Subgroups — #18088035

Order 4864.

1164 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926561	C₂	1	1	yes	maximal, characteristic
2	#14572154	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926315	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926315	C₂	1	1	yes	maximal, characteristic, complemented
5	#14563361	C₂	1	1	yes	maximal, characteristic, complemented
6	#14563346	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#568	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂×#10597372	C₂²	1	1	yes	characteristic
11	C₂×#10597372	C₂²	1	1	yes	characteristic
12	#11926561	—	2	2	no	—
13	#11926561	C₄	1	4	yes	complemented
14	C₂×#10597294	—	2	2	no	—
15	#11926553	C₄	1	2	yes	complemented
16	#11926549	C₄	1	2	yes	complemented
17	#11926545	—	2	2	no	—
18	#11926540	—	2	2	no	—
19	#11926315	—	2	2	no	—
20	#11926315	—	2	2	no	—
21	#11926308	—	2	2	no	—
22	#11926305	—	2	2	no	—
23	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#568	—	2	2	no	—
25	C₁₉×#568	—	2	2	no	—
26	C₁₉×#568	—	2	2	no	—
27	C₁₉×#568	—	2	2	no	—
28	C₂×C₁₉×#131	—	2	2	no	—
29	C₂×C₁₉×#131	C₄	1	4	yes	complemented
30	C₂²×M₁₆×C₁₉	—	2	2	no	—
31	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
32	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂×#41×C₁₉	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
40	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
41	C₂×#41×C₁₉	D₄	1	2	yes	—
42	C₂×#41×C₁₉	D₄	1	2	yes	—
43	C₂×#41×C₁₉	D₄	1	2	yes	—
44	C₂×#41×C₁₉	Q₈	1	2	yes	—
45	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	—	2	1	no	—
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₁₉×#131	—	2	8	no	—
51	C₁₉×#131	—	2	8	no	—
52	C₁₉×#131	—	2	8	no	—
53	C₁₉×#131	—	2	8	no	—
54	C₂×M₁₆×C₁₉	—	2	8	no	—
55	C₂×M₁₆×C₁₉	—	2	8	no	—
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	—	2	1	no	—
62	C₂×M₁₆×C₁₉	—	2	1	no	—
63	C₂×M₁₆×C₁₉	—	2	4	no	—
64	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
65	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
66	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
67	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
68	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
69	C₂²×C₈×C₁₉	—	2	1	no	—
70	C₂²×C₈×C₁₉	—	2	4	no	—
71	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
72	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
73	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
74	#10597372	—	2	1	no	—
75	#10597372	—	2	1	no	—
76	#10597372	—	2	1	no	—
77	#10597372	—	2	1	no	—
78	#10597372	—	2	1	no	—
79	#10597372	—	2	1	no	—
80	#10597372	C₂×C₄	1	2	yes	—
81	#10597372	C₂×C₄	1	2	yes	—
82	C₂×C₄⋊Dic₁₉	—	2	1	no	—
83	C₂×C₄⋊Dic₁₉	—	2	1	no	—
84	C₂×C₄×Dic₁₉	—	2	1	no	—
85	C₂×C₄×Dic₁₉	—	2	1	no	—
86	C₂×#64520	—	2	1	no	—
87	C₂×#64520	—	2	1	no	—
88	C₂×#64520	—	2	1	no	—
89	C₂×#64520	—	2	1	no	—
90	C₂×#64520	—	2	1	no	—
91	C₂×#64520	—	2	1	no	—
92	C₂×#64520	—	2	1	no	—
93	C₂×#64520	—	2	1	no	—
94	C₂×#64520	—	2	1	no	—
95	C₂×#64520	—	2	1	no	—
96	C₂×#64520	C₂×C₄	1	2	yes	—
97	C₂×#64520	C₂×C₄	1	2	yes	—
98	C₂²×C₁₉⋊C₈	—	2	1	no	—
99	C₂²×C₁₉⋊C₈	—	2	1	no	—
100	#10597294	—	2	8	no	—
101	#10597292	—	2	4	no	—
102	#10597289	—	2	4	no	—
103	C₂⁴×C₁₉	—	2	1	no	—
104	C₂⁴×C₁₉	#41	1	1	yes	characteristic
105	#41×C₁₉	—	2	2	no	—
106	#41×C₁₉	—	2	2	no	—
107	#41×C₁₉	—	2	2	no	—
108	#41×C₁₉	—	2	2	no	—
109	#41×C₁₉	—	2	2	no	—
110	#41×C₁₉	—	2	2	no	—
111	#41×C₁₉	—	2	2	no	—
112	#41×C₁₉	—	2	2	no	—
113	#41×C₁₉	—	2	2	no	—
114	#41×C₁₉	—	2	2	no	—
115	#41×C₁₉	—	2	2	no	—
116	#41×C₁₉	—	2	2	no	—
117	#41×C₁₉	C₂²⋊C₄	1	4	yes	—
118	#41×C₁₉	C₂²⋊C₄	1	4	yes	—
119	#41×C₁₉	C₄⋊C₄	1	4	yes	—
120	#41×C₁₉	C₄⋊C₄	1	4	yes	—
121	C₂×Q₈×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	C₄²	1	2	yes	—
125	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
126	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	—	2	2	no	—
132	C₂×D₄×C₁₉	—	2	2	no	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	C₄²	1	2	yes	—
137	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
138	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
160	C₂²×Dic₁₉	—	4	1	no	—
161	C₂²×Dic₁₉	—	4	1	no	—
162	M₁₆×C₁₉	—	2	16	no	—
163	M₁₆×C₁₉	—	2	2	no	—
164	M₁₆×C₁₉	—	2	2	no	—
165	M₁₆×C₁₉	—	2	2	no	—
166	M₁₆×C₁₉	—	2	2	no	—
167	M₁₆×C₁₉	—	2	2	no	—
168	M₁₆×C₁₉	—	2	2	no	—
169	M₁₆×C₁₉	—	2	2	no	—
170	M₁₆×C₁₉	C₂²⋊C₄	1	4	yes	—
171	C₂×C₈×C₁₉	—	2	16	no	—
172	C₂×C₈×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	2	2	no	—
175	C₂×C₈×C₁₉	—	2	2	no	—
176	C₂×C₈×C₁₉	—	2	2	no	—
177	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
178	C₂²⋊Dic₁₉	—	2	2	no	—
179	C₂²⋊Dic₁₉	—	2	2	no	—
180	C₂²⋊Dic₁₉	—	4	1	no	—
181	C₂²⋊Dic₁₉	—	4	1	no	—
182	C₄⋊Dic₁₉	—	2	2	no	—
183	C₄⋊Dic₁₉	—	2	2	no	—
184	C₄⋊Dic₁₉	—	4	1	no	—
185	C₄⋊Dic₁₉	—	4	1	no	—
186	C₄×Dic₁₉	—	2	2	no	—
187	C₄×Dic₁₉	—	2	2	no	—
188	C₄×Dic₁₉	—	4	1	no	—
189	C₄×Dic₁₉	—	4	1	no	—
190	#64520	—	2	2	no	—
191	#64520	—	2	2	no	—
192	#64520	—	2	2	no	—
193	#64520	—	2	2	no	—
194	#64520	—	4	1	no	—
195	#64520	—	4	1	no	—
196	#64520	—	4	1	no	—
197	#64520	—	4	1	no	—
198	C₂×C₁₉⋊C₈	—	2	2	no	—
199	C₂×C₁₉⋊C₈	—	2	2	no	—
200	C₂×C₁₉⋊C₈	—	4	1	no	—
201	C₂×C₁₉⋊C₈	—	4	1	no	—
202	C₂×C₁₉⋊C₈	—	4	1	no	—
203	C₂×C₁₉⋊C₈	—	4	1	no	—
204	#10778	—	19	1	no	maximal, Sylow
205	C₂³×C₁₉	—	2	2	no	—
206	C₂³×C₁₉	—	2	2	no	—
207	C₂³×C₁₉	—	2	2	no	—
208	C₂³×C₁₉	—	8	1	no	—
209	C₂³×C₁₉	—	8	2	no	—
210	C₂³×C₁₉	#117	1	1	yes	characteristic
211	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
212	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
213	C₂³×C₁₉	#121	1	1	yes	characteristic
214	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
215	C₂³×C₁₉	#123	1	1	yes	characteristic
216	C₂³×C₁₉	#123	1	1	yes	characteristic
217	Q₈×C₁₉	—	2	2	no	—
218	Q₈×C₁₉	—	2	2	no	—
219	Q₈×C₁₉	—	2	2	no	—
220	Q₈×C₁₉	#95	1	4	yes	—
221	D₄×C₁₉	—	2	4	no	—
222	D₄×C₁₉	—	2	4	no	—
223	D₄×C₁₉	—	2	4	no	—
224	D₄×C₁₉	—	2	4	no	—
225	D₄×C₁₉	—	2	2	no	—
226	D₄×C₁₉	—	2	2	no	—
227	D₄×C₁₉	—	2	2	no	—
228	D₄×C₁₉	#95	1	4	yes	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	2	4	no	—
235	C₂×C₄×C₁₉	—	2	4	no	—
236	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
253	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
254	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
255	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
256	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
257	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
258	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
263	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
264	C₂×Dic₁₉	—	4	2	no	—
265	C₂×Dic₁₉	—	4	2	no	—
266	C₂×Dic₁₉	—	8	2	no	—
267	C₂×Dic₁₉	—	8	2	no	—
268	C₈×C₁₉	—	2	4	no	—
269	C₈×C₁₉	—	2	4	no	—
270	C₁₉⋊C₈	—	4	2	no	—
271	C₁₉⋊C₈	—	4	2	no	—
272	C₂×#568	D₁₉	1	1	yes	characteristic
273	C₂×#421	—	19	1	no	—
274	#2896	—	19	1	no	—
275	C₂×#344	—	19	1	no	—
276	C₂×#344	—	19	1	no	—
277	#1738	—	19	1	no	—
278	#1733	—	19	1	no	—
279	C₂²×C₁₉	—	2	4	no	—
280	C₂²×C₁₉	—	4	1	no	—
281	C₂²×C₁₉	—	4	1	no	—
282	C₂²×C₁₉	—	4	1	no	—
283	C₂²×C₁₉	—	4	1	no	—
284	C₂²×C₁₉	—	4	1	no	—
285	C₂²×C₁₉	—	4	1	no	—
286	C₂²×C₁₉	—	4	1	no	—
287	C₂²×C₁₉	—	4	4	no	—
288	C₂²×C₁₉	—	8	2	no	—
289	C₂²×C₁₉	—	8	2	no	—
290	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
291	C₂²×C₁₉	#380	1	1	yes	characteristic
292	C₂²×C₁₉	#381	1	1	yes	characteristic
293	C₂²×C₁₉	#385	1	1	yes	characteristic
294	C₂²×C₁₉	#385	1	1	yes	characteristic
295	C₂²×C₁₉	#386	1	1	yes	characteristic
296	C₂²×C₁₉	#386	1	1	yes	characteristic
297	C₄×C₁₉	—	2	4	no	—
298	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
299	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
300	C₄×C₁₉	#379	1	1	yes	characteristic
301	C₄×C₁₉	#380	1	1	yes	characteristic
302	C₄×C₁₉	#385	1	1	yes	characteristic
303	C₄×C₁₉	#385	1	1	yes	characteristic
304	C₄×C₁₉	#386	1	1	yes	characteristic
305	C₄×C₁₉	#386	1	1	yes	characteristic
306	Dic₁₉	—	8	2	no	—
307	Dic₁₉	—	8	2	no	—
308	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
309	#568	—	2	2	no	—
310	#568	—	2	2	no	—
311	#568	—	2	2	no	—
312	#568	—	2	2	no	—
313	C₂×#131	—	2	2	no	—
314	C₂×#131	Dic₁₉	1	4	yes	complemented
315	C₂²×M₁₆	—	2	2	no	—
316	C₂²×M₁₆	—	19	1	no	—
317	C₂²×M₁₆	—	19	1	no	—
318	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
319	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
320	C₂×#117	—	19	1	no	—
321	C₂×#117	—	19	1	no	—
322	#421	—	19	4	no	—
323	#421	—	38	2	no	—
324	C₂×#104	—	38	2	no	—
325	#419	—	19	2	no	—
326	#418	—	19	2	no	—
327	#417	—	38	2	no	—
328	#416	—	38	2	no	—
329	#344	—	38	2	no	—
330	#344	—	38	2	no	—
331	#341	—	38	2	no	—
332	#339	—	38	2	no	—
333	C₂×C₁₉	—	2	1	no	—
334	C₂×C₁₉	—	2	1	no	—
335	C₂×C₁₉	—	2	1	no	—
336	C₂×C₁₉	—	2	1	no	—
337	C₂×C₁₉	—	2	1	no	—
338	C₂×C₁₉	—	2	1	no	—
339	C₂×C₁₉	—	2	1	no	—
340	C₂×C₁₉	—	4	4	no	—
341	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
342	C₂×#41	—	2	1	no	—
343	C₂×#41	—	2	1	no	—
344	C₂×#41	—	2	1	no	—
345	C₂×#41	—	2	1	no	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	—	2	1	no	—
348	C₂×#41	Dic₃₈	1	2	yes	—
349	C₂×#41	C₄×D₁₉	1	2	yes	—
350	C₂×#41	D₇₆	1	2	yes	—
351	C₂×#41	C₂×Dic₁₉	1	2	yes	—
352	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
353	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
354	C₂²×Q₈	C₄×D₁₉	1	1	yes	characteristic
355	C₂²×D₄	—	2	1	no	—
356	C₂²×D₄	C₄×D₁₉	1	1	yes	characteristic
357	C₂³×C₄	—	2	1	no	—
358	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
359	#131	—	2	8	no	—
360	#131	—	2	8	no	—
361	#131	—	2	8	no	—
362	#131	—	2	8	no	—
363	C₂×M₁₆	—	2	8	no	—
364	C₂×M₁₆	—	2	8	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂×M₁₆	—	2	4	no	—
373	C₂×M₁₆	—	19	2	no	—
374	C₂×M₁₆	—	19	2	no	—
375	C₂×M₁₆	—	38	1	no	—
376	C₂×M₁₆	—	38	1	no	—
377	C₂×M₁₆	—	38	1	no	—
378	C₂×M₁₆	—	38	1	no	—
379	C₂×M₁₆	—	38	1	no	—
380	C₂×M₁₆	—	38	1	no	—
381	C₂×M₁₆	—	38	1	no	—
382	C₂×M₁₆	—	38	1	no	—
383	C₂×M₁₆	—	38	1	no	—
384	C₂×M₁₆	—	38	1	no	—
385	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
386	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
387	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
388	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
389	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	—	2	4	no	—
392	C₂²×C₈	—	38	1	no	—
393	C₂²×C₈	—	38	1	no	—
394	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
395	#117	—	19	2	no	—
396	#117	—	19	2	no	—
397	#117	—	38	1	no	—
398	#117	—	38	1	no	—
399	#117	—	38	1	no	—
400	#117	—	38	1	no	—
401	#117	—	38	1	no	—
402	#117	—	38	1	no	—
403	C₂×C₄⋊C₄	—	38	1	no	—
404	C₂×C₄⋊C₄	—	38	1	no	—
405	C₂×C₂²⋊C₄	—	38	1	no	—
406	C₂×C₂²⋊C₄	—	38	1	no	—
407	C₂×C₄²	—	38	1	no	—
408	C₂×C₄²	—	38	1	no	—
409	#104	—	38	8	no	—
410	#103	—	38	4	no	—
411	#102	—	38	4	no	—
412	C₁₉	#10778	1	1	yes	characteristic, complemented, Sylow
413	C₂⁴	—	2	1	no	—
414	C₂⁴	#64541	1	1	yes	characteristic
415	#41	—	2	2	no	—
416	#41	—	2	2	no	—
417	#41	—	2	2	no	—
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	2	2	no	—
422	#41	—	2	2	no	—
423	#41	—	2	2	no	—
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	#41	—	2	2	no	—
427	#41	Dic₁₉⋊C₄	1	4	yes	—
428	#41	C₄⋊Dic₁₉	1	4	yes	—
429	#41	(C₂×D₁₉)⋊C₄	1	4	yes	—
430	#41	C₂²⋊Dic₁₉	1	4	yes	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	C₄×Dic₁₉	1	2	yes	—
435	C₂×Q₈	Dic₁₉⋊C₄	1	2	yes	—
436	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	C₄×Dic₁₉	1	2	yes	—
447	C₂×D₄	Dic₁₉⋊C₄	1	2	yes	—
448	C₂×D₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	76	1	no	—
457	C₂²×C₄	—	76	1	no	—
458	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
462	C₂²×C₄	#64541	1	1	yes	characteristic
463	C₂²×C₄	#64541	1	1	yes	characteristic
464	C₂²×C₄	#64541	1	1	yes	characteristic
465	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
466	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
467	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
468	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
472	M₁₆	—	2	16	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	2	no	—
475	M₁₆	—	2	2	no	—
476	M₁₆	—	2	2	no	—
477	M₁₆	—	2	2	no	—
478	M₁₆	—	2	2	no	—
479	M₁₆	—	2	2	no	—
480	M₁₆	—	38	2	no	—
481	M₁₆	—	38	2	no	—
482	M₁₆	—	38	2	no	—
483	M₁₆	—	38	2	no	—
484	M₁₆	—	76	1	no	—
485	M₁₆	—	76	1	no	—
486	M₁₆	—	76	1	no	—
487	M₁₆	—	76	1	no	—
488	M₁₆	C₂²⋊Dic₁₉	1	4	yes	—
489	C₂×C₈	—	2	16	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	38	2	no	—
496	C₂×C₈	—	38	2	no	—
497	C₂×C₈	—	76	1	no	—
498	C₂×C₈	—	76	1	no	—
499	C₂×C₈	—	76	1	no	—
500	C₂×C₈	—	76	1	no	—
501	C₂×C₈	C₂²⋊Dic₁₉	1	4	yes	—
502	C₄⋊C₄	—	38	2	no	—
503	C₄⋊C₄	—	38	2	no	—
504	C₄⋊C₄	—	76	1	no	—
505	C₄⋊C₄	—	76	1	no	—
506	C₂²⋊C₄	—	38	2	no	—
507	C₂²⋊C₄	—	38	2	no	—
508	C₂²⋊C₄	—	76	1	no	—
509	C₂²⋊C₄	—	76	1	no	—
510	C₄²	—	38	2	no	—
511	C₄²	—	38	2	no	—
512	C₄²	—	76	1	no	—
513	C₄²	—	76	1	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	8	1	no	—
518	C₂³	—	8	2	no	—
519	C₂³	#10597370	1	1	yes	characteristic
520	C₂³	#10597372	1	1	yes	characteristic
521	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
522	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
523	C₂³	#10597375	1	1	yes	characteristic
524	C₂³	#10597375	1	1	yes	characteristic
525	C₂³	#10597376	1	1	yes	characteristic
526	Q₈	—	2	2	no	—
527	Q₈	—	2	2	no	—
528	Q₈	—	2	2	no	—
529	Q₈	C₁₉⋊#95	1	4	yes	—
530	D₄	—	2	4	no	—
531	D₄	—	2	4	no	—
532	D₄	—	2	4	no	—
533	D₄	—	2	4	no	—
534	D₄	—	2	2	no	—
535	D₄	—	2	2	no	—
536	D₄	—	2	2	no	—
537	D₄	C₁₉⋊#95	1	4	yes	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	76	2	no	—
546	C₂×C₄	—	76	2	no	—
547	C₂×C₄	—	152	2	no	—
548	C₂×C₄	—	152	2	no	—
549	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
550	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
551	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
552	C₂×C₄	#10597370	1	1	yes	characteristic
553	C₂×C₄	#10597370	1	1	yes	characteristic
554	C₂×C₄	#10597370	1	1	yes	characteristic
555	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
556	C₂×C₄	#10597372	1	1	yes	characteristic
557	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
558	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
559	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
560	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
561	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
562	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
563	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
564	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
565	C₂×C₄	#10597375	1	1	yes	characteristic
566	C₂×C₄	#10597375	1	1	yes	characteristic
567	C₂×C₄	#10597376	1	1	yes	characteristic
568	C₂×C₄	#10597376	1	1	yes	characteristic
569	C₂×C₄	#10597376	1	1	yes	characteristic
570	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
571	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
572	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
573	C₂×C₄	#10597399	1	1	yes	characteristic
574	C₂×C₄	#10597399	1	1	yes	characteristic
575	C₂×C₄	#10597399	1	1	yes	characteristic
576	C₂×C₄	#10597399	1	1	yes	characteristic
577	C₈	—	2	4	no	—
578	C₈	—	2	4	no	—
579	C₈	—	76	2	no	—
580	C₈	—	76	2	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	8	2	no	—
591	C₂²	—	8	2	no	—
592	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
593	C₂²	#11926404	1	1	yes	characteristic
594	C₂²	#11926407	1	1	yes	characteristic
595	C₂²	#11926417	1	1	yes	characteristic
596	C₂²	#11926417	1	1	yes	characteristic
597	C₂²	#11926423	1	1	yes	characteristic
598	C₂²	#11926423	1	1	yes	characteristic
599	C₄	—	2	4	no	—
600	C₄	—	152	2	no	—
601	C₄	—	152	2	no	—
602	C₄	C₂×C₁₉⋊#95	1	1	yes	characteristic
603	C₄	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
604	C₄	#11926400	1	1	yes	characteristic
605	C₄	#11926404	1	1	yes	characteristic
606	C₄	#11926417	1	1	yes	characteristic
607	C₄	#11926417	1	1	yes	characteristic
608	C₄	#11926423	1	1	yes	characteristic
609	C₄	#11926423	1	1	yes	characteristic
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	2	1	no	—
614	C₂	—	2	1	no	—
615	C₂	—	2	1	no	—
616	C₂	—	2	1	no	—
617	C₂	—	4	4	no	—
618	C₂	#14561858	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11926400
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#568	C₂
socle	C₂×C₁₉	C₂²⋊#95
prime radical	C₂²×#41×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#568	D₁₉
hypocenter	C₁₉	#10778
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#568

Complements

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

N	H ≅ G/N	type
3. C₂×#11926315	C₂	semidirect
4. C₂×#11926315	C₂	semidirect
5. #14563361	C₂	semidirect
6. #14563346	C₂	semidirect
13. #11926561	C₄	semidirect
15. #11926553	C₄	semidirect
16. #11926549	C₄	semidirect
29. C₂×C₁₉×#131	C₄	semidirect
314. C₂×#131	Dic₁₉	semidirect
412. C₁₉	#10778	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926561	2
#14572154	2
C₂×#11926315	2
#14563361	2
#14563346	2
C₂×C₁₉×#568	2
#10778	19