Subgroups — #18084842

Order 4864.

744 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926744	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11926739	C₂	1	1	yes	maximal, characteristic
3	#14564440	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₈⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561518	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2538	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64527	—	2	1	no	—
9	C₂²×#64525	—	2	1	no	—
10	C₂×#10597320	C₂²	1	1	yes	characteristic
11	#11926744	—	2	2	no	—
12	#11926744	—	2	2	no	—
13	#11926739	—	2	2	no	—
14	#11926739	—	2	2	no	—
15	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#10597266	—	2	1	no	—
18	C₂×#10597266	—	2	1	no	—
19	C₂×#10597266	—	2	2	no	—
20	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
21	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
22	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
23	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
24	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#396	—	2	2	no	—
27	C₁₉×#390	—	2	1	no	—
28	C₁₉×#389	—	2	1	no	—
29	C₁₉×#384	C₂²	1	1	yes	characteristic
30	C₁₉×#380	—	2	1	no	—
31	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	—	2	1	no	—
34	C₂²×D₇₆	—	2	1	no	—
35	C₂²×D₇₆	—	2	1	no	—
36	C₂²×D₇₆	—	2	1	no	—
37	C₁₉×C₂²⋊Q₈	—	4	2	no	—
38	C₁₉×C₂²⋊Q₈	—	4	2	no	—
39	C₄×Q₈×C₁₉	—	2	1	no	—
40	C₄×Q₈×C₁₉	—	2	1	no	—
41	C₄×Q₈×C₁₉	—	2	1	no	—
42	C₄×Q₈×C₁₉	—	2	1	no	—
43	C₄×D₄×C₁₉	—	2	1	no	—
44	C₄×D₄×C₁₉	—	2	1	no	—
45	C₄×D₄×C₁₉	—	2	1	no	—
46	C₄×D₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄²×C₁₉	—	2	1	no	—
58	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
59	C₂×#64527	—	2	4	no	—
60	C₂×#64527	—	4	2	no	—
61	C₂×#64527	—	4	2	no	—
62	C₂×#64525	—	2	4	no	—
63	C₂×#64525	—	4	2	no	—
64	C₂×#64525	—	4	2	no	—
65	C₂²×C₁₉⋊C₈	—	2	1	no	—
66	C₂²×C₁₉⋊C₈	—	2	1	no	—
67	C₂²×C₁₉⋊C₈	—	2	1	no	—
68	#10597320	—	2	1	no	—
69	#10597320	—	2	1	no	—
70	#10597320	—	2	1	no	—
71	#10597320	D₄	1	2	yes	—
72	C₁₉×#95	—	2	2	no	—
73	#10597266	—	2	4	no	—
74	#10597266	—	2	4	no	—
75	#10597266	—	4	4	no	—
76	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
77	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
78	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
79	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
80	C₄×C₁₉⋊C₈	—	2	1	no	—
81	C₄×C₁₉⋊C₈	—	2	1	no	—
82	C₂⁴×C₁₉	—	2	1	no	—
83	C₂³×D₁₉	—	4	1	no	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	—	2	1	no	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	2	1	no	—
88	C₂×Q₈×C₁₉	—	2	1	no	—
89	C₂×Q₈×C₁₉	D₈	1	2	yes	complemented
90	C₂×D₄×C₁₉	—	2	1	no	—
91	C₂×D₄×C₁₉	—	2	1	no	—
92	C₂×D₄×C₁₉	—	2	1	no	—
93	C₂×D₄×C₁₉	—	2	1	no	—
94	C₂×D₄×C₁₉	—	2	1	no	—
95	C₂×D₄×C₁₉	SD₁₆	1	2	yes	complemented
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	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	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	—	4	1	no	—
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	C₂×D₇₆	—	2	2	no	—
110	C₂×D₇₆	—	2	2	no	—
111	C₂×D₇₆	—	2	2	no	—
112	C₂×D₇₆	—	4	2	no	—
113	C₂×D₇₆	—	4	2	no	—
114	C₂×D₇₆	—	4	1	no	—
115	C₂×D₇₆	—	4	1	no	—
116	C₂×D₇₆	—	4	1	no	—
117	C₂×D₇₆	—	4	1	no	—
118	C₂×D₇₆	—	4	1	no	—
119	C₂×D₇₆	—	4	1	no	—
120	C₂×D₇₆	—	4	1	no	—
121	C₂×D₇₆	—	4	1	no	—
122	C₂×D₇₆	—	4	1	no	—
123	C₂×D₇₆	—	4	1	no	—
124	C₂×D₇₆	—	4	1	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₄⋊C₄×C₁₉	—	4	2	no	—
130	C₄⋊C₄×C₁₉	—	4	4	no	—
131	C₄⋊C₄×C₁₉	—	4	1	no	—
132	C₄⋊C₄×C₁₉	—	4	1	no	—
133	C₄⋊C₄×C₁₉	—	4	1	no	—
134	C₄⋊C₄×C₁₉	—	4	1	no	—
135	C₄⋊C₄×C₁₉	—	4	1	no	—
136	C₄⋊C₄×C₁₉	—	4	1	no	—
137	C₂²⋊C₄×C₁₉	—	4	4	no	—
138	C₂²⋊C₄×C₁₉	—	4	1	no	—
139	C₂²⋊C₄×C₁₉	—	4	1	no	—
140	C₂²⋊C₄×C₁₉	—	8	2	no	—
141	C₄²×C₁₉	—	4	1	no	—
142	C₄²×C₁₉	—	4	1	no	—
143	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₁₉	#41	1	1	yes	characteristic
147	#64527	—	4	8	no	—
148	#64525	—	4	8	no	—
149	C₂×C₁₉⋊C₈	—	2	2	no	—
150	C₂×C₁₉⋊C₈	—	2	2	no	—
151	C₂×C₁₉⋊C₈	—	2	2	no	—
152	C₂×C₁₉⋊C₈	—	4	1	no	—
153	C₂×C₁₉⋊C₈	—	4	1	no	—
154	C₂×C₁₉⋊C₈	—	4	1	no	—
155	C₂×C₁₉⋊C₈	—	4	1	no	—
156	C₂×C₁₉⋊C₈	—	4	1	no	—
157	C₂×C₁₉⋊C₈	—	4	1	no	—
158	#10229	—	19	1	no	maximal, Sylow
159	C₂³×C₁₉	—	2	2	no	—
160	C₂³×C₁₉	—	4	1	no	—
161	C₂³×C₁₉	—	4	1	no	—
162	C₂³×C₁₉	—	4	1	no	—
163	C₂³×C₁₉	—	4	1	no	—
164	C₂³×C₁₉	—	4	1	no	—
165	C₂³×C₁₉	—	4	1	no	—
166	C₂³×C₁₉	#120	1	1	yes	characteristic
167	C₂²×D₁₉	—	4	2	no	—
168	C₂²×D₁₉	—	8	1	no	—
169	C₂²×D₁₉	—	8	1	no	—
170	C₂²×D₁₉	—	8	1	no	—
171	C₂²×D₁₉	—	8	1	no	—
172	C₂²×D₁₉	—	8	1	no	—
173	C₂²×D₁₉	—	8	1	no	—
174	Q₈×C₁₉	—	2	2	no	—
175	Q₈×C₁₉	—	2	2	no	—
176	Q₈×C₁₉	—	4	1	no	—
177	Q₈×C₁₉	—	4	1	no	—
178	D₄×C₁₉	—	2	2	no	—
179	D₄×C₁₉	—	2	2	no	—
180	D₄×C₁₉	—	4	1	no	—
181	D₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	1	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	1	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	2	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	8	1	no	—
197	C₂×C₄×C₁₉	—	8	1	no	—
198	C₂×C₄×C₁₉	—	8	1	no	—
199	C₂×C₄×C₁₉	—	8	1	no	—
200	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
201	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
202	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
205	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
208	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
209	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
210	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
211	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
214	D₇₆	—	4	4	no	—
215	D₇₆	—	4	2	no	—
216	D₇₆	—	4	2	no	—
217	D₇₆	—	4	2	no	—
218	D₇₆	—	4	2	no	—
219	D₇₆	—	8	2	no	—
220	D₇₆	—	8	1	no	—
221	D₇₆	—	8	1	no	—
222	D₇₆	—	8	1	no	—
223	D₇₆	—	8	1	no	—
224	C₁₉⋊C₈	—	4	2	no	—
225	C₁₉⋊C₈	—	4	2	no	—
226	C₁₉⋊C₈	—	4	2	no	—
227	C₂×#460	—	19	1	no	—
228	C₂×#459	—	19	1	no	—
229	#2538	D₁₉	1	1	yes	characteristic, complemented
230	#1957	—	19	1	no	—
231	C₂×Q₈⋊C₈	—	19	1	no	—
232	C₂×D₄⋊C₈	—	19	1	no	—
233	#1296	—	19	1	no	—
234	C₂²×C₁₉	—	4	2	no	—
235	C₂²×C₁₉	—	4	2	no	—
236	C₂²×C₁₉	—	4	2	no	—
237	C₂²×C₁₉	—	8	1	no	—
238	C₂²×C₁₉	—	8	1	no	—
239	C₂²×C₁₉	—	8	1	no	—
240	C₂²×C₁₉	—	8	1	no	—
241	C₂²×C₁₉	#392	1	1	yes	characteristic
242	C₂²×C₁₉	#447	1	1	yes	characteristic
243	C₂²×C₁₉	#448	1	1	yes	characteristic
244	C₂²×C₁₉	#449	1	1	yes	characteristic
245	C₂²×C₁₉	#449	1	1	yes	characteristic
246	C₂²×C₁₉	#453	1	1	yes	characteristic
247	C₂²×C₁₉	#454	1	1	yes	characteristic
248	C₂×D₁₉	—	8	2	no	—
249	C₂×D₁₉	—	8	2	no	—
250	C₂×D₁₉	—	8	2	no	—
251	C₂×D₁₉	—	16	1	no	—
252	C₂×D₁₉	—	16	1	no	—
253	C₂×D₁₉	—	16	1	no	—
254	C₂×D₁₉	—	16	1	no	—
255	C₄×C₁₉	—	2	1	no	—
256	C₄×C₁₉	—	2	1	no	—
257	C₄×C₁₉	—	4	2	no	—
258	C₄×C₁₉	—	8	2	no	—
259	C₄×C₁₉	—	8	1	no	—
260	C₄×C₁₉	—	8	1	no	—
261	C₄×C₁₉	#447	1	1	yes	characteristic
262	C₄×C₁₉	#449	1	1	yes	characteristic
263	C₄×C₁₉	#450	1	1	yes	characteristic
264	C₄×C₁₉	#452	1	1	yes	characteristic
265	C₄×C₁₉	#465	1	1	yes	characteristic
266	C₄×C₁₉	#466	1	1	yes	characteristic
267	C₄×C₁₉	#468	1	1	yes	characteristic
268	C₄×C₁₉	#469	1	1	yes	characteristic
269	C₂²×SD₁₆	—	38	1	no	—
270	C₂²×D₈	—	38	1	no	—
271	C₂×#127	—	19	1	no	—
272	C₂×C₂²⋊Q₈	—	2	1	no	—
273	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
274	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
275	#460	—	38	2	no	—
276	#460	—	38	2	no	—
277	#459	—	38	2	no	—
278	#459	—	38	2	no	—
279	C₂×C₄⋊C₈	—	19	1	no	—
280	C₂×C₄⋊C₈	—	19	1	no	—
281	C₂×#102	—	38	1	no	—
282	C₂×#102	—	38	1	no	—
283	C₂×#102	—	38	2	no	—
284	C₂×C₄×C₈	—	19	1	no	—
285	#396	—	2	2	no	—
286	#390	—	2	1	no	—
287	#389	—	2	1	no	—
288	#384	C₂×D₁₉	1	1	yes	characteristic
289	#380	—	2	1	no	—
290	Q₈⋊C₈	—	38	2	no	—
291	D₄⋊C₈	—	38	2	no	—
292	C₂×C₁₉	—	8	2	no	—
293	C₂×C₁₉	#1621	1	1	yes	characteristic
294	C₂×C₁₉	#1622	1	1	yes	characteristic
295	C₂×C₁₉	#1627	1	1	yes	characteristic
296	C₂×C₁₉	#1628	1	1	yes	characteristic
297	C₂×C₁₉	#1999	1	1	yes	characteristic
298	C₂×C₁₉	#2000	1	1	yes	characteristic
299	C₂×C₁₉	#2006	1	1	yes	characteristic
300	D₁₉	—	16	2	no	—
301	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
302	C₂²×D₄	—	38	1	no	—
303	C₂²×D₄	—	38	1	no	—
304	C₂²×D₄	—	38	1	no	—
305	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
306	C₂³×C₄	—	2	1	no	—
307	C₂×SD₁₆	—	38	4	no	—
308	C₂×SD₁₆	—	76	2	no	—
309	C₂×SD₁₆	—	76	2	no	—
310	C₂×D₈	—	38	4	no	—
311	C₂×D₈	—	76	2	no	—
312	C₂×D₈	—	76	2	no	—
313	C₂²×C₈	—	38	1	no	—
314	C₂²×C₈	—	38	1	no	—
315	C₂²×C₈	—	38	1	no	—
316	#127	—	19	2	no	—
317	#127	—	38	1	no	—
318	#127	—	38	1	no	—
319	#127	—	38	1	no	—
320	C₂²⋊Q₈	—	4	2	no	—
321	C₂²⋊Q₈	—	4	2	no	—
322	C₄×Q₈	—	2	1	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×Q₈	—	2	1	no	—
325	C₄×Q₈	—	2	1	no	—
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
342	C₄⋊C₈	—	19	2	no	—
343	C₄⋊C₈	—	19	2	no	—
344	C₄⋊C₈	—	38	1	no	—
345	C₄⋊C₈	—	38	1	no	—
346	#102	—	38	4	no	—
347	#102	—	38	4	no	—
348	#102	—	76	4	no	—
349	C₄×C₈	—	38	1	no	—
350	C₄×C₈	—	38	1	no	—
351	#95	—	2	2	no	—
352	C₁₉	#10229	1	1	yes	characteristic, complemented, Sylow
353	C₂⁴	—	2	1	no	—
354	C₂⁴	—	76	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	#64525	1	2	yes	complemented
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	38	2	no	—
367	C₂×D₄	—	38	2	no	—
368	C₂×D₄	—	38	2	no	—
369	C₂×D₄	—	76	2	no	—
370	C₂×D₄	—	76	2	no	—
371	C₂×D₄	—	76	1	no	—
372	C₂×D₄	—	76	1	no	—
373	C₂×D₄	—	76	1	no	—
374	C₂×D₄	—	76	1	no	—
375	C₂×D₄	—	76	1	no	—
376	C₂×D₄	—	76	1	no	—
377	C₂×D₄	—	76	1	no	—
378	C₂×D₄	—	76	1	no	—
379	C₂×D₄	—	76	1	no	—
380	C₂×D₄	—	76	1	no	—
381	C₂×D₄	—	76	1	no	—
382	C₂×D₄	#64527	1	2	yes	complemented
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	—	4	1	no	—
391	C₂²×C₄	—	4	1	no	—
392	C₂²×C₄	—	4	1	no	—
393	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
394	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
395	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
396	SD₁₆	—	76	8	no	—
397	D₈	—	76	8	no	—
398	C₂×C₈	—	38	2	no	—
399	C₂×C₈	—	38	2	no	—
400	C₂×C₈	—	38	2	no	—
401	C₂×C₈	—	76	1	no	—
402	C₂×C₈	—	76	1	no	—
403	C₂×C₈	—	76	1	no	—
404	C₂×C₈	—	76	1	no	—
405	C₂×C₈	—	76	1	no	—
406	C₂×C₈	—	76	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	—	4	4	no	—
413	C₄⋊C₄	—	4	1	no	—
414	C₄⋊C₄	—	4	1	no	—
415	C₄⋊C₄	—	4	1	no	—
416	C₄⋊C₄	—	4	1	no	—
417	C₄⋊C₄	—	4	1	no	—
418	C₄⋊C₄	—	4	1	no	—
419	C₂²⋊C₄	—	4	4	no	—
420	C₂²⋊C₄	—	4	1	no	—
421	C₂²⋊C₄	—	4	1	no	—
422	C₂²⋊C₄	—	8	2	no	—
423	C₄²	—	4	1	no	—
424	C₄²	—	4	1	no	—
425	C₄²	D₄×D₁₉	1	1	yes	characteristic
426	C₄²	D₄×D₁₉	1	1	yes	characteristic
427	C₄²	D₄×D₁₉	1	1	yes	characteristic
428	C₄²	#64543	1	1	yes	characteristic
429	C₂³	—	2	2	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	76	2	no	—
437	C₂³	—	152	1	no	—
438	C₂³	—	152	1	no	—
439	C₂³	—	152	1	no	—
440	C₂³	—	152	1	no	—
441	C₂³	—	152	1	no	—
442	C₂³	—	152	1	no	—
443	C₂³	#10597399	1	1	yes	characteristic
444	Q₈	—	2	2	no	—
445	Q₈	—	2	2	no	—
446	Q₈	—	4	1	no	—
447	Q₈	—	4	1	no	—
448	D₄	—	2	2	no	—
449	D₄	—	2	2	no	—
450	D₄	—	4	1	no	—
451	D₄	—	4	1	no	—
452	D₄	—	76	4	no	—
453	D₄	—	76	2	no	—
454	D₄	—	76	2	no	—
455	D₄	—	76	2	no	—
456	D₄	—	76	2	no	—
457	D₄	—	152	2	no	—
458	D₄	—	152	1	no	—
459	D₄	—	152	1	no	—
460	D₄	—	152	1	no	—
461	D₄	—	152	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	8	1	no	—
477	C₂×C₄	—	8	1	no	—
478	C₂×C₄	—	8	1	no	—
479	C₂×C₄	—	8	1	no	—
480	C₂×C₄	C₂×#64525	1	1	yes	characteristic
481	C₂×C₄	#10597378	1	1	yes	characteristic
482	C₂×C₄	#10597383	1	1	yes	characteristic
483	C₂×C₄	#10597383	1	1	yes	characteristic
484	C₂×C₄	#10597384	1	1	yes	characteristic
485	C₂×C₄	#10597385	1	1	yes	characteristic
486	C₂×C₄	#10597385	1	1	yes	characteristic
487	C₂×C₄	#10597386	1	1	yes	characteristic
488	C₂×C₄	C₂×#64527	1	1	yes	characteristic
489	C₂×C₄	#10597388	1	1	yes	characteristic
490	C₂×C₄	#10597395	1	1	yes	characteristic
491	C₂×C₄	#10597395	1	1	yes	characteristic
492	C₂×C₄	#10597396	1	1	yes	characteristic
493	C₂×C₄	#10597396	1	1	yes	characteristic
494	C₈	—	76	2	no	—
495	C₈	—	76	2	no	—
496	C₈	—	76	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	—	8	1	no	—
504	C₂²	—	304	1	no	—
505	C₂²	—	304	1	no	—
506	C₂²	—	304	1	no	—
507	C₂²	—	304	1	no	—
508	C₂²	—	152	2	no	—
509	C₂²	—	152	2	no	—
510	C₂²	—	152	2	no	—
511	C₂²	#11926452	1	1	yes	characteristic
512	C₂²	#11926678	1	1	yes	characteristic
513	C₂²	#11926683	1	1	yes	characteristic
514	C₂²	#11926689	1	1	yes	characteristic
515	C₂²	#11926689	1	1	yes	characteristic
516	C₂²	#11926712	1	1	yes	characteristic
517	C₂²	#11926717	1	1	yes	characteristic
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	4	2	no	—
521	C₄	—	8	1	no	—
522	C₄	—	8	1	no	—
523	C₄	—	8	2	no	—
524	C₄	#11926677	1	1	yes	characteristic
525	C₄	#11926687	1	1	yes	characteristic
526	C₄	#11926694	1	1	yes	characteristic
527	C₄	#11926704	1	1	yes	characteristic
528	C₄	#11926775	1	1	yes	characteristic
529	C₄	#11926778	1	1	yes	characteristic
530	C₄	#11926792	1	1	yes	characteristic
531	C₄	#11926795	1	1	yes	characteristic
532	C₂	—	8	2	no	—
533	C₂	—	304	2	no	—
534	C₂	#14562700	1	1	yes	characteristic
535	C₂	#14562707	1	1	yes	characteristic
536	C₂	#14562738	1	1	yes	characteristic
537	C₂	#14562745	1	1	yes	characteristic
538	C₂	#14564631	1	1	yes	characteristic
539	C₂	#14564636	1	1	yes	characteristic
540	C₂	#14564677	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2538	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×#11926739	C₂
hypercenter	#2538	D₁₉
hypocenter	C₁₉	#10229
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2538

Complements

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

N	H ≅ G/N	type
1. C₂×#11926744	C₂	semidirect
3. #14564440	C₂	semidirect
4. C₂×Q₈⋊(C₁₉⋊C₈)	C₂	semidirect
5. C₂×D₄⋊(C₁₉⋊C₈)	C₂	semidirect
6. #14561518	C₂	semidirect
7. C₁₉×#2538	C₂	semidirect
89. C₂×Q₈×C₁₉	D₈	semidirect
95. C₂×D₄×C₁₉	SD₁₆	semidirect
229. #2538	D₁₉	semidirect
352. C₁₉	#10229	semidirect
360. C₂×Q₈	#64525	semidirect
382. C₂×D₄	#64527	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926744	2
C₂×#11926739	2
#14564440	2
C₂×Q₈⋊(C₁₉⋊C₈)	2
C₂×D₄⋊(C₁₉⋊C₈)	2
#14561518	2
C₁₉×#2538	2
#10229	19