Subgroups — #18083602

Order 4864.

802 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926920	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926744	C₂	1	1	yes	maximal, characteristic, complemented
3	#14564562	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926288	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2548	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64527	—	2	1	no	—
9	C₂²×#64525	—	2	2	no	—
10	C₂×#10597320	C₂²	1	1	yes	characteristic
11	#11926920	—	2	2	no	—
12	#11926920	—	2	2	no	—
13	#11926744	—	2	2	no	—
14	#11926744	—	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	2	no	—
19	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	#11926288	—	2	2	no	—
21	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
22	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#124	—	2	1	no	—
24	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#394	—	2	2	no	—
26	C₁₉×#390	—	2	1	no	—
27	C₁₉×#390	—	2	2	no	—
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
30	C₂²×D₄×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	D₄	1	2	yes	—
33	C₂²×D₇₆	—	2	1	no	—
34	C₂²×D₇₆	—	2	1	no	—
35	C₂²×D₇₆	—	2	1	no	—
36	C₁₉×#127	—	2	1	no	—
37	C₁₉×#127	—	2	1	no	—
38	C₁₉×#127	—	2	1	no	—
39	C₁₉×#127	—	2	1	no	—
40	C₁₉×#124	—	4	2	no	—
41	C₁₉×#124	—	4	2	no	—
42	C₄×Q₈×C₁₉	—	2	1	no	—
43	C₄×Q₈×C₁₉	—	2	1	no	—
44	C₄×Q₈×C₁₉	—	2	1	no	—
45	C₄×Q₈×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
51	C₂×C₄²×C₁₉	—	2	1	no	—
52	C₂×C₄²×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
54	C₂×#64527	—	2	4	no	—
55	C₂×#64527	—	4	2	no	—
56	C₂×#64527	—	4	2	no	—
57	C₂×#64525	—	2	8	no	—
58	C₂×#64525	—	4	8	no	—
59	C₂²×C₁₉⋊C₈	—	2	1	no	—
60	C₂²×C₁₉⋊C₈	—	2	1	no	—
61	C₂²×C₁₉⋊C₈	—	2	1	no	—
62	#10597320	—	2	1	no	—
63	#10597320	—	2	1	no	—
64	#10597320	—	2	1	no	—
65	#10597320	D₄	1	2	yes	—
66	C₁₉×#95	—	2	1	no	—
67	#10597266	—	2	4	no	—
68	#10597266	—	4	4	no	—
69	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
70	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
72	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
73	C₄×C₁₉⋊C₈	—	2	1	no	—
74	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
75	C₂⁴×C₁₉	—	2	2	no	—
76	C₂³×D₁₉	—	4	1	no	—
77	C₂×Q₈×C₁₉	—	2	1	no	—
78	C₂×Q₈×C₁₉	—	2	1	no	—
79	C₂×Q₈×C₁₉	—	2	1	no	—
80	C₂×Q₈×C₁₉	—	2	1	no	—
81	C₂×Q₈×C₁₉	—	2	1	no	—
82	C₂×Q₈×C₁₉	D₈	1	2	yes	complemented
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	—	2	2	no	—
85	C₂×D₄×C₁₉	—	4	4	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	4	1	no	—
91	C₂×D₄×C₁₉	—	4	1	no	—
92	C₂×D₄×C₁₉	—	4	2	no	—
93	C₂×D₄×C₁₉	—	4	1	no	—
94	C₂×D₄×C₁₉	—	4	1	no	—
95	C₂×D₄×C₁₉	—	4	2	no	—
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	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂×D₇₆	—	2	2	no	—
103	C₂×D₇₆	—	2	2	no	—
104	C₂×D₇₆	—	2	2	no	—
105	C₂×D₇₆	—	4	4	no	—
106	C₂×D₇₆	—	4	1	no	—
107	C₂×D₇₆	—	4	1	no	—
108	C₂×D₇₆	—	4	2	no	—
109	C₂×D₇₆	—	4	1	no	—
110	C₂×D₇₆	—	4	1	no	—
111	C₂×D₇₆	—	4	2	no	—
112	C₂×D₇₆	—	4	1	no	—
113	C₂×D₇₆	—	4	1	no	—
114	C₂×D₇₆	—	4	1	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	4	1	no	—
120	C₄⋊C₄×C₁₉	—	4	1	no	—
121	C₂²⋊C₄×C₁₉	—	4	8	no	—
122	C₂²⋊C₄×C₁₉	—	8	4	no	—
123	C₄²×C₁₉	—	4	1	no	—
124	C₄²×C₁₉	—	4	1	no	—
125	C₄²×C₁₉	—	4	1	no	—
126	C₄²×C₁₉	—	4	1	no	—
127	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₉	#41	1	1	yes	characteristic
131	#64527	—	4	8	no	—
132	#64525	—	4	16	no	—
133	C₂×C₁₉⋊C₈	—	2	4	no	—
134	C₂×C₁₉⋊C₈	—	2	2	no	—
135	C₂×C₁₉⋊C₈	—	2	2	no	—
136	C₂×C₁₉⋊C₈	—	4	1	no	—
137	C₂×C₁₉⋊C₈	—	4	1	no	—
138	C₂×C₁₉⋊C₈	—	4	1	no	—
139	C₂×C₁₉⋊C₈	—	4	2	no	—
140	#10047	—	19	1	no	maximal, Sylow
141	C₂³×C₁₉	—	4	2	no	—
142	C₂³×C₁₉	—	4	2	no	—
143	C₂³×C₁₉	—	4	2	no	—
144	C₂³×C₁₉	—	4	4	no	—
145	C₂³×C₁₉	—	4	4	no	—
146	C₂³×C₁₉	#120	1	1	yes	characteristic
147	C₂²×D₁₉	—	4	2	no	—
148	C₂²×D₁₉	—	8	1	no	—
149	C₂²×D₁₉	—	8	1	no	—
150	C₂²×D₁₉	—	8	2	no	—
151	C₂²×D₁₉	—	8	2	no	—
152	Q₈×C₁₉	—	2	2	no	—
153	Q₈×C₁₉	—	2	2	no	—
154	Q₈×C₁₉	—	4	1	no	—
155	Q₈×C₁₉	—	4	1	no	—
156	D₄×C₁₉	—	4	4	no	—
157	D₄×C₁₉	—	8	2	no	—
158	D₄×C₁₉	—	8	1	no	—
159	D₄×C₁₉	—	8	1	no	—
160	D₄×C₁₉	—	8	2	no	—
161	D₄×C₁₉	—	8	1	no	—
162	D₄×C₁₉	—	8	1	no	—
163	D₄×C₁₉	—	8	1	no	—
164	D₄×C₁₉	—	8	1	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#135	1	2	yes	—
183	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
186	D₇₆	—	4	4	no	—
187	D₇₆	—	4	2	no	—
188	D₇₆	—	4	2	no	—
189	D₇₆	—	4	4	no	—
190	D₇₆	—	8	2	no	—
191	D₇₆	—	8	1	no	—
192	D₇₆	—	8	1	no	—
193	D₇₆	—	8	1	no	—
194	D₇₆	—	8	1	no	—
195	C₁₉⋊C₈	—	2	4	no	—
196	C₁₉⋊C₈	—	4	2	no	—
197	C₁₉⋊C₈	—	8	1	no	—
198	C₂×#493	—	19	1	no	—
199	C₂×#460	—	19	1	no	—
200	#2548	D₁₉	1	1	yes	characteristic, complemented
201	#1982	—	19	1	no	—
202	C₂×#331	—	19	1	no	—
203	C₂×Q₈⋊C₈	—	19	1	no	—
204	#1279	—	19	1	no	—
205	C₂²×C₁₉	—	8	4	no	—
206	C₂²×C₁₉	—	8	4	no	—
207	C₂²×C₁₉	—	8	2	no	—
208	C₂²×C₁₉	—	8	2	no	—
209	C₂²×C₁₉	—	8	2	no	—
210	C₂²×C₁₉	#392	1	1	yes	characteristic
211	C₂²×C₁₉	#447	1	1	yes	characteristic
212	C₂²×C₁₉	#449	1	1	yes	characteristic
213	C₂²×C₁₉	#449	1	2	yes	—
214	C₂²×C₁₉	#453	1	2	yes	—
215	C₂×D₁₉	—	8	2	no	—
216	C₂×D₁₉	—	8	2	no	—
217	C₂×D₁₉	—	8	2	no	—
218	C₂×D₁₉	—	16	2	no	—
219	C₂×D₁₉	—	16	2	no	—
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	4	2	no	—
223	C₄×C₁₉	—	8	2	no	—
224	C₄×C₁₉	—	8	1	no	—
225	C₄×C₁₉	#447	1	1	yes	characteristic
226	C₄×C₁₉	#449	1	1	yes	characteristic
227	C₄×C₁₉	#463	1	2	yes	—
228	C₄×C₁₉	#466	1	1	yes	characteristic
229	C₄×C₁₉	#469	1	1	yes	characteristic
230	C₄×C₁₉	#495	1	1	yes	characteristic
231	C₄×C₁₉	#496	1	1	yes	characteristic
232	C₂²×SD₁₆	—	38	1	no	—
233	C₂²×D₈	—	38	2	no	—
234	C₂×#127	—	19	1	no	—
235	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
236	C₂×#124	—	2	1	no	—
237	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
238	#493	—	38	2	no	—
239	#493	—	38	2	no	—
240	#460	—	38	2	no	—
241	#460	—	38	2	no	—
242	C₂×C₄⋊C₈	—	19	1	no	—
243	C₂×C₄⋊C₈	—	19	1	no	—
244	C₂×#102	—	38	1	no	—
245	C₂×#102	—	38	2	no	—
246	C₂×C₄×C₈	—	19	1	no	—
247	#394	—	2	2	no	—
248	#390	—	2	2	no	—
249	#390	—	2	1	no	—
250	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
251	#331	—	38	2	no	—
252	Q₈⋊C₈	—	38	2	no	—
253	C₂×C₁₉	—	16	2	no	—
254	C₂×C₁₉	#1620	1	2	yes	—
255	C₂×C₁₉	#1621	1	2	yes	—
256	C₂×C₁₉	#1999	1	1	yes	characteristic
257	C₂×C₁₉	#2002	1	1	yes	characteristic
258	C₂×C₁₉	#2012	1	1	yes	characteristic
259	D₁₉	—	16	2	no	—
260	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
261	C₂²×D₄	—	2	1	no	—
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	—	38	1	no	—
264	C₂²×D₄	—	38	1	no	—
265	C₂²×D₄	—	38	1	no	—
266	C₂²×D₄	C₂²⋊D₁₉	1	2	yes	—
267	C₂×SD₁₆	—	38	4	no	—
268	C₂×SD₁₆	—	76	2	no	—
269	C₂×SD₁₆	—	76	2	no	—
270	C₂×D₈	—	38	8	no	—
271	C₂×D₈	—	76	8	no	—
272	C₂²×C₈	—	38	1	no	—
273	C₂²×C₈	—	38	1	no	—
274	C₂²×C₈	—	38	1	no	—
275	#127	—	2	1	no	—
276	#127	—	2	1	no	—
277	#127	—	2	1	no	—
278	#127	—	2	1	no	—
279	#127	—	19	2	no	—
280	#127	—	38	1	no	—
281	#127	—	38	1	no	—
282	#127	—	38	1	no	—
283	#124	—	4	2	no	—
284	#124	—	4	2	no	—
285	C₄×Q₈	—	2	1	no	—
286	C₄×Q₈	—	2	1	no	—
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
292	C₂×C₂²⋊C₄	—	2	4	no	—
293	C₂×C₂²⋊C₄	—	2	4	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
297	C₄⋊C₈	—	19	2	no	—
298	C₄⋊C₈	—	38	1	no	—
299	C₄⋊C₈	—	38	1	no	—
300	C₄⋊C₈	—	38	1	no	—
301	#102	—	38	4	no	—
302	#102	—	76	4	no	—
303	C₄×C₈	—	19	2	no	—
304	C₄×C₈	—	38	1	no	—
305	#95	—	2	1	no	—
306	C₁₉	#10047	1	1	yes	characteristic, complemented, Sylow
307	C₂⁴	—	2	2	no	—
308	C₂⁴	—	76	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	#64525	1	2	yes	complemented
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	4	4	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	2	no	—
326	C₂×D₄	—	4	2	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	38	2	no	—
329	C₂×D₄	—	38	2	no	—
330	C₂×D₄	—	38	2	no	—
331	C₂×D₄	—	76	4	no	—
332	C₂×D₄	—	76	1	no	—
333	C₂×D₄	—	76	1	no	—
334	C₂×D₄	—	76	1	no	—
335	C₂×D₄	—	76	1	no	—
336	C₂×D₄	—	76	1	no	—
337	C₂×D₄	—	76	2	no	—
338	C₂×D₄	—	76	1	no	—
339	C₂×D₄	—	76	2	no	—
340	C₂×D₄	—	76	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
347	SD₁₆	—	76	8	no	—
348	D₈	—	76	16	no	—
349	C₂×C₈	—	38	4	no	—
350	C₂×C₈	—	38	2	no	—
351	C₂×C₈	—	38	2	no	—
352	C₂×C₈	—	76	1	no	—
353	C₂×C₈	—	76	1	no	—
354	C₂×C₈	—	76	1	no	—
355	C₂×C₈	—	76	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₂²⋊C₄	—	4	8	no	—
363	C₂²⋊C₄	—	8	4	no	—
364	C₄²	—	4	1	no	—
365	C₄²	—	4	1	no	—
366	C₄²	—	4	1	no	—
367	C₄²	—	4	1	no	—
368	C₄²	D₄×D₁₉	1	1	yes	characteristic
369	C₄²	D₄×D₁₉	1	1	yes	characteristic
370	C₄²	D₄×D₁₉	1	1	yes	characteristic
371	C₄²	#64543	1	1	yes	characteristic
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	4	4	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	4	no	—
377	C₂³	—	76	2	no	—
378	C₂³	—	152	1	no	—
379	C₂³	—	152	1	no	—
380	C₂³	—	152	2	no	—
381	C₂³	—	152	2	no	—
382	C₂³	#10597399	1	1	yes	characteristic
383	Q₈	—	2	2	no	—
384	Q₈	—	2	2	no	—
385	Q₈	—	4	1	no	—
386	Q₈	—	4	1	no	—
387	D₄	—	4	4	no	—
388	D₄	—	8	2	no	—
389	D₄	—	8	1	no	—
390	D₄	—	8	1	no	—
391	D₄	—	8	1	no	—
392	D₄	—	8	1	no	—
393	D₄	—	8	1	no	—
394	D₄	—	8	2	no	—
395	D₄	—	8	1	no	—
396	D₄	—	76	4	no	—
397	D₄	—	76	2	no	—
398	D₄	—	76	2	no	—
399	D₄	—	76	4	no	—
400	D₄	—	152	2	no	—
401	D₄	—	152	1	no	—
402	D₄	—	152	1	no	—
403	D₄	—	152	1	no	—
404	D₄	—	152	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	C₂×#64525	1	1	yes	characteristic
415	C₂×C₄	#10597378	1	1	yes	characteristic
416	C₂×C₄	#10597383	1	1	yes	characteristic
417	C₂×C₄	#10597383	1	1	yes	characteristic
418	C₂×C₄	#10597384	1	1	yes	characteristic
419	C₂×C₄	#10597385	1	1	yes	characteristic
420	C₂×C₄	#10597385	1	1	yes	characteristic
421	C₂×C₄	#10597386	1	1	yes	characteristic
422	C₂×C₄	#10597395	1	1	yes	characteristic
423	C₂×C₄	#10597395	1	2	yes	—
424	C₂×C₄	#10597396	1	2	yes	—
425	C₂×C₄	#10597396	1	1	yes	characteristic
426	C₈	—	38	4	no	—
427	C₈	—	76	2	no	—
428	C₈	—	152	1	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	8	4	no	—
433	C₂²	—	8	4	no	—
434	C₂²	—	304	2	no	—
435	C₂²	—	304	2	no	—
436	C₂²	—	152	2	no	—
437	C₂²	—	152	2	no	—
438	C₂²	—	152	2	no	—
439	C₂²	#11926452	1	1	yes	characteristic
440	C₂²	#11926678	1	1	yes	characteristic
441	C₂²	#11926689	1	1	yes	characteristic
442	C₂²	#11926689	1	2	yes	—
443	C₂²	#11926712	1	2	yes	—
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	4	2	no	—
447	C₄	—	8	1	no	—
448	C₄	—	8	2	no	—
449	C₄	#11926677	1	1	yes	characteristic
450	C₄	#11926687	1	1	yes	characteristic
451	C₄	#11926756	1	2	yes	—
452	C₄	#11926778	1	1	yes	characteristic
453	C₄	#11926795	1	1	yes	characteristic
454	C₄	#11926926	1	1	yes	characteristic
455	C₄	#11926934	1	1	yes	characteristic
456	C₂	—	16	2	no	—
457	C₂	—	304	2	no	—
458	C₂	#14562694	1	2	yes	—
459	C₂	#14562700	1	2	yes	—
460	C₂	#14564631	1	1	yes	characteristic
461	C₂	#14564648	1	1	yes	characteristic
462	C₂	#14564712	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2548	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×#11926920	C₂
hypercenter	#2548	D₁₉
hypocenter	C₁₉	#10047
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2548

Complements

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

N	H ≅ G/N	type
2. C₂×#11926744	C₂	semidirect
3. #14564562	C₂	semidirect
4. C₂×#11926288	C₂	semidirect
5. C₂×Q₈⋊(C₁₉⋊C₈)	C₂	semidirect
6. #14561476	C₂	semidirect
7. C₁₉×#2548	C₂	semidirect
82. C₂×Q₈×C₁₉	D₈	semidirect
200. #2548	D₁₉	semidirect
306. C₁₉	#10047	semidirect
314. C₂×Q₈	#64525	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926920	2
C₂×#11926744	2
#14564562	2
C₂×#11926288	2
C₂×Q₈⋊(C₁₉⋊C₈)	2
#14561476	2
C₁₉×#2548	2
#10047	19