Subgroups — #18088227

Order 4864.

612 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572053	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926316	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926315	C₂	1	1	yes	maximal, characteristic
4	#14563361	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉⋊#338	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉⋊#338	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1738	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂²×#64520	C₂²	1	1	yes	characteristic
11	C₂×#10597372	C₂²	1	1	yes	characteristic
12	#11926502	C₄	1	4	yes	—
13	#11926499	—	2	2	no	—
14	M₁₆×Dic₁₉	—	2	2	no	—
15	#11926316	—	2	2	no	—
16	#11926315	—	2	2	no	—
17	#11926308	C₄	1	4	yes	complemented
18	C₁₉⋊#338	—	2	2	no	—
19	C₁₉⋊#338	—	2	2	no	—
20	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#341	C₄	1	4	yes	complemented
24	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂×M₁₆×C₁₉	—	2	1	no	—
26	C₂×M₁₆×C₁₉	—	2	1	no	—
27	C₂×M₁₆×C₁₉	—	2	1	no	—
28	C₂×M₁₆×C₁₉	—	2	1	no	—
29	C₂×M₁₆×C₁₉	—	2	1	no	—
30	C₂×M₁₆×C₁₉	—	2	1	no	—
31	C₂×M₁₆×C₁₉	—	2	1	no	—
32	C₂×M₁₆×C₁₉	—	2	1	no	—
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂×M₁₆×C₁₉	—	2	1	no	—
38	C₂×M₁₆×C₁₉	—	2	1	no	—
39	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
40	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
41	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
42	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
43	C₂²×C₈×C₁₉	—	2	1	no	—
44	C₂²×C₈×C₁₉	—	2	1	no	—
45	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
46	C₂×C₂²⋊Dic₁₉	Q₈	1	2	yes	—
47	#10597372	—	2	1	no	—
48	#10597372	—	2	1	no	—
49	#10597372	C₂×C₄	1	2	yes	—
50	#10597372	D₄	1	2	yes	—
51	C₂×C₄⋊Dic₁₉	—	2	1	no	—
52	C₂×C₄×Dic₁₉	—	2	1	no	—
53	C₂×#64520	—	2	1	no	—
54	C₂×#64520	—	2	1	no	—
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	—	2	1	no	—
66	C₂×#64520	—	2	1	no	—
67	C₂×#64520	—	2	1	no	—
68	C₂×#64520	C₂×C₄	1	2	yes	—
69	C₂×#64520	D₄	1	2	yes	—
70	C₂×#64520	D₄	1	2	yes	—
71	C₂²×C₁₉⋊C₈	—	2	1	no	—
72	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
73	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
74	#10597272	—	2	4	no	—
75	C₈×Dic₁₉	—	2	4	no	—
76	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	#41	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×Dic₁₉	—	2	2	no	—
92	M₁₆×C₁₉	—	2	2	no	—
93	M₁₆×C₁₉	—	2	2	no	—
94	M₁₆×C₁₉	—	2	2	no	—
95	M₁₆×C₁₉	—	2	2	no	—
96	M₁₆×C₁₉	—	2	2	no	—
97	M₁₆×C₁₉	—	4	1	no	—
98	M₁₆×C₁₉	—	4	1	no	—
99	M₁₆×C₁₉	—	4	1	no	—
100	M₁₆×C₁₉	—	4	1	no	—
101	M₁₆×C₁₉	—	4	1	no	—
102	M₁₆×C₁₉	—	4	1	no	—
103	M₁₆×C₁₉	C₄²	1	4	yes	—
104	C₂×C₈×C₁₉	—	2	2	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	2	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	—	4	1	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₂²⋊Dic₁₉	—	2	2	no	—
114	C₂²⋊Dic₁₉	C₄⋊C₄	1	4	yes	—
115	C₄⋊Dic₁₉	—	2	2	no	—
116	C₄⋊Dic₁₉	—	2	2	no	—
117	C₄×Dic₁₉	—	2	2	no	—
118	C₄×Dic₁₉	—	2	2	no	—
119	#64520	—	2	2	no	—
120	#64520	—	2	2	no	—
121	#64520	—	2	2	no	—
122	#64520	—	2	2	no	—
123	#64520	—	2	2	no	—
124	#64520	—	2	2	no	—
125	#64520	—	4	1	no	—
126	#64520	—	4	1	no	—
127	#64520	—	4	1	no	—
128	#64520	—	4	1	no	—
129	#64520	—	4	1	no	—
130	#64520	—	4	1	no	—
131	C₂×C₁₉⋊C₈	—	2	2	no	—
132	C₂×C₁₉⋊C₈	—	2	2	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	—	4	1	no	—
138	C₂×C₁₉⋊C₈	—	4	1	no	—
139	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	—
140	#10812	—	19	1	no	maximal, Sylow
141	C₂³×C₁₉	—	8	1	no	—
142	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
144	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
145	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
146	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
147	C₂³×C₁₉	#125	1	1	yes	characteristic
148	C₂³×C₁₉	#125	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₄×D₄	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	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
177	C₂×Dic₁₉	—	2	4	no	—
178	C₂×Dic₁₉	—	8	2	no	—
179	C₈×C₁₉	—	2	4	no	—
180	C₈×C₁₉	—	4	2	no	—
181	C₈×C₁₉	—	4	2	no	—
182	C₁₉⋊C₈	—	2	4	no	—
183	C₁₉⋊C₈	—	4	2	no	—
184	C₁₉⋊C₈	—	4	2	no	—
185	#2873	—	19	1	no	—
186	C₂×#344	—	19	1	no	—
187	C₂×#344	—	19	1	no	—
188	#1738	—	19	1	no	—
189	#1738	D₁₉	1	1	yes	characteristic
190	C₂×#338	—	19	1	no	—
191	C₂×#338	—	19	1	no	—
192	C₂²×C₁₉	—	4	1	no	—
193	C₂²×C₁₉	—	4	1	no	—
194	C₂²×C₁₉	—	4	1	no	—
195	C₂²×C₁₉	—	4	1	no	—
196	C₂²×C₁₉	—	4	1	no	—
197	C₂²×C₁₉	—	4	1	no	—
198	C₂²×C₁₉	—	4	1	no	—
199	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
200	C₂²×C₁₉	#380	1	1	yes	characteristic
201	C₂²×C₁₉	#382	1	1	yes	characteristic
202	C₂²×C₁₉	#387	1	1	yes	characteristic
203	C₂²×C₁₉	#387	1	1	yes	characteristic
204	C₂²×C₁₉	#387	1	1	yes	characteristic
205	C₂²×C₁₉	#387	1	1	yes	characteristic
206	C₄×C₁₉	#376	1	1	yes	characteristic
207	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
208	C₄×C₁₉	#381	1	1	yes	characteristic
209	C₄×C₁₉	#383	1	1	yes	characteristic
210	C₄×C₁₉	#388	1	1	yes	characteristic
211	C₄×C₁₉	#388	1	1	yes	characteristic
212	C₄×C₁₉	#388	1	1	yes	characteristic
213	C₄×C₁₉	#388	1	1	yes	characteristic
214	Dic₁₉	—	4	4	no	—
215	C₂²×M₁₆	—	19	1	no	—
216	C₂²×M₁₆	—	19	1	no	—
217	C₂²×M₁₆	—	19	1	no	—
218	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
219	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
220	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
221	C₂×#117	—	19	1	no	—
222	#405	—	19	4	no	—
223	#405	—	38	2	no	—
224	C₄×M₁₆	—	38	2	no	—
225	#344	—	38	2	no	—
226	#344	—	38	2	no	—
227	#341	—	19	4	no	—
228	#341	Dic₁₉	1	4	yes	complemented
229	#338	—	38	2	no	—
230	#338	—	38	2	no	—
231	C₂×C₁₉	—	2	1	no	—
232	C₂×C₁₉	—	2	1	no	—
233	C₂×C₁₉	—	2	1	no	—
234	C₂×C₁₉	—	2	1	no	—
235	C₂×C₁₉	—	2	1	no	—
236	C₂×C₁₉	—	2	1	no	—
237	C₂×C₁₉	—	2	1	no	—
238	C₂×C₁₉	#1434	1	1	yes	characteristic
239	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
240	C₂×M₁₆	—	2	1	no	—
241	C₂×M₁₆	—	2	1	no	—
242	C₂×M₁₆	—	2	1	no	—
243	C₂×M₁₆	—	2	1	no	—
244	C₂×M₁₆	—	2	1	no	—
245	C₂×M₁₆	—	2	1	no	—
246	C₂×M₁₆	—	2	1	no	—
247	C₂×M₁₆	—	2	1	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	2	1	no	—
250	C₂×M₁₆	—	2	1	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	2	1	no	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	19	2	no	—
255	C₂×M₁₆	—	19	2	no	—
256	C₂×M₁₆	—	19	2	no	—
257	C₂×M₁₆	—	38	1	no	—
258	C₂×M₁₆	—	38	1	no	—
259	C₂×M₁₆	—	38	1	no	—
260	C₂×M₁₆	—	38	1	no	—
261	C₂×M₁₆	—	38	1	no	—
262	C₂×M₁₆	—	38	1	no	—
263	C₂×M₁₆	—	38	1	no	—
264	C₂×M₁₆	—	38	1	no	—
265	C₂×M₁₆	—	38	1	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	C₄×D₁₉	1	2	yes	—
273	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
274	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
275	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	19	2	no	—
279	C₂²×C₈	—	19	2	no	—
280	C₂²×C₈	—	38	1	no	—
281	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
282	#117	—	19	2	no	—
283	#117	—	19	2	no	—
284	#117	—	38	1	no	—
285	#117	—	38	1	no	—
286	C₂×C₄⋊C₄	—	38	1	no	—
287	C₂×C₂²⋊C₄	—	19	2	no	—
288	C₂×C₄²	—	38	1	no	—
289	#97	—	38	4	no	—
290	C₄×C₈	—	38	4	no	—
291	C₁₉	#10812	1	1	yes	characteristic, complemented, Sylow
292	C₂⁴	Q₈×D₁₉	1	1	yes	characteristic
293	C₂²×C₄	—	38	2	no	—
294	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
296	C₂²×C₄	#64541	1	1	yes	characteristic
297	C₂²×C₄	#64541	1	1	yes	characteristic
298	C₂²×C₄	#64541	1	1	yes	characteristic
299	C₂²×C₄	#64541	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	D₄×D₁₉	1	1	yes	characteristic
303	C₂²×C₄	#64543	1	1	yes	characteristic
304	C₂²×C₄	#64543	1	1	yes	characteristic
305	C₂²×C₄	#64543	1	1	yes	characteristic
306	C₂²×C₄	#64545	1	1	yes	characteristic
307	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
308	M₁₆	—	2	2	no	—
309	M₁₆	—	2	2	no	—
310	M₁₆	—	2	2	no	—
311	M₁₆	—	2	2	no	—
312	M₁₆	—	2	2	no	—
313	M₁₆	—	4	1	no	—
314	M₁₆	—	4	1	no	—
315	M₁₆	—	4	1	no	—
316	M₁₆	—	4	1	no	—
317	M₁₆	—	4	1	no	—
318	M₁₆	—	4	1	no	—
319	M₁₆	—	38	2	no	—
320	M₁₆	—	38	2	no	—
321	M₁₆	—	38	2	no	—
322	M₁₆	—	38	2	no	—
323	M₁₆	—	38	2	no	—
324	M₁₆	—	38	2	no	—
325	M₁₆	—	76	1	no	—
326	M₁₆	—	76	1	no	—
327	M₁₆	—	76	1	no	—
328	M₁₆	—	76	1	no	—
329	M₁₆	—	76	1	no	—
330	M₁₆	—	76	1	no	—
331	M₁₆	C₄×Dic₁₉	1	4	yes	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	19	4	no	—
342	C₂×C₈	—	38	2	no	—
343	C₂×C₈	—	38	2	no	—
344	C₂×C₈	—	38	2	no	—
345	C₂×C₈	—	38	2	no	—
346	C₂×C₈	—	38	2	no	—
347	C₂×C₈	—	38	2	no	—
348	C₂×C₈	—	76	1	no	—
349	C₂×C₈	—	76	1	no	—
350	C₄⋊C₄	—	38	2	no	—
351	C₄⋊C₄	—	38	2	no	—
352	C₂²⋊C₄	—	19	4	no	—
353	C₂²⋊C₄	—	38	2	no	—
354	C₄²	—	38	2	no	—
355	C₄²	—	38	2	no	—
356	C₂³	—	8	1	no	—
357	C₂³	#10597333	1	1	yes	characteristic
358	C₂³	#10597335	1	1	yes	characteristic
359	C₂³	#10597335	1	1	yes	characteristic
360	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
361	C₂³	#10597342	1	1	yes	characteristic
362	C₂³	#10597342	1	1	yes	characteristic
363	C₂³	Q₈×Dic₁₉	1	1	yes	characteristic
364	C₂×C₄	—	38	4	no	—
365	C₂×C₄	—	152	2	no	—
366	C₂×C₄	#10597318	1	1	yes	characteristic
367	C₂×C₄	#10597318	1	1	yes	characteristic
368	C₂×C₄	#10597318	1	1	yes	characteristic
369	C₂×C₄	#10597318	1	1	yes	characteristic
370	C₂×C₄	#10597323	1	1	yes	characteristic
371	C₂×C₄	#10597325	1	1	yes	characteristic
372	C₂×C₄	#10597325	1	1	yes	characteristic
373	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
374	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
375	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
376	C₂×C₄	#10597329	1	1	yes	characteristic
377	C₂×C₄	#10597329	1	1	yes	characteristic
378	C₂×C₄	#10597330	1	1	yes	characteristic
379	C₂×C₄	#10597330	1	1	yes	characteristic
380	C₂×C₄	#10597331	1	1	yes	characteristic
381	C₂×C₄	#10597331	1	1	yes	characteristic
382	C₂×C₄	#10597338	1	1	yes	characteristic
383	C₂×C₄	#10597339	1	1	yes	characteristic
384	C₂×C₄	#10597340	1	1	yes	characteristic
385	C₂×C₄	#10597340	1	1	yes	characteristic
386	C₂×C₄	#10597344	1	1	yes	characteristic
387	C₂×C₄	#10597344	1	1	yes	characteristic
388	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
389	C₂×C₄	#10597372	1	1	yes	characteristic
390	C₂×C₄	#10597372	1	1	yes	characteristic
391	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
392	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
393	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
394	C₈	—	2	4	no	—
395	C₈	—	4	2	no	—
396	C₈	—	4	2	no	—
397	C₈	—	38	4	no	—
398	C₈	—	76	2	no	—
399	C₈	—	76	2	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
408	C₂²	#11926403	1	1	yes	characteristic
409	C₂²	#11926408	1	1	yes	characteristic
410	C₂²	#11926426	1	1	yes	characteristic
411	C₂²	#11926426	1	1	yes	characteristic
412	C₂²	#11926430	1	1	yes	characteristic
413	C₂²	#11926430	1	1	yes	characteristic
414	C₄	—	76	4	no	—
415	C₄	#11926390	1	1	yes	characteristic
416	C₄	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
417	C₄	#11926406	1	1	yes	characteristic
418	C₄	#11926411	1	1	yes	characteristic
419	C₄	#11926433	1	1	yes	characteristic
420	C₄	#11926433	1	1	yes	characteristic
421	C₄	#11926437	1	1	yes	characteristic
422	C₄	#11926437	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	2	1	no	—
430	C₂	#14561860	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊C₄×Dic₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1738	C₂
socle	C₂×C₁₉	#1434
prime radical	C₂⁴×C₁₉	C₂×Q₈
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1738	D₁₉
hypocenter	C₁₉	#10812
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ #1738

Complements

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

N	H ≅ G/N	type
17. #11926308	C₄	semidirect
23. C₁₉×#341	C₄	semidirect
228. #341	Dic₁₉	semidirect
291. C₁₉	#10812	semidirect

Maximal subgroups

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

subgroup	index
#14572053	2
C₂×#11926316	2
C₂×#11926315	2
#14563361	2
C₂×C₁₉⋊#338	2
C₁₉×#1738	2
#10812	19