Subgroups — #18086331

Order 4864.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926740	C₂	1	1	yes	maximal, characteristic
2	#14564441	C₂	1	1	yes	maximal, characteristic, complemented
3	#14564429	C₂	1	1	yes	maximal, characteristic, complemented
4	#14563636	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926287	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#335	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₁₅₂	—	2	1	no	—
9	C₂×#10597320	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
11	#11926740	—	2	2	no	—
12	#11926740	—	2	2	no	—
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#10597278	—	2	1	no	—
15	C₂×#10597278	—	2	1	no	—
16	C₂×#10597278	—	2	1	no	—
17	C₂×#10597278	—	2	1	no	—
18	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
19	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
20	#11926414	C₂²	1	1	yes	characteristic
21	#11926307	—	2	1	no	—
22	#11926287	—	2	2	no	—
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#335	—	2	2	no	—
27	C₂²×D₇₆	—	2	1	no	—
28	C₂²×D₇₆	—	2	1	no	—
29	C₂²×D₇₆	—	2	1	no	—
30	C₂²×D₇₆	D₄	1	1	yes	characteristic
31	C₂²×C₄×D₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
38	C₂×C₄⋊Dic₁₉	—	2	1	no	—
39	C₂×C₄⋊Dic₁₉	—	2	1	no	—
40	C₂×C₄⋊Dic₁₉	—	2	1	no	—
41	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
42	C₂²×C₁₉⋊C₈	—	2	1	no	—
43	C₂×D₁₅₂	—	2	4	no	—
44	C₂×D₁₅₂	—	4	2	no	—
45	C₂×D₁₅₂	—	4	2	no	—
46	#10597320	—	2	1	no	—
47	#10597320	—	2	1	no	—
48	#10597320	—	2	1	no	—
49	#10597320	D₄	1	2	yes	—
50	C₄×D₇₆	—	2	1	no	—
51	C₄×D₇₆	—	2	1	no	—
52	C₄×D₇₆	—	2	1	no	—
53	C₄×D₇₆	—	2	1	no	—
54	C₁₉×C₄⋊C₈	—	2	1	no	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₁₉×C₄⋊C₈	—	2	1	no	—
57	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
58	C₄×C₈×C₁₉	—	2	1	no	—
59	C₄×C₈×C₁₉	—	2	1	no	—
60	#10597278	—	2	4	no	—
61	#10597278	—	4	2	no	—
62	#10597278	—	4	2	no	—
63	#10597278	—	4	2	no	—
64	(C₂×D₁₉)⋊C₈	—	4	2	no	—
65	(C₂×D₁₉)⋊C₈	—	4	2	no	—
66	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
67	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
68	C₂³×D₁₉	—	2	1	no	—
69	C₂³×D₁₉	—	4	1	no	—
70	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
73	C₂²×Dic₁₉	—	2	1	no	—
74	C₂²×Dic₁₉	—	4	1	no	—
75	C₂×D₇₆	—	2	1	no	—
76	C₂×D₇₆	—	2	1	no	—
77	C₂×D₇₆	—	2	1	no	—
78	C₂×D₇₆	—	2	1	no	—
79	C₂×D₇₆	—	2	2	no	—
80	C₂×D₇₆	—	2	2	no	—
81	C₂×D₇₆	—	2	1	no	—
82	C₂×D₇₆	—	2	2	no	—
83	C₂×D₇₆	—	4	1	no	—
84	C₂×D₇₆	—	4	1	no	—
85	C₂×D₇₆	—	4	1	no	—
86	C₂×D₇₆	—	4	1	no	—
87	C₂×D₇₆	—	4	1	no	—
88	C₂×D₇₆	—	4	1	no	—
89	C₂×D₇₆	—	4	1	no	—
90	C₂×D₇₆	—	4	1	no	—
91	C₂×D₇₆	—	4	1	no	—
92	C₂×D₇₆	—	4	1	no	—
93	C₂×D₇₆	—	4	1	no	—
94	C₂×D₇₆	—	8	1	no	—
95	C₂×D₇₆	—	8	1	no	—
96	C₂×D₇₆	D₈	1	2	yes	—
97	C₂×C₄×D₁₉	—	4	1	no	—
98	C₂×C₄×D₁₉	—	4	1	no	—
99	C₂×C₄×D₁₉	—	4	1	no	—
100	C₂×C₄×D₁₉	—	4	1	no	—
101	C₂×C₄×D₁₉	—	4	1	no	—
102	C₂×C₄×D₁₉	—	4	1	no	—
103	C₂×C₈×C₁₉	—	2	1	no	—
104	C₂×C₈×C₁₉	—	2	1	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	1	no	—
107	C₂×C₈×C₁₉	—	2	1	no	—
108	C₂×C₈×C₁₉	—	2	1	no	—
109	C₂×C₈×C₁₉	—	4	1	no	—
110	C₂×C₈×C₁₉	—	4	1	no	—
111	C₂×C₈×C₁₉	—	4	1	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₂×C₈×C₁₉	D₈	1	2	yes	complemented
115	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₁₉	#41	1	1	yes	characteristic
118	C₄²×C₁₉	#41	1	1	yes	characteristic
119	(C₂×D₁₉)⋊C₄	—	4	1	no	—
120	(C₂×D₁₉)⋊C₄	—	4	1	no	—
121	C₄⋊Dic₁₉	—	2	1	no	—
122	C₄⋊Dic₁₉	—	2	1	no	—
123	C₄⋊Dic₁₉	—	4	1	no	—
124	C₄⋊Dic₁₉	—	4	1	no	—
125	C₄⋊Dic₁₉	—	4	1	no	—
126	C₄⋊Dic₁₉	—	4	1	no	—
127	C₄⋊Dic₁₉	—	8	1	no	—
128	C₂×C₁₉⋊C₈	—	4	1	no	—
129	C₂×C₁₉⋊C₈	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	4	1	no	—
131	D₁₅₂	—	4	8	no	—
132	#10472	—	19	1	no	maximal, Sylow
133	C₂³×C₁₉	#121	1	1	yes	characteristic
134	C₂²×D₁₉	—	2	2	no	—
135	C₂²×D₁₉	—	4	1	no	—
136	C₂²×D₁₉	—	4	1	no	—
137	C₂²×D₁₉	—	4	1	no	—
138	C₂²×D₁₉	—	4	1	no	—
139	C₂²×D₁₉	—	4	1	no	—
140	C₂²×D₁₉	—	4	1	no	—
141	C₂²×D₁₉	—	4	2	no	—
142	C₂²×D₁₉	—	8	1	no	—
143	C₂²×D₁₉	—	8	1	no	—
144	C₂²×D₁₉	—	8	1	no	—
145	C₂²×D₁₉	—	8	1	no	—
146	C₂²×D₁₉	—	8	1	no	—
147	C₂²×D₁₉	—	8	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
160	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
161	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
164	C₂×Dic₁₉	—	4	1	no	—
165	C₂×Dic₁₉	—	4	1	no	—
166	C₂×Dic₁₉	—	4	1	no	—
167	C₂×Dic₁₉	—	8	1	no	—
168	C₂×Dic₁₉	—	8	1	no	—
169	C₂×Dic₁₉	—	8	1	no	—
170	D₇₆	—	2	2	no	—
171	D₇₆	—	2	2	no	—
172	D₇₆	—	4	2	no	—
173	D₇₆	—	4	1	no	—
174	D₇₆	—	4	2	no	—
175	D₇₆	—	4	2	no	—
176	D₇₆	—	4	2	no	—
177	D₇₆	—	4	1	no	—
178	D₇₆	—	8	2	no	—
179	D₇₆	—	8	2	no	—
180	D₇₆	—	8	1	no	—
181	D₇₆	—	8	1	no	—
182	D₇₆	—	8	1	no	—
183	D₇₆	—	8	1	no	—
184	C₄×D₁₉	—	8	1	no	—
185	C₄×D₁₉	—	8	1	no	—
186	C₄×D₁₉	—	8	1	no	—
187	C₄×D₁₉	—	8	1	no	—
188	C₈×C₁₉	—	2	2	no	—
189	C₈×C₁₉	—	4	2	no	—
190	C₈×C₁₉	—	4	1	no	—
191	C₈×C₁₉	—	8	1	no	—
192	C₁₉⋊C₈	—	8	1	no	—
193	C₂×#459	—	19	1	no	—
194	#1957	—	19	1	no	—
195	#1954	—	19	1	no	—
196	#1802	—	19	1	no	—
197	C₂×#335	D₁₉	1	1	yes	characteristic, complemented
198	C₂×#331	—	19	1	no	—
199	#1296	—	19	1	no	—
200	C₂²×C₁₉	#394	1	1	yes	characteristic
201	C₂²×C₁₉	#459	1	1	yes	characteristic
202	C₂²×C₁₉	#463	1	1	yes	characteristic
203	C₂²×C₁₉	#466	1	1	yes	characteristic
204	C₂²×C₁₉	#468	1	1	yes	characteristic
205	C₂²×C₁₉	#471	1	1	yes	characteristic
206	C₂²×C₁₉	#472	1	1	yes	characteristic
207	C₂×D₁₉	—	4	2	no	—
208	C₂×D₁₉	—	4	2	no	—
209	C₂×D₁₉	—	4	2	no	—
210	C₂×D₁₉	—	8	1	no	—
211	C₂×D₁₉	—	8	1	no	—
212	C₂×D₁₉	—	8	1	no	—
213	C₂×D₁₉	—	8	1	no	—
214	C₂×D₁₉	—	8	2	no	—
215	C₂×D₁₉	—	8	2	no	—
216	C₂×D₁₉	—	8	2	no	—
217	C₂×D₁₉	—	16	1	no	—
218	C₂×D₁₉	—	16	1	no	—
219	C₂×D₁₉	—	16	1	no	—
220	C₂×D₁₉	—	16	1	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	#447	1	1	yes	characteristic
224	C₄×C₁₉	#452	1	1	yes	characteristic
225	C₄×C₁₉	#459	1	1	yes	characteristic
226	C₄×C₁₉	#463	1	1	yes	characteristic
227	C₄×C₁₉	#466	1	1	yes	characteristic
228	C₄×C₁₉	#469	1	1	yes	characteristic
229	C₄×C₁₉	#480	1	1	yes	characteristic
230	C₄×C₁₉	#482	1	1	yes	characteristic
231	Dic₁₉	—	8	1	no	—
232	Dic₁₉	—	16	1	no	—
233	C₂²×D₈	—	38	1	no	—
234	C₂×#127	—	19	1	no	—
235	C₂×C₄×D₄	—	19	1	no	—
236	#459	—	38	2	no	—
237	#459	—	38	2	no	—
238	C₂×C₄⋊C₈	—	19	1	no	—
239	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
240	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
241	C₂×#102	—	38	1	no	—
242	C₂×#102	—	38	1	no	—
243	C₂×#102	—	38	1	no	—
244	C₂×#102	—	38	1	no	—
245	C₂×C₂²⋊C₈	—	38	1	no	—
246	C₂×C₂²⋊C₈	—	38	1	no	—
247	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
248	#384	—	19	1	no	—
249	#340	—	38	1	no	—
250	#335	—	2	2	no	—
251	#331	—	38	2	no	—
252	C₂×C₁₉	#1667	1	1	yes	characteristic
253	C₂×C₁₉	#1681	1	1	yes	characteristic
254	C₂×C₁₉	#1685	1	1	yes	characteristic
255	C₂×C₁₉	#1697	1	1	yes	characteristic
256	C₂×C₁₉	#2033	1	1	yes	characteristic
257	C₂×C₁₉	#2051	1	1	yes	characteristic
258	C₂×C₁₉	#2054	1	1	yes	characteristic
259	D₁₉	—	8	2	no	—
260	D₁₉	—	16	2	no	—
261	C₂²×D₄	—	19	1	no	—
262	C₂²×D₄	—	38	1	no	—
263	C₂²×D₄	—	38	1	no	—
264	C₂²×D₄	—	38	1	no	—
265	C₂³×C₄	—	38	1	no	—
266	C₂×D₈	—	38	4	no	—
267	C₂×D₈	—	76	2	no	—
268	C₂×D₈	—	76	2	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	38	1	no	—
272	C₂²×C₈	D₇₆	1	1	yes	characteristic
273	C₂²×C₈	D₇₆	1	1	yes	characteristic
274	#127	—	19	2	no	—
275	#127	—	38	1	no	—
276	#127	—	38	1	no	—
277	#127	—	38	1	no	—
278	C₄×D₄	—	38	1	no	—
279	C₄×D₄	—	38	1	no	—
280	C₄×D₄	—	38	1	no	—
281	C₄×D₄	—	38	1	no	—
282	C₂×C₄⋊C₄	—	19	1	no	—
283	C₂×C₄⋊C₄	—	38	1	no	—
284	C₂×C₄⋊C₄	—	38	1	no	—
285	C₂×C₄⋊C₄	—	38	1	no	—
286	C₂×C₂²⋊C₄	—	38	1	no	—
287	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	38	1	no	—
292	C₄⋊C₈	—	38	1	no	—
293	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
294	#102	—	38	4	no	—
295	#102	—	76	2	no	—
296	#102	—	76	2	no	—
297	#102	—	76	2	no	—
298	C₂²⋊C₈	—	76	2	no	—
299	C₂²⋊C₈	—	76	2	no	—
300	C₄×C₈	—	2	1	no	—
301	C₄×C₈	—	2	1	no	—
302	C₁₉	#10472	1	1	yes	characteristic, complemented, Sylow
303	C₂⁴	—	38	1	no	—
304	C₂⁴	—	76	1	no	—
305	C₂×D₄	—	19	2	no	—
306	C₂×D₄	—	38	1	no	—
307	C₂×D₄	—	38	2	no	—
308	C₂×D₄	—	38	1	no	—
309	C₂×D₄	—	38	2	no	—
310	C₂×D₄	—	38	2	no	—
311	C₂×D₄	—	38	1	no	—
312	C₂×D₄	—	38	1	no	—
313	C₂×D₄	—	38	1	no	—
314	C₂×D₄	—	76	1	no	—
315	C₂×D₄	—	76	1	no	—
316	C₂×D₄	—	76	1	no	—
317	C₂×D₄	—	76	1	no	—
318	C₂×D₄	—	76	1	no	—
319	C₂×D₄	—	76	1	no	—
320	C₂×D₄	—	76	1	no	—
321	C₂×D₄	—	76	1	no	—
322	C₂×D₄	—	76	1	no	—
323	C₂×D₄	—	76	1	no	—
324	C₂×D₄	—	76	1	no	—
325	C₂×D₄	—	152	1	no	—
326	C₂×D₄	—	152	1	no	—
327	C₂²×C₄	—	38	1	no	—
328	C₂²×C₄	—	76	1	no	—
329	C₂²×C₄	—	76	1	no	—
330	C₂²×C₄	—	76	1	no	—
331	C₂²×C₄	—	76	1	no	—
332	C₂²×C₄	—	76	1	no	—
333	C₂²×C₄	—	76	1	no	—
334	C₂²×C₄	—	76	1	no	—
335	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
336	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
337	C₂²×C₄	#64545	1	1	yes	characteristic
338	D₈	—	76	8	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	4	1	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	76	1	no	—
351	C₂×C₈	—	76	1	no	—
352	C₂×C₈	—	76	1	no	—
353	C₂×C₈	D₁₅₂	1	2	yes	complemented
354	C₄⋊C₄	—	38	1	no	—
355	C₄⋊C₄	—	38	1	no	—
356	C₄⋊C₄	—	76	1	no	—
357	C₄⋊C₄	—	76	1	no	—
358	C₄⋊C₄	—	76	1	no	—
359	C₄⋊C₄	—	76	1	no	—
360	C₄⋊C₄	—	152	1	no	—
361	C₂²⋊C₄	—	76	1	no	—
362	C₂²⋊C₄	—	76	1	no	—
363	C₄²	#64541	1	1	yes	characteristic
364	C₄²	D₄×D₁₉	1	1	yes	characteristic
365	C₄²	#64545	1	1	yes	characteristic
366	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
367	C₂³	—	38	2	no	—
368	C₂³	—	76	1	no	—
369	C₂³	—	76	1	no	—
370	C₂³	—	76	1	no	—
371	C₂³	—	76	1	no	—
372	C₂³	—	76	1	no	—
373	C₂³	—	76	1	no	—
374	C₂³	—	76	2	no	—
375	C₂³	—	152	1	no	—
376	C₂³	—	152	1	no	—
377	C₂³	—	152	1	no	—
378	C₂³	—	152	1	no	—
379	C₂³	—	152	1	no	—
380	C₂³	—	152	1	no	—
381	C₂³	#10597341	1	1	yes	characteristic
382	D₄	—	38	2	no	—
383	D₄	—	38	2	no	—
384	D₄	—	76	1	no	—
385	D₄	—	76	2	no	—
386	D₄	—	76	1	no	—
387	D₄	—	76	2	no	—
388	D₄	—	76	2	no	—
389	D₄	—	76	2	no	—
390	D₄	—	152	2	no	—
391	D₄	—	152	2	no	—
392	D₄	—	152	1	no	—
393	D₄	—	152	1	no	—
394	D₄	—	152	1	no	—
395	D₄	—	152	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	76	1	no	—
399	C₂×C₄	—	76	1	no	—
400	C₂×C₄	—	76	1	no	—
401	C₂×C₄	—	152	1	no	—
402	C₂×C₄	—	152	1	no	—
403	C₂×C₄	—	152	1	no	—
404	C₂×C₄	—	152	1	no	—
405	C₂×C₄	—	152	1	no	—
406	C₂×C₄	—	152	1	no	—
407	C₂×C₄	—	152	1	no	—
408	C₂×C₄	#10597340	1	1	yes	characteristic
409	C₂×C₄	#10597340	1	1	yes	characteristic
410	C₂×C₄	#10597341	1	1	yes	characteristic
411	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
412	C₂×C₄	#10597350	1	1	yes	characteristic
413	C₂×C₄	#10597354	1	1	yes	characteristic
414	C₂×C₄	#10597354	1	1	yes	characteristic
415	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
416	C₂×C₄	#10597357	1	1	yes	characteristic
417	C₂×C₄	#10597364	1	1	yes	characteristic
418	C₂×C₄	#10597365	1	1	yes	characteristic
419	C₂×C₄	#10597376	1	1	yes	characteristic
420	C₂×C₄	#10597383	1	1	yes	characteristic
421	C₂×C₄	#10597393	1	1	yes	characteristic
422	C₈	—	2	2	no	—
423	C₈	—	4	1	no	—
424	C₈	—	4	2	no	—
425	C₈	—	8	1	no	—
426	C₈	—	152	1	no	—
427	C₂²	—	304	1	no	—
428	C₂²	—	304	1	no	—
429	C₂²	—	304	1	no	—
430	C₂²	—	304	1	no	—
431	C₂²	—	76	2	no	—
432	C₂²	—	76	2	no	—
433	C₂²	—	76	2	no	—
434	C₂²	—	152	2	no	—
435	C₂²	—	152	2	no	—
436	C₂²	—	152	2	no	—
437	C₂²	—	152	1	no	—
438	C₂²	—	152	1	no	—
439	C₂²	—	152	1	no	—
440	C₂²	—	152	1	no	—
441	C₂²	#11926461	1	1	yes	characteristic
442	C₂²	#11926740	1	1	yes	characteristic
443	C₂²	#11926760	1	1	yes	characteristic
444	C₂²	#11926781	1	1	yes	characteristic
445	C₂²	#11926791	1	1	yes	characteristic
446	C₂²	#11926808	1	1	yes	characteristic
447	C₂²	#11926815	1	1	yes	characteristic
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	304	1	no	—
451	C₄	—	152	1	no	—
452	C₄	#11926676	1	1	yes	characteristic
453	C₄	#11926705	1	1	yes	characteristic
454	C₄	#11926740	1	1	yes	characteristic
455	C₄	#11926760	1	1	yes	characteristic
456	C₄	#11926780	1	1	yes	characteristic
457	C₄	#11926797	1	1	yes	characteristic
458	C₄	#11926859	1	1	yes	characteristic
459	C₄	#11926871	1	1	yes	characteristic
460	C₂	—	304	2	no	—
461	C₂	—	152	2	no	—
462	C₂	#14562991	1	1	yes	characteristic
463	C₂	#14563073	1	1	yes	characteristic
464	C₂	#14563101	1	1	yes	characteristic
465	C₂	#14563169	1	1	yes	characteristic
466	C₂	#14564819	1	1	yes	characteristic
467	C₂	#14564929	1	1	yes	characteristic
468	C₂	#14564946	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597341
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#335	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂×#11926740	C₂
hypercenter	C₂×#335	D₁₉
hypocenter	C₁₉	#10472
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
2. #14564441	C₂	semidirect
3. #14564429	C₂	semidirect
4. #14563636	C₂	semidirect
5. C₂×#11926287	C₂	semidirect
6. #14561519	C₂	semidirect
7. C₂×C₁₉×#335	C₂	semidirect
114. C₂×C₈×C₁₉	D₈	semidirect
197. C₂×#335	D₁₉	semidirect
302. C₁₉	#10472	semidirect
353. C₂×C₈	D₁₅₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926740	2
#14564441	2
#14564429	2
#14563636	2
C₂×#11926287	2
#14561519	2
C₂×C₁₉×#335	2
#10472	19