Subgroups — #18088173

Order 4864.

802 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926312	C₂	1	2	yes	maximal
3	C₂×#11926312	C₂	1	2	yes	maximal
4	#14563329	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1728	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64520	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₄×Dic₁₉	C₄	1	2	yes	—
10	C₄×C₄⋊Dic₁₉	—	2	1	no	—
11	C₄×C₄⋊Dic₁₉	—	2	1	no	—
12	C₄×C₄⋊Dic₁₉	—	2	1	no	—
13	C₄×C₄⋊Dic₁₉	—	2	1	no	—
14	C₂×C₁₉⋊#95	C₄	1	2	yes	—
15	#11926312	—	2	4	no	—
16	#11926312	C₄	1	8	yes	complemented
17	#11926299	—	2	1	no	—
18	#11926299	—	2	1	no	—
19	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#336	—	2	1	no	—
22	C₁₉×#336	—	2	1	no	—
23	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂³×Dic₁₉	C₂×C₄	1	2	yes	—
27	C₂³×Dic₁₉	C₂×C₄	1	2	yes	—
28	C₂×M₁₆×C₁₉	—	2	2	no	—
29	C₂×M₁₆×C₁₉	—	2	2	no	—
30	C₂×M₁₆×C₁₉	—	2	2	no	—
31	C₂×M₁₆×C₁₉	—	2	2	no	—
32	C₂×M₁₆×C₁₉	—	2	2	no	—
33	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
34	C₂²×C₈×C₁₉	—	2	2	no	—
35	C₂×C₄²×C₁₉	—	2	2	no	—
36	C₂×C₄²×C₁₉	—	2	2	no	—
37	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄⋊Dic₁₉	—	2	1	no	—
42	C₂×C₄⋊Dic₁₉	—	2	1	no	—
43	C₂×C₄⋊Dic₁₉	—	2	1	no	—
44	C₂×C₄⋊Dic₁₉	—	2	1	no	—
45	C₂×C₄⋊Dic₁₉	—	2	2	no	—
46	C₂×C₄⋊Dic₁₉	—	2	1	no	—
47	C₂×C₄⋊Dic₁₉	—	2	1	no	—
48	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
49	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
50	C₂×C₄⋊Dic₁₉	Q₈	1	2	yes	—
51	C₂×C₄×Dic₁₉	—	2	2	no	—
52	C₂×C₄×Dic₁₉	—	2	2	no	—
53	C₂×C₄×Dic₁₉	—	4	4	no	—
54	C₂×#64520	—	2	2	no	—
55	C₂×#64520	—	2	2	no	—
56	C₂×#64520	—	2	2	no	—
57	C₂×#64520	—	2	2	no	—
58	C₂×#64520	—	2	2	no	—
59	C₂×#64520	C₂×C₄	1	4	yes	—
60	C₂²×C₁₉⋊C₈	—	2	2	no	—
61	C₁₉⋊#95	—	2	2	no	—
62	C₁₉⋊#95	—	2	2	no	—
63	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	4	1	no	—
71	C₂²×C₄×C₁₉	—	4	1	no	—
72	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	#41	1	2	yes	—
82	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	#41	1	2	yes	—
84	C₂²×C₄×C₁₉	#41	1	2	yes	—
85	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
86	C₂²×Dic₁₉	—	2	2	no	—
87	C₂²×Dic₁₉	—	2	2	no	—
88	C₂²×Dic₁₉	—	2	2	no	—
89	C₂²×Dic₁₉	—	2	2	no	—
90	C₂²×Dic₁₉	—	4	2	no	—
91	C₂²×Dic₁₉	—	4	2	no	—
92	C₂²×Dic₁₉	—	4	2	no	—
93	C₂²×Dic₁₉	—	4	2	no	—
94	C₂²×Dic₁₉	C₄²	1	4	yes	—
95	C₂²×Dic₁₉	C₄⋊C₄	1	4	yes	—
96	M₁₆×C₁₉	—	2	4	no	—
97	M₁₆×C₁₉	—	2	4	no	—
98	M₁₆×C₁₉	—	4	2	no	—
99	M₁₆×C₁₉	—	4	2	no	—
100	C₂×C₈×C₁₉	—	2	4	no	—
101	C₂×C₈×C₁₉	—	4	2	no	—
102	C₂×C₈×C₁₉	—	4	2	no	—
103	C₄²×C₁₉	—	2	2	no	—
104	C₄²×C₁₉	—	2	2	no	—
105	C₄²×C₁₉	—	2	2	no	—
106	C₄²×C₁₉	—	2	2	no	—
107	C₄⋊Dic₁₉	—	2	4	no	—
108	C₄⋊Dic₁₉	—	2	4	no	—
109	C₄⋊Dic₁₉	—	2	2	no	—
110	C₄⋊Dic₁₉	—	2	2	no	—
111	C₄⋊Dic₁₉	—	2	2	no	—
112	C₄⋊Dic₁₉	—	2	2	no	—
113	C₄×Dic₁₉	—	4	4	no	—
114	C₄×Dic₁₉	—	4	4	no	—
115	#64520	—	2	4	no	—
116	#64520	—	2	4	no	—
117	#64520	—	4	2	no	—
118	#64520	—	4	2	no	—
119	C₂×C₁₉⋊C₈	—	2	4	no	—
120	C₂×C₁₉⋊C₈	—	4	2	no	—
121	C₂×C₁₉⋊C₈	—	4	2	no	—
122	#10802	—	19	1	no	maximal, Sylow
123	C₂³×C₁₉	—	2	1	no	—
124	C₂³×C₁₉	—	2	1	no	—
125	C₂³×C₁₉	—	2	1	no	—
126	C₂³×C₁₉	—	2	1	no	—
127	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
128	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂³×C₁₉	#117	1	1	yes	characteristic
131	C₂³×C₁₉	#117	1	1	yes	characteristic
132	C₂³×C₁₉	#117	1	1	yes	characteristic
133	C₂³×C₁₉	#117	1	1	yes	characteristic
134	C₂×C₄×C₁₉	—	2	4	no	—
135	C₂×C₄×C₁₉	—	2	4	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	#100	1	2	yes	—
149	C₂×C₄×C₁₉	#101	1	2	yes	—
150	C₂×C₄×C₁₉	#117	1	2	yes	—
151	C₂×C₄×C₁₉	#117	1	2	yes	—
152	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
155	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
156	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#123	1	2	yes	—
161	C₂×C₄×C₁₉	#123	1	2	yes	—
162	C₂×C₄×C₁₉	#124	1	2	yes	—
163	C₂×C₄×C₁₉	#125	1	2	yes	—
164	C₂×C₄×C₁₉	#126	1	2	yes	—
165	C₂×C₄×C₁₉	#126	1	2	yes	—
166	C₂×Dic₁₉	—	2	4	no	—
167	C₂×Dic₁₉	—	2	4	no	—
168	C₂×Dic₁₉	—	4	4	no	—
169	C₂×Dic₁₉	—	4	4	no	—
170	C₂×Dic₁₉	—	4	2	no	—
171	C₂×Dic₁₉	—	4	2	no	—
172	C₂×Dic₁₉	—	4	2	no	—
173	C₂×Dic₁₉	—	4	2	no	—
174	C₂×Dic₁₉	—	4	4	no	—
175	C₂×Dic₁₉	—	4	4	no	—
176	C₈×C₁₉	—	4	4	no	—
177	C₁₉⋊C₈	—	4	4	no	—
178	C₂×C₄×C₄⋊C₄	—	19	1	no	—
179	C₂×#343	—	19	2	no	—
180	C₂×#343	—	19	2	no	—
181	#1728	—	19	1	no	—
182	#1728	D₁₉	1	1	yes	characteristic
183	C₂²×C₁₉	—	2	1	no	—
184	C₂²×C₁₉	—	2	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	—	2	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	#376	1	1	yes	characteristic
196	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
197	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
198	C₂²×C₁₉	#380	1	1	yes	characteristic
199	C₂²×C₁₉	#381	1	1	yes	characteristic
200	C₂²×C₁₉	#382	1	1	yes	characteristic
201	C₂²×C₁₉	#383	1	1	yes	characteristic
202	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
203	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
204	C₂²×C₁₉	#413	1	1	yes	characteristic
205	C₂²×C₁₉	#413	1	1	yes	characteristic
206	C₄×C₁₉	—	2	2	no	—
207	C₄×C₁₉	—	2	2	no	—
208	C₄×C₁₉	—	4	1	no	—
209	C₄×C₁₉	—	4	1	no	—
210	C₄×C₁₉	#387	1	2	yes	—
211	C₄×C₁₉	#387	1	2	yes	—
212	C₄×C₁₉	#388	1	2	yes	—
213	C₄×C₁₉	#388	1	2	yes	—
214	Dic₁₉	—	4	4	no	—
215	Dic₁₉	—	4	4	no	—
216	C₂²×M₁₆	—	19	2	no	—
217	C₂²×M₁₆	C₂×D₁₉	1	2	yes	—
218	C₂²×C₄⋊C₄	—	19	1	no	—
219	C₂²×C₄⋊C₄	—	19	1	no	—
220	C₂²×C₄²	—	19	2	no	—
221	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
222	C₄×C₄⋊C₄	—	38	1	no	—
223	C₄×C₄⋊C₄	—	38	1	no	—
224	C₄×C₄⋊C₄	—	38	1	no	—
225	C₄×C₄⋊C₄	—	38	1	no	—
226	C₂×#95	—	19	2	no	—
227	#343	—	19	8	no	—
228	#343	—	38	4	no	—
229	#336	—	2	1	no	—
230	#336	—	2	1	no	—
231	#336	—	38	1	no	—
232	#336	—	38	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	#1434	1	1	yes	characteristic
238	C₂×C₁₉	C₄×#100	1	1	yes	characteristic
239	C₂×C₁₉	C₄×#101	1	1	yes	characteristic
240	C₂×C₁₉	#1800	1	1	yes	characteristic
241	C₂×C₁₉	#1801	1	1	yes	characteristic
242	C₂×C₁₉	#1821	1	1	yes	characteristic
243	C₂×C₁₉	#1822	1	1	yes	characteristic
244	C₂³×C₄	—	19	2	no	—
245	C₂³×C₄	—	19	2	no	—
246	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
247	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
248	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	—	19	4	no	—
255	C₂×M₁₆	—	38	2	no	—
256	C₂×M₁₆	—	38	2	no	—
257	C₂×M₁₆	—	38	2	no	—
258	C₂×M₁₆	—	38	2	no	—
259	C₂×M₁₆	—	38	2	no	—
260	C₂×M₁₆	C₄×D₁₉	1	4	yes	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	38	2	no	—
263	C₂×C₄⋊C₄	—	19	4	no	—
264	C₂×C₄⋊C₄	—	19	2	no	—
265	C₂×C₄⋊C₄	—	19	2	no	—
266	C₂×C₄⋊C₄	—	38	1	no	—
267	C₂×C₄⋊C₄	—	38	1	no	—
268	C₂×C₄⋊C₄	—	38	2	no	—
269	C₂×C₄⋊C₄	—	38	1	no	—
270	C₂×C₄⋊C₄	—	38	1	no	—
271	C₂×C₄⋊C₄	—	38	1	no	—
272	C₂×C₄⋊C₄	—	38	1	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	38	2	no	—
276	C₂×C₄²	—	38	2	no	—
277	C₂×C₄²	—	76	4	no	—
278	C₂×C₄²	D₇₆	1	1	yes	characteristic
279	C₂×C₄²	D₇₆	1	1	yes	characteristic
280	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
281	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
282	#95	—	38	2	no	—
283	#95	—	38	2	no	—
284	C₁₉	#10802	1	1	yes	characteristic, complemented, Sylow
285	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	19	4	no	—
295	C₂²×C₄	—	19	4	no	—
296	C₂²×C₄	—	38	2	no	—
297	C₂²×C₄	—	38	2	no	—
298	C₂²×C₄	—	38	2	no	—
299	C₂²×C₄	—	38	2	no	—
300	C₂²×C₄	—	76	2	no	—
301	C₂²×C₄	—	76	2	no	—
302	C₂²×C₄	—	76	2	no	—
303	C₂²×C₄	—	76	2	no	—
304	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
305	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
306	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
307	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
309	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
310	C₂²×C₄	#64541	1	2	yes	—
311	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
312	C₂²×C₄	#64543	1	2	yes	—
313	C₂²×C₄	#64543	1	2	yes	—
314	C₂²×C₄	#64543	1	1	yes	characteristic
315	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
316	C₂²×C₄	#64545	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
318	M₁₆	—	2	4	no	—
319	M₁₆	—	2	4	no	—
320	M₁₆	—	4	2	no	—
321	M₁₆	—	4	2	no	—
322	M₁₆	—	38	4	no	—
323	M₁₆	—	38	4	no	—
324	M₁₆	—	76	2	no	—
325	M₁₆	—	76	2	no	—
326	C₂×C₈	—	2	4	no	—
327	C₂×C₈	—	4	2	no	—
328	C₂×C₈	—	4	2	no	—
329	C₂×C₈	—	38	4	no	—
330	C₂×C₈	—	76	2	no	—
331	C₂×C₈	—	76	2	no	—
332	C₄⋊C₄	—	38	2	no	—
333	C₄⋊C₄	—	38	2	no	—
334	C₄⋊C₄	—	38	4	no	—
335	C₄⋊C₄	—	38	2	no	—
336	C₄⋊C₄	—	38	2	no	—
337	C₄⋊C₄	—	38	4	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	76	4	no	—
343	C₄²	—	76	4	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	C₄²×D₁₉	1	1	yes	characteristic
349	C₂³	#10597318	1	1	yes	characteristic
350	C₂³	#10597323	1	1	yes	characteristic
351	C₂³	#10597323	1	1	yes	characteristic
352	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
353	C₂³	#10597338	1	1	yes	characteristic
354	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	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	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	38	4	no	—
370	C₂×C₄	—	38	4	no	—
371	C₂×C₄	—	76	4	no	—
372	C₂×C₄	—	76	4	no	—
373	C₂×C₄	—	76	2	no	—
374	C₂×C₄	—	76	2	no	—
375	C₂×C₄	—	76	2	no	—
376	C₂×C₄	—	76	2	no	—
377	C₂×C₄	—	76	4	no	—
378	C₂×C₄	—	76	4	no	—
379	C₂×C₄	#10597280	1	2	yes	—
380	C₂×C₄	#10597281	1	2	yes	—
381	C₂×C₄	C₄×D₇₆	1	2	yes	—
382	C₂×C₄	#10597323	1	2	yes	—
383	C₂×C₄	#10597325	1	2	yes	—
384	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
385	C₂×C₄	#10597331	1	2	yes	—
386	C₂×C₄	#10597332	1	2	yes	—
387	C₂×C₄	#10597333	1	2	yes	—
388	C₂×C₄	#10597335	1	2	yes	—
389	C₂×C₄	#10597338	1	2	yes	—
390	C₂×C₄	#10597341	1	1	yes	characteristic
391	C₂×C₄	#10597343	1	1	yes	characteristic
392	C₂×C₄	#10597344	1	2	yes	—
393	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
394	C₂×C₄	#10597381	1	2	yes	—
395	C₂×C₄	#10597384	1	1	yes	characteristic
396	C₂×C₄	#10597392	1	1	yes	characteristic
397	C₈	—	4	4	no	—
398	C₈	—	76	4	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	#11926389	1	1	yes	characteristic
412	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
413	C₂²	#11926395	1	1	yes	characteristic
414	C₂²	#11926401	1	1	yes	characteristic
415	C₂²	#11926405	1	1	yes	characteristic
416	C₂²	#11926408	1	1	yes	characteristic
417	C₂²	#11926411	1	1	yes	characteristic
418	C₂²	C₂×#10597280	1	1	yes	characteristic
419	C₂²	C₂×#10597281	1	1	yes	characteristic
420	C₂²	#11926526	1	1	yes	characteristic
421	C₂²	#11926526	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	76	4	no	—
427	C₄	—	76	4	no	—
428	C₄	#11926425	1	2	yes	—
429	C₄	#11926429	1	2	yes	—
430	C₄	#11926432	1	2	yes	—
431	C₄	#11926436	1	2	yes	—
432	C₂	—	2	1	no	—
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	2	1	no	—
436	C₂	#14561859	1	1	yes	characteristic
437	C₂	C₄×#10597280	1	1	yes	characteristic
438	C₂	C₄×#10597281	1	1	yes	characteristic
439	C₂	#14563624	1	1	yes	characteristic
440	C₂	#14563628	1	1	yes	characteristic
441	C₂	#14563713	1	1	yes	characteristic
442	C₂	#14563716	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂³×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1728	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1728	D₁₉
hypocenter	C₁₉	#10802
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #1728

Complements

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

N	H ≅ G/N	type
16. #11926312	C₄	semidirect
284. C₁₉	#10802	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₄⋊Dic₁₉	2
C₂×#11926312	2
#14563329	2
C₁₉×#1728	2
#10802	19