Subgroups — #18074582

Order 4864.

760 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563655	C₂	1	1	yes	maximal, characteristic
2	C₄×#10597292	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562134	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562090	C₂	1	1	yes	maximal, characteristic, complemented
5	#14562064	C₂	1	1	yes	maximal, characteristic, complemented
6	#14562017	C₂	1	1	yes	maximal, characteristic
7	Q₈×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926568	C₂²	1	1	yes	characteristic
10	C₂×#10597294	—	2	1	no	—
11	C₂×#10597292	—	2	1	no	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	#11926306	—	2	1	no	—
15	#11926303	—	2	1	no	—
16	#11926281	—	2	2	no	—
17	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
18	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
19	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
20	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
21	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
22	Q₈²×C₁₉	C₄	1	1	yes	characteristic, complemented
23	C₁₉×#557	—	2	1	no	—
24	C₁₉×#557	C₄	1	1	yes	characteristic, complemented
25	C₁₉×#554	—	2	2	no	—
26	C₁₉×#554	—	2	1	no	—
27	C₁₉×#554	—	2	1	no	—
28	C₁₉×#554	C₄	1	1	yes	characteristic, complemented
29	D₄×Q₈×C₁₉	—	2	1	no	—
30	D₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
31	C₁₉×#533	—	2	2	no	—
32	C₁₉×#533	—	2	1	no	—
33	C₁₉×#533	—	2	1	no	—
34	C₁₉×#533	C₂²	1	1	yes	characteristic
35	C₄×#41×C₁₉	—	2	1	no	—
36	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
38	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
39	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
40	C₂²×Q₈×C₁₉	—	2	1	no	—
41	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
42	C₁₉×C₄⋊Q₈	—	2	2	no	—
43	C₁₉×C₄⋊Q₈	—	2	1	no	—
44	C₁₉×C₄⋊Q₈	—	2	2	no	—
45	C₁₉×C₄⋊Q₈	—	2	1	no	—
46	C₁₉×C₄⋊Q₈	—	2	1	no	—
47	C₁₉×C₄⋊Q₈	—	2	1	no	—
48	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
49	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
50	C₁₉×#125	—	2	2	no	—
51	C₁₉×#125	—	2	2	no	—
52	C₁₉×#125	—	2	2	no	—
53	C₁₉×#125	—	2	1	no	—
54	C₁₉×#125	—	2	1	no	—
55	C₁₉×#125	—	2	1	no	—
56	C₁₉×C₂²⋊Q₈	—	2	2	no	—
57	C₁₉×C₂²⋊Q₈	—	2	2	no	—
58	C₁₉×C₂²⋊Q₈	—	2	2	no	—
59	C₁₉×C₂²⋊Q₈	—	2	2	no	—
60	C₁₉×C₂²⋊Q₈	—	2	2	no	—
61	C₁₉×C₂²⋊Q₈	—	2	1	no	—
62	C₁₉×C₂²⋊Q₈	—	2	2	no	—
63	C₁₉×C₂²⋊Q₈	—	2	1	no	—
64	C₁₉×C₂²⋊Q₈	—	2	1	no	—
65	C₁₉×C₂²⋊Q₈	—	2	2	no	—
66	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
67	C₄×Q₈×C₁₉	—	2	2	no	—
68	C₄×Q₈×C₁₉	—	2	2	no	—
69	C₄×Q₈×C₁₉	—	2	2	no	—
70	C₄×Q₈×C₁₉	—	2	1	no	—
71	C₄×Q₈×C₁₉	—	2	1	no	—
72	C₄×Q₈×C₁₉	—	2	1	no	—
73	C₄×Q₈×C₁₉	—	2	1	no	—
74	C₄×Q₈×C₁₉	—	2	1	no	—
75	C₄×Q₈×C₁₉	—	2	1	no	—
76	C₄×Q₈×C₁₉	—	2	1	no	—
77	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
78	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
79	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
80	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
81	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
82	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
83	C₄×Q₈×C₁₉	D₄	1	2	yes	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₄×D₄×C₁₉	—	2	2	no	—
86	C₄×D₄×C₁₉	—	2	1	no	—
87	C₄×D₄×C₁₉	—	2	1	no	—
88	C₄×D₄×C₁₉	—	2	1	no	—
89	C₄×D₄×C₁₉	—	2	1	no	—
90	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
91	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
92	C₁₉×#117	—	2	2	no	—
93	C₁₉×#117	—	2	1	no	—
94	C₁₉×#117	—	2	1	no	—
95	C₁₉×#117	D₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₉	—	2	2	no	—
101	C₂×C₄²×C₁₉	—	2	1	no	—
102	C₂×C₄²×C₁₉	—	2	1	no	—
103	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊Dic₁₉	—	2	1	no	—
105	C₂×C₄×Dic₁₉	—	2	1	no	—
106	C₂×#64520	—	2	1	no	—
107	C₂²×C₁₉⋊C₈	—	2	1	no	—
108	#10597294	—	4	2	no	—
109	#10597292	—	2	4	no	—
110	C₁₉⋊#95	—	2	1	no	—
111	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
112	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
113	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
114	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
115	C₄×C₁₉⋊C₈	—	2	1	no	—
116	C₄×C₁₉⋊C₈	—	2	1	no	—
117	C₄×C₁₉⋊C₈	—	2	1	no	—
118	#41×C₁₉	—	2	1	no	—
119	#41×C₁₉	—	2	1	no	—
120	#41×C₁₉	SD₁₆	1	2	yes	—
121	#41×C₁₉	Q₁₆	1	2	yes	—
122	C₂×Q₈×C₁₉	—	2	2	no	—
123	C₂×Q₈×C₁₉	—	2	2	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	2	no	—
127	C₂×Q₈×C₁₉	—	4	1	no	—
128	C₂×Q₈×C₁₉	—	4	2	no	—
129	C₂×Q₈×C₁₉	—	4	2	no	—
130	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
132	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
133	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×Dic₁₉	—	4	1	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
168	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
169	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
170	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
171	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	2	1	no	—
176	C₂²⋊C₄×C₁₉	—	2	1	no	—
177	C₂²⋊C₄×C₁₉	—	2	1	no	—
178	C₄²×C₁₉	—	2	2	no	—
179	C₄²×C₁₉	—	2	2	no	—
180	C₄²×C₁₉	—	2	1	no	—
181	C₄²×C₁₉	—	2	1	no	—
182	C₄²×C₁₉	—	2	1	no	—
183	C₄²×C₁₉	—	2	1	no	—
184	C₄²×C₁₉	—	2	2	no	—
185	C₄²×C₁₉	—	2	1	no	—
186	C₄²×C₁₉	—	2	1	no	—
187	C₄²×C₁₉	—	2	1	no	—
188	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
189	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₄⋊Dic₁₉	—	2	2	no	—
193	C₄⋊Dic₁₉	—	4	1	no	—
194	C₄×Dic₁₉	—	4	1	no	—
195	C₄×Dic₁₉	—	4	1	no	—
196	#64520	—	4	1	no	—
197	#64520	—	4	1	no	—
198	C₂×C₁₉⋊C₈	—	2	2	no	—
199	C₂×C₁₉⋊C₈	—	4	1	no	—
200	C₂×C₁₉⋊C₈	—	4	1	no	—
201	C₂×C₁₉⋊C₈	—	4	1	no	—
202	C₂×C₁₉⋊C₈	—	4	1	no	—
203	#8439	—	19	1	no	maximal, Sylow
204	C₂³×C₁₉	—	2	1	no	—
205	C₂³×C₁₉	#120	1	1	yes	characteristic
206	Q₈×C₁₉	—	2	1	no	—
207	Q₈×C₁₉	—	2	1	no	—
208	Q₈×C₁₉	—	2	1	no	—
209	Q₈×C₁₉	—	2	1	no	—
210	Q₈×C₁₉	—	4	2	no	—
211	Q₈×C₁₉	—	4	2	no	—
212	Q₈×C₁₉	—	4	4	no	—
213	Q₈×C₁₉	—	4	1	no	—
214	Q₈×C₁₉	—	4	1	no	—
215	Q₈×C₁₉	—	8	2	no	—
216	Q₈×C₁₉	#103	1	2	yes	complemented
217	Q₈×C₁₉	#104	1	2	yes	complemented
218	D₄×C₁₉	—	2	2	no	—
219	D₄×C₁₉	—	2	2	no	—
220	D₄×C₁₉	—	2	1	no	—
221	D₄×C₁₉	#103	1	2	yes	complemented
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	2	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	4	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	8	1	no	—
241	C₂×C₄×C₁₉	—	8	1	no	—
242	C₂×C₄×C₁₉	—	8	2	no	—
243	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
248	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
251	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
252	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
253	C₂×Dic₁₉	—	4	2	no	—
254	C₂×Dic₁₉	—	8	1	no	—
255	C₂×Dic₁₉	—	8	1	no	—
256	C₁₉⋊C₈	—	4	2	no	—
257	C₁₉⋊C₈	—	8	1	no	—
258	C₁₉⋊C₈	—	8	1	no	—
259	Q₈×#41	D₁₉	1	1	yes	characteristic
260	#1806	—	19	1	no	—
261	C₄×#103	—	19	1	no	—
262	#1503	—	19	1	no	—
263	#1493	—	19	1	no	—
264	#1487	—	19	1	no	—
265	#1476	—	19	1	no	—
266	C₂²×C₁₉	—	2	1	no	—
267	C₂²×C₁₉	—	2	1	no	—
268	C₂²×C₁₉	—	2	2	no	—
269	C₂²×C₁₉	—	4	1	no	—
270	C₂²×C₁₉	—	4	1	no	—
271	C₂²×C₁₉	#379	1	1	yes	characteristic
272	C₂²×C₁₉	#448	1	1	yes	characteristic
273	C₂²×C₁₉	#451	1	1	yes	characteristic
274	C₄×C₁₉	—	2	1	no	—
275	C₄×C₁₉	—	2	1	no	—
276	C₄×C₁₉	—	2	2	no	—
277	C₄×C₁₉	—	2	1	no	—
278	C₄×C₁₉	—	2	2	no	—
279	C₄×C₁₉	—	4	1	no	—
280	C₄×C₁₉	—	4	2	no	—
281	C₄×C₁₉	—	4	1	no	—
282	C₄×C₁₉	—	4	1	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	—	4	2	no	—
285	C₄×C₁₉	—	4	1	no	—
286	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
287	C₄×C₁₉	#419	1	1	yes	characteristic
288	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
289	C₄×C₁₉	#421	1	1	yes	characteristic
290	C₄×C₁₉	#448	1	1	yes	characteristic
291	C₄×C₁₉	#451	1	1	yes	characteristic
292	Dic₁₉	—	8	2	no	—
293	Q₈²	Dic₁₉	1	1	yes	characteristic, complemented
294	#557	—	2	1	no	—
295	#557	Dic₁₉	1	1	yes	characteristic, complemented
296	#554	—	2	2	no	—
297	#554	—	2	1	no	—
298	#554	—	2	1	no	—
299	#554	Dic₁₉	1	1	yes	characteristic, complemented
300	D₄×Q₈	—	2	1	no	—
301	D₄×Q₈	Dic₁₉	1	1	yes	characteristic, complemented
302	#533	—	2	2	no	—
303	#533	—	2	1	no	—
304	#533	—	2	1	no	—
305	#533	C₂×D₁₉	1	1	yes	characteristic
306	C₄×#41	—	2	1	no	—
307	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
308	C₂×C₄×Q₈	—	2	1	no	—
309	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
310	#431	—	19	1	no	—
311	#423	—	19	1	no	—
312	C₂×#104	—	38	1	no	—
313	C₂×#103	—	38	1	no	—
314	C₂×C₄×C₈	—	19	1	no	—
315	C₄×C₄⋊C₄	—	19	1	no	—
316	#340	—	38	1	no	—
317	#339	—	38	1	no	—
318	#328	—	38	2	no	—
319	Q₈⋊C₈	—	38	1	no	—
320	Q₈⋊C₈	—	38	1	no	—
321	Q₈⋊C₈	—	38	1	no	—
322	Q₈⋊C₈	—	38	2	no	—
323	D₄⋊C₈	—	38	1	no	—
324	C₂×C₁₉	—	2	1	no	—
325	C₂×C₁₉	—	2	1	no	—
326	C₂×C₁₉	—	4	2	no	—
327	C₂×C₁₉	#1787	1	1	yes	characteristic
328	C₂×C₁₉	#1789	1	1	yes	characteristic
329	C₂×C₁₉	#1794	1	1	yes	characteristic
330	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
331	C₂²×Q₈	—	2	1	no	—
332	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
333	C₂×M₁₆	—	38	1	no	—
334	C₂²×C₈	—	38	1	no	—
335	C₄⋊Q₈	—	2	2	no	—
336	C₄⋊Q₈	—	2	1	no	—
337	C₄⋊Q₈	—	2	2	no	—
338	C₄⋊Q₈	—	2	1	no	—
339	C₄⋊Q₈	—	2	1	no	—
340	C₄⋊Q₈	—	2	1	no	—
341	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
342	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
343	#125	—	2	2	no	—
344	#125	—	2	2	no	—
345	#125	—	2	2	no	—
346	#125	—	2	1	no	—
347	#125	—	2	1	no	—
348	#125	—	2	1	no	—
349	C₂²⋊Q₈	—	2	2	no	—
350	C₂²⋊Q₈	—	2	2	no	—
351	C₂²⋊Q₈	—	2	2	no	—
352	C₂²⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	—	2	2	no	—
354	C₂²⋊Q₈	—	2	1	no	—
355	C₂²⋊Q₈	—	2	2	no	—
356	C₂²⋊Q₈	—	2	1	no	—
357	C₂²⋊Q₈	—	2	1	no	—
358	C₂²⋊Q₈	—	2	2	no	—
359	C₂²⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
360	C₄×Q₈	—	2	2	no	—
361	C₄×Q₈	—	2	2	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	—	2	1	no	—
368	C₄×Q₈	—	2	1	no	—
369	C₄×Q₈	—	2	1	no	—
370	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
371	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
372	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
373	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
374	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
375	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
376	C₄×Q₈	C₂²⋊D₁₉	1	2	yes	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
384	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
385	#117	—	2	2	no	—
386	#117	—	2	1	no	—
387	#117	—	2	1	no	—
388	#117	C₂²⋊D₁₉	1	1	yes	characteristic
389	C₂×C₄⋊C₄	—	2	2	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	38	1	no	—
393	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
394	C₂×C₄²	—	2	2	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	—	38	1	no	—
398	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
399	C₄⋊C₈	—	38	1	no	—
400	C₄⋊C₈	—	38	1	no	—
401	C₄⋊C₈	—	38	1	no	—
402	#104	—	76	2	no	—
403	#103	—	38	4	no	—
404	C₂²⋊C₈	—	38	1	no	—
405	C₄×C₈	—	38	1	no	—
406	C₄×C₈	—	38	1	no	—
407	C₄×C₈	—	38	1	no	—
408	#95	—	38	1	no	—
409	C₁₉	#8439	1	1	yes	characteristic, complemented, Sylow
410	#41	—	2	1	no	—
411	#41	—	2	1	no	—
412	#41	#64527	1	2	yes	—
413	#41	#64528	1	2	yes	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	4	1	no	—
420	C₂×Q₈	—	4	2	no	—
421	C₂×Q₈	—	4	2	no	—
422	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
423	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
424	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
425	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	76	1	no	—
436	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
439	M₁₆	—	76	1	no	—
440	M₁₆	—	76	1	no	—
441	C₂×C₈	—	38	2	no	—
442	C₂×C₈	—	76	1	no	—
443	C₂×C₈	—	76	1	no	—
444	C₂×C₈	—	76	1	no	—
445	C₂×C₈	—	76	1	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	38	2	no	—
467	C₄⋊C₄	—	76	1	no	—
468	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
469	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
470	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
471	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
472	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	76	1	no	—
490	C₄²	—	76	1	no	—
491	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
492	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
493	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
494	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
495	C₂³	—	2	1	no	—
496	C₂³	#10597399	1	1	yes	characteristic
497	Q₈	—	2	1	no	—
498	Q₈	—	2	1	no	—
499	Q₈	—	2	1	no	—
500	Q₈	—	2	1	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	4	2	no	—
503	Q₈	—	4	4	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	8	2	no	—
507	Q₈	#10597292	1	2	yes	complemented
508	Q₈	#10597294	1	2	yes	complemented
509	D₄	—	2	2	no	—
510	D₄	—	2	2	no	—
511	D₄	—	2	1	no	—
512	D₄	#10597292	1	2	yes	complemented
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	4	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	8	1	no	—
532	C₂×C₄	—	8	1	no	—
533	C₂×C₄	—	8	2	no	—
534	C₂×C₄	—	76	2	no	—
535	C₂×C₄	—	152	1	no	—
536	C₂×C₄	—	152	1	no	—
537	C₂×C₄	C₂×#64527	1	1	yes	characteristic
538	C₂×C₄	#10597388	1	1	yes	characteristic
539	C₂×C₄	#10597388	1	1	yes	characteristic
540	C₂×C₄	C₂×#64528	1	1	yes	characteristic
541	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
542	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
543	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
544	C₂×C₄	#10597399	1	1	yes	characteristic
545	C₂×C₄	#10597399	1	1	yes	characteristic
546	C₂×C₄	#10597399	1	1	yes	characteristic
547	C₈	—	76	2	no	—
548	C₈	—	152	1	no	—
549	C₈	—	152	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	#11926400	1	1	yes	characteristic
556	C₂²	#11926683	1	1	yes	characteristic
557	C₂²	#11926700	1	1	yes	characteristic
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	2	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	2	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	1	no	—
570	C₄	—	152	2	no	—
571	C₄	C₂×#10597292	1	1	yes	characteristic
572	C₄	#11926553	1	1	yes	characteristic
573	C₄	C₂×#10597294	1	1	yes	characteristic
574	C₄	#11926561	1	1	yes	characteristic
575	C₄	#11926683	1	1	yes	characteristic
576	C₄	#11926700	1	1	yes	characteristic
577	C₂	—	2	1	no	—
578	C₂	—	2	1	no	—
579	C₂	—	4	2	no	—
580	C₂	#14563570	1	1	yes	characteristic
581	C₂	#14563579	1	1	yes	characteristic
582	C₂	#14563599	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	Q₈×#41×C₁₉	C₂
socle	C₂²×C₁₉	#379
prime radical	C₂×#41×C₁₉	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	Q₈×#41	D₁₉
hypocenter	C₁₉	#8439
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ Q₈×#41

Complements

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

N	H ≅ G/N	type
2. C₄×#10597292	C₂	semidirect
3. #14562134	C₂	semidirect
4. #14562090	C₂	semidirect
5. #14562064	C₂	semidirect
22. Q₈²×C₁₉	C₄	semidirect
24. C₁₉×#557	C₄	semidirect
28. C₁₉×#554	C₄	semidirect
30. D₄×Q₈×C₁₉	C₄	semidirect
216. Q₈×C₁₉	#103	semidirect
217. Q₈×C₁₉	#104	semidirect
221. D₄×C₁₉	#103	semidirect
293. Q₈²	Dic₁₉	semidirect
295. #557	Dic₁₉	semidirect
299. #554	Dic₁₉	semidirect
301. D₄×Q₈	Dic₁₉	semidirect
409. C₁₉	#8439	semidirect
507. Q₈	#10597292	semidirect
508. Q₈	#10597294	semidirect
512. D₄	#10597292	semidirect

Maximal subgroups

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

subgroup	index
#14563655	2
C₄×#10597292	2
#14562134	2
#14562090	2
#14562064	2
#14562017	2
Q₈×#41×C₁₉	2
#8439	19