Subgroups — #14575110

Order 2432.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597357	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927189	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927179	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926931	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926796	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926772	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926760	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926696	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926686	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926679	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926676	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926654	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926614	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#459	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#64543	C₂²	1	1	yes	characteristic, complemented
17	C₂×D₄×D₁₉	—	2	1	no	—
18	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
20	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#127	C₂²	1	1	yes	characteristic, complemented
24	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
25	#10597384	—	2	1	no	—
26	#10597384	C₂²	1	1	yes	characteristic
27	#10597384	C₂²	1	1	yes	characteristic, complemented
28	#10597383	—	2	1	no	—
29	#10597383	—	2	1	no	—
30	C₂×#64526	C₂²	1	1	yes	characteristic, complemented
31	C₂×#64526	C₂²	1	1	yes	characteristic, complemented
32	C₂×#64525	C₂²	1	1	yes	characteristic
33	C₂×#64525	C₂²	1	1	yes	characteristic, complemented
34	C₂×#64525	C₂²	1	1	yes	characteristic, complemented
35	#10597376	—	2	1	no	—
36	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
37	#10597357	—	2	4	no	—
38	D₈×D₁₉	—	2	4	no	—
39	C₂×D₁₅₂	C₂²	1	1	yes	characteristic
40	C₂×#64516	C₂²	1	1	yes	characteristic, complemented
41	C₂×#64515	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
43	#10597343	C₂²	1	1	yes	characteristic, complemented
44	#10597341	C₂²	1	1	yes	characteristic, complemented
45	#10597332	—	2	1	no	—
46	#10597328	—	2	1	no	—
47	#10597321	C₂²	1	1	yes	characteristic, complemented
48	C₄×D₇₆	C₂²	1	1	yes	characteristic
49	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
52	C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
53	#10597289	C₂²	1	1	yes	characteristic, complemented
54	#10597278	C₂²	1	1	yes	characteristic, complemented
55	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	#10597273	C₂²	1	1	yes	characteristic, complemented
58	#10597266	C₂²	1	1	yes	characteristic, complemented
59	#10597265	C₂²	1	1	yes	characteristic, complemented
60	#10597260	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₉	—	2	1	no	—
62	C₂³×D₁₉	—	2	1	no	—
63	C₂³×D₁₉	—	2	1	no	—
64	C₂×D₄×C₁₉	—	2	1	no	—
65	C₂×D₄×C₁₉	—	2	1	no	—
66	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂×C₂²⋊D₁₉	—	2	1	no	—
71	C₂×C₂²⋊D₁₉	—	2	1	no	—
72	C₂×C₂²⋊D₁₉	—	2	1	no	—
73	C₂×C₂²⋊D₁₉	—	2	1	no	—
74	C₂×C₂²⋊D₁₉	—	2	1	no	—
75	C₂×C₂²⋊D₁₉	—	2	1	no	—
76	C₂²×Dic₁₉	—	2	1	no	—
77	#64543	—	2	2	no	—
78	#64543	—	4	1	no	—
79	D₄×D₁₉	—	2	2	no	—
80	D₄×D₁₉	—	2	2	no	—
81	D₄×D₁₉	—	2	2	no	—
82	D₄×D₁₉	—	4	1	no	—
83	D₄×D₁₉	—	4	1	no	—
84	D₄×D₁₉	—	4	1	no	—
85	D₄×D₁₉	—	4	4	no	—
86	C₂×D₇₆	—	2	1	no	—
87	C₂×D₇₆	D₄	1	1	yes	characteristic
88	C₂×D₇₆	C₂³	1	1	yes	characteristic
89	C₂×D₇₆	C₂³	1	1	yes	characteristic
90	C₂×C₄×D₁₉	—	2	1	no	—
91	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
93	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
94	D₈×C₁₉	—	2	2	no	—
95	D₈×C₁₉	—	2	2	no	—
96	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₂²⋊Dic₁₉	—	2	1	no	—
102	C₂²⋊Dic₁₉	—	2	1	no	—
103	#64526	—	2	2	no	—
104	#64526	—	4	1	no	—
105	#64525	—	2	2	no	—
106	#64525	—	4	1	no	—
107	#64525	D₄	1	4	yes	complemented
108	(C₂×D₁₉)⋊C₄	—	2	1	no	—
109	(C₂×D₁₉)⋊C₄	—	2	1	no	—
110	(C₂×D₁₉)⋊C₄	—	2	1	no	—
111	(C₂×D₁₉)⋊C₄	—	2	1	no	—
112	(C₂×D₁₉)⋊C₄	—	2	1	no	—
113	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
114	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
115	C₄⋊Dic₁₉	—	2	1	no	—
116	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
117	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
118	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
119	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
120	D₁₅₂	—	2	2	no	—
121	#64516	—	2	2	no	—
122	#64515	—	2	2	no	—
123	C₈×D₁₉	—	2	2	no	—
124	C₂³×C₁₉	—	2	1	no	—
125	C₂³×C₁₉	—	2	1	no	—
126	C₂³×C₁₉	—	2	1	no	—
127	C₂²×D₁₉	—	2	1	no	—
128	C₂²×D₁₉	—	2	1	no	—
129	C₂²×D₁₉	—	4	2	no	—
130	C₂²×D₁₉	—	4	2	no	—
131	C₂²×D₁₉	—	4	2	no	—
132	C₂²×D₁₉	—	4	2	no	—
133	C₂²×D₁₉	—	4	2	no	—
134	C₂²×D₁₉	—	4	2	no	—
135	C₂²×D₁₉	—	8	1	no	—
136	C₂²×D₁₉	—	8	1	no	—
137	C₂²×D₁₉	—	8	1	no	—
138	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
140	D₄×C₁₉	—	2	1	no	—
141	D₄×C₁₉	—	2	1	no	—
142	D₄×C₁₉	—	2	1	no	—
143	D₄×C₁₉	—	2	1	no	—
144	D₄×C₁₉	—	2	1	no	—
145	D₄×C₁₉	—	4	2	no	—
146	D₄×C₁₉	—	8	1	no	—
147	D₄×C₁₉	C₂×D₄	1	2	yes	complemented
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	8	1	no	—
150	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
153	C₂²⋊D₁₉	—	4	2	no	—
154	C₂²⋊D₁₉	—	4	2	no	—
155	C₂²⋊D₁₉	—	4	2	no	—
156	C₂²⋊D₁₉	—	4	2	no	—
157	C₂²⋊D₁₉	—	4	2	no	—
158	C₂²⋊D₁₉	—	4	2	no	—
159	C₂×Dic₁₉	—	2	1	no	—
160	C₂×Dic₁₉	—	2	1	no	—
161	C₂×Dic₁₉	—	4	2	no	—
162	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
164	D₇₆	—	2	2	no	—
165	D₇₆	—	2	1	no	—
166	D₇₆	—	2	1	no	—
167	D₇₆	—	2	1	no	—
168	D₇₆	—	8	1	no	—
169	D₇₆	C₂×D₄	1	2	yes	—
170	C₄×D₁₉	—	2	1	no	—
171	C₄×D₁₉	—	2	1	no	—
172	C₄×D₁₉	—	2	1	no	—
173	C₄×D₁₉	—	2	1	no	—
174	C₄×D₁₉	—	4	2	no	—
175	Dic₃₈	—	2	1	no	—
176	Dic₃₈	—	2	1	no	—
177	C₈×C₁₉	—	2	1	no	—
178	C₈×C₁₉	—	2	1	no	—
179	C₁₉⋊C₈	—	2	1	no	—
180	C₁₉⋊C₈	C₂×D₄	1	2	yes	complemented
181	#3264	—	19	1	no	maximal, Sylow
182	C₂²×C₁₉	—	2	2	no	—
183	C₂²×C₁₉	—	4	1	no	—
184	C₂²×C₁₉	—	4	1	no	—
185	C₂²×C₁₉	—	4	1	no	—
186	C₂²×C₁₉	—	4	1	no	—
187	C₂²×C₁₉	—	4	1	no	—
188	C₂²×C₁₉	—	4	1	no	—
189	C₂²×C₁₉	—	4	1	no	—
190	C₂²×C₁₉	—	4	1	no	—
191	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×D₁₉	—	2	1	no	—
193	C₂×D₁₉	—	2	1	no	—
194	C₂×D₁₉	—	2	1	no	—
195	C₂×D₁₉	—	2	2	no	—
196	C₂×D₁₉	—	2	1	no	—
197	C₂×D₁₉	—	2	1	no	—
198	C₂×D₁₉	—	4	1	no	—
199	C₂×D₁₉	—	4	1	no	—
200	C₂×D₁₉	—	4	1	no	—
201	C₂×D₁₉	—	4	1	no	—
202	C₂×D₁₉	—	4	1	no	—
203	C₂×D₁₉	—	8	4	no	—
204	C₂×D₁₉	—	8	4	no	—
205	C₂×D₁₉	—	8	4	no	—
206	C₂×D₁₉	AGL(1,ℤ/8)	1	2	yes	complemented
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	2	1	no	—
209	C₄×C₁₉	—	4	1	no	—
210	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
211	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
212	Dic₁₉	—	2	1	no	—
213	Dic₁₉	—	2	1	no	—
214	Dic₁₉	—	4	1	no	—
215	Dic₁₉	—	4	1	no	—
216	C₂×AGL(1,ℤ/8)	—	19	1	no	—
217	C₂²×D₈	—	19	1	no	—
218	#546	—	19	1	no	—
219	D₄²	—	19	1	no	—
220	#496	—	19	1	no	—
221	#469	—	19	1	no	—
222	#465	—	19	1	no	—
223	#463	—	19	1	no	—
224	#459	D₁₉	1	1	yes	characteristic, complemented
225	#450	—	19	1	no	—
226	#449	—	19	1	no	—
227	#447	—	19	1	no	—
228	#447	—	19	1	no	—
229	#442	—	19	1	no	—
230	#435	—	19	1	no	—
231	C₂×C₁₉	—	4	2	no	—
232	C₂×C₁₉	—	8	1	no	—
233	C₂×C₁₉	—	8	1	no	—
234	C₂×C₁₉	D₄²	1	1	yes	characteristic
235	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₂×C₁₉	#576	1	1	yes	characteristic
237	D₁₉	—	2	2	no	—
238	D₁₉	—	4	1	no	—
239	D₁₉	—	4	2	no	—
240	D₁₉	—	8	1	no	—
241	C₂×#41	—	19	1	no	—
242	C₂²×D₄	—	19	1	no	—
243	C₂²×D₄	—	19	1	no	—
244	C₂²×D₄	—	19	1	no	—
245	C₂²×D₄	—	38	1	no	—
246	AGL(1,ℤ/8)	—	38	4	no	—
247	C₂×SD₁₆	—	19	1	no	—
248	C₂×SD₁₆	—	19	1	no	—
249	C₂×SD₁₆	—	19	1	no	—
250	C₂×D₈	—	19	1	no	—
251	C₂×D₈	—	19	1	no	—
252	C₂×D₈	—	19	1	no	—
253	C₂×D₈	—	19	1	no	—
254	C₂×D₈	—	38	4	no	—
255	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic, complemented
256	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic, complemented
257	C₂×M₁₆	—	19	1	no	—
258	C₂²×C₈	—	19	1	no	—
259	#127	C₂×D₁₉	1	1	yes	characteristic, complemented
260	#124	—	19	1	no	—
261	#123	—	38	1	no	—
262	C₂²⋊Q₈	—	19	1	no	—
263	#121	—	19	1	no	—
264	#121	—	19	1	no	—
265	#121	—	19	1	no	—
266	#121	—	38	1	no	—
267	#121	—	38	1	no	—
268	#120	—	38	1	no	—
269	#120	—	38	1	no	—
270	#120	—	38	1	no	—
271	C₄×D₄	—	19	1	no	—
272	C₄×D₄	—	19	1	no	—
273	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
274	C₂×C₂²⋊C₄	—	38	1	no	—
275	#106	—	19	1	no	—
276	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic, complemented
277	#103	—	19	1	no	—
278	#102	—	19	1	no	—
279	#102	—	19	1	no	—
280	#102	—	19	1	no	—
281	#102	C₂×D₁₉	1	1	yes	characteristic, complemented
282	#102	C₂×D₁₉	1	1	yes	characteristic, complemented
283	C₂²⋊C₈	—	19	1	no	—
284	C₂²⋊C₈	—	19	1	no	—
285	#97	—	19	1	no	—
286	C₁₉	#3264	1	1	yes	characteristic, complemented, Sylow
287	C₂⁴	—	38	1	no	—
288	C₂⁴	—	38	1	no	—
289	C₂⁴	—	38	1	no	—
290	#41	—	38	2	no	—
291	#41	—	76	1	no	—
292	C₂×Q₈	—	19	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	19	1	no	—
296	C₂×D₄	—	19	1	no	—
297	C₂×D₄	—	19	1	no	—
298	C₂×D₄	—	38	1	no	—
299	C₂×D₄	—	38	1	no	—
300	C₂×D₄	—	38	1	no	—
301	C₂×D₄	—	38	1	no	—
302	C₂×D₄	—	38	2	no	—
303	C₂×D₄	—	38	2	no	—
304	C₂×D₄	—	38	2	no	—
305	C₂×D₄	—	38	1	no	—
306	C₂×D₄	—	38	1	no	—
307	C₂×D₄	—	38	1	no	—
308	C₂×D₄	—	76	1	no	—
309	C₂×D₄	—	76	1	no	—
310	C₂×D₄	—	76	1	no	—
311	C₂×D₄	—	76	4	no	—
312	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
313	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
314	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	19	1	no	—
317	C₂²×C₄	—	19	1	no	—
318	C₂²×C₄	—	38	1	no	—
319	C₂²×C₄	—	38	1	no	—
320	SD₁₆	—	38	2	no	—
321	SD₁₆	—	38	2	no	—
322	SD₁₆	—	76	1	no	—
323	D₈	—	2	2	no	—
324	D₈	—	2	2	no	—
325	D₈	—	19	4	no	—
326	D₈	—	38	2	no	—
327	D₈	—	38	2	no	—
328	D₈	—	76	1	no	—
329	M₁₆	—	38	2	no	—
330	C₂×C₈	—	19	1	no	—
331	C₂×C₈	—	19	1	no	—
332	C₂×C₈	—	38	2	no	—
333	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
334	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
335	C₄⋊C₄	—	19	1	no	—
336	C₄⋊C₄	—	19	1	no	—
337	C₄⋊C₄	—	38	1	no	—
338	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
339	C₂²⋊C₄	—	2	1	no	—
340	C₂²⋊C₄	—	19	1	no	—
341	C₂²⋊C₄	—	19	1	no	—
342	C₂²⋊C₄	—	38	1	no	—
343	C₂²⋊C₄	—	38	1	no	—
344	C₂²⋊C₄	—	38	1	no	—
345	C₂²⋊C₄	—	38	1	no	—
346	C₂²⋊C₄	—	38	1	no	—
347	C₂²⋊C₄	—	38	1	no	—
348	C₂²⋊C₄	—	38	1	no	—
349	C₄²	C₂²×D₁₉	1	1	yes	characteristic
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	19	1	no	—
354	C₂³	—	19	1	no	—
355	C₂³	—	38	1	no	—
356	C₂³	—	38	1	no	—
357	C₂³	—	76	2	no	—
358	C₂³	—	76	2	no	—
359	C₂³	—	76	2	no	—
360	C₂³	—	76	2	no	—
361	C₂³	—	76	2	no	—
362	C₂³	—	76	2	no	—
363	C₂³	—	152	1	no	—
364	C₂³	—	152	1	no	—
365	C₂³	—	152	1	no	—
366	Q₈	—	38	1	no	—
367	Q₈	—	38	1	no	—
368	D₄	—	2	1	no	—
369	D₄	—	2	1	no	—
370	D₄	—	2	1	no	—
371	D₄	—	2	1	no	—
372	D₄	—	2	1	no	—
373	D₄	—	4	2	no	—
374	D₄	—	8	1	no	—
375	D₄	—	19	2	no	—
376	D₄	—	38	2	no	—
377	D₄	—	38	1	no	—
378	D₄	—	38	1	no	—
379	D₄	—	38	1	no	—
380	D₄	—	76	2	no	—
381	D₄	—	76	2	no	—
382	D₄	—	76	2	no	—
383	D₄	—	76	2	no	—
384	D₄	—	76	2	no	—
385	D₄	—	76	2	no	—
386	D₄	—	152	1	no	—
387	D₄	D₄×D₁₉	1	2	yes	complemented
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	8	1	no	—
390	C₂×C₄	—	19	1	no	—
391	C₂×C₄	—	19	1	no	—
392	C₂×C₄	—	38	1	no	—
393	C₂×C₄	—	38	1	no	—
394	C₂×C₄	—	38	1	no	—
395	C₂×C₄	—	38	1	no	—
396	C₂×C₄	—	38	1	no	—
397	C₂×C₄	—	38	1	no	—
398	C₂×C₄	—	76	2	no	—
399	C₂×C₄	—	76	2	no	—
400	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
401	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	19	2	no	—
406	C₈	—	38	1	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	19	2	no	—
417	C₂²	—	38	1	no	—
418	C₂²	—	38	1	no	—
419	C₂²	—	38	1	no	—
420	C₂²	—	38	1	no	—
421	C₂²	—	38	1	no	—
422	C₂²	—	38	2	no	—
423	C₂²	—	76	1	no	—
424	C₂²	—	76	1	no	—
425	C₂²	—	76	1	no	—
426	C₂²	—	76	1	no	—
427	C₂²	—	76	1	no	—
428	C₂²	—	152	4	no	—
429	C₂²	—	152	4	no	—
430	C₂²	—	152	4	no	—
431	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	38	1	no	—
436	C₄	—	38	1	no	—
437	C₄	—	76	1	no	—
438	C₄	—	76	1	no	—
439	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
440	C₄	#10597435	1	1	yes	characteristic
441	C₂	—	4	2	no	—
442	C₂	—	8	1	no	—
443	C₂	—	8	1	no	—
444	C₂	—	38	2	no	—
445	C₂	—	76	1	no	—
446	C₂	—	76	2	no	—
447	C₂	—	152	1	no	—
448	C₂	#11927178	1	1	yes	characteristic
449	C₂	AGL(1,ℤ/8)×D₁₉	1	1	yes	characteristic
450	C₂	#11927345	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#459	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	#459	D₁₉
hypocenter	C₁₉	#3264
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #459

Complements

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

N	H ≅ G/N	type
1. C₂×#10597357	C₂	semidirect
2. C₂×D₈×D₁₉	C₂	semidirect
3. #11927189	C₂	semidirect
4. #11927179	C₂	semidirect
5. #11926931	C₂	semidirect
6. #11926796	C₂	semidirect
7. #11926772	C₂	semidirect
8. #11926760	C₂	semidirect
9. #11926696	C₂	semidirect
10. #11926686	C₂	semidirect
11. #11926679	C₂	semidirect
12. #11926676	C₂	semidirect
13. #11926654	C₂	semidirect
14. #11926614	C₂	semidirect
15. C₁₉×#459	C₂	semidirect
16. C₂×#64543	C₂²	semidirect
19. C₂×D₄×D₁₉	C₂²	semidirect
20. C₂×D₄×D₁₉	C₂²	semidirect
21. C₂×D₈×C₁₉	C₂²	semidirect
22. C₂×D₈×C₁₉	C₂²	semidirect
23. C₁₉×#127	C₂²	semidirect
24. C₄×D₄×C₁₉	C₂²	semidirect
27. #10597384	C₂²	semidirect
30. C₂×#64526	C₂²	semidirect
31. C₂×#64526	C₂²	semidirect
33. C₂×#64525	C₂²	semidirect
34. C₂×#64525	C₂²	semidirect
40. C₂×#64516	C₂²	semidirect
41. C₂×#64515	C₂²	semidirect
42. C₂×C₈×D₁₉	C₂²	semidirect
43. #10597343	C₂²	semidirect
44. #10597341	C₂²	semidirect
47. #10597321	C₂²	semidirect
49. C₄×D₇₆	C₂²	semidirect
50. C₁₉×C₄⋊C₈	C₂²	semidirect
51. C₁₉×#102	C₂²	semidirect
52. C₁₉×#102	C₂²	semidirect
53. #10597289	C₂²	semidirect
54. #10597278	C₂²	semidirect
55. (C₂×D₁₉)⋊C₈	C₂²	semidirect
56. (C₂×D₁₉)⋊C₈	C₂²	semidirect
57. #10597273	C₂²	semidirect
58. #10597266	C₂²	semidirect
59. #10597265	C₂²	semidirect
60. #10597260	C₂²	semidirect
107. #64525	D₄	semidirect
147. D₄×C₁₉	C₂×D₄	semidirect
180. C₁₉⋊C₈	C₂×D₄	semidirect
206. C₂×D₁₉	AGL(1,ℤ/8)	semidirect
224. #459	D₁₉	semidirect
255. C₂×D₈	C₂×D₁₉	semidirect
256. C₂×D₈	C₂×D₁₉	semidirect
259. #127	C₂×D₁₉	semidirect
273. C₄×D₄	C₂×D₁₉	semidirect
276. C₄⋊C₈	C₂×D₁₉	semidirect
281. #102	C₂×D₁₉	semidirect
282. #102	C₂×D₁₉	semidirect
286. C₁₉	#3264	semidirect
387. D₄	D₄×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597357	2
C₂×D₈×D₁₉	2
#11927189	2
#11927179	2
#11926931	2
#11926796	2
#11926772	2
#11926760	2
#11926696	2
#11926686	2
#11926679	2
#11926676	2
#11926654	2
#11926614	2
C₁₉×#459	2
#3264	19