Subgroups — #18088113

Order 4864.

1426 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10597294	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926305	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926304	C₂	1	1	yes	maximal, characteristic, complemented
5	#14563328	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×C₁₉⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₉×#104	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	#41×Dic₁₉	—	2	2	no	—
10	#41×Dic₁₉	—	2	2	no	—
11	#41×Dic₁₉	—	2	2	no	—
12	#41×Dic₁₉	—	2	2	no	—
13	C₂×Q₈×Dic₁₉	C₄	1	2	yes	complemented
14	C₂×D₄×Dic₁₉	—	2	2	no	—
15	C₂×D₄×Dic₁₉	C₄	1	2	yes	complemented
16	C₂×#10597372	—	2	1	no	—
17	C₂×#10597372	C₂²	1	1	yes	characteristic
18	C₂²×C₄×Dic₁₉	—	2	1	no	—
19	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
21	C₂×#10597294	—	2	2	no	—
22	C₂×#10597294	—	2	2	no	—
23	C₂×#10597294	C₄	1	4	yes	complemented
24	C₂×C₁₉⋊#95	—	2	2	no	—
25	#11926305	—	2	2	no	—
26	#11926304	—	2	2	no	—
27	#11926298	—	2	1	no	—
28	#11926298	—	2	1	no	—
29	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#104	—	2	2	no	—
33	C₂×C₁₉×#104	—	2	2	no	—
34	C₂×C₁₉×#104	C₄	1	4	yes	complemented
35	C₂×#41×C₁₉	—	2	1	no	—
36	C₂×#41×C₁₉	—	2	1	no	—
37	C₂×#41×C₁₉	—	2	1	no	—
38	C₂×#41×C₁₉	—	2	1	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	—	2	1	no	—
41	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
42	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
43	C₂×#41×C₁₉	D₄	1	2	yes	—
44	C₂×#41×C₁₉	D₄	1	2	yes	—
45	C₂×#41×C₁₉	D₄	1	2	yes	—
46	C₂×#41×C₁₉	Q₈	1	2	yes	—
47	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	—	2	1	no	—
51	C₂³×C₄×C₁₉	—	2	1	no	—
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂³×Dic₁₉	—	2	1	no	—
54	C₂³×Dic₁₉	—	2	2	no	—
55	C₂³×Dic₁₉	D₄	1	2	yes	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	—	2	1	no	—
59	C₂×M₁₆×C₁₉	—	2	1	no	—
60	C₂×M₁₆×C₁₉	—	2	1	no	—
61	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	complemented
62	C₂²×C₈×C₁₉	—	2	1	no	—
63	C₂×C₄²×C₁₉	—	2	1	no	—
64	C₂×C₄²×C₁₉	—	2	1	no	—
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	—	2	1	no	—
67	C₂×C₄²×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	complemented
69	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
70	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
71	Q₈×Dic₁₉	—	2	4	no	—
72	Q₈×Dic₁₉	—	2	4	no	—
73	D₄×Dic₁₉	—	2	8	no	—
74	D₄×Dic₁₉	—	2	8	no	—
75	D₄×Dic₁₉	—	2	4	no	—
76	D₄×Dic₁₉	—	2	4	no	—
77	#10597372	—	2	4	no	—
78	#10597372	—	2	4	no	—
79	#10597372	—	2	1	no	—
80	#10597372	—	2	1	no	—
81	#10597372	D₄	1	2	yes	—
82	#10597372	D₄	1	2	yes	—
83	C₂×C₄⋊Dic₁₉	—	2	2	no	—
84	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
85	C₂×C₄×Dic₁₉	—	2	4	no	—
86	C₂×C₄×Dic₁₉	—	2	4	no	—
87	C₂×C₄×Dic₁₉	—	2	1	no	—
88	C₂×C₄×Dic₁₉	—	2	1	no	—
89	C₂×C₄×Dic₁₉	—	2	1	no	—
90	C₂×C₄×Dic₁₉	—	2	1	no	—
91	C₂×C₄×Dic₁₉	—	2	1	no	—
92	C₂×C₄×Dic₁₉	—	2	2	no	—
93	C₂×C₄×Dic₁₉	—	2	1	no	—
94	C₂×C₄×Dic₁₉	—	2	1	no	—
95	C₂×C₄×Dic₁₉	—	2	1	no	—
96	C₂×C₄×Dic₁₉	—	2	1	no	—
97	C₂×C₄×Dic₁₉	—	2	1	no	—
98	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
99	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	complemented
100	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
101	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
102	C₂×#64520	—	2	1	no	—
103	C₂×#64520	—	2	1	no	—
104	C₂×#64520	—	2	1	no	—
105	C₂×#64520	—	2	1	no	—
106	C₂×#64520	—	2	1	no	—
107	C₂×#64520	C₂×C₄	1	2	yes	complemented
108	C₂²×C₁₉⋊C₈	—	2	1	no	—
109	C₁₉×#104	—	2	8	no	—
110	#10597294	—	2	8	no	—
111	C₁₉⋊#95	—	2	8	no	—
112	C₂⁴×C₁₉	—	2	1	no	—
113	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
114	#41×C₁₉	—	2	2	no	—
115	#41×C₁₉	—	2	2	no	—
116	#41×C₁₉	—	2	2	no	—
117	#41×C₁₉	—	2	2	no	—
118	#41×C₁₉	—	2	2	no	—
119	#41×C₁₉	—	2	2	no	—
120	#41×C₁₉	—	2	2	no	—
121	#41×C₁₉	—	2	2	no	—
122	#41×C₁₉	—	2	2	no	—
123	#41×C₁₉	—	2	2	no	—
124	#41×C₁₉	—	2	2	no	—
125	#41×C₁₉	—	2	2	no	—
126	#41×C₁₉	C₂²⋊C₄	1	4	yes	—
127	#41×C₁₉	C₂²⋊C₄	1	4	yes	—
128	#41×C₁₉	C₄⋊C₄	1	4	yes	—
129	#41×C₁₉	C₄⋊C₄	1	4	yes	—
130	C₂×Q₈×C₁₉	—	2	1	no	—
131	C₂×Q₈×C₁₉	—	2	1	no	—
132	C₂×Q₈×C₁₉	—	2	1	no	—
133	C₂×Q₈×C₁₉	C₄²	1	2	yes	—
134	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
135	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
136	C₂×D₄×C₁₉	—	2	2	no	—
137	C₂×D₄×C₁₉	—	2	2	no	—
138	C₂×D₄×C₁₉	—	2	2	no	—
139	C₂×D₄×C₁₉	—	2	2	no	—
140	C₂×D₄×C₁₉	—	2	2	no	—
141	C₂×D₄×C₁₉	—	2	2	no	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	C₄²	1	2	yes	—
146	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
147	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	2	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	4	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	4	2	no	—
158	C₂²×C₄×C₁₉	—	4	1	no	—
159	C₂²×C₄×C₁₉	—	4	1	no	—
160	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
174	C₂²×Dic₁₉	—	2	8	no	—
175	C₂²×Dic₁₉	—	2	4	no	—
176	C₂²×Dic₁₉	—	2	2	no	—
177	C₂²×Dic₁₉	—	2	2	no	—
178	C₂²×Dic₁₉	—	2	2	no	—
179	C₂²×Dic₁₉	—	2	2	no	—
180	C₂²×Dic₁₉	—	2	4	no	—
181	C₂²×Dic₁₉	—	4	2	no	—
182	C₂²×Dic₁₉	—	4	4	no	—
183	C₂²×Dic₁₉	—	4	2	no	—
184	C₂²×Dic₁₉	—	4	1	no	—
185	C₂²×Dic₁₉	—	4	1	no	—
186	C₂²×Dic₁₉	—	4	4	no	—
187	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
188	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
189	M₁₆×C₁₉	—	2	2	no	—
190	M₁₆×C₁₉	—	2	2	no	—
191	M₁₆×C₁₉	—	4	1	no	—
192	M₁₆×C₁₉	—	4	1	no	—
193	C₂×C₈×C₁₉	—	2	2	no	—
194	C₂×C₈×C₁₉	—	4	1	no	—
195	C₂×C₈×C₁₉	—	4	1	no	—
196	C₄²×C₁₉	—	2	2	no	—
197	C₄²×C₁₉	—	2	2	no	—
198	C₄²×C₁₉	—	4	1	no	—
199	C₄²×C₁₉	—	4	1	no	—
200	C₂²⋊Dic₁₉	—	2	8	no	—
201	C₂²⋊Dic₁₉	—	2	2	no	—
202	C₂²⋊Dic₁₉	—	2	2	no	—
203	C₄⋊Dic₁₉	—	2	8	no	—
204	C₄⋊Dic₁₉	—	2	2	no	—
205	C₄⋊Dic₁₉	C₂²⋊C₄	1	4	yes	—
206	C₄×Dic₁₉	—	2	8	no	—
207	C₄×Dic₁₉	—	2	2	no	—
208	C₄×Dic₁₉	—	2	2	no	—
209	C₄×Dic₁₉	—	2	1	no	—
210	C₄×Dic₁₉	—	2	1	no	—
211	C₄×Dic₁₉	—	2	2	no	—
212	C₄×Dic₁₉	—	2	2	no	—
213	C₄×Dic₁₉	—	2	1	no	—
214	C₄×Dic₁₉	—	2	1	no	—
215	C₄×Dic₁₉	—	2	2	no	—
216	C₄×Dic₁₉	—	2	2	no	—
217	C₄×Dic₁₉	—	4	1	no	—
218	C₄×Dic₁₉	—	4	1	no	—
219	#64520	—	2	2	no	—
220	#64520	—	2	2	no	—
221	#64520	—	4	1	no	—
222	#64520	—	4	1	no	—
223	C₂×C₁₉⋊C₈	—	2	2	no	—
224	C₂×C₁₉⋊C₈	—	4	1	no	—
225	C₂×C₁₉⋊C₈	—	4	1	no	—
226	#10790	—	19	1	no	maximal, Sylow
227	C₂³×C₁₉	—	2	2	no	—
228	C₂³×C₁₉	—	2	2	no	—
229	C₂³×C₁₉	—	2	2	no	—
230	C₂³×C₁₉	—	2	2	no	—
231	C₂³×C₁₉	—	2	2	no	—
232	C₂³×C₁₉	—	4	2	no	—
233	C₂³×C₁₉	—	4	2	no	—
234	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
236	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
237	C₂³×C₁₉	#120	1	1	yes	characteristic
238	C₂³×C₁₉	#120	1	1	yes	characteristic
239	C₂³×C₁₉	#121	1	1	yes	characteristic
240	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
241	Q₈×C₁₉	—	2	2	no	—
242	Q₈×C₁₉	—	2	2	no	—
243	Q₈×C₁₉	—	2	2	no	—
244	Q₈×C₁₉	#95	1	4	yes	complemented
245	D₄×C₁₉	—	2	4	no	—
246	D₄×C₁₉	—	2	4	no	—
247	D₄×C₁₉	—	2	4	no	—
248	D₄×C₁₉	—	2	4	no	—
249	D₄×C₁₉	—	2	2	no	—
250	D₄×C₁₉	—	2	2	no	—
251	D₄×C₁₉	—	2	2	no	—
252	D₄×C₁₉	#95	1	4	yes	complemented
253	C₂×C₄×C₁₉	—	2	2	no	—
254	C₂×C₄×C₁₉	—	2	2	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	4	no	—
257	C₂×C₄×C₁₉	—	2	4	no	—
258	C₂×C₄×C₁₉	—	2	4	no	—
259	C₂×C₄×C₁₉	—	2	4	no	—
260	C₂×C₄×C₁₉	—	2	4	no	—
261	C₂×C₄×C₁₉	—	4	4	no	—
262	C₂×C₄×C₁₉	—	4	2	no	—
263	C₂×C₄×C₁₉	—	4	4	no	—
264	C₂×C₄×C₁₉	—	4	2	no	—
265	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
274	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
275	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
276	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
277	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
278	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
279	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
280	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
281	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
282	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
283	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
284	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
285	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
286	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
287	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
288	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
289	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
290	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
291	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
292	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
293	C₂×Dic₁₉	—	2	2	no	—
294	C₂×Dic₁₉	—	2	2	no	—
295	C₂×Dic₁₉	—	2	4	no	—
296	C₂×Dic₁₉	—	2	2	no	—
297	C₂×Dic₁₉	—	2	4	no	—
298	C₂×Dic₁₉	—	2	2	no	—
299	C₂×Dic₁₉	—	2	2	no	—
300	C₂×Dic₁₉	—	4	4	no	—
301	C₂×Dic₁₉	—	4	4	no	—
302	C₂×Dic₁₉	—	4	16	no	—
303	C₂×Dic₁₉	—	4	4	no	—
304	C₂×Dic₁₉	—	4	2	no	—
305	C₂×Dic₁₉	—	4	4	no	—
306	C₂×Dic₁₉	—	4	2	no	—
307	C₂×Dic₁₉	—	4	2	no	—
308	C₂×Dic₁₉	—	4	2	no	—
309	C₂×Dic₁₉	#104	1	4	yes	complemented
310	C₈×C₁₉	—	4	2	no	—
311	C₁₉⋊C₈	—	4	2	no	—
312	C₂×C₄×#41	—	19	1	no	—
313	C₂²×#104	—	19	1	no	—
314	C₂²×#104	D₁₉	1	1	yes	characteristic
315	C₂×#339	—	19	1	no	—
316	C₂×#339	—	19	1	no	—
317	#1728	—	19	1	no	—
318	C₄×#95	—	19	1	no	—
319	C₂²×C₁₉	—	2	2	no	—
320	C₂²×C₁₉	—	2	2	no	—
321	C₂²×C₁₉	—	2	1	no	—
322	C₂²×C₁₉	—	2	1	no	—
323	C₂²×C₁₉	—	2	1	no	—
324	C₂²×C₁₉	—	2	1	no	—
325	C₂²×C₁₉	—	2	2	no	—
326	C₂²×C₁₉	—	2	2	no	—
327	C₂²×C₁₉	—	2	4	no	—
328	C₂²×C₁₉	—	4	4	no	—
329	C₂²×C₁₉	—	4	2	no	—
330	C₂²×C₁₉	—	4	2	no	—
331	C₂²×C₁₉	—	4	4	no	—
332	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
333	C₂²×C₁₉	#379	1	1	yes	characteristic
334	C₂²×C₁₉	#380	1	1	yes	characteristic
335	C₂²×C₁₉	#385	1	1	yes	characteristic
336	C₂²×C₁₉	#385	1	1	yes	characteristic
337	C₂²×C₁₉	#386	1	1	yes	characteristic
338	C₂²×C₁₉	#386	1	1	yes	characteristic
339	C₂²×C₁₉	C₂×#104	1	2	yes	—
340	C₂²×C₁₉	#421	1	2	yes	—
341	C₄×C₁₉	—	2	4	no	—
342	C₄×C₁₉	—	4	4	no	—
343	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
344	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
345	C₄×C₁₉	#380	1	1	yes	characteristic
346	C₄×C₁₉	#381	1	1	yes	characteristic
347	C₄×C₁₉	#385	1	1	yes	characteristic
348	C₄×C₁₉	#385	1	1	yes	characteristic
349	C₄×C₁₉	#386	1	1	yes	characteristic
350	C₄×C₁₉	#386	1	1	yes	characteristic
351	Dic₁₉	—	2	4	no	—
352	Dic₁₉	—	4	4	no	—
353	Dic₁₉	—	4	2	no	—
354	Dic₁₉	—	4	4	no	—
355	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
356	C₂²×M₁₆	—	19	1	no	—
357	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
358	C₄×#41	—	38	2	no	—
359	C₄×#41	—	38	2	no	—
360	C₄×#41	—	38	2	no	—
361	C₄×#41	—	38	2	no	—
362	C₂×C₄×Q₈	—	19	2	no	—
363	C₂×C₄×D₄	—	19	2	no	—
364	C₂×C₄×D₄	—	38	2	no	—
365	C₂×#117	—	19	1	no	—
366	C₂×#117	—	38	1	no	—
367	C₂²×C₄²	—	19	1	no	—
368	C₂²×C₄²	—	19	1	no	—
369	C₂²×C₄²	—	38	1	no	—
370	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
371	C₂×#104	—	2	2	no	—
372	C₂×#104	—	2	2	no	—
373	C₂×#104	—	19	4	no	—
374	C₂×#104	—	38	2	no	—
375	C₂×#104	—	38	2	no	—
376	C₂×#104	Dic₁₉	1	4	yes	complemented
377	C₂×#95	—	38	2	no	—
378	#339	—	38	2	no	—
379	#339	—	38	2	no	—
380	#336	—	38	1	no	—
381	#336	—	38	1	no	—
382	C₂×C₁₉	—	2	1	no	—
383	C₂×C₁₉	—	2	1	no	—
384	C₂×C₁₉	—	2	1	no	—
385	C₂×C₁₉	—	2	1	no	—
386	C₂×C₁₉	—	4	4	no	—
387	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
388	C₂×C₁₉	C₄×#104	1	1	yes	characteristic
389	C₂×C₁₉	#1759	1	1	yes	characteristic
390	C₂×C₁₉	#1789	1	2	yes	—
391	C₂×C₁₉	#1806	1	2	yes	—
392	C₂×#41	—	2	1	no	—
393	C₂×#41	—	2	1	no	—
394	C₂×#41	—	2	1	no	—
395	C₂×#41	—	2	1	no	—
396	C₂×#41	—	2	1	no	—
397	C₂×#41	—	2	1	no	—
398	C₂×#41	Dic₃₈	1	2	yes	—
399	C₂×#41	C₄×D₁₉	1	2	yes	—
400	C₂×#41	D₇₆	1	2	yes	—
401	C₂×#41	C₂×Dic₁₉	1	2	yes	—
402	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
403	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
404	C₂²×Q₈	C₄×D₁₉	1	1	yes	characteristic
405	C₂²×D₄	—	2	1	no	—
406	C₂²×D₄	C₄×D₁₉	1	1	yes	characteristic
407	C₂³×C₄	—	2	1	no	—
408	C₂³×C₄	—	2	1	no	—
409	C₂³×C₄	—	19	2	no	—
410	C₂³×C₄	—	38	2	no	—
411	C₂³×C₄	—	38	1	no	—
412	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
413	C₂×M₁₆	—	2	1	no	—
414	C₂×M₁₆	—	2	1	no	—
415	C₂×M₁₆	—	2	1	no	—
416	C₂×M₁₆	—	2	1	no	—
417	C₂×M₁₆	—	2	1	no	—
418	C₂×M₁₆	—	19	2	no	—
419	C₂×M₁₆	—	38	1	no	—
420	C₂×M₁₆	—	38	1	no	—
421	C₂×M₁₆	—	38	1	no	—
422	C₂×M₁₆	—	38	1	no	—
423	C₂×M₁₆	—	38	1	no	—
424	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	complemented
425	C₂²×C₈	—	2	1	no	—
426	C₂²×C₈	—	38	1	no	—
427	C₄×Q₈	—	38	4	no	—
428	C₄×Q₈	—	38	4	no	—
429	C₄×D₄	—	38	4	no	—
430	C₄×D₄	—	38	8	no	—
431	C₄×D₄	—	38	8	no	—
432	C₄×D₄	—	38	4	no	—
433	#117	—	19	2	no	—
434	#117	—	19	2	no	—
435	#117	—	38	4	no	—
436	#117	—	38	4	no	—
437	#117	—	38	1	no	—
438	#117	—	38	1	no	—
439	C₂×C₄⋊C₄	—	19	2	no	—
440	C₂×C₄⋊C₄	—	38	2	no	—
441	C₂×C₂²⋊C₄	—	38	2	no	—
442	C₂×C₂²⋊C₄	—	38	1	no	—
443	C₂×C₄²	—	2	1	no	—
444	C₂×C₄²	—	2	1	no	—
445	C₂×C₄²	—	2	1	no	—
446	C₂×C₄²	—	2	1	no	—
447	C₂×C₄²	—	2	1	no	—
448	C₂×C₄²	—	19	2	no	—
449	C₂×C₄²	—	19	1	no	—
450	C₂×C₄²	—	19	1	no	—
451	C₂×C₄²	—	19	2	no	—
452	C₂×C₄²	—	38	2	no	—
453	C₂×C₄²	—	38	4	no	—
454	C₂×C₄²	—	38	4	no	—
455	C₂×C₄²	—	38	1	no	—
456	C₂×C₄²	—	38	1	no	—
457	C₂×C₄²	—	38	1	no	—
458	C₂×C₄²	—	38	1	no	—
459	C₂×C₄²	—	38	1	no	—
460	C₂×C₄²	—	38	1	no	—
461	C₂×C₄²	—	38	1	no	—
462	C₂×C₄²	—	38	1	no	—
463	C₂×C₄²	—	38	1	no	—
464	C₂×C₄²	—	38	1	no	—
465	C₂×C₄²	C₂×Dic₁₉	1	2	yes	complemented
466	#104	—	2	8	no	—
467	#104	—	38	8	no	—
468	#95	—	38	8	no	—
469	C₁₉	#10790	1	1	yes	characteristic, complemented, Sylow
470	C₂⁴	—	2	1	no	—
471	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
472	#41	—	2	2	no	—
473	#41	—	2	2	no	—
474	#41	—	2	2	no	—
475	#41	—	2	2	no	—
476	#41	—	2	2	no	—
477	#41	—	2	2	no	—
478	#41	—	2	2	no	—
479	#41	—	2	2	no	—
480	#41	—	2	2	no	—
481	#41	—	2	2	no	—
482	#41	—	2	2	no	—
483	#41	—	2	2	no	—
484	#41	Dic₁₉⋊C₄	1	4	yes	—
485	#41	C₄⋊Dic₁₉	1	4	yes	—
486	#41	(C₂×D₁₉)⋊C₄	1	4	yes	—
487	#41	C₂²⋊Dic₁₉	1	4	yes	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	C₄×Dic₁₉	1	2	yes	—
492	C₂×Q₈	Dic₁₉⋊C₄	1	2	yes	—
493	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
494	C₂×D₄	—	2	2	no	—
495	C₂×D₄	—	2	2	no	—
496	C₂×D₄	—	2	2	no	—
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	2	2	no	—
499	C₂×D₄	—	2	2	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	C₄×Dic₁₉	1	2	yes	—
504	C₂×D₄	Dic₁₉⋊C₄	1	2	yes	—
505	C₂×D₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	4	2	no	—
516	C₂²×C₄	—	4	1	no	—
517	C₂²×C₄	—	4	1	no	—
518	C₂²×C₄	—	19	2	no	—
519	C₂²×C₄	—	19	2	no	—
520	C₂²×C₄	—	38	4	no	—
521	C₂²×C₄	—	38	4	no	—
522	C₂²×C₄	—	38	8	no	—
523	C₂²×C₄	—	38	2	no	—
524	C₂²×C₄	—	38	2	no	—
525	C₂²×C₄	—	38	2	no	—
526	C₂²×C₄	—	38	2	no	—
527	C₂²×C₄	—	76	4	no	—
528	C₂²×C₄	—	76	2	no	—
529	C₂²×C₄	—	76	4	no	—
530	C₂²×C₄	—	76	2	no	—
531	C₂²×C₄	—	76	1	no	—
532	C₂²×C₄	—	76	1	no	—
533	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
534	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
535	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
536	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
537	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
538	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
539	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
540	C₂²×C₄	#64543	1	1	yes	characteristic
541	C₂²×C₄	#64543	1	1	yes	characteristic
542	C₂²×C₄	#64543	1	1	yes	characteristic
543	C₂²×C₄	#64543	1	1	yes	characteristic
544	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
545	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
546	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
547	M₁₆	—	2	2	no	—
548	M₁₆	—	2	2	no	—
549	M₁₆	—	4	1	no	—
550	M₁₆	—	4	1	no	—
551	M₁₆	—	38	2	no	—
552	M₁₆	—	38	2	no	—
553	M₁₆	—	76	1	no	—
554	M₁₆	—	76	1	no	—
555	C₂×C₈	—	2	2	no	—
556	C₂×C₈	—	4	1	no	—
557	C₂×C₈	—	4	1	no	—
558	C₂×C₈	—	38	2	no	—
559	C₂×C₈	—	76	1	no	—
560	C₂×C₈	—	76	1	no	—
561	C₄⋊C₄	—	19	4	no	—
562	C₄⋊C₄	—	38	8	no	—
563	C₄⋊C₄	—	38	2	no	—
564	C₂²⋊C₄	—	38	8	no	—
565	C₂²⋊C₄	—	38	2	no	—
566	C₂²⋊C₄	—	38	2	no	—
567	C₄²	—	2	2	no	—
568	C₄²	—	2	2	no	—
569	C₄²	—	4	1	no	—
570	C₄²	—	4	1	no	—
571	C₄²	—	38	8	no	—
572	C₄²	—	38	1	no	—
573	C₄²	—	38	1	no	—
574	C₄²	—	38	2	no	—
575	C₄²	—	38	2	no	—
576	C₄²	—	38	1	no	—
577	C₄²	—	38	1	no	—
578	C₄²	—	38	2	no	—
579	C₄²	—	38	2	no	—
580	C₄²	—	38	2	no	—
581	C₄²	—	38	2	no	—
582	C₄²	—	76	1	no	—
583	C₄²	—	76	1	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	4	2	no	—
590	C₂³	—	4	2	no	—
591	C₂³	#10597324	1	1	yes	characteristic
592	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
593	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
594	C₂³	#10597328	1	1	yes	characteristic
595	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
596	C₂³	#10597383	1	1	yes	characteristic
597	C₂³	#10597385	1	1	yes	characteristic
598	Q₈	—	2	2	no	—
599	Q₈	—	2	2	no	—
600	Q₈	—	2	2	no	—
601	Q₈	C₁₉⋊#95	1	4	yes	complemented
602	D₄	—	2	4	no	—
603	D₄	—	2	4	no	—
604	D₄	—	2	4	no	—
605	D₄	—	2	4	no	—
606	D₄	—	2	2	no	—
607	D₄	—	2	2	no	—
608	D₄	—	2	2	no	—
609	D₄	C₁₉⋊#95	1	4	yes	complemented
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	4	4	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	4	4	no	—
621	C₂×C₄	—	4	2	no	—
622	C₂×C₄	—	19	4	no	—
623	C₂×C₄	—	38	2	no	—
624	C₂×C₄	—	38	2	no	—
625	C₂×C₄	—	38	4	no	—
626	C₂×C₄	—	38	2	no	—
627	C₂×C₄	—	38	2	no	—
628	C₂×C₄	—	38	4	no	—
629	C₂×C₄	—	38	2	no	—
630	C₂×C₄	—	76	4	no	—
631	C₂×C₄	—	76	4	no	—
632	C₂×C₄	—	76	16	no	—
633	C₂×C₄	—	76	4	no	—
634	C₂×C₄	—	76	2	no	—
635	C₂×C₄	—	76	4	no	—
636	C₂×C₄	—	76	2	no	—
637	C₂×C₄	—	76	2	no	—
638	C₂×C₄	—	76	2	no	—
639	C₂×C₄	#10597323	1	1	yes	characteristic
640	C₂×C₄	#10597323	1	1	yes	characteristic
641	C₂×C₄	#10597324	1	1	yes	characteristic
642	C₂×C₄	#10597324	1	1	yes	characteristic
643	C₂×C₄	#10597324	1	1	yes	characteristic
644	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
645	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
646	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
647	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
648	C₂×C₄	#10597328	1	1	yes	characteristic
649	C₂×C₄	#10597332	1	1	yes	characteristic
650	C₂×C₄	#10597332	1	1	yes	characteristic
651	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
652	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
653	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
654	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
655	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
656	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
657	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
658	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
659	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
660	C₂×C₄	#10597381	1	1	yes	characteristic
661	C₂×C₄	#10597381	1	1	yes	characteristic
662	C₂×C₄	#10597383	1	1	yes	characteristic
663	C₂×C₄	#10597385	1	1	yes	characteristic
664	C₂×C₄	#10597385	1	1	yes	characteristic
665	C₂×C₄	#10597385	1	1	yes	characteristic
666	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
667	C₈	—	4	2	no	—
668	C₈	—	76	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	4	no	—
678	C₂²	—	4	4	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	4	no	—
682	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
683	C₂²	#11926399	1	1	yes	characteristic
684	C₂²	#11926402	1	1	yes	characteristic
685	C₂²	#11926416	1	1	yes	characteristic
686	C₂²	#11926419	1	1	yes	characteristic
687	C₂²	#11926421	1	1	yes	characteristic
688	C₂²	#11926424	1	1	yes	characteristic
689	C₂²	#104×D₁₉	1	2	yes	—
690	C₂²	#11926559	1	2	yes	—
691	C₄	—	2	4	no	—
692	C₄	—	4	4	no	—
693	C₄	—	38	4	no	—
694	C₄	—	76	4	no	—
695	C₄	—	76	2	no	—
696	C₄	—	76	4	no	—
697	C₄	C₂×C₁₉⋊#95	1	1	yes	characteristic
698	C₄	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
699	C₄	#11926402	1	1	yes	characteristic
700	C₄	#11926405	1	1	yes	characteristic
701	C₄	#11926416	1	1	yes	characteristic
702	C₄	#11926419	1	1	yes	characteristic
703	C₄	#11926421	1	1	yes	characteristic
704	C₄	#11926424	1	1	yes	characteristic
705	C₂	—	2	1	no	—
706	C₂	—	2	1	no	—
707	C₂	—	2	1	no	—
708	C₂	—	2	1	no	—
709	C₂	—	4	4	no	—
710	C₂	#14561857	1	1	yes	characteristic
711	C₂	#104×Dic₁₉	1	1	yes	characteristic
712	C₂	#14563447	1	1	yes	characteristic
713	C₂	#14563577	1	2	yes	—
714	C₂	#14563653	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₁₉×#104	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×#104	D₁₉
hypocenter	C₁₉	#10790
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂²×#104

Complements

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

N	H ≅ G/N	type
3. C₂×#11926305	C₂	semidirect
4. C₂×#11926304	C₂	semidirect
5. #14563328	C₂	semidirect
6. C₄×C₁₉⋊#95	C₂	semidirect
13. C₂×Q₈×Dic₁₉	C₄	semidirect
15. C₂×D₄×Dic₁₉	C₄	semidirect
23. C₂×#10597294	C₄	semidirect
34. C₂×C₁₉×#104	C₄	semidirect
61. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
68. C₂×C₄²×C₁₉	C₂×C₄	semidirect
99. C₂×C₄×Dic₁₉	C₂×C₄	semidirect
107. C₂×#64520	C₂×C₄	semidirect
244. Q₈×C₁₉	#95	semidirect
252. D₄×C₁₉	#95	semidirect
309. C₂×Dic₁₉	#104	semidirect
376. C₂×#104	Dic₁₉	semidirect
424. C₂×M₁₆	C₂×Dic₁₉	semidirect
465. C₂×C₄²	C₂×Dic₁₉	semidirect
469. C₁₉	#10790	semidirect
601. Q₈	C₁₉⋊#95	semidirect
609. D₄	C₁₉⋊#95	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×Dic₁₉	2
C₂²×#10597294	2
C₂×#11926305	2
C₂×#11926304	2
#14563328	2
C₄×C₁₉⋊#95	2
C₂²×C₁₉×#104	2
#10790	19