Subgroups — #18073540

Order 4864.

522 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572330	C₂	1	1	yes	maximal, characteristic
2	#14563413	C₂	1	1	yes	maximal, characteristic, complemented
3	#14563409	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562126	C₂	1	1	yes	maximal, characteristic
5	#14561523	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561521	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1501	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597394	C₄	1	1	yes	characteristic, complemented
9	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	#11926616	—	2	1	no	—
11	#11926616	—	2	1	no	—
12	D₄×C₁₉⋊C₈	—	2	1	no	—
13	D₄×C₁₉⋊C₈	—	2	1	no	—
14	#11926571	C₄	1	1	yes	characteristic, complemented
15	#11926511	C₄	1	1	yes	characteristic, complemented
16	#11926508	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
18	#11926500	C₄	1	1	yes	characteristic, complemented
19	C₂×#10597260	—	2	1	no	—
20	C₂×C₈×Dic₁₉	—	2	1	no	—
21	C₄×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
22	#11926299	—	2	1	no	—
23	#11926298	—	2	1	no	—
24	#11926281	C₄	1	2	yes	complemented
25	#11926278	C₄	1	2	yes	complemented
26	C₁₉×#525	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#328	C₄	1	2	yes	complemented
30	C₁₉×#327	C₄	1	2	yes	complemented
31	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₁₉×#123	—	2	1	no	—
35	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
36	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
37	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
38	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
39	C₁₉×#120	—	2	1	no	—
40	C₄×D₄×C₁₉	—	2	1	no	—
41	C₄×D₄×C₁₉	—	2	1	no	—
42	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₄²×C₁₉	—	2	1	no	—
45	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
46	#10597394	—	4	2	no	—
47	C₂×C₄×Dic₁₉	—	2	1	no	—
48	C₂×#64520	—	2	1	no	—
49	C₂×#64520	C₂×C₄	1	1	yes	characteristic
50	C₂×#64520	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₁₉⋊C₈	—	2	1	no	—
52	C₂²×C₁₉⋊C₈	—	2	1	no	—
53	C₂²×C₁₉⋊C₈	—	4	2	no	—
54	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
57	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
58	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
59	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
60	C₁₉×C₂²⋊C₈	—	2	1	no	—
61	C₁₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
62	C₁₉×#95	C₂×C₄	1	2	yes	—
63	C₁₉⋊#95	C₂×C₄	1	2	yes	—
64	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
67	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
68	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
69	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
70	C₈×Dic₁₉	—	4	2	no	—
71	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
72	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
73	#10597260	—	2	1	no	—
74	#10597260	—	4	2	no	—
75	C₄×C₁₉⋊C₈	—	2	1	no	—
76	C₂⁴×C₁₉	#41	1	1	yes	characteristic
77	#41×C₁₉	—	4	1	no	—
78	#41×C₁₉	—	4	1	no	—
79	C₂×Q₈×C₁₉	C₄²	1	1	yes	characteristic
80	C₂×D₄×C₁₉	—	2	1	no	—
81	C₂×D₄×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	—	2	1	no	—
83	C₂×D₄×C₁₉	C₄²	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
94	C₂²×Dic₁₉	—	2	2	no	—
95	C₂×C₈×C₁₉	—	2	2	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₂×C₈×C₁₉	—	4	1	no	—
98	C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₄⋊C₄×C₁₉	C₄²	1	1	yes	characteristic
101	C₄⋊C₄×C₁₉	C₄²	1	1	yes	characteristic
102	C₂²⋊C₄×C₁₉	—	2	1	no	—
103	C₂²⋊C₄×C₁₉	—	2	1	no	—
104	C₂²⋊C₄×C₁₉	—	2	1	no	—
105	C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂²⋊C₄×C₁₉	—	2	1	no	—
107	C₂²⋊C₄×C₁₉	—	4	2	no	—
108	C₄²×C₁₉	—	2	1	no	—
109	C₄²×C₁₉	—	4	1	no	—
110	C₄²×C₁₉	—	4	1	no	—
111	C₂²⋊Dic₁₉	—	2	4	no	—
112	C₄×Dic₁₉	—	4	1	no	—
113	C₄×Dic₁₉	—	4	1	no	—
114	#64520	—	4	2	no	—
115	#64520	—	4	1	no	—
116	#64520	—	4	1	no	—
117	C₂×C₁₉⋊C₈	—	2	2	no	—
118	C₂×C₁₉⋊C₈	—	2	2	no	—
119	C₂×C₁₉⋊C₈	—	2	2	no	—
120	C₂×C₁₉⋊C₈	—	2	1	no	—
121	C₂×C₁₉⋊C₈	—	2	1	no	—
122	C₂×C₁₉⋊C₈	—	2	2	no	—
123	C₂×C₁₉⋊C₈	—	4	1	no	—
124	C₂×C₁₉⋊C₈	—	4	1	no	—
125	C₂×C₁₉⋊C₈	—	4	1	no	—
126	C₂×C₁₉⋊C₈	—	4	2	no	—
127	C₂×C₁₉⋊C₈	—	4	1	no	—
128	C₂×C₁₉⋊C₈	—	4	1	no	—
129	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
133	#8240	—	19	1	no	maximal, Sylow
134	C₂³×C₁₉	—	2	2	no	—
135	C₂³×C₁₉	—	2	2	no	—
136	C₂³×C₁₉	—	2	1	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	#117	1	1	yes	characteristic
139	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
140	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
141	Q₈×C₁₉	—	4	1	no	—
142	D₄×C₁₉	—	4	1	no	—
143	D₄×C₁₉	—	4	2	no	—
144	D₄×C₁₉	—	4	2	no	—
145	D₄×C₁₉	—	4	2	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	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	2	1	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
167	C₂×Dic₁₉	—	2	4	no	—
168	C₂×Dic₁₉	—	4	2	no	—
169	C₂×Dic₁₉	—	4	2	no	—
170	C₈×C₁₉	—	4	2	no	—
171	C₁₉⋊C₈	—	2	1	no	—
172	C₁₉⋊C₈	—	2	1	no	—
173	C₁₉⋊C₈	—	2	1	no	—
174	C₁₉⋊C₈	—	4	2	no	—
175	C₁₉⋊C₈	—	4	1	no	—
176	C₁₉⋊C₈	—	4	1	no	—
177	C₁₉⋊C₈	#99	1	2	yes	—
178	#2929	—	19	1	no	—
179	#1752	—	19	1	no	—
180	C₈×C₂²⋊C₄	—	19	1	no	—
181	#1501	—	19	1	no	—
182	#1501	D₁₉	1	1	yes	characteristic
183	#1298	—	19	1	no	—
184	#1297	—	19	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	—	2	1	no	—
188	C₂²×C₁₉	—	2	1	no	—
189	C₂²×C₁₉	—	2	1	no	—
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	4	4	no	—
193	C₂²×C₁₉	—	4	1	no	—
194	C₂²×C₁₉	—	4	1	no	—
195	C₂²×C₁₉	—	4	1	no	—
196	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
197	C₂²×C₁₉	#443	1	2	yes	—
198	C₂²×C₁₉	#444	1	2	yes	—
199	C₄×C₁₉	—	2	1	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	4	1	no	—
203	C₄×C₁₉	—	4	1	no	—
204	C₄×C₁₉	—	4	1	no	—
205	C₄×C₁₉	—	8	2	no	—
206	C₄×C₁₉	C₂×#99	1	1	yes	characteristic
207	C₄×C₁₉	#410	1	1	yes	characteristic
208	Dic₁₉	—	4	4	no	—
209	C₂×#131	—	19	1	no	—
210	C₂³×C₈	—	19	1	no	—
211	#525	C₂×D₁₉	1	1	yes	characteristic
212	#435	—	38	1	no	—
213	#435	—	38	1	no	—
214	C₈×D₄	—	38	1	no	—
215	C₈×D₄	—	38	1	no	—
216	#424	—	19	1	no	—
217	#408	—	19	1	no	—
218	#407	—	19	1	no	—
219	C₂×C₂²⋊C₈	—	19	1	no	—
220	C₂×C₂²⋊C₈	C₂×D₁₉	1	1	yes	characteristic
221	#405	—	19	1	no	—
222	C₂×#97	—	38	1	no	—
223	C₂×C₄×C₈	—	38	1	no	—
224	C₄×C₂²⋊C₄	—	19	1	no	—
225	C₄×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
226	#336	—	38	1	no	—
227	#336	—	38	1	no	—
228	#328	—	19	2	no	—
229	#328	Dic₁₉	1	2	yes	complemented
230	#327	—	19	2	no	—
231	#327	Dic₁₉	1	2	yes	complemented
232	C₂×C₁₉	—	2	2	no	—
233	C₂×C₁₉	—	2	2	no	—
234	C₂×C₁₉	—	4	1	no	—
235	C₂×C₁₉	—	8	1	no	—
236	C₂×C₁₉	C₄×#99	1	1	yes	characteristic
237	C₂×C₁₉	#1764	1	1	yes	characteristic
238	C₂×C₁₉	#1765	1	1	yes	characteristic
239	C₂×#41	C₄×D₁₉	1	1	yes	characteristic
240	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
241	#131	—	76	2	no	—
242	C₂×M₁₆	—	19	1	no	—
243	C₂×M₁₆	—	19	1	no	—
244	C₂×M₁₆	—	38	1	no	—
245	C₂²×C₈	—	2	1	no	—
246	C₂²×C₈	—	19	1	no	—
247	C₂²×C₈	—	19	1	no	—
248	C₂²×C₈	—	19	1	no	—
249	C₂²×C₈	—	19	1	no	—
250	C₂²×C₈	—	19	1	no	—
251	C₂²×C₈	—	19	1	no	—
252	C₂²×C₈	—	38	1	no	—
253	C₂²×C₈	—	38	1	no	—
254	C₂²×C₈	—	76	2	no	—
255	#123	—	2	1	no	—
256	C₂²⋊Q₈	C₄×D₁₉	1	1	yes	characteristic
257	C₂²⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
258	#121	C₄×D₁₉	1	1	yes	characteristic
259	#121	C₂×Dic₁₉	1	1	yes	characteristic
260	#120	—	2	1	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	#117	C₄×D₁₉	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	38	1	no	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	—	38	1	no	—
268	C₄⋊C₈	—	38	1	no	—
269	C₄⋊C₈	—	38	1	no	—
270	C₂²⋊C₈	—	2	1	no	—
271	C₂²⋊C₈	—	19	2	no	—
272	C₂²⋊C₈	—	38	1	no	—
273	C₂²⋊C₈	—	38	1	no	—
274	C₂²⋊C₈	—	38	1	no	—
275	C₂²⋊C₈	—	38	1	no	—
276	C₂²⋊C₈	—	38	1	no	—
277	C₂²⋊C₈	C₂×Dic₁₉	1	2	yes	—
278	#97	—	38	1	no	—
279	#97	—	76	2	no	—
280	C₄×C₈	—	38	1	no	—
281	C₄×C₈	—	76	2	no	—
282	#95	—	19	2	no	—
283	#95	C₂×Dic₁₉	1	2	yes	—
284	C₁₉	#8240	1	1	yes	characteristic, complemented, Sylow
285	C₂⁴	#64543	1	1	yes	characteristic
286	#41	—	4	1	no	—
287	#41	—	4	1	no	—
288	C₂×Q₈	C₄×Dic₁₉	1	1	yes	characteristic
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	C₄×Dic₁₉	1	1	yes	characteristic
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	38	2	no	—
298	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
300	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
301	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
302	C₂²×C₄	#64543	1	1	yes	characteristic
303	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
304	M₁₆	—	76	2	no	—
305	M₁₆	—	76	1	no	—
306	M₁₆	—	76	1	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	—	19	1	no	—
311	C₂×C₈	—	19	1	no	—
312	C₂×C₈	—	19	1	no	—
313	C₂×C₈	—	19	1	no	—
314	C₂×C₈	—	38	2	no	—
315	C₂×C₈	—	38	2	no	—
316	C₂×C₈	—	38	2	no	—
317	C₂×C₈	—	38	1	no	—
318	C₂×C₈	—	38	1	no	—
319	C₂×C₈	—	38	2	no	—
320	C₂×C₈	—	76	1	no	—
321	C₂×C₈	—	76	1	no	—
322	C₂×C₈	—	76	1	no	—
323	C₂×C₈	—	76	2	no	—
324	C₂×C₈	—	76	1	no	—
325	C₂×C₈	—	76	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	C₄×Dic₁₉	1	1	yes	characteristic
329	C₄⋊C₄	C₄×Dic₁₉	1	1	yes	characteristic
330	C₂²⋊C₄	—	2	1	no	—
331	C₂²⋊C₄	—	2	1	no	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	2	1	no	—
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	38	4	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	4	1	no	—
339	C₄²	—	4	1	no	—
340	C₄²	—	76	1	no	—
341	C₄²	—	76	1	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	4	1	no	—
346	C₂³	#10597323	1	1	yes	characteristic
347	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
348	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
349	Q₈	—	4	1	no	—
350	D₄	—	4	1	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	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	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	38	4	no	—
372	C₂×C₄	—	76	2	no	—
373	C₂×C₄	—	76	2	no	—
374	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
375	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
376	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
377	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
378	C₈	—	4	2	no	—
379	C₈	—	19	2	no	—
380	C₈	—	38	1	no	—
381	C₈	—	38	1	no	—
382	C₈	—	38	1	no	—
383	C₈	—	76	2	no	—
384	C₈	—	76	1	no	—
385	C₈	—	76	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
398	C₂²	#11926661	1	2	yes	—
399	C₂²	#11926663	1	2	yes	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	4	1	no	—
406	C₄	—	8	2	no	—
407	C₄	—	76	4	no	—
408	C₄	#99×D₁₉	1	1	yes	characteristic
409	C₄	#11926516	1	1	yes	characteristic
410	C₂	—	2	2	no	—
411	C₂	—	2	2	no	—
412	C₂	—	4	1	no	—
413	C₂	—	8	1	no	—
414	C₂	#99×Dic₁₉	1	1	yes	characteristic
415	C₂	#14563475	1	1	yes	characteristic
416	C₂	#14563480	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1501	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	C₁₉×#525	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1501	D₁₉
hypocenter	C₁₉	#8240
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1501

Complements

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

N	H ≅ G/N	type
2. #14563413	C₂	semidirect
3. #14563409	C₂	semidirect
5. #14561523	C₂	semidirect
6. #14561521	C₂	semidirect
8. C₂×#10597394	C₄	semidirect
14. #11926571	C₄	semidirect
15. #11926511	C₄	semidirect
18. #11926500	C₄	semidirect
24. #11926281	C₄	semidirect
25. #11926278	C₄	semidirect
29. C₁₉×#328	C₄	semidirect
30. C₁₉×#327	C₄	semidirect
229. #328	Dic₁₉	semidirect
231. #327	Dic₁₉	semidirect
284. C₁₉	#8240	semidirect

Maximal subgroups

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

subgroup	index
#14572330	2
#14563413	2
#14563409	2
#14562126	2
#14561523	2
#14561521	2
C₁₉×#1501	2
#8240	19