Subgroups — #18077906

Order 4864.

754 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#64520	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563615	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal, complemented
4	#14561476	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₉×#121	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64520	—	2	1	no	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
9	C₄×#64520	—	2	4	no	—
10	C₂×#10597260	—	2	1	no	—
11	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
12	#11926299	—	2	1	no	—
13	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
14	C₂×C₁₉×#121	C₄	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₉	—	2	1	no	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#390	C₄	1	1	yes	characteristic
19	C₁₉×#389	C₄	1	1	yes	characteristic
20	C₁₉×#388	—	2	1	no	—
21	C₁₉×#386	—	2	1	no	—
22	C₁₉×#380	C₄	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
25	C₂²×D₄×C₁₉	—	2	1	no	—
26	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
31	C₁₉×#121	—	2	2	no	—
32	C₁₉×#121	—	2	2	no	—
33	C₄×D₄×C₁₉	—	2	2	no	—
34	C₄×D₄×C₁₉	—	2	2	no	—
35	C₄×D₄×C₁₉	—	4	4	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₄²×C₁₉	—	2	2	no	—
46	C₂×C₄²×C₁₉	—	2	2	no	—
47	C₂×C₄²×C₁₉	—	2	1	no	—
48	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
52	C₂×#64520	—	2	4	no	—
53	C₂×#64520	—	2	4	no	—
54	C₂×#64520	—	2	4	no	—
55	C₂²×C₁₉⋊C₈	—	2	2	no	—
56	C₂²×C₁₉⋊C₈	—	2	2	no	—
57	C₁₉×#95	—	2	1	no	—
58	C₁₉×#95	—	2	1	no	—
59	C₁₉×#95	—	2	1	no	—
60	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
61	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
62	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
63	#10597260	—	2	4	no	—
64	C₄×C₁₉⋊C₈	—	2	2	no	—
65	C₄×C₁₉⋊C₈	D₄	1	4	yes	complemented
66	C₂⁴×C₁₉	—	2	1	no	—
67	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×D₄×C₁₉	—	2	4	no	—
69	C₂×D₄×C₁₉	—	2	2	no	—
70	C₂×D₄×C₁₉	—	2	1	no	—
71	C₂×D₄×C₁₉	—	2	2	no	—
72	C₂×D₄×C₁₉	—	4	2	no	—
73	C₂×D₄×C₁₉	—	4	2	no	—
74	C₂×D₄×C₁₉	M₁₆	1	2	yes	complemented
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	4	2	no	—
91	C₂²×C₄×C₁₉	—	4	2	no	—
92	C₂²×C₄×C₁₉	—	4	1	no	—
93	C₂²×C₄×C₁₉	—	4	1	no	—
94	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₄⋊C₄×C₁₉	—	2	2	no	—
102	C₄⋊C₄×C₁₉	—	2	2	no	—
103	C₄⋊C₄×C₁₉	—	4	2	no	—
104	C₄⋊C₄×C₁₉	M₁₆	1	2	yes	complemented
105	C₂²⋊C₄×C₁₉	—	2	4	no	—
106	C₂²⋊C₄×C₁₉	—	4	2	no	—
107	C₂²⋊C₄×C₁₉	—	4	2	no	—
108	C₂²⋊C₄×C₁₉	—	4	2	no	—
109	C₂²⋊C₄×C₁₉	—	4	1	no	—
110	C₂²⋊C₄×C₁₉	—	4	1	no	—
111	C₄²×C₁₉	—	2	2	no	—
112	C₄²×C₁₉	—	2	1	no	—
113	C₄²×C₁₉	—	2	2	no	—
114	C₄²×C₁₉	—	2	1	no	—
115	C₄²×C₁₉	—	4	2	no	—
116	C₄²×C₁₉	C₂×D₄	1	2	yes	—
117	C₄²×C₁₉	#41	1	2	yes	—
118	#64520	—	2	16	no	—
119	C₂×C₁₉⋊C₈	—	2	4	no	—
120	C₂×C₁₉⋊C₈	—	2	4	no	—
121	C₂×C₁₉⋊C₈	—	2	4	no	—
122	C₂×C₁₉⋊C₈	—	4	2	no	—
123	C₂×C₁₉⋊C₈	—	4	2	no	—
124	C₂×C₁₉⋊C₈	—	4	2	no	—
125	#9078	—	19	1	no	maximal, Sylow
126	C₂³×C₁₉	—	2	1	no	—
127	C₂³×C₁₉	—	2	1	no	—
128	C₂³×C₁₉	—	2	1	no	—
129	C₂³×C₁₉	—	2	1	no	—
130	C₂³×C₁₉	—	2	1	no	—
131	C₂³×C₁₉	—	2	1	no	—
132	C₂³×C₁₉	—	2	2	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	—	4	1	no	—
136	C₂³×C₁₉	—	4	1	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	#104	1	2	yes	—
140	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	D₄×C₁₉	—	2	4	no	—
142	D₄×C₁₉	—	4	8	no	—
143	D₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	2	4	no	—
145	C₂×C₄×C₁₉	—	2	4	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	2	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	2	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	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	8	2	no	—
170	C₂×C₄×C₁₉	—	8	2	no	—
171	C₂×C₄×C₁₉	#104	1	2	yes	—
172	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#121	1	2	yes	—
175	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#131	1	2	yes	—
179	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
180	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
182	C₁₉⋊C₈	—	2	8	no	—
183	C₁₉⋊C₈	—	8	2	no	—
184	C₂×C₄×M₁₆	—	19	1	no	—
185	C₄×#121	D₁₉	1	1	yes	characteristic
186	#1797	—	19	1	no	—
187	C₂×D₄⋊C₈	—	19	2	no	—
188	#1279	—	19	2	no	—
189	C₂²×C₁₉	—	2	2	no	—
190	C₂²×C₁₉	—	2	2	no	—
191	C₂²×C₁₉	—	2	2	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	2	no	—
197	C₂²×C₁₉	—	4	2	no	—
198	C₂²×C₁₉	—	4	2	no	—
199	C₂²×C₁₉	—	8	1	no	—
200	C₂²×C₁₉	—	8	1	no	—
201	C₂²×C₁₉	—	8	1	no	—
202	C₂²×C₁₉	—	8	1	no	—
203	C₂²×C₁₉	#386	1	1	yes	characteristic
204	C₂²×C₁₉	#407	1	1	yes	characteristic
205	C₂²×C₁₉	#408	1	1	yes	characteristic
206	C₂²×C₁₉	#417	1	1	yes	characteristic
207	C₂²×C₁₉	#418	1	1	yes	characteristic
208	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
209	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
210	C₄×C₁₉	—	2	1	no	—
211	C₄×C₁₉	—	2	2	no	—
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	4	1	no	—
214	C₄×C₁₉	—	4	1	no	—
215	C₄×C₁₉	—	4	2	no	—
216	C₄×C₁₉	—	8	1	no	—
217	C₄×C₁₉	—	8	1	no	—
218	C₄×C₁₉	#435	1	2	yes	—
219	C₄×C₁₉	#436	1	2	yes	—
220	C₄×C₁₉	#468	1	2	yes	—
221	C₄×C₁₉	#469	1	2	yes	—
222	C₂²×M₁₆	—	38	1	no	—
223	C₂×#121	Dic₁₉	1	1	yes	characteristic
224	C₂×C₄×D₄	—	2	1	no	—
225	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
226	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
227	C₂×C₄⋊C₈	—	19	2	no	—
228	C₂×C₂²⋊C₈	—	38	1	no	—
229	C₄×M₁₆	—	38	4	no	—
230	C₂×#97	—	38	1	no	—
231	C₂×C₄×C₈	—	19	2	no	—
232	#390	Dic₁₉	1	1	yes	characteristic
233	#389	Dic₁₉	1	1	yes	characteristic
234	#388	—	2	1	no	—
235	#386	—	2	1	no	—
236	#380	Dic₁₉	1	1	yes	characteristic
237	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
238	C₄×C₂²⋊C₄	—	2	1	no	—
239	#336	—	38	1	no	—
240	D₄⋊C₈	—	38	4	no	—
241	C₂×C₁₉	—	4	2	no	—
242	C₂×C₁₉	—	8	2	no	—
243	C₂×C₁₉	#1483	1	1	yes	characteristic
244	C₂×C₁₉	#1484	1	1	yes	characteristic
245	C₂×C₁₉	#1489	1	1	yes	characteristic
246	C₂×C₁₉	#1490	1	1	yes	characteristic
247	C₂×C₁₉	#1870	1	1	yes	characteristic
248	C₂×C₁₉	#1895	1	1	yes	characteristic
249	C₂×C₁₉	#1896	1	1	yes	characteristic
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
252	C₂³×C₄	—	2	1	no	—
253	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
254	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
255	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
256	C₂×M₁₆	—	38	4	no	—
257	C₂×M₁₆	—	38	4	no	—
258	C₂×M₁₆	—	38	4	no	—
259	C₂²×C₈	—	38	2	no	—
260	C₂²×C₈	—	38	2	no	—
261	#121	—	2	2	no	—
262	#121	—	2	2	no	—
263	C₄×D₄	—	2	2	no	—
264	C₄×D₄	—	2	2	no	—
265	C₄×D₄	—	4	4	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
279	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
280	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
281	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
282	C₄⋊C₈	—	38	2	no	—
283	C₄⋊C₈	—	38	2	no	—
284	C₂²⋊C₈	—	76	2	no	—
285	#97	—	38	4	no	—
286	C₄×C₈	—	19	4	no	—
287	C₄×C₈	—	38	2	no	—
288	#95	—	2	1	no	—
289	#95	—	2	1	no	—
290	#95	—	2	1	no	—
291	C₁₉	#9078	1	1	yes	characteristic, complemented, Sylow
292	C₂⁴	—	2	1	no	—
293	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	#64520	1	2	yes	complemented
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
321	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
322	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
323	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
326	M₁₆	—	38	16	no	—
327	C₂×C₈	—	38	4	no	—
328	C₂×C₈	—	38	4	no	—
329	C₂×C₈	—	38	4	no	—
330	C₂×C₈	—	76	2	no	—
331	C₂×C₈	—	76	2	no	—
332	C₂×C₈	—	76	2	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	#64520	1	2	yes	complemented
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	1	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	4	2	no	—
349	C₄²	D₄×D₁₉	1	2	yes	—
350	C₄²	#64543	1	2	yes	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	1	no	—
364	C₂³	#10597294	1	2	yes	—
365	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
366	D₄	—	2	4	no	—
367	D₄	—	4	8	no	—
368	D₄	—	4	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	8	2	no	—
395	C₂×C₄	—	8	2	no	—
396	C₂×C₄	#10597294	1	2	yes	—
397	C₂×C₄	C₂×#64520	1	1	yes	characteristic
398	C₂×C₄	C₂×#64520	1	1	yes	characteristic
399	C₂×C₄	#10597378	1	2	yes	—
400	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
401	C₂×C₄	#10597381	1	1	yes	characteristic
402	C₂×C₄	#10597383	1	1	yes	characteristic
403	C₂×C₄	#10597385	1	2	yes	—
404	C₂×C₄	#10597394	1	2	yes	—
405	C₂×C₄	#10597395	1	1	yes	characteristic
406	C₂×C₄	#10597397	1	1	yes	characteristic
407	C₈	—	38	8	no	—
408	C₈	—	152	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	#11926424	1	1	yes	characteristic
424	C₂²	#11926508	1	1	yes	characteristic
425	C₂²	#11926511	1	1	yes	characteristic
426	C₂²	#11926545	1	1	yes	characteristic
427	C₂²	#11926549	1	1	yes	characteristic
428	C₂²	C₂×#10597294	1	1	yes	characteristic
429	C₂²	C₂×#10597294	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	1	no	—
435	C₄	—	4	1	no	—
436	C₄	—	8	1	no	—
437	C₄	—	8	1	no	—
438	C₄	#11926616	1	2	yes	—
439	C₄	#11926622	1	2	yes	—
440	C₄	#11926788	1	2	yes	—
441	C₄	#11926795	1	2	yes	—
442	C₂	—	4	2	no	—
443	C₂	—	8	2	no	—
444	C₂	#14562048	1	1	yes	characteristic
445	C₂	#14562052	1	1	yes	characteristic
446	C₂	#14562074	1	1	yes	characteristic
447	C₂	#14562078	1	1	yes	characteristic
448	C₂	#14563933	1	1	yes	characteristic
449	C₂	#14564074	1	1	yes	characteristic
450	C₂	#14564079	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#121	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂×C₁₉×#121	C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#121	D₁₉
hypocenter	C₁₉	#9078
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₄×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×#64520	C₂	semidirect
2. #14563615	C₂	semidirect
3. C₂×D₄⋊(C₁₉⋊C₈)	C₂	semidirect
4. #14561476	C₂	semidirect
65. C₄×C₁₉⋊C₈	D₄	semidirect
74. C₂×D₄×C₁₉	M₁₆	semidirect
104. C₄⋊C₄×C₁₉	M₁₆	semidirect
291. C₁₉	#9078	semidirect
300. C₂×D₄	#64520	semidirect
337. C₄⋊C₄	#64520	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#64520	2
#14563615	2
C₂×D₄⋊(C₁₉⋊C₈)	2
#14561476	2
C₄×C₁₉×#121	2
#9078	19