Subgroups — #18084854

Order 4864.

728 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926824	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11926749	C₂	1	1	yes	maximal, characteristic, complemented
3	#14564595	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄⋊(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×#2537	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64526	—	2	1	no	—
9	C₂×#10597315	C₂²	1	1	yes	characteristic
10	#11926824	—	2	2	no	—
11	#11926824	—	2	2	no	—
12	#11926749	—	2	2	no	—
13	#11926749	—	2	2	no	—
14	C₂×#10597264	—	2	1	no	—
15	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#10597267	—	2	1	no	—
18	C₂×#10597289	—	2	1	no	—
19	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	#11926306	—	2	2	no	—
21	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
22	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
23	C₂×C₁₉×#121	—	2	1	no	—
24	C₂×C₁₉×#121	—	2	1	no	—
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#394	—	2	2	no	—
28	C₁₉×#384	C₂²	1	1	yes	characteristic
29	C₁₉×#380	—	2	1	no	—
30	C₁₉×#380	—	2	1	no	—
31	C₂²×D₄×C₁₉	—	2	2	no	—
32	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	—	2	1	no	—
35	C₂³×C₄×C₁₉	—	2	1	no	—
36	C₂²×Dic₃₈	—	2	1	no	—
37	C₁₉×#121	—	4	2	no	—
38	C₁₉×#121	—	4	2	no	—
39	C₁₉×#121	—	4	2	no	—
40	C₁₉×#121	—	4	2	no	—
41	C₄×D₄×C₁₉	—	2	1	no	—
42	C₄×D₄×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	C₄×D₄×C₁₉	—	2	1	no	—
48	C₄×D₄×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	2	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
59	C₂×#64526	—	2	4	no	—
60	C₂×#64526	—	4	2	no	—
61	C₂×#64526	—	4	2	no	—
62	C₂×C₄⋊Dic₁₉	—	2	1	no	—
63	C₂×C₄⋊Dic₁₉	—	2	1	no	—
64	C₂²×C₁₉⋊C₈	—	2	1	no	—
65	C₂²×C₁₉⋊C₈	—	2	1	no	—
66	C₂²×C₁₉⋊C₈	—	2	1	no	—
67	#10597315	—	2	1	no	—
68	#10597315	—	2	1	no	—
69	#10597315	—	2	1	no	—
70	#10597315	D₄	1	2	yes	complemented
71	C₁₉×#95	—	2	2	no	—
72	#10597289	—	2	4	no	—
73	#10597267	—	2	4	no	—
74	#10597264	—	2	4	no	—
75	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
76	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
77	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	complemented
78	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	complemented
79	C₄×C₁₉⋊C₈	—	2	1	no	—
80	C₄×C₁₉⋊C₈	—	2	1	no	—
81	C₂⁴×C₁₉	—	2	1	no	—
82	C₂⁴×C₁₉	—	2	1	no	—
83	C₂×D₄×C₁₉	—	2	1	no	—
84	C₂×D₄×C₁₉	—	2	1	no	—
85	C₂×D₄×C₁₉	—	2	1	no	—
86	C₂×D₄×C₁₉	—	2	1	no	—
87	C₂×D₄×C₁₉	—	2	1	no	—
88	C₂×D₄×C₁₉	—	2	1	no	—
89	C₂×D₄×C₁₉	—	2	1	no	—
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	—	4	4	no	—
94	C₂×D₄×C₁₉	—	4	4	no	—
95	C₂×D₄×C₁₉	—	8	2	no	—
96	C₂×D₄×C₁₉	D₈	1	2	yes	—
97	C₂×D₄×C₁₉	SD₁₆	1	2	yes	complemented
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	2	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	—	4	1	no	—
107	C₂²×C₄×C₁₉	—	4	1	no	—
108	C₂²×C₄×C₁₉	—	4	1	no	—
109	C₂²×C₄×C₁₉	—	4	1	no	—
110	C₂²×C₄×C₁₉	—	4	1	no	—
111	C₂²×C₄×C₁₉	—	4	1	no	—
112	C₂²×C₄×C₁₉	—	4	1	no	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×Dic₁₉	—	4	1	no	—
117	C₂×Dic₃₈	—	2	2	no	—
118	C₂×Dic₃₈	—	4	1	no	—
119	C₂×Dic₃₈	—	4	1	no	—
120	C₂×Dic₃₈	—	4	1	no	—
121	C₂×Dic₃₈	—	4	1	no	—
122	C₂×Dic₃₈	—	4	1	no	—
123	C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	4	2	no	—
128	C₄⋊C₄×C₁₉	—	4	1	no	—
129	C₄⋊C₄×C₁₉	—	4	1	no	—
130	C₄⋊C₄×C₁₉	—	4	1	no	—
131	C₄⋊C₄×C₁₉	—	4	1	no	—
132	C₂²⋊C₄×C₁₉	—	4	4	no	—
133	C₂²⋊C₄×C₁₉	—	4	4	no	—
134	C₂²⋊C₄×C₁₉	—	4	1	no	—
135	C₂²⋊C₄×C₁₉	—	4	1	no	—
136	C₂²⋊C₄×C₁₉	—	4	1	no	—
137	C₂²⋊C₄×C₁₉	—	4	1	no	—
138	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₉	#41	1	1	yes	characteristic
142	#64526	—	4	8	no	—
143	C₄⋊Dic₁₉	—	2	2	no	—
144	C₄⋊Dic₁₉	—	2	2	no	—
145	C₄⋊Dic₁₉	—	4	1	no	—
146	C₄⋊Dic₁₉	—	4	1	no	—
147	C₂×C₁₉⋊C₈	—	2	2	no	—
148	C₂×C₁₉⋊C₈	—	2	2	no	—
149	C₂×C₁₉⋊C₈	—	2	2	no	—
150	C₂×C₁₉⋊C₈	—	4	1	no	—
151	C₂×C₁₉⋊C₈	—	4	1	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	#10231	—	19	1	no	maximal, Sylow
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	—	4	1	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	—	4	1	no	—
167	C₂³×C₁₉	—	4	1	no	—
168	C₂³×C₁₉	—	4	1	no	—
169	C₂³×C₁₉	—	4	1	no	—
170	C₂³×C₁₉	—	4	1	no	—
171	C₂³×C₁₉	#120	1	1	yes	characteristic
172	D₄×C₁₉	—	2	2	no	—
173	D₄×C₁₉	—	2	2	no	—
174	D₄×C₁₉	—	2	2	no	—
175	D₄×C₁₉	—	2	2	no	—
176	D₄×C₁₉	—	4	1	no	—
177	D₄×C₁₉	—	4	1	no	—
178	D₄×C₁₉	—	4	1	no	—
179	D₄×C₁₉	—	4	1	no	—
180	D₄×C₁₉	—	8	8	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	2	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	—	8	1	no	—
193	C₂×C₄×C₁₉	—	8	1	no	—
194	C₂×C₄×C₁₉	—	8	1	no	—
195	C₂×C₄×C₁₉	—	8	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	C₂×Dic₁₉	—	4	2	no	—
215	C₂×Dic₁₉	—	8	1	no	—
216	C₂×Dic₁₉	—	8	1	no	—
217	Dic₃₈	—	4	2	no	—
218	Dic₃₈	—	4	2	no	—
219	Dic₃₈	—	8	1	no	—
220	Dic₃₈	—	8	1	no	—
221	C₁₉⋊C₈	—	4	2	no	—
222	C₁₉⋊C₈	—	4	2	no	—
223	C₁₉⋊C₈	—	4	2	no	—
224	C₂×#474	—	19	1	no	—
225	C₂×#461	—	19	1	no	—
226	#2537	D₁₉	1	1	yes	characteristic
227	#1990	—	19	1	no	—
228	C₂×D₄⋊C₈	—	19	1	no	—
229	C₂×D₄⋊C₈	—	19	1	no	—
230	#1296	—	19	1	no	—
231	C₂²×C₁₉	—	4	2	no	—
232	C₂²×C₁₉	—	4	2	no	—
233	C₂²×C₁₉	—	4	2	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	—	8	1	no	—
242	C₂²×C₁₉	—	8	1	no	—
243	C₂²×C₁₉	—	8	1	no	—
244	C₂²×C₁₉	—	8	1	no	—
245	C₂²×C₁₉	#392	1	1	yes	characteristic
246	C₂²×C₁₉	#447	1	1	yes	characteristic
247	C₂²×C₁₉	#449	1	1	yes	characteristic
248	C₂²×C₁₉	#450	1	1	yes	characteristic
249	C₂²×C₁₉	#452	1	1	yes	characteristic
250	C₂²×C₁₉	#455	1	1	yes	characteristic
251	C₂²×C₁₉	#456	1	1	yes	characteristic
252	C₄×C₁₉	—	2	1	no	—
253	C₄×C₁₉	—	2	1	no	—
254	C₄×C₁₉	—	8	2	no	—
255	C₄×C₁₉	—	8	1	no	—
256	C₄×C₁₉	—	8	1	no	—
257	C₄×C₁₉	#447	1	1	yes	characteristic
258	C₄×C₁₉	#448	1	1	yes	characteristic
259	C₄×C₁₉	#449	1	1	yes	characteristic
260	C₄×C₁₉	#449	1	1	yes	characteristic
261	C₄×C₁₉	#465	1	1	yes	characteristic
262	C₄×C₁₉	#466	1	1	yes	characteristic
263	C₄×C₁₉	#468	1	1	yes	characteristic
264	C₄×C₁₉	#469	1	1	yes	characteristic
265	Dic₁₉	—	8	2	no	—
266	C₂²×SD₁₆	—	38	1	no	—
267	C₂×C₄⋊Q₈	—	19	1	no	—
268	C₂×#121	—	2	1	no	—
269	C₂×#121	—	2	1	no	—
270	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
271	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
272	#474	—	38	2	no	—
273	#474	—	38	2	no	—
274	#461	—	38	2	no	—
275	#461	—	38	2	no	—
276	C₂×#107	—	38	1	no	—
277	C₂×C₄⋊C₈	—	19	1	no	—
278	C₂×C₄⋊C₈	—	19	1	no	—
279	C₂×#103	—	38	1	no	—
280	C₂×#102	—	38	1	no	—
281	C₂×C₄×C₈	—	19	1	no	—
282	#394	—	2	2	no	—
283	#384	C₂×D₁₉	1	1	yes	characteristic
284	#380	—	2	1	no	—
285	#380	—	2	1	no	—
286	#340	—	38	2	no	—
287	D₄⋊C₈	—	38	2	no	—
288	D₄⋊C₈	—	38	2	no	—
289	C₂×C₁₉	—	8	2	no	—
290	C₂×C₁₉	—	8	2	no	—
291	C₂×C₁₉	#1639	1	1	yes	characteristic
292	C₂×C₁₉	#1646	1	1	yes	characteristic
293	C₂×C₁₉	#1647	1	1	yes	characteristic
294	C₂×C₁₉	#1654	1	1	yes	characteristic
295	C₂×C₁₉	#1999	1	1	yes	characteristic
296	C₂×C₁₉	#2000	1	1	yes	characteristic
297	C₂×C₁₉	#2007	1	1	yes	characteristic
298	C₂²×Q₈	—	38	1	no	—
299	C₂²×D₄	—	2	2	no	—
300	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
301	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
302	C₂³×C₄	—	2	1	no	—
303	C₂³×C₄	—	2	1	no	—
304	C₂×SD₁₆	—	38	4	no	—
305	C₂×SD₁₆	—	76	2	no	—
306	C₂×SD₁₆	—	76	2	no	—
307	C₂²×C₈	—	38	1	no	—
308	C₂²×C₈	—	38	1	no	—
309	C₂²×C₈	—	38	1	no	—
310	C₄⋊Q₈	—	19	2	no	—
311	C₄⋊Q₈	—	38	1	no	—
312	C₄⋊Q₈	—	38	1	no	—
313	C₄⋊Q₈	—	38	1	no	—
314	#121	—	4	2	no	—
315	#121	—	4	2	no	—
316	#121	—	4	2	no	—
317	#121	—	4	2	no	—
318	C₄×D₄	—	2	1	no	—
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	—	2	1	no	—
323	C₄×D₄	—	2	1	no	—
324	C₄×D₄	—	2	1	no	—
325	C₄×D₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	38	1	no	—
329	C₂×C₄⋊C₄	—	38	1	no	—
330	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
338	#107	—	38	4	no	—
339	C₄⋊C₈	—	19	2	no	—
340	C₄⋊C₈	—	19	2	no	—
341	C₄⋊C₈	—	38	1	no	—
342	C₄⋊C₈	—	38	1	no	—
343	#103	—	38	4	no	—
344	#102	—	38	4	no	—
345	C₄×C₈	—	38	1	no	—
346	C₄×C₈	—	38	1	no	—
347	#95	—	2	2	no	—
348	C₁₉	#10231	1	1	yes	characteristic, complemented, Sylow
349	C₂⁴	—	2	1	no	—
350	C₂⁴	—	2	1	no	—
351	C₂×Q₈	—	38	2	no	—
352	C₂×Q₈	—	76	1	no	—
353	C₂×Q₈	—	76	1	no	—
354	C₂×Q₈	—	76	1	no	—
355	C₂×Q₈	—	76	1	no	—
356	C₂×Q₈	—	76	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
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	—	2	1	no	—
367	C₂×D₄	—	4	4	no	—
368	C₂×D₄	—	4	4	no	—
369	C₂×D₄	—	8	2	no	—
370	C₂×D₄	#64525	1	2	yes	—
371	C₂×D₄	#64526	1	2	yes	complemented
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	4	1	no	—
376	C₂²×C₄	—	4	1	no	—
377	C₂²×C₄	—	4	1	no	—
378	C₂²×C₄	—	4	1	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	—	4	1	no	—
381	C₂²×C₄	—	4	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	—	4	1	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	—	4	1	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	—	76	1	no	—
388	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
391	SD₁₆	—	76	8	no	—
392	C₂×C₈	—	38	2	no	—
393	C₂×C₈	—	38	2	no	—
394	C₂×C₈	—	38	2	no	—
395	C₂×C₈	—	76	1	no	—
396	C₂×C₈	—	76	1	no	—
397	C₂×C₈	—	76	1	no	—
398	C₂×C₈	—	76	1	no	—
399	C₂×C₈	—	76	1	no	—
400	C₂×C₈	—	76	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	4	2	no	—
406	C₄⋊C₄	—	4	1	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	—	4	1	no	—
410	C₄⋊C₄	—	38	2	no	—
411	C₄⋊C₄	—	38	2	no	—
412	C₄⋊C₄	—	76	1	no	—
413	C₄⋊C₄	—	76	1	no	—
414	C₂²⋊C₄	—	4	4	no	—
415	C₂²⋊C₄	—	4	4	no	—
416	C₂²⋊C₄	—	4	1	no	—
417	C₂²⋊C₄	—	4	1	no	—
418	C₂²⋊C₄	—	4	1	no	—
419	C₂²⋊C₄	—	4	1	no	—
420	C₄²	D₄×D₁₉	1	1	yes	characteristic
421	C₄²	D₄×D₁₉	1	1	yes	characteristic
422	C₄²	D₄×D₁₉	1	1	yes	characteristic
423	C₄²	#64543	1	1	yes	characteristic
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	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	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	#10597399	1	1	yes	characteristic
439	Q₈	—	76	2	no	—
440	Q₈	—	76	2	no	—
441	Q₈	—	152	1	no	—
442	Q₈	—	152	1	no	—
443	D₄	—	2	2	no	—
444	D₄	—	2	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	4	1	no	—
448	D₄	—	4	1	no	—
449	D₄	—	4	1	no	—
450	D₄	—	4	1	no	—
451	D₄	—	8	8	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	8	1	no	—
464	C₂×C₄	—	8	1	no	—
465	C₂×C₄	—	8	1	no	—
466	C₂×C₄	—	8	1	no	—
467	C₂×C₄	—	8	1	no	—
468	C₂×C₄	—	8	1	no	—
469	C₂×C₄	—	8	1	no	—
470	C₂×C₄	—	8	1	no	—
471	C₂×C₄	—	76	2	no	—
472	C₂×C₄	—	152	1	no	—
473	C₂×C₄	—	152	1	no	—
474	C₂×C₄	C₂×#64525	1	1	yes	characteristic
475	C₂×C₄	#10597378	1	1	yes	characteristic
476	C₂×C₄	#10597378	1	1	yes	characteristic
477	C₂×C₄	C₂×#64526	1	1	yes	characteristic
478	C₂×C₄	#10597383	1	1	yes	characteristic
479	C₂×C₄	#10597383	1	1	yes	characteristic
480	C₂×C₄	#10597384	1	1	yes	characteristic
481	C₂×C₄	#10597385	1	1	yes	characteristic
482	C₂×C₄	#10597385	1	1	yes	characteristic
483	C₂×C₄	#10597386	1	1	yes	characteristic
484	C₂×C₄	#10597395	1	1	yes	characteristic
485	C₂×C₄	#10597396	1	1	yes	characteristic
486	C₂×C₄	#10597396	1	1	yes	characteristic
487	C₂×C₄	#10597397	1	1	yes	characteristic
488	C₈	—	76	2	no	—
489	C₈	—	76	2	no	—
490	C₈	—	76	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	8	1	no	—
498	C₂²	—	8	1	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	—	8	1	no	—
504	C₂²	—	8	1	no	—
505	C₂²	#11926452	1	1	yes	characteristic
506	C₂²	#11926678	1	1	yes	characteristic
507	C₂²	#11926689	1	1	yes	characteristic
508	C₂²	#11926695	1	1	yes	characteristic
509	C₂²	#11926706	1	1	yes	characteristic
510	C₂²	#11926722	1	1	yes	characteristic
511	C₂²	#11926727	1	1	yes	characteristic
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	8	1	no	—
515	C₄	—	8	1	no	—
516	C₄	—	8	2	no	—
517	C₄	—	152	2	no	—
518	C₄	#11926677	1	1	yes	characteristic
519	C₄	#11926682	1	1	yes	characteristic
520	C₄	#11926687	1	1	yes	characteristic
521	C₄	#11926687	1	1	yes	characteristic
522	C₄	#11926771	1	1	yes	characteristic
523	C₄	#11926778	1	1	yes	characteristic
524	C₄	#11926788	1	1	yes	characteristic
525	C₄	#11926795	1	1	yes	characteristic
526	C₂	—	8	2	no	—
527	C₂	—	8	2	no	—
528	C₂	#14562814	1	1	yes	characteristic
529	C₂	#14562863	1	1	yes	characteristic
530	C₂	#14562870	1	1	yes	characteristic
531	C₂	#14562919	1	1	yes	characteristic
532	C₂	#14564631	1	1	yes	characteristic
533	C₂	#14564638	1	1	yes	characteristic
534	C₂	#14564682	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#2537	C₂
socle	C₂³×C₁₉	#120
hypercenter	#2537	D₁₉
hypocenter	C₁₉	#10231
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2537

Complements

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

N	H ≅ G/N	type
1. C₂×#11926824	C₂	semidirect
2. C₂×#11926749	C₂	semidirect
3. #14564595	C₂	semidirect
4. C₂×D₄⋊(C₁₉⋊C₈)	C₂	semidirect
5. C₂×D₄⋊(C₁₉⋊C₈)	C₂	semidirect
6. #14561518	C₂	semidirect
70. #10597315	D₄	semidirect
77. C₄⋊(C₁₉⋊C₈)	D₄	semidirect
78. C₄⋊(C₁₉⋊C₈)	D₄	semidirect
97. C₂×D₄×C₁₉	SD₁₆	semidirect
348. C₁₉	#10231	semidirect
371. C₂×D₄	#64526	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926824	2
C₂×#11926749	2
#14564595	2
C₂×D₄⋊(C₁₉⋊C₈)	2
#14561518	2
C₁₉×#2537	2
#10231	19