Subgroups — #18078624

Order 4864.

478 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	#41×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#14563655	C₂	1	1	yes	maximal, characteristic
3	#14562134	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562090	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561532	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3076	C₂	1	1	yes	maximal, characteristic
8	Q₈×C₁₉⋊C₈	—	2	1	no	—
9	D₄×C₁₉⋊C₈	—	2	2	no	—
10	D₄×C₁₉⋊C₈	—	2	1	no	—
11	#11926597	—	2	1	no	—
12	#11926597	C₂²	1	1	yes	characteristic
13	#11926568	C₂²	1	1	yes	characteristic
14	C₂×#10597294	—	2	1	no	—
15	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
16	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
18	#11926303	—	2	1	no	—
19	#11926281	—	2	2	no	—
20	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
21	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
22	C₁₉×#533	C₂²	1	1	yes	characteristic
23	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#479	—	2	1	no	—
25	C₁₉×#478	—	2	1	no	—
26	C₁₉×#477	C₄	1	1	yes	characteristic, complemented
27	C₁₉×#476	C₄	1	1	yes	characteristic, complemented
28	C₁₉×#475	C₄	1	1	yes	characteristic, complemented
29	C₁₉×#474	C₄	1	1	yes	characteristic, complemented
30	C₁₉×#427	—	2	1	no	—
31	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₁₉×#416	—	2	1	no	—
33	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₉	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
36	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
37	C₁₉×#125	—	2	1	no	—
38	C₁₉×C₂²⋊Q₈	—	2	1	no	—
39	C₁₉×C₂²⋊Q₈	—	2	1	no	—
40	C₄×Q₈×C₁₉	—	2	1	no	—
41	C₄×Q₈×C₁₉	—	2	1	no	—
42	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
44	C₄×D₄×C₁₉	—	2	1	no	—
45	C₄×D₄×C₁₉	—	2	1	no	—
46	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
48	C₁₉×#117	—	2	1	no	—
49	C₁₉×#117	—	2	1	no	—
50	C₁₉×#117	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₉	—	2	1	no	—
52	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊Dic₁₉	—	2	1	no	—
54	C₂×C₄×Dic₁₉	—	2	1	no	—
55	C₂×#64520	—	2	1	no	—
56	C₂²×C₁₉⋊C₈	—	2	2	no	—
57	C₂²×C₁₉⋊C₈	—	2	1	no	—
58	C₁₉×#107	—	2	1	no	—
59	C₁₉×#107	—	2	1	no	—
60	C₁₉×#106	—	2	1	no	—
61	C₁₉×#106	—	2	1	no	—
62	C₁₉×C₄⋊C₈	—	2	1	no	—
63	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
64	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
65	C₁₉×#103	—	2	1	no	—
66	C₁₉×#103	—	2	1	no	—
67	C₁₉×#102	—	2	1	no	—
68	C₁₉×#102	—	2	1	no	—
69	#10597294	—	4	2	no	—
70	C₁₉⋊#95	—	2	1	no	—
71	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
72	C₂²⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
73	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
74	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
75	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
76	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
77	C₄×C₁₉⋊C₈	—	2	2	no	—
78	C₄×C₁₉⋊C₈	—	2	1	no	—
79	C₄×C₁₉⋊C₈	—	2	1	no	—
80	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
81	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
82	#41×C₁₉	—	2	1	no	—
83	#41×C₁₉	—	2	1	no	—
84	#41×C₁₉	SD₁₆	1	2	yes	—
85	#41×C₁₉	Q₁₆	1	2	yes	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	2	1	no	—
88	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×D₄×C₁₉	—	2	1	no	—
90	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
97	C₂²×Dic₁₉	—	4	1	no	—
98	C₂×C₈×C₁₉	—	2	1	no	—
99	C₂×C₈×C₁₉	—	2	1	no	—
100	C₂×C₈×C₁₉	—	4	1	no	—
101	C₂×C₈×C₁₉	—	4	1	no	—
102	C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	4	1	no	—
109	C₄⋊C₄×C₁₉	—	4	1	no	—
110	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
111	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂²⋊C₄×C₁₉	—	4	1	no	—
116	C₄²×C₁₉	—	2	1	no	—
117	C₄²×C₁₉	—	2	1	no	—
118	C₄²×C₁₉	—	2	1	no	—
119	C₄²×C₁₉	—	4	1	no	—
120	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₁₉	#41	1	1	yes	characteristic
124	C₄⋊Dic₁₉	—	2	2	no	—
125	C₄⋊Dic₁₉	—	4	1	no	—
126	C₄×Dic₁₉	—	4	1	no	—
127	C₄×Dic₁₉	—	4	1	no	—
128	#64520	—	4	1	no	—
129	#64520	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	2	1	no	—
131	C₂×C₁₉⋊C₈	—	2	2	no	—
132	C₂×C₁₉⋊C₈	—	2	1	no	—
133	C₂×C₁₉⋊C₈	—	4	2	no	—
134	C₂×C₁₉⋊C₈	—	4	4	no	—
135	C₂×C₁₉⋊C₈	—	4	1	no	—
136	#9207	—	19	1	no	maximal, Sylow
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	#121	1	1	yes	characteristic
139	Q₈×C₁₉	—	2	1	no	—
140	Q₈×C₁₉	—	4	1	no	—
141	Q₈×C₁₉	—	4	1	no	—
142	Q₈×C₁₉	—	8	1	no	—
143	Q₈×C₁₉	#103	1	2	yes	—
144	D₄×C₁₉	—	2	2	no	—
145	D₄×C₁₉	—	2	2	no	—
146	D₄×C₁₉	—	2	1	no	—
147	D₄×C₁₉	#103	1	2	yes	—
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	2	no	—
152	C₂×C₄×C₁₉	—	2	2	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	2	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	1	no	—
161	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
171	C₂×Dic₁₉	—	4	2	no	—
172	C₂×Dic₁₉	—	8	1	no	—
173	C₂×Dic₁₉	—	8	1	no	—
174	C₈×C₁₉	—	4	1	no	—
175	C₈×C₁₉	—	4	1	no	—
176	C₁₉⋊C₈	—	2	2	no	—
177	C₁₉⋊C₈	—	4	2	no	—
178	C₁₉⋊C₈	—	4	1	no	—
179	C₁₉⋊C₈	—	8	1	no	—
180	#3076	D₁₉	1	1	yes	characteristic
181	C₈×#41	—	19	1	no	—
182	#1806	—	19	1	no	—
183	#1503	—	19	1	no	—
184	#1493	—	19	1	no	—
185	#1301	—	19	1	no	—
186	#1279	—	19	1	no	—
187	C₂²×C₁₉	—	2	1	no	—
188	C₂²×C₁₉	—	2	1	no	—
189	C₂²×C₁₉	—	2	2	no	—
190	C₂²×C₁₉	—	4	1	no	—
191	C₂²×C₁₉	—	4	1	no	—
192	C₂²×C₁₉	#386	1	1	yes	characteristic
193	C₂²×C₁₉	#465	1	1	yes	characteristic
194	C₂²×C₁₉	#467	1	1	yes	characteristic
195	C₄×C₁₉	—	2	1	no	—
196	C₄×C₁₉	—	2	2	no	—
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	2	1	no	—
199	C₄×C₁₉	—	4	1	no	—
200	C₄×C₁₉	—	4	1	no	—
201	C₄×C₁₉	—	8	1	no	—
202	C₄×C₁₉	—	8	1	no	—
203	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
204	C₄×C₁₉	#416	1	1	yes	characteristic
205	C₄×C₁₉	#443	1	1	yes	characteristic
206	C₄×C₁₉	#444	1	1	yes	characteristic
207	C₄×C₁₉	#465	1	1	yes	characteristic
208	C₄×C₁₉	#467	1	1	yes	characteristic
209	Dic₁₉	—	8	2	no	—
210	#533	C₂×D₁₉	1	1	yes	characteristic
211	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
212	#479	—	2	1	no	—
213	#478	—	2	1	no	—
214	#477	Dic₁₉	1	1	yes	characteristic, complemented
215	#476	Dic₁₉	1	1	yes	characteristic, complemented
216	#475	Dic₁₉	1	1	yes	characteristic, complemented
217	#474	Dic₁₉	1	1	yes	characteristic, complemented
218	C₈×Q₈	—	38	1	no	—
219	C₈×D₄	—	38	2	no	—
220	C₈×D₄	—	38	1	no	—
221	#431	—	19	1	no	—
222	#431	—	38	1	no	—
223	#427	—	2	1	no	—
224	#423	—	19	1	no	—
225	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
226	C₂×#104	—	38	1	no	—
227	#416	—	2	1	no	—
228	C₂×C₄×C₈	—	19	1	no	—
229	C₂×C₄×C₈	—	38	1	no	—
230	C₄×C₄⋊C₄	—	19	1	no	—
231	#339	—	38	1	no	—
232	#328	—	38	2	no	—
233	Q₈⋊C₈	—	38	1	no	—
234	Q₈⋊C₈	—	38	1	no	—
235	C₂×C₁₉	—	2	1	no	—
236	C₂×C₁₉	—	2	1	no	—
237	C₂×C₁₉	—	4	2	no	—
238	C₂×C₁₉	#1876	1	1	yes	characteristic
239	C₂×C₁₉	#1892	1	1	yes	characteristic
240	C₂×C₁₉	#1906	1	1	yes	characteristic
241	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
242	C₂×M₁₆	—	38	1	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	38	2	no	—
245	C₂²×C₈	—	38	1	no	—
246	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
247	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
248	#125	—	2	1	no	—
249	C₂²⋊Q₈	—	2	1	no	—
250	C₂²⋊Q₈	—	2	1	no	—
251	C₄×Q₈	—	2	1	no	—
252	C₄×Q₈	—	2	1	no	—
253	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
254	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
258	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
259	#117	—	2	1	no	—
260	#117	—	2	1	no	—
261	#117	C₂²⋊D₁₉	1	1	yes	characteristic
262	C₂×C₄⋊C₄	—	38	1	no	—
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	—	38	1	no	—
265	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
266	#107	—	2	1	no	—
267	#107	—	2	1	no	—
268	#106	—	2	1	no	—
269	#106	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	38	2	no	—
272	C₄⋊C₈	—	38	1	no	—
273	C₄⋊C₈	—	38	1	no	—
274	C₄⋊C₈	—	38	1	no	—
275	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
276	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
277	#104	—	76	2	no	—
278	#103	—	2	1	no	—
279	#103	—	2	1	no	—
280	#102	—	2	1	no	—
281	#102	—	2	1	no	—
282	C₂²⋊C₈	—	19	2	no	—
283	C₂²⋊C₈	—	38	2	no	—
284	C₄×C₈	—	19	1	no	—
285	C₄×C₈	—	19	1	no	—
286	C₄×C₈	—	38	2	no	—
287	C₄×C₈	—	38	1	no	—
288	C₄×C₈	—	38	1	no	—
289	#95	—	38	1	no	—
290	C₁₉	#9207	1	1	yes	characteristic, complemented, Sylow
291	#41	—	2	1	no	—
292	#41	—	2	1	no	—
293	#41	#64527	1	2	yes	—
294	#41	#64528	1	2	yes	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	76	1	no	—
304	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
305	C₂²×C₄	#64543	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
307	M₁₆	—	76	1	no	—
308	M₁₆	—	76	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	38	1	no	—
314	C₂×C₈	—	38	1	no	—
315	C₂×C₈	—	38	2	no	—
316	C₂×C₈	—	76	2	no	—
317	C₂×C₈	—	76	4	no	—
318	C₂×C₈	—	76	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	38	2	no	—
328	C₄⋊C₄	—	76	1	no	—
329	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
330	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
331	C₂²⋊C₄	—	2	1	no	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	2	1	no	—
334	C₂²⋊C₄	—	4	1	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	4	1	no	—
339	C₄²	—	76	1	no	—
340	C₄²	—	76	1	no	—
341	C₄²	D₄×D₁₉	1	1	yes	characteristic
342	C₄²	#64543	1	1	yes	characteristic
343	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
344	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
345	C₂³	—	2	1	no	—
346	C₂³	#10597385	1	1	yes	characteristic
347	Q₈	—	2	1	no	—
348	Q₈	—	4	1	no	—
349	Q₈	—	4	1	no	—
350	Q₈	—	8	1	no	—
351	Q₈	#10597292	1	2	yes	—
352	D₄	—	2	2	no	—
353	D₄	—	2	2	no	—
354	D₄	—	2	1	no	—
355	D₄	#10597292	1	2	yes	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	76	2	no	—
370	C₂×C₄	—	152	1	no	—
371	C₂×C₄	—	152	1	no	—
372	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
373	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
374	C₂×C₄	#10597381	1	1	yes	characteristic
375	C₂×C₄	#10597383	1	1	yes	characteristic
376	C₂×C₄	#10597385	1	1	yes	characteristic
377	C₂×C₄	C₂×#64527	1	1	yes	characteristic
378	C₂×C₄	C₂×#64528	1	1	yes	characteristic
379	C₂×C₄	#10597396	1	1	yes	characteristic
380	C₂×C₄	#10597396	1	1	yes	characteristic
381	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
382	C₈	—	4	1	no	—
383	C₈	—	4	1	no	—
384	C₈	—	38	2	no	—
385	C₈	—	76	1	no	—
386	C₈	—	76	2	no	—
387	C₈	—	152	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	#11926424	1	1	yes	characteristic
394	C₂²	#11926775	1	1	yes	characteristic
395	C₂²	#11926783	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	2	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	1	no	—
404	C₄	—	152	2	no	—
405	C₄	C₂×#10597292	1	1	yes	characteristic
406	C₄	#11926540	1	1	yes	characteristic
407	C₄	#11926661	1	1	yes	characteristic
408	C₄	#11926666	1	1	yes	characteristic
409	C₄	#11926775	1	1	yes	characteristic
410	C₄	#11926783	1	1	yes	characteristic
411	C₂	—	2	1	no	—
412	C₂	—	2	1	no	—
413	C₂	—	4	2	no	—
414	C₂	#14563964	1	1	yes	characteristic
415	C₂	#14564059	1	1	yes	characteristic
416	C₂	#14564138	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597385
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3076	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂×#41×C₁₉	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3076	D₁₉
hypocenter	C₁₉	#9207
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3076

Complements

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

N	H ≅ G/N	type
3. #14562134	C₂	semidirect
4. #14562090	C₂	semidirect
5. #14561532	C₂	semidirect
6. #14561474	C₂	semidirect
26. C₁₉×#477	C₄	semidirect
27. C₁₉×#476	C₄	semidirect
28. C₁₉×#475	C₄	semidirect
29. C₁₉×#474	C₄	semidirect
214. #477	Dic₁₉	semidirect
215. #476	Dic₁₉	semidirect
216. #475	Dic₁₉	semidirect
217. #474	Dic₁₉	semidirect
290. C₁₉	#9207	semidirect

Maximal subgroups

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

subgroup	index
#41×C₁₉⋊C₈	2
#14563655	2
#14562134	2
#14562090	2
#14561532	2
#14561474	2
C₁₉×#3076	2
#9207	19