Subgroups — #18091249

Order 4864.

822 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926587	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926586	C₂	1	1	yes	maximal, characteristic
3	#14566251	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926312	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926304	C₂	1	1	yes	maximal, characteristic
6	#14561865	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂×#10597372	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	#11926587	—	2	2	no	—
13	#11926587	—	2	2	no	—
14	#11926586	—	2	2	no	—
15	#11926586	—	2	2	no	—
16	C₂×#10597275	—	2	1	no	—
17	C₂×#10597264	—	2	1	no	—
18	C₂×#10597274	—	2	1	no	—
19	C₂×#10597265	—	2	1	no	—
20	#11926442	—	2	1	no	—
21	#11926442	—	2	1	no	—
22	#11926440	—	2	1	no	—
23	#11926440	—	2	1	no	—
24	#11926402	—	2	2	no	—
25	C₂×C₁₉⋊#95	—	2	2	no	—
26	#11926312	C₄	1	4	yes	complemented
27	#11926304	—	2	2	no	—
28	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#339	—	2	2	no	—
32	C₂³×C₄×C₁₉	—	2	1	no	—
33	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂³×Dic₁₉	—	2	1	no	—
35	C₂³×Dic₁₉	D₄	1	2	yes	—
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	D₄	1	2	yes	—
41	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
42	C₂²×C₈×C₁₉	—	2	1	no	—
43	C₁₉×#117	—	2	1	no	—
44	C₁₉×#117	—	2	1	no	—
45	C₁₉×#117	—	2	1	no	—
46	C₁₉×#117	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	—	2	1	no	—
51	C₂×C₄²×C₁₉	—	2	1	no	—
52	C₂×C₄²×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	—	2	1	no	—
54	C₂×C₄²×C₁₉	—	2	1	no	—
55	C₂×C₄²×C₁₉	—	2	1	no	—
56	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
57	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
58	#10597372	—	2	1	no	—
59	#10597372	—	2	1	no	—
60	#10597372	—	2	1	no	—
61	#10597372	—	2	1	no	—
62	C₂×C₄⋊Dic₁₉	—	2	1	no	—
63	C₂×C₄⋊Dic₁₉	—	2	1	no	—
64	C₂×C₄⋊Dic₁₉	—	2	1	no	—
65	C₂×C₄⋊Dic₁₉	—	2	1	no	—
66	C₂×C₄⋊Dic₁₉	—	2	1	no	—
67	C₂×C₄⋊Dic₁₉	—	2	1	no	—
68	C₂×C₄⋊Dic₁₉	—	2	1	no	—
69	C₂×C₄⋊Dic₁₉	—	2	1	no	—
70	C₂×C₄⋊Dic₁₉	—	2	1	no	—
71	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
73	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
74	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
75	C₂×C₄⋊Dic₁₉	Q₈	1	2	yes	—
76	C₂×Dic₁₉⋊C₄	—	2	2	no	—
77	C₂×Dic₁₉⋊C₄	—	2	2	no	—
78	C₂×C₄×Dic₁₉	—	2	1	no	—
79	C₂×#64520	—	2	1	no	—
80	C₂×#64520	—	2	1	no	—
81	C₂×#64520	—	2	1	no	—
82	C₂×#64520	C₂×C₄	1	2	yes	—
83	C₂×#64520	D₄	1	2	yes	—
84	C₂×#64520	Q₈	1	2	yes	—
85	C₂²×C₁₉⋊C₈	—	2	1	no	—
86	C₁₉⋊#95	—	2	2	no	—
87	C₁₉⋊#95	—	2	2	no	—
88	C₁₉⋊#95	—	4	4	no	—
89	#10597275	—	2	4	no	—
90	#10597274	—	2	4	no	—
91	#10597265	—	2	4	no	—
92	#10597264	—	2	4	no	—
93	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
117	C₂²×Dic₁₉	—	2	2	no	—
118	C₂²×Dic₁₉	—	2	2	no	—
119	C₂²×Dic₁₉	—	2	1	no	—
120	C₂²×Dic₁₉	—	2	1	no	—
121	C₂²×Dic₁₉	—	2	2	no	—
122	C₂²×Dic₁₉	—	4	2	no	—
123	C₂²×Dic₁₉	—	4	2	no	—
124	C₂²×Dic₁₉	—	4	2	no	—
125	C₂²×Dic₁₉	—	4	2	no	—
126	C₂²×Dic₁₉	—	4	1	no	—
127	C₂²×Dic₁₉	—	4	1	no	—
128	C₂²×Dic₁₉	C₄⋊C₄	1	4	yes	—
129	M₁₆×C₁₉	—	2	2	no	—
130	M₁₆×C₁₉	—	2	2	no	—
131	M₁₆×C₁₉	—	2	2	no	—
132	M₁₆×C₁₉	C₄⋊C₄	1	4	yes	complemented
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₂²⋊C₄×C₁₉	—	4	1	no	—
141	C₂²⋊C₄×C₁₉	—	4	1	no	—
142	C₄²×C₁₉	—	2	2	no	—
143	C₄²×C₁₉	—	2	2	no	—
144	C₄²×C₁₉	—	4	1	no	—
145	C₄²×C₁₉	—	4	1	no	—
146	C₄²×C₁₉	—	4	1	no	—
147	C₄²×C₁₉	—	4	1	no	—
148	C₂²⋊Dic₁₉	—	4	1	no	—
149	C₂²⋊Dic₁₉	—	4	1	no	—
150	C₄⋊Dic₁₉	—	2	2	no	—
151	C₄⋊Dic₁₉	—	2	2	no	—
152	C₄⋊Dic₁₉	—	2	2	no	—
153	C₄⋊Dic₁₉	—	2	2	no	—
154	C₄⋊Dic₁₉	—	2	2	no	—
155	C₄⋊Dic₁₉	—	2	1	no	—
156	C₄⋊Dic₁₉	—	2	2	no	—
157	C₄⋊Dic₁₉	—	2	1	no	—
158	C₄⋊Dic₁₉	—	2	1	no	—
159	C₄⋊Dic₁₉	—	2	1	no	—
160	C₄⋊Dic₁₉	—	4	1	no	—
161	C₄⋊Dic₁₉	—	4	1	no	—
162	Dic₁₉⋊C₄	—	8	2	no	—
163	Dic₁₉⋊C₄	—	8	2	no	—
164	C₄×Dic₁₉	—	4	1	no	—
165	C₄×Dic₁₉	—	4	1	no	—
166	#64520	—	2	2	no	—
167	#64520	—	2	2	no	—
168	#64520	—	2	2	no	—
169	#64520	C₄⋊C₄	1	4	yes	complemented
170	C₂×C₁₉⋊C₈	—	2	2	no	—
171	C₂×C₁₉⋊C₈	—	2	2	no	—
172	C₂×C₁₉⋊C₈	—	2	2	no	—
173	#11342	—	19	1	no	maximal, Sylow
174	C₂³×C₁₉	—	2	1	no	—
175	C₂³×C₁₉	—	2	1	no	—
176	C₂³×C₁₉	—	2	1	no	—
177	C₂³×C₁₉	—	2	1	no	—
178	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂³×C₁₉	#120	1	1	yes	characteristic
180	C₂³×C₁₉	#121	1	1	yes	characteristic
181	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
182	C₂³×C₁₉	#123	1	1	yes	characteristic
183	C₂³×C₁₉	#127	1	1	yes	characteristic
184	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
205	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
206	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
207	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
208	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
210	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
216	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
217	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
218	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
219	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
220	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
223	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
226	C₂×Dic₁₉	—	2	4	no	—
227	C₂×Dic₁₉	—	4	2	no	—
228	C₂×Dic₁₉	—	4	2	no	—
229	C₂×Dic₁₉	—	4	4	no	—
230	C₂×Dic₁₉	—	4	4	no	—
231	C₂×Dic₁₉	—	4	1	no	—
232	C₂×Dic₁₉	—	4	1	no	—
233	C₂×Dic₁₉	—	4	2	no	—
234	C₂×Dic₁₉	—	4	1	no	—
235	C₂×Dic₁₉	—	4	1	no	—
236	C₂×Dic₁₉	—	4	1	no	—
237	C₂×Dic₁₉	—	4	1	no	—
238	C₂×Dic₁₉	—	8	2	no	—
239	C₂×Dic₁₉	—	8	2	no	—
240	C₂×Dic₁₉	—	8	1	no	—
241	C₂×Dic₁₉	—	8	1	no	—
242	C₈×C₁₉	—	2	4	no	—
243	C₁₉⋊C₈	—	2	4	no	—
244	C₂×#428	—	19	1	no	—
245	C₂×#428	—	19	1	no	—
246	#2316	—	19	1	no	—
247	C₂×#343	—	19	1	no	—
248	C₂×#339	—	19	1	no	—
249	C₂×#339	D₁₉	1	1	yes	characteristic
250	C₄⋊#95	—	19	1	no	—
251	C₂²×C₁₉	—	2	1	no	—
252	C₂²×C₁₉	—	2	1	no	—
253	C₂²×C₁₉	—	2	1	no	—
254	C₂²×C₁₉	—	2	1	no	—
255	C₂²×C₁₉	—	2	1	no	—
256	C₂²×C₁₉	—	2	1	no	—
257	C₂²×C₁₉	—	2	1	no	—
258	C₂²×C₁₉	—	2	1	no	—
259	C₂²×C₁₉	—	2	1	no	—
260	C₂²×C₁₉	—	2	1	no	—
261	C₂²×C₁₉	—	2	1	no	—
262	C₂²×C₁₉	—	2	1	no	—
263	C₂²×C₁₉	#384	1	1	yes	characteristic
264	C₂²×C₁₉	#385	1	1	yes	characteristic
265	C₂²×C₁₉	#389	1	1	yes	characteristic
266	C₂²×C₁₉	#392	1	1	yes	characteristic
267	C₂²×C₁₉	#395	1	1	yes	characteristic
268	C₂²×C₁₉	#398	1	1	yes	characteristic
269	C₂²×C₁₉	#399	1	1	yes	characteristic
270	C₂²×C₁₉	#453	1	1	yes	characteristic
271	C₂²×C₁₉	#454	1	1	yes	characteristic
272	C₂²×C₁₉	#455	1	1	yes	characteristic
273	C₂²×C₁₉	#456	1	1	yes	characteristic
274	C₄×C₁₉	—	4	4	no	—
275	C₄×C₁₉	—	8	1	no	—
276	C₄×C₁₉	—	8	1	no	—
277	C₄×C₁₉	#385	1	1	yes	characteristic
278	C₄×C₁₉	#385	1	1	yes	characteristic
279	C₄×C₁₉	#389	1	1	yes	characteristic
280	C₄×C₁₉	#389	1	1	yes	characteristic
281	C₄×C₁₉	#395	1	1	yes	characteristic
282	C₄×C₁₉	#395	1	1	yes	characteristic
283	C₄×C₁₉	#398	1	1	yes	characteristic
284	C₄×C₁₉	#398	1	1	yes	characteristic
285	Dic₁₉	—	4	4	no	—
286	Dic₁₉	—	8	1	no	—
287	Dic₁₉	—	8	2	no	—
288	Dic₁₉	—	8	1	no	—
289	C₂²×M₁₆	—	19	1	no	—
290	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
291	C₂×#117	—	19	1	no	—
292	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
293	C₂²×C₄⋊C₄	—	19	1	no	—
294	C₂²×C₄⋊C₄	—	19	1	no	—
295	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
296	#428	—	38	2	no	—
297	#428	—	38	2	no	—
298	#428	—	38	2	no	—
299	#428	—	38	2	no	—
300	C₂×#107	—	38	1	no	—
301	C₂×#107	—	38	1	no	—
302	C₂×#106	—	38	1	no	—
303	C₂×#106	—	38	1	no	—
304	#389	—	38	1	no	—
305	#389	—	38	1	no	—
306	#389	—	38	1	no	—
307	#389	—	38	1	no	—
308	#380	—	38	2	no	—
309	C₂×#95	—	38	2	no	—
310	#343	—	19	4	no	—
311	#339	—	2	2	no	—
312	#339	—	38	2	no	—
313	C₂×C₁₉	—	2	1	no	—
314	C₂×C₁₉	—	2	1	no	—
315	C₂×C₁₉	—	2	1	no	—
316	C₂×C₁₉	—	2	1	no	—
317	C₂×C₁₉	#1444	1	1	yes	characteristic
318	C₂×C₁₉	#1856	1	1	yes	characteristic
319	C₂×C₁₉	#1857	1	1	yes	characteristic
320	C₂×C₁₉	#2006	1	1	yes	characteristic
321	C₂×C₁₉	#2007	1	1	yes	characteristic
322	C₂×C₁₉	#2060	1	1	yes	characteristic
323	C₂×C₁₉	#2061	1	1	yes	characteristic
324	C₂³×C₄	—	2	1	no	—
325	C₂³×C₄	—	19	2	no	—
326	C₂³×C₄	—	38	1	no	—
327	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
328	C₂×M₁₆	—	2	1	no	—
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	2	1	no	—
331	C₂×M₁₆	—	19	2	no	—
332	C₂×M₁₆	—	19	2	no	—
333	C₂×M₁₆	—	19	2	no	—
334	C₂×M₁₆	—	38	1	no	—
335	C₂×M₁₆	—	38	1	no	—
336	C₂×M₁₆	—	38	1	no	—
337	C₂×M₁₆	Dic₃₈	1	2	yes	—
338	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
339	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
340	C₂²×C₈	—	2	1	no	—
341	C₂²×C₈	—	38	1	no	—
342	#117	—	2	1	no	—
343	#117	—	2	1	no	—
344	#117	—	2	1	no	—
345	#117	—	2	1	no	—
346	#117	—	38	1	no	—
347	#117	—	38	1	no	—
348	#117	—	38	1	no	—
349	#117	—	38	1	no	—
350	C₂×C₄⋊C₄	—	19	2	no	—
351	C₂×C₄⋊C₄	—	19	2	no	—
352	C₂×C₄⋊C₄	—	19	2	no	—
353	C₂×C₄⋊C₄	—	19	1	no	—
354	C₂×C₄⋊C₄	—	19	1	no	—
355	C₂×C₄⋊C₄	—	38	1	no	—
356	C₂×C₄⋊C₄	—	38	1	no	—
357	C₂×C₄⋊C₄	—	38	1	no	—
358	C₂×C₄⋊C₄	—	38	1	no	—
359	C₂×C₄⋊C₄	—	38	1	no	—
360	C₂×C₄⋊C₄	—	38	1	no	—
361	C₂×C₄⋊C₄	—	38	1	no	—
362	C₂×C₄⋊C₄	—	38	1	no	—
363	C₂×C₄⋊C₄	—	38	1	no	—
364	C₂×C₄⋊C₄	—	38	2	no	—
365	C₂×C₄⋊C₄	—	38	2	no	—
366	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
367	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	38	1	no	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	—	38	1	no	—
377	C₂×C₄²	Dic₃₈	1	2	yes	—
378	#107	—	38	4	no	—
379	#107	—	38	4	no	—
380	#106	—	38	4	no	—
381	#106	—	38	4	no	—
382	#95	—	38	2	no	—
383	#95	—	38	2	no	—
384	#95	—	76	4	no	—
385	C₁₉	#11342	1	1	yes	characteristic, complemented, Sylow
386	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	4	1	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	—	4	1	no	—
395	C₂²×C₄	—	4	1	no	—
396	C₂²×C₄	—	19	4	no	—
397	C₂²×C₄	—	38	2	no	—
398	C₂²×C₄	—	38	2	no	—
399	C₂²×C₄	—	38	1	no	—
400	C₂²×C₄	—	38	1	no	—
401	C₂²×C₄	—	38	2	no	—
402	C₂²×C₄	—	76	2	no	—
403	C₂²×C₄	—	76	2	no	—
404	C₂²×C₄	—	76	2	no	—
405	C₂²×C₄	—	76	2	no	—
406	C₂²×C₄	—	76	1	no	—
407	C₂²×C₄	—	76	1	no	—
408	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
409	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
410	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
412	C₂²×C₄	#64541	1	1	yes	characteristic
413	C₂²×C₄	#64541	1	1	yes	characteristic
414	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
415	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
416	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
417	C₂²×C₄	#64543	1	1	yes	characteristic
418	C₂²×C₄	#64543	1	1	yes	characteristic
419	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
420	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
421	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
422	M₁₆	—	2	2	no	—
423	M₁₆	—	2	2	no	—
424	M₁₆	—	2	2	no	—
425	M₁₆	—	19	4	no	—
426	M₁₆	—	38	2	no	—
427	M₁₆	—	38	2	no	—
428	M₁₆	—	38	2	no	—
429	M₁₆	Dic₁₉⋊C₄	1	4	yes	complemented
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	38	2	no	—
434	C₂×C₈	—	38	2	no	—
435	C₂×C₈	—	38	2	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	38	2	no	—
441	C₄⋊C₄	—	38	2	no	—
442	C₄⋊C₄	—	38	2	no	—
443	C₄⋊C₄	—	38	2	no	—
444	C₄⋊C₄	—	38	1	no	—
445	C₄⋊C₄	—	38	2	no	—
446	C₄⋊C₄	—	38	1	no	—
447	C₄⋊C₄	—	38	2	no	—
448	C₄⋊C₄	—	38	1	no	—
449	C₄⋊C₄	—	38	1	no	—
450	C₄⋊C₄	—	76	1	no	—
451	C₄⋊C₄	—	76	1	no	—
452	C₄⋊C₄	—	152	2	no	—
453	C₄⋊C₄	—	152	2	no	—
454	C₂²⋊C₄	—	4	1	no	—
455	C₂²⋊C₄	—	4	1	no	—
456	C₂²⋊C₄	—	76	1	no	—
457	C₂²⋊C₄	—	76	1	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	4	1	no	—
461	C₄²	—	4	1	no	—
462	C₄²	—	4	1	no	—
463	C₄²	—	4	1	no	—
464	C₄²	—	76	1	no	—
465	C₄²	—	76	1	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	1	no	—
470	C₂³	#10597324	1	1	yes	characteristic
471	C₂³	#10597328	1	1	yes	characteristic
472	C₂³	#10597329	1	1	yes	characteristic
473	C₂³	#10597330	1	1	yes	characteristic
474	C₂³	#10597334	1	1	yes	characteristic
475	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
476	C₂³	#10597386	1	1	yes	characteristic
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	38	4	no	—
491	C₂×C₄	—	76	2	no	—
492	C₂×C₄	—	76	2	no	—
493	C₂×C₄	—	76	4	no	—
494	C₂×C₄	—	76	4	no	—
495	C₂×C₄	—	76	1	no	—
496	C₂×C₄	—	76	1	no	—
497	C₂×C₄	—	76	2	no	—
498	C₂×C₄	—	76	1	no	—
499	C₂×C₄	—	76	1	no	—
500	C₂×C₄	—	76	1	no	—
501	C₂×C₄	—	76	1	no	—
502	C₂×C₄	—	152	2	no	—
503	C₂×C₄	—	152	2	no	—
504	C₂×C₄	—	152	1	no	—
505	C₂×C₄	—	152	1	no	—
506	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
507	C₂×C₄	#10597315	1	1	yes	characteristic
508	C₂×C₄	#10597316	1	1	yes	characteristic
509	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
510	C₂×C₄	#10597324	1	1	yes	characteristic
511	C₂×C₄	#10597324	1	1	yes	characteristic
512	C₂×C₄	#10597324	1	1	yes	characteristic
513	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
514	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
515	C₂×C₄	#10597328	1	1	yes	characteristic
516	C₂×C₄	#10597329	1	1	yes	characteristic
517	C₂×C₄	#10597330	1	1	yes	characteristic
518	C₂×C₄	#10597334	1	1	yes	characteristic
519	C₂×C₄	#10597334	1	1	yes	characteristic
520	C₂×C₄	#10597334	1	1	yes	characteristic
521	C₂×C₄	#10597335	1	1	yes	characteristic
522	C₂×C₄	#10597335	1	1	yes	characteristic
523	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
524	C₂×C₄	#10597342	1	1	yes	characteristic
525	C₂×C₄	#10597342	1	1	yes	characteristic
526	C₂×C₄	#10597343	1	1	yes	characteristic
527	C₂×C₄	#10597343	1	1	yes	characteristic
528	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
529	C₂×C₄	#10597370	1	1	yes	characteristic
530	C₂×C₄	#10597376	1	1	yes	characteristic
531	C₂×C₄	#10597381	1	1	yes	characteristic
532	C₂×C₄	#10597383	1	1	yes	characteristic
533	C₂×C₄	#10597390	1	1	yes	characteristic
534	C₈	—	2	4	no	—
535	C₈	—	38	4	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	#11926413	1	1	yes	characteristic
549	C₂²	#11926418	1	1	yes	characteristic
550	C₂²	#11926441	1	1	yes	characteristic
551	C₂²	#11926453	1	1	yes	characteristic
552	C₂²	#11926465	1	1	yes	characteristic
553	C₂²	#11926478	1	1	yes	characteristic
554	C₂²	#11926480	1	1	yes	characteristic
555	C₂²	#11926713	1	1	yes	characteristic
556	C₂²	#11926718	1	1	yes	characteristic
557	C₂²	#11926723	1	1	yes	characteristic
558	C₂²	#11926728	1	1	yes	characteristic
559	C₄	—	4	4	no	—
560	C₄	—	8	1	no	—
561	C₄	—	8	1	no	—
562	C₄	—	76	4	no	—
563	C₄	—	152	2	no	—
564	C₄	—	152	1	no	—
565	C₄	—	152	1	no	—
566	C₄	#11926416	1	1	yes	characteristic
567	C₄	#11926418	1	1	yes	characteristic
568	C₄	#11926441	1	1	yes	characteristic
569	C₄	#11926442	1	1	yes	characteristic
570	C₄	#11926464	1	1	yes	characteristic
571	C₄	#11926465	1	1	yes	characteristic
572	C₄	#11926474	1	1	yes	characteristic
573	C₄	#11926478	1	1	yes	characteristic
574	C₂	—	2	1	no	—
575	C₂	—	2	1	no	—
576	C₂	—	2	1	no	—
577	C₂	—	2	1	no	—
578	C₂	#14561899	1	1	yes	characteristic
579	C₂	#14563846	1	1	yes	characteristic
580	C₂	#14563851	1	1	yes	characteristic
581	C₂	#14564678	1	1	yes	characteristic
582	C₂	#14564683	1	1	yes	characteristic
583	C₂	#14564979	1	1	yes	characteristic
584	C₂	#14564984	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597328
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#339	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#339	D₁₉
hypocenter	C₁₉	#11342
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
26. #11926312	C₄	semidirect
132. M₁₆×C₁₉	C₄⋊C₄	semidirect
169. #64520	C₄⋊C₄	semidirect
385. C₁₉	#11342	semidirect
429. M₁₆	Dic₁₉⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926587	2
C₂×#11926586	2
#14566251	2
C₂×#11926312	2
C₂×#11926304	2
#14561865	2
C₂×C₁₉×#339	2
#11342	19