Subgroups — #14578420

Order 2432.

1412 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927381	C₂	1	1	yes	maximal, characteristic, complemented
2	2₋¹⁺⁴×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927360	C₂	1	3	yes	maximal, complemented
4	#11927359	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927357	C₂	1	3	yes	maximal, complemented
6	#11927356	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927353	C₂	1	3	yes	maximal, complemented
8	#11927352	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927351	C₂	1	3	yes	maximal, complemented
10	#11927343	C₂	1	3	yes	maximal, complemented
11	#11927341	C₂	1	3	yes	maximal, complemented
12	C₂×#10597364	C₂	1	3	yes	maximal, complemented
13	#137×D₁₉	C₂	1	3	yes	maximal, complemented
14	#11927309	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#578	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
17	C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
18	#10597436	—	2	3	no	—
19	#10597436	C₂²	1	3	yes	complemented
20	#10597436	C₂²	1	1	yes	characteristic, complemented
21	#10597435	—	2	3	no	—
22	#10597435	C₂²	1	3	yes	complemented
23	#10597435	C₂²	1	1	yes	characteristic, complemented
24	#41×D₁₉	—	2	3	no	—
25	#41×D₁₉	—	2	3	no	—
26	#41×D₁₉	C₂²	1	3	yes	—
27	#41×D₁₉	C₂²	1	1	yes	characteristic
28	#41×D₁₉	C₂²	1	3	yes	complemented
29	#10597433	—	2	1	no	—
30	#10597433	—	2	1	no	—
31	#10597433	C₂²	1	3	yes	complemented
32	#10597433	C₂²	1	3	yes	complemented
33	C₂×#64545	—	2	1	no	—
34	C₂×#64545	C₂²	1	3	yes	—
35	C₂×Q₈×D₁₉	—	2	1	no	—
36	C₂×Q₈×D₁₉	C₂²	1	3	yes	complemented
37	C₁₉×#137	C₂²	1	3	yes	complemented
38	C₁₉×#137	C₂²	1	3	yes	complemented
39	C₁₉×#135	C₂²	1	3	yes	complemented
40	C₂×Q₁₆×C₁₉	C₂²	1	3	yes	complemented
41	C₁₉×#131	C₂²	1	1	yes	characteristic, complemented
42	#10597397	C₂²	1	3	yes	complemented
43	#10597396	C₂²	1	3	yes	complemented
44	#10597396	C₂²	1	3	yes	complemented
45	#10597395	C₂²	1	3	yes	complemented
46	#10597394	C₂²	1	1	yes	characteristic, complemented
47	C₂×#64528	C₂²	1	3	yes	complemented
48	#10597388	C₂²	1	3	yes	complemented
49	#10597388	C₂²	1	3	yes	complemented
50	C₂×#64527	C₂²	1	3	yes	complemented
51	#10597365	C₂²	1	6	yes	complemented
52	#10597364	C₂²	1	6	yes	complemented
53	#10597364	C₂²	1	3	yes	complemented
54	#10597364	C₂²	1	6	yes	complemented
55	#10597364	C₂²	1	6	yes	complemented
56	#10597364	C₂²	1	3	yes	complemented
57	Q₁₆×D₁₉	C₂²	1	6	yes	complemented
58	#10597362	C₂²	1	6	yes	complemented
59	#10597361	C₂²	1	3	yes	complemented
60	#10597361	C₂²	1	3	yes	complemented
61	#10597360	C₂²	1	3	yes	complemented
62	#10597360	C₂²	1	3	yes	complemented
63	SD₁₆×D₁₉	C₂²	1	6	yes	complemented
64	#10597357	C₂²	1	1	yes	characteristic, complemented
65	#10597357	C₂²	1	3	yes	complemented
66	#10597355	C₂²	1	3	yes	complemented
67	#10597354	C₂²	1	3	yes	complemented
68	#10597353	C₂²	1	3	yes	complemented
69	M₁₆×D₁₉	C₂²	1	3	yes	complemented
70	#10597350	C₂²	1	3	yes	complemented
71	C₂×#64516	C₂²	1	3	yes	complemented
72	#10597347	C₂²	1	3	yes	complemented
73	C₂×#64515	C₂²	1	3	yes	complemented
74	#41×C₁₉	—	2	3	no	—
75	#41×C₁₉	—	2	3	no	—
76	#41×C₁₉	C₂³	1	3	yes	—
77	#41×C₁₉	C₂³	1	3	yes	—
78	#41×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×Q₈×C₁₉	—	2	1	no	—
80	C₂×Q₈×C₁₉	—	2	1	no	—
81	C₂×Q₈×C₁₉	C₂³	1	3	yes	—
82	C₂×Q₈×C₁₉	C₂³	1	3	yes	—
83	#64545	—	2	1	no	—
84	#64545	—	2	3	no	—
85	#64545	—	2	3	no	—
86	#64545	—	2	3	no	—
87	#64545	—	2	3	no	—
88	#64545	D₄	1	1	yes	characteristic
89	#64545	C₂³	1	3	yes	—
90	#64545	C₂³	1	6	yes	—
91	#64545	C₂³	1	3	yes	—
92	Q₈×D₁₉	—	2	1	no	—
93	Q₈×D₁₉	—	2	3	no	—
94	Q₈×D₁₉	—	2	3	no	—
95	Q₈×D₁₉	—	2	3	no	—
96	Q₈×D₁₉	—	2	3	no	—
97	Q₈×D₁₉	D₄	1	1	yes	characteristic
98	Q₈×D₁₉	C₂³	1	3	yes	—
99	Q₈×D₁₉	C₂³	1	6	yes	—
100	Q₈×D₁₉	C₂³	1	3	yes	—
101	#64543	—	2	3	no	—
102	#64543	—	2	6	no	—
103	#64543	—	2	3	no	—
104	#64543	—	2	3	no	—
105	#64543	D₄	1	3	yes	—
106	#64543	C₂³	1	1	yes	characteristic
107	#64543	C₂³	1	3	yes	—
108	D₄×D₁₉	—	2	3	no	—
109	D₄×D₁₉	—	2	3	no	—
110	D₄×D₁₉	—	2	3	no	—
111	D₄×D₁₉	—	2	6	no	—
112	D₄×D₁₉	D₄	1	3	yes	—
113	D₄×D₁₉	C₂³	1	3	yes	—
114	D₄×D₁₉	C₂³	1	1	yes	characteristic
115	#64541	—	2	6	no	—
116	#64541	—	2	6	no	—
117	#64541	—	2	3	no	—
118	#64541	—	2	3	no	—
119	#64541	—	2	3	no	—
120	#64541	—	2	3	no	—
121	#64541	C₂³	1	3	yes	—
122	#64541	C₂³	1	3	yes	—
123	#64541	C₂³	1	3	yes	—
124	C₂×D₇₆	—	2	3	no	—
125	C₂×D₇₆	—	2	3	no	—
126	C₂×D₇₆	C₂³	1	3	yes	—
127	C₂×C₄×D₁₉	—	2	3	no	—
128	C₂×C₄×D₁₉	—	2	3	no	—
129	C₂×C₄×D₁₉	—	2	3	no	—
130	C₂×C₄×D₁₉	—	2	3	no	—
131	C₂×C₄×D₁₉	C₂³	1	3	yes	—
132	C₂×Dic₃₈	—	2	3	no	—
133	C₂×Dic₃₈	—	2	3	no	—
134	C₂×Dic₃₈	C₂³	1	3	yes	—
135	Q₁₆×C₁₉	C₂³	1	3	yes	—
136	Q₁₆×C₁₉	C₂³	1	6	yes	—
137	SD₁₆×C₁₉	C₂³	1	3	yes	—
138	SD₁₆×C₁₉	C₂³	1	3	yes	—
139	D₈×C₁₉	C₂³	1	1	yes	characteristic
140	M₁₆×C₁₉	C₂³	1	3	yes	—
141	C₂×C₈×C₁₉	C₂³	1	3	yes	—
142	#64528	C₂³	1	3	yes	—
143	#64528	C₂³	1	6	yes	—
144	#64528	C₂³	1	3	yes	—
145	#64527	C₂³	1	3	yes	—
146	#64527	C₂³	1	6	yes	—
147	#64527	C₂³	1	3	yes	—
148	#64526	C₂³	1	1	yes	characteristic
149	#64526	C₂³	1	3	yes	—
150	#64525	C₂³	1	3	yes	—
151	#64525	C₂³	1	1	yes	characteristic
152	#64520	C₂³	1	3	yes	—
153	C₂×C₁₉⋊C₈	C₂³	1	3	yes	—
154	Dic₇₆	C₂³	1	3	yes	—
155	D₁₅₂	C₂³	1	3	yes	—
156	#64516	C₂³	1	3	yes	—
157	#64516	C₂³	1	6	yes	—
158	#64516	C₂³	1	1	yes	characteristic
159	#64515	C₂³	1	1	yes	characteristic
160	#64515	C₂³	1	3	yes	—
161	#64515	C₂³	1	3	yes	—
162	#64515	C₂³	1	3	yes	—
163	C₈×D₁₉	C₂³	1	6	yes	—
164	C₂²×D₁₉	—	2	3	no	—
165	C₂²×D₁₉	—	2	1	no	—
166	C₂²×D₁₉	—	2	3	no	—
167	C₂²×D₁₉	C₂×D₄	1	3	yes	—
168	Q₈×C₁₉	—	2	3	no	—
169	Q₈×C₁₉	—	2	3	no	—
170	Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
171	Q₈×C₁₉	C₂⁴	1	3	yes	—
172	Q₈×C₁₉	C₂⁴	1	3	yes	—
173	D₄×C₁₉	—	2	3	no	—
174	D₄×C₁₉	—	2	3	no	—
175	D₄×C₁₉	C₂×D₄	1	3	yes	—
176	D₄×C₁₉	C₂⁴	1	1	yes	characteristic
177	D₄×C₁₉	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₁₉	—	2	3	no	—
179	C₂×C₄×C₁₉	—	2	3	no	—
180	C₂×C₄×C₁₉	—	2	3	no	—
181	C₂×C₄×C₁₉	—	2	3	no	—
182	C₂×C₄×C₁₉	C₂⁴	1	3	yes	—
183	C₂²⋊D₁₉	—	2	3	no	—
184	C₂²⋊D₁₉	—	2	3	no	—
185	C₂²⋊D₁₉	—	2	1	no	—
186	C₂²⋊D₁₉	—	2	3	no	—
187	C₂²⋊D₁₉	—	2	3	no	—
188	C₂²⋊D₁₉	—	2	1	no	—
189	C₂²⋊D₁₉	C₂×D₄	1	6	yes	—
190	C₂×Dic₁₉	—	2	3	no	—
191	C₂×Dic₁₉	—	2	3	no	—
192	C₂×Dic₁₉	—	2	1	no	—
193	C₂×Dic₁₉	C₂×D₄	1	3	yes	—
194	D₇₆	—	2	3	no	—
195	D₇₆	—	2	6	no	—
196	D₇₆	—	2	3	no	—
197	D₇₆	—	2	3	no	—
198	D₇₆	C₂×D₄	1	3	yes	—
199	D₇₆	C₂⁴	1	3	yes	—
200	D₇₆	C₂⁴	1	1	yes	characteristic
201	C₄×D₁₉	—	2	3	no	—
202	C₄×D₁₉	—	2	3	no	—
203	C₄×D₁₉	—	2	6	no	—
204	C₄×D₁₉	—	2	3	no	—
205	C₄×D₁₉	—	2	3	no	—
206	C₄×D₁₉	—	2	3	no	—
207	C₄×D₁₉	—	2	6	no	—
208	C₄×D₁₉	—	2	3	no	—
209	C₄×D₁₉	C₂×D₄	1	3	yes	—
210	C₄×D₁₉	C₂×D₄	1	3	yes	—
211	C₄×D₁₉	C₂⁴	1	3	yes	—
212	C₄×D₁₉	C₂⁴	1	1	yes	characteristic
213	Dic₃₈	—	2	3	no	—
214	Dic₃₈	—	2	6	no	—
215	Dic₃₈	—	2	3	no	—
216	Dic₃₈	—	2	3	no	—
217	Dic₃₈	C₂×D₄	1	3	yes	—
218	Dic₃₈	C₂⁴	1	3	yes	—
219	Dic₃₈	C₂⁴	1	1	yes	characteristic
220	C₈×C₁₉	C₂⁴	1	3	yes	—
221	C₈×C₁₉	C₂⁴	1	1	yes	characteristic
222	C₁₉⋊C₈	C₂⁴	1	3	yes	—
223	C₁₉⋊C₈	C₂⁴	1	1	yes	characteristic
224	#3586	—	19	1	no	maximal, Sylow
225	C₂²×C₁₉	—	2	1	no	—
226	C₂²×C₁₉	—	2	1	no	—
227	C₂²×C₁₉	C₂²×D₄	1	3	yes	—
228	C₂×D₁₉	—	2	1	no	—
229	C₂×D₁₉	—	2	3	no	—
230	C₂×D₁₉	—	4	3	no	—
231	C₂×D₁₉	—	4	2	no	—
232	C₂×D₁₉	—	8	3	no	—
233	C₂×D₁₉	—	8	3	no	—
234	C₂×D₁₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×D₁₉	C₂²×D₄	1	3	yes	—
236	C₄×C₁₉	—	2	3	no	—
237	C₄×C₁₉	—	2	3	no	—
238	C₄×C₁₉	C₂²×D₄	1	3	yes	—
239	C₄×C₁₉	C₂⁵	1	1	yes	characteristic
240	Dic₁₉	—	2	3	no	—
241	Dic₁₉	—	2	1	no	—
242	Dic₁₉	C₂²×D₄	1	3	yes	—
243	Dic₁₉	C₂²×D₄	1	1	yes	characteristic
244	#585	—	19	1	no	—
245	C₂×2₋¹⁺⁴	—	19	1	no	—
246	#578	—	19	1	no	—
247	#578	—	19	3	no	—
248	#578	—	19	3	no	—
249	#578	D₁₉	1	1	yes	characteristic, complemented
250	#577	—	19	1	no	—
251	#577	—	19	3	no	—
252	#577	—	19	3	no	—
253	#577	—	19	1	no	—
254	#575	—	19	3	no	—
255	#575	—	19	3	no	—
256	C₂×#137	—	19	3	no	—
257	C₂×#137	—	19	3	no	—
258	#568	—	19	1	no	—
259	C₂×C₁₉	—	2	3	no	—
260	C₂×C₁₉	—	4	1	no	—
261	C₂×C₁₉	—	4	1	no	—
262	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
263	D₁₉	—	2	1	no	—
264	D₁₉	—	2	3	no	—
265	D₁₉	—	4	1	no	—
266	D₁₉	—	4	3	no	—
267	2₋¹⁺⁴	—	19	3	no	—
268	2₋¹⁺⁴	—	19	1	no	—
269	2₋¹⁺⁴	—	19	3	no	—
270	2₋¹⁺⁴	—	19	3	no	—
271	2₋¹⁺⁴	—	38	1	no	—
272	2₋¹⁺⁴	—	38	1	no	—
273	2₋¹⁺⁴	—	38	3	no	—
274	2₋¹⁺⁴	C₂×D₁₉	1	1	yes	characteristic, complemented
275	2₋¹⁺⁴	C₂×D₁₉	1	1	yes	characteristic, complemented
276	H(5,𝔽₂)	—	19	3	no	—
277	H(5,𝔽₂)	—	19	1	no	—
278	H(5,𝔽₂)	—	38	3	no	—
279	C₂×#41	—	19	1	no	—
280	C₂×#41	—	19	3	no	—
281	C₂×#41	—	19	3	no	—
282	C₂×#41	—	19	3	no	—
283	C₂×#41	—	38	3	no	—
284	C₂×#41	—	38	1	no	—
285	C₂×#41	—	38	3	no	—
286	C₂²×Q₈	—	19	3	no	—
287	C₂²×Q₈	—	38	1	no	—
288	#137	—	19	3	no	—
289	#137	—	19	3	no	—
290	#137	—	19	3	no	—
291	#137	—	19	6	no	—
292	#137	—	19	3	no	—
293	#137	—	19	6	no	—
294	#137	—	19	6	no	—
295	#137	—	19	3	no	—
296	#137	—	19	3	no	—
297	#137	—	19	3	no	—
298	#137	—	19	3	no	—
299	#137	C₂×D₁₉	1	3	yes	complemented
300	#137	C₂×D₁₉	1	3	yes	complemented
301	AGL(1,ℤ/8)	—	19	3	no	—
302	AGL(1,ℤ/8)	—	19	3	no	—
303	AGL(1,ℤ/8)	—	19	3	no	—
304	AGL(1,ℤ/8)	—	19	1	no	—
305	AGL(1,ℤ/8)	—	19	3	no	—
306	AGL(1,ℤ/8)	—	19	3	no	—
307	#135	—	19	3	no	—
308	#135	—	19	3	no	—
309	#135	—	19	6	no	—
310	#135	—	19	6	no	—
311	#135	—	19	3	no	—
312	#135	C₂×D₁₉	1	3	yes	complemented
313	C₂×Q₁₆	—	19	3	no	—
314	C₂×Q₁₆	—	19	6	no	—
315	C₂×Q₁₆	C₂×D₁₉	1	3	yes	complemented
316	C₂×SD₁₆	—	19	3	no	—
317	C₂×SD₁₆	—	19	6	no	—
318	C₂×SD₁₆	—	19	3	no	—
319	#131	—	19	1	no	—
320	#131	—	19	3	no	—
321	#131	—	19	3	no	—
322	#131	C₂×D₁₉	1	1	yes	characteristic, complemented
323	C₂×M₁₆	—	19	3	no	—
324	C₂×M₁₆	—	19	3	no	—
325	C₁₉	#3586	1	1	yes	characteristic, complemented, Sylow
326	#41	—	2	3	no	—
327	#41	—	2	3	no	—
328	#41	—	19	1	no	—
329	#41	—	19	3	no	—
330	#41	—	19	3	no	—
331	#41	—	19	3	no	—
332	#41	—	19	6	no	—
333	#41	—	19	3	no	—
334	#41	—	19	3	no	—
335	#41	—	19	1	no	—
336	#41	—	19	3	no	—
337	#41	—	19	3	no	—
338	#41	—	38	3	no	—
339	#41	—	38	3	no	—
340	#41	—	38	6	no	—
341	#41	—	38	6	no	—
342	#41	—	38	3	no	—
343	#41	—	38	3	no	—
344	#41	—	38	3	no	—
345	#41	—	38	3	no	—
346	#41	—	38	3	no	—
347	#41	—	38	3	no	—
348	#41	—	38	6	no	—
349	#41	—	38	3	no	—
350	#41	—	38	3	no	—
351	#41	—	38	1	no	—
352	#41	—	38	3	no	—
353	#41	C₂²×D₁₉	1	3	yes	—
354	#41	C₂²×D₁₉	1	3	yes	—
355	#41	C₂²×D₁₉	1	1	yes	characteristic
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	19	1	no	—
359	C₂×Q₈	—	19	6	no	—
360	C₂×Q₈	—	19	3	no	—
361	C₂×Q₈	—	19	3	no	—
362	C₂×Q₈	—	19	3	no	—
363	C₂×Q₈	—	38	3	no	—
364	C₂×Q₈	—	38	3	no	—
365	C₂×Q₈	—	38	3	no	—
366	C₂×Q₈	—	38	3	no	—
367	C₂×Q₈	—	38	3	no	—
368	C₂×Q₈	—	38	3	no	—
369	C₂×Q₈	—	38	1	no	—
370	C₂×Q₈	C₂²×D₁₉	1	3	yes	—
371	C₂×Q₈	C₂²×D₁₉	1	3	yes	—
372	C₂×D₄	—	19	3	no	—
373	C₂×D₄	—	19	3	no	—
374	C₂×D₄	—	19	1	no	—
375	C₂×D₄	—	19	3	no	—
376	C₂×D₄	—	38	3	no	—
377	C₂×D₄	—	38	3	no	—
378	C₂×D₄	—	38	6	no	—
379	C₂×D₄	—	38	3	no	—
380	C₂×D₄	—	38	3	no	—
381	C₂×D₄	—	38	3	no	—
382	C₂²×C₄	—	19	3	no	—
383	C₂²×C₄	—	38	3	no	—
384	C₂²×C₄	—	38	3	no	—
385	C₂²×C₄	—	38	3	no	—
386	C₂²×C₄	—	38	3	no	—
387	Q₁₆	—	19	6	no	—
388	Q₁₆	—	19	3	no	—
389	Q₁₆	—	19	3	no	—
390	Q₁₆	—	19	3	no	—
391	Q₁₆	C₂²×D₁₉	1	6	yes	—
392	Q₁₆	C₂²×D₁₉	1	3	yes	—
393	SD₁₆	—	19	3	no	—
394	SD₁₆	—	19	6	no	—
395	SD₁₆	—	19	3	no	—
396	SD₁₆	—	19	3	no	—
397	SD₁₆	—	19	1	no	—
398	SD₁₆	—	19	6	no	—
399	SD₁₆	—	19	3	no	—
400	SD₁₆	—	19	1	no	—
401	SD₁₆	C₂²×D₁₉	1	3	yes	—
402	SD₁₆	C₂²×D₁₉	1	3	yes	—
403	D₈	—	19	1	no	—
404	D₈	—	19	3	no	—
405	D₈	—	19	3	no	—
406	D₈	C₂²×D₁₉	1	1	yes	characteristic
407	M₁₆	—	19	3	no	—
408	M₁₆	—	19	3	no	—
409	M₁₆	—	19	1	no	—
410	M₁₆	—	19	3	no	—
411	M₁₆	—	19	3	no	—
412	M₁₆	C₂²×D₁₉	1	3	yes	—
413	C₂×C₈	—	19	3	no	—
414	C₂×C₈	—	19	6	no	—
415	C₂×C₈	C₂²×D₁₉	1	3	yes	—
416	C₂³	—	19	3	no	—
417	C₂³	—	38	1	no	—
418	C₂³	—	38	3	no	—
419	C₂³	—	38	3	no	—
420	Q₈	—	2	3	no	—
421	Q₈	—	2	3	no	—
422	Q₈	—	19	3	no	—
423	Q₈	—	19	3	no	—
424	Q₈	—	19	1	no	—
425	Q₈	—	38	3	no	—
426	Q₈	—	38	6	no	—
427	Q₈	—	38	3	no	—
428	Q₈	—	38	3	no	—
429	Q₈	D₄×D₁₉	1	1	yes	characteristic
430	Q₈	C₂³×D₁₉	1	3	yes	—
431	Q₈	C₂³×D₁₉	1	3	yes	—
432	D₄	—	2	3	no	—
433	D₄	—	2	3	no	—
434	D₄	—	19	6	no	—
435	D₄	—	19	3	no	—
436	D₄	—	19	1	no	—
437	D₄	—	19	3	no	—
438	D₄	—	38	3	no	—
439	D₄	—	38	6	no	—
440	D₄	—	38	3	no	—
441	D₄	—	38	3	no	—
442	D₄	—	38	1	no	—
443	D₄	—	38	1	no	—
444	D₄	—	38	3	no	—
445	D₄	—	38	3	no	—
446	D₄	—	38	3	no	—
447	D₄	—	38	3	no	—
448	D₄	D₄×D₁₉	1	3	yes	—
449	D₄	C₂³×D₁₉	1	1	yes	characteristic
450	D₄	C₂³×D₁₉	1	1	yes	characteristic
451	C₂×C₄	—	2	3	no	—
452	C₂×C₄	—	2	3	no	—
453	C₂×C₄	—	2	3	no	—
454	C₂×C₄	—	2	3	no	—
455	C₂×C₄	—	19	3	no	—
456	C₂×C₄	—	19	3	no	—
457	C₂×C₄	—	19	3	no	—
458	C₂×C₄	—	19	3	no	—
459	C₂×C₄	—	19	1	no	—
460	C₂×C₄	—	38	3	no	—
461	C₂×C₄	—	38	6	no	—
462	C₂×C₄	—	38	3	no	—
463	C₂×C₄	—	38	3	no	—
464	C₂×C₄	—	38	3	no	—
465	C₂×C₄	—	38	6	no	—
466	C₂×C₄	—	38	1	no	—
467	C₂×C₄	—	38	3	no	—
468	C₂×C₄	—	38	3	no	—
469	C₂×C₄	—	38	3	no	—
470	C₂×C₄	—	38	3	no	—
471	C₂×C₄	C₂³×D₁₉	1	3	yes	—
472	C₈	—	19	1	no	—
473	C₈	—	19	3	no	—
474	C₈	C₂³×D₁₉	1	3	yes	—
475	C₈	C₂³×D₁₉	1	1	yes	characteristic
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	19	1	no	—
479	C₂²	—	19	3	no	—
480	C₂²	—	38	1	no	—
481	C₂²	—	38	3	no	—
482	C₂²	—	76	3	no	—
483	C₂²	—	76	2	no	—
484	C₂²	—	152	3	no	—
485	C₂²	—	152	3	no	—
486	C₂²	C₂×D₄×D₁₉	1	3	yes	—
487	C₄	—	2	3	no	—
488	C₄	—	2	3	no	—
489	C₄	—	19	1	no	—
490	C₄	—	19	3	no	—
491	C₄	—	38	1	no	—
492	C₄	—	38	3	no	—
493	C₄	C₂×D₄×D₁₉	1	3	yes	—
494	C₄	C₂⁴×D₁₉	1	1	yes	characteristic
495	C₂	—	2	3	no	—
496	C₂	—	4	1	no	—
497	C₂	—	4	1	no	—
498	C₂	—	38	1	no	—
499	C₂	—	38	3	no	—
500	C₂	—	76	1	no	—
501	C₂	—	76	3	no	—
502	C₂	C₂²×D₄×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₁₉
commutator, cosocle	C₄×C₁₉	C₂⁵
Frattini	C₄	C₂⁴×D₁₉
Fitting	C₁₉×#578	C₂
socle	C₂×C₁₉	C₂³×D₄
hypercenter	#578	D₁₉
hypocenter	C₁₉	#3586
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ #41 ◁ #578

Complements

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

N	H ≅ G/N	type
1. #11927381	C₂	semidirect
2. 2₋¹⁺⁴×D₁₉	C₂	semidirect
3. #11927360	C₂	semidirect
4. #11927359	C₂	semidirect
5. #11927357	C₂	semidirect
6. #11927356	C₂	semidirect
7. #11927353	C₂	semidirect
8. #11927352	C₂	semidirect
9. #11927351	C₂	semidirect
10. #11927343	C₂	semidirect
11. #11927341	C₂	semidirect
12. C₂×#10597364	C₂	semidirect
13. #137×D₁₉	C₂	semidirect
14. #11927309	C₂	semidirect
15. C₁₉×#578	C₂	semidirect
16. C₁₉×2₋¹⁺⁴	C₂²	semidirect
17. C₁₉×2₋¹⁺⁴	C₂²	semidirect
19. #10597436	C₂²	semidirect
20. #10597436	C₂²	semidirect
22. #10597435	C₂²	semidirect
23. #10597435	C₂²	semidirect
28. #41×D₁₉	C₂²	semidirect
31. #10597433	C₂²	semidirect
32. #10597433	C₂²	semidirect
36. C₂×Q₈×D₁₉	C₂²	semidirect
37. C₁₉×#137	C₂²	semidirect
38. C₁₉×#137	C₂²	semidirect
39. C₁₉×#135	C₂²	semidirect
40. C₂×Q₁₆×C₁₉	C₂²	semidirect
41. C₁₉×#131	C₂²	semidirect
42. #10597397	C₂²	semidirect
43. #10597396	C₂²	semidirect
44. #10597396	C₂²	semidirect
45. #10597395	C₂²	semidirect
46. #10597394	C₂²	semidirect
47. C₂×#64528	C₂²	semidirect
48. #10597388	C₂²	semidirect
49. #10597388	C₂²	semidirect
50. C₂×#64527	C₂²	semidirect
51. #10597365	C₂²	semidirect
52. #10597364	C₂²	semidirect
53. #10597364	C₂²	semidirect
54. #10597364	C₂²	semidirect
55. #10597364	C₂²	semidirect
56. #10597364	C₂²	semidirect
57. Q₁₆×D₁₉	C₂²	semidirect
58. #10597362	C₂²	semidirect
59. #10597361	C₂²	semidirect
60. #10597361	C₂²	semidirect
61. #10597360	C₂²	semidirect
62. #10597360	C₂²	semidirect
63. SD₁₆×D₁₉	C₂²	semidirect
64. #10597357	C₂²	semidirect
65. #10597357	C₂²	semidirect
66. #10597355	C₂²	semidirect
67. #10597354	C₂²	semidirect
68. #10597353	C₂²	semidirect
69. M₁₆×D₁₉	C₂²	semidirect
70. #10597350	C₂²	semidirect
71. C₂×#64516	C₂²	semidirect
72. #10597347	C₂²	semidirect
73. C₂×#64515	C₂²	semidirect
249. #578	D₁₉	semidirect
274. 2₋¹⁺⁴	C₂×D₁₉	semidirect
275. 2₋¹⁺⁴	C₂×D₁₉	semidirect
299. #137	C₂×D₁₉	semidirect
300. #137	C₂×D₁₉	semidirect
312. #135	C₂×D₁₉	semidirect
315. C₂×Q₁₆	C₂×D₁₉	semidirect
322. #131	C₂×D₁₉	semidirect
325. C₁₉	#3586	semidirect

Maximal subgroups

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

subgroup	index
#11927381	2
2₋¹⁺⁴×D₁₉	2
#11927360	2
#11927359	2
#11927357	2
#11927356	2
#11927353	2
#11927352	2
#11927351	2
#11927343	2
#11927341	2
C₂×#10597364	2
#137×D₁₉	2
#11927309	2
C₁₉×#578	2
#3586	19