	—
472	C₂	#14564236	1	2	yes	—
473	C₂	#14564341	1	1	yes	characteristic
474	C₂	#14564348	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1735	C₂
socle	C₂³×C₁₉	C₄×D₄
prime radical	C₂⁴×C₁₉	#41
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1735	D₁₉
hypocenter	C₁₉	#11291
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ #1735

Complements

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

N	H ≅ G/N	type
23. C₁₉×#340	C₄	semidirect
24. C₁₉×#340	C₄	semidirect
247. #340	Dic₁₉	semidirect
248. #340	Dic₁₉	semidirect
314. C₁₉	#11291	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
C₁₉×#1735	2
#11291	19