Subgroups — #14578411

Order 2432.

1464 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927380	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597430	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927354	C₂	1	4	yes	maximal, complemented
4	#11927350	C₂	1	4	yes	maximal, complemented
5	#11927348	C₂	1	4	yes	maximal, complemented
6	#11927345	C₂	1	4	yes	maximal, complemented
7	#11927344	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927342	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927340	C₂	1	4	yes	maximal, complemented
10	C₂×#10597378	C₂	1	1	yes	maximal, characteristic, complemented
11	AGL(1,ℤ/8)×D₁₉	C₂	1	4	yes	maximal, complemented
12	#11927310	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
15	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₂²⋊D₁₉	—	2	2	no	—
17	#10597436	—	2	1	no	—
18	#10597436	C₂²	1	2	yes	complemented
19	#10597435	—	2	1	no	—
20	#10597435	C₂²	1	2	yes	complemented
21	#41×D₁₉	—	2	2	no	—
22	#41×D₁₉	C₂²	1	4	yes	complemented
23	#10597433	C₂²	1	2	yes	complemented
24	#10597430	—	2	2	no	—
25	#10597430	—	2	2	no	—
26	#10597430	—	2	2	no	—
27	#10597430	C₂²	1	4	yes	complemented
28	#10597430	C₂²	1	4	yes	complemented
29	#10597430	C₂²	1	2	yes	complemented
30	C₂×#64543	—	2	1	no	—
31	C₂×#64543	C₂²	1	2	yes	complemented
32	C₂×D₄×D₁₉	—	2	1	no	—
33	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
34	C₂×#64541	—	2	2	no	—
35	C₂×#64541	C₂²	1	1	yes	characteristic
36	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
37	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
39	C₁₉×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
40	C₂×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
41	C₂×D₈×C₁₉	C₂²	1	2	yes	complemented
42	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
43	#10597397	C₂²	1	2	yes	complemented
44	#10597396	C₂²	1	4	yes	complemented
45	#10597395	C₂²	1	2	yes	complemented
46	#10597388	C₂²	1	2	yes	complemented
47	C₂×#64526	C₂²	1	2	yes	complemented
48	#10597378	C₂²	1	4	yes	complemented
49	#10597378	C₂²	1	2	yes	complemented
50	#10597378	C₂²	1	4	yes	complemented
51	C₂×#64525	C₂²	1	2	yes	complemented
52	C₂×#64520	C₂²	1	1	yes	characteristic, complemented
53	#10597362	C₂²	1	8	yes	complemented
54	#10597361	C₂²	1	8	yes	complemented
55	#10597360	C₂²	1	8	yes	complemented
56	SD₁₆×D₁₉	C₂²	1	8	yes	complemented
57	#10597358	C₂²	1	8	yes	complemented
58	#10597357	C₂²	1	8	yes	complemented
59	#10597357	C₂²	1	8	yes	complemented
60	D₈×D₁₉	C₂²	1	8	yes	complemented
61	#10597355	C₂²	1	2	yes	complemented
62	#10597355	C₂²	1	2	yes	complemented
63	#10597354	C₂²	1	2	yes	complemented
64	#10597354	C₂²	1	2	yes	complemented
65	#10597353	C₂²	1	4	yes	complemented
66	M₁₆×D₁₉	C₂²	1	4	yes	complemented
67	#10597350	C₂²	1	4	yes	complemented
68	#10597347	C₂²	1	4	yes	complemented
69	C₂⁴×C₁₉	—	2	1	no	—
70	C₂³×D₁₉	—	2	2	no	—
71	#41×C₁₉	—	2	1	no	—
72	#41×C₁₉	—	2	1	no	—
73	#41×C₁₉	C₂³	1	2	yes	—
74	#41×C₁₉	C₂³	1	2	yes	complemented
75	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic, complemented
76	C₂×D₄×C₁₉	—	2	1	no	—
77	C₂×D₄×C₁₉	—	2	1	no	—
78	C₂×D₄×C₁₉	—	2	1	no	—
79	C₂×D₄×C₁₉	—	2	1	no	—
80	C₂×D₄×C₁₉	C₂³	1	2	yes	—
81	C₂×D₄×C₁₉	C₂³	1	2	yes	—
82	C₂×D₄×C₁₉	C₂³	1	2	yes	—
83	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic, complemented
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊D₁₉	—	2	1	no	—
87	C₂×C₂²⋊D₁₉	—	2	1	no	—
88	C₂×C₂²⋊D₁₉	—	2	2	no	—
89	C₂×C₂²⋊D₁₉	—	2	4	no	—
90	C₂×C₂²⋊D₁₉	—	2	8	no	—
91	C₂×C₂²⋊D₁₉	—	2	8	no	—
92	C₂×C₂²⋊D₁₉	—	2	2	no	—
93	C₂×C₂²⋊D₁₉	D₄	1	2	yes	—
94	C₂²×Dic₁₉	—	2	2	no	—
95	#64545	—	2	2	no	—
96	#64545	C₂³	1	4	yes	complemented
97	Q₈×D₁₉	—	2	2	no	—
98	Q₈×D₁₉	C₂³	1	4	yes	complemented
99	#64543	—	2	4	no	—
100	#64543	—	2	4	no	—
101	#64543	—	2	4	no	—
102	#64543	—	2	4	no	—
103	#64543	—	2	4	no	—
104	#64543	—	2	2	no	—
105	#64543	C₂³	1	8	yes	—
106	#64543	C₂³	1	4	yes	complemented
107	D₄×D₁₉	—	2	4	no	—
108	D₄×D₁₉	—	2	4	no	—
109	D₄×D₁₉	—	2	4	no	—
110	D₄×D₁₉	—	2	4	no	—
111	D₄×D₁₉	—	2	2	no	—
112	D₄×D₁₉	—	2	4	no	—
113	D₄×D₁₉	C₂³	1	8	yes	—
114	D₄×D₁₉	C₂³	1	4	yes	complemented
115	#64541	—	2	1	no	—
116	#64541	—	2	1	no	—
117	#64541	—	2	1	no	—
118	#64541	—	2	1	no	—
119	#64541	—	2	4	no	—
120	#64541	—	2	2	no	—
121	#64541	—	2	4	no	—
122	#64541	—	2	2	no	—
123	#64541	D₄	1	2	yes	—
124	#64541	D₄	1	2	yes	—
125	#64541	C₂³	1	2	yes	—
126	#64541	C₂³	1	2	yes	—
127	#64541	C₂³	1	2	yes	—
128	#64541	C₂³	1	2	yes	—
129	#64541	C₂³	1	2	yes	—
130	#64541	C₂³	1	2	yes	complemented
131	C₂×D₇₆	—	2	2	no	—
132	C₂×D₇₆	D₄	1	1	yes	characteristic
133	C₂×D₇₆	C₂³	1	1	yes	characteristic
134	C₂×D₇₆	C₂³	1	1	yes	characteristic, complemented
135	C₂×C₄×D₁₉	—	2	1	no	—
136	C₂×C₄×D₁₉	—	2	1	no	—
137	C₂×C₄×D₁₉	—	2	4	no	—
138	C₂×C₄×D₁₉	C₂³	1	2	yes	—
139	C₂×Dic₃₈	—	2	2	no	—
140	C₂×Dic₃₈	D₄	1	1	yes	characteristic
141	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
142	C₂×Dic₃₈	C₂³	1	1	yes	characteristic, complemented
143	SD₁₆×C₁₉	C₂³	1	8	yes	complemented
144	D₈×C₁₉	C₂³	1	8	yes	complemented
145	M₁₆×C₁₉	C₂³	1	2	yes	—
146	M₁₆×C₁₉	C₂³	1	2	yes	complemented
147	C₂×C₈×C₁₉	C₂³	1	2	yes	complemented
148	#64528	C₂³	1	4	yes	complemented
149	#64527	C₂³	1	4	yes	complemented
150	#64526	C₂³	1	8	yes	complemented
151	#64526	C₂³	1	4	yes	complemented
152	#64525	C₂³	1	8	yes	complemented
153	#64525	C₂³	1	4	yes	complemented
154	#64520	C₂³	1	2	yes	—
155	#64520	C₂³	1	2	yes	complemented
156	C₂×C₁₉⋊C₈	C₂³	1	2	yes	complemented
157	Dic₇₆	C₂³	1	4	yes	complemented
158	D₁₅₂	C₂³	1	4	yes	complemented
159	#64516	C₂³	1	4	yes	complemented
160	#64516	C₂³	1	4	yes	complemented
161	#64515	C₂³	1	8	yes	complemented
162	C₈×D₁₉	C₂³	1	8	yes	complemented
163	C₂³×C₁₉	—	2	2	no	—
164	C₂³×C₁₉	—	2	1	no	—
165	C₂³×C₁₉	—	2	2	no	—
166	C₂³×C₁₉	—	2	2	no	—
167	C₂³×C₁₉	—	8	2	no	—
168	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×D₁₉	—	2	1	no	—
170	C₂²×D₁₉	—	2	1	no	—
171	C₂²×D₁₉	—	2	4	no	—
172	C₂²×D₁₉	—	2	8	no	—
173	C₂²×D₁₉	—	8	4	no	—
174	C₂²×D₁₉	C₂×D₄	1	2	yes	—
175	Q₈×C₁₉	—	2	1	no	—
176	Q₈×C₁₉	C₂⁴	1	2	yes	—
177	D₄×C₁₉	—	2	2	no	—
178	D₄×C₁₉	—	2	2	no	—
179	D₄×C₁₉	—	2	2	no	—
180	D₄×C₁₉	—	2	2	no	—
181	D₄×C₁₉	—	2	2	no	—
182	D₄×C₁₉	—	2	1	no	—
183	D₄×C₁₉	C₂⁴	1	2	yes	—
184	D₄×C₁₉	C₂⁴	1	4	yes	—
185	C₂×C₄×C₁₉	—	2	1	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
194	C₂²⋊D₁₉	—	2	2	no	—
195	C₂²⋊D₁₉	—	2	2	no	—
196	C₂²⋊D₁₉	—	2	2	no	—
197	C₂²⋊D₁₉	—	2	2	no	—
198	C₂²⋊D₁₉	—	2	4	no	—
199	C₂²⋊D₁₉	—	2	8	no	—
200	C₂²⋊D₁₉	—	2	4	no	—
201	C₂²⋊D₁₉	—	2	8	no	—
202	C₂²⋊D₁₉	C₂×D₄	1	4	yes	—
203	C₂²⋊D₁₉	C₂×D₄	1	4	yes	—
204	C₂×Dic₁₉	—	2	1	no	—
205	C₂×Dic₁₉	—	2	1	no	—
206	C₂×Dic₁₉	—	2	4	no	—
207	C₂×Dic₁₉	—	2	8	no	—
208	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
209	D₇₆	—	2	4	no	—
210	D₇₆	—	2	1	no	—
211	D₇₆	—	2	1	no	—
212	D₇₆	C₂×D₄	1	2	yes	—
213	D₇₆	C₂×D₄	1	2	yes	—
214	D₇₆	C₂⁴	1	2	yes	—
215	D₇₆	C₂⁴	1	2	yes	—
216	C₄×D₁₉	—	2	4	no	—
217	C₄×D₁₉	—	2	2	no	—
218	C₄×D₁₉	—	2	2	no	—
219	C₄×D₁₉	—	2	2	no	—
220	C₄×D₁₉	—	2	2	no	—
221	C₄×D₁₉	—	2	4	no	—
222	C₄×D₁₉	C₂×D₄	1	4	yes	—
223	C₄×D₁₉	C₂⁴	1	4	yes	—
224	Dic₃₈	—	2	1	no	—
225	Dic₃₈	—	2	1	no	—
226	Dic₃₈	—	2	4	no	—
227	Dic₃₈	C₂×D₄	1	2	yes	—
228	Dic₃₈	C₂×D₄	1	2	yes	—
229	Dic₃₈	C₂⁴	1	2	yes	—
230	Dic₃₈	C₂⁴	1	2	yes	—
231	C₈×C₁₉	C₂⁴	1	4	yes	—
232	C₁₉⋊C₈	C₂⁴	1	4	yes	—
233	#3585	—	19	1	no	maximal, Sylow
234	C₂²×C₁₉	—	2	2	no	—
235	C₂²×C₁₉	—	2	4	no	—
236	C₂²×C₁₉	—	4	1	no	—
237	C₂²×C₁₉	—	4	4	no	—
238	C₂²×C₁₉	—	8	1	no	—
239	C₂²×C₁₉	—	8	2	no	—
240	C₂²×C₁₉	—	8	2	no	—
241	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
242	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
243	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
244	C₂×D₁₉	—	2	2	no	—
245	C₂×D₁₉	—	2	2	no	—
246	C₂×D₁₉	—	4	2	no	—
247	C₂×D₁₉	—	4	2	no	—
248	C₂×D₁₉	—	8	4	no	—
249	C₂×D₁₉	—	8	8	no	—
250	C₂×D₁₉	—	8	1	no	—
251	C₂×D₁₉	C₂²×D₄	1	4	yes	—
252	C₄×C₁₉	—	2	2	no	—
253	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
254	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
255	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
256	C₄×C₁₉	C₂⁵	1	1	yes	characteristic
257	Dic₁₉	—	2	2	no	—
258	Dic₁₉	—	2	2	no	—
259	Dic₁₉	C₂²×D₄	1	4	yes	—
260	#585	—	19	1	no	—
261	C₂×H(5,𝔽₂)	—	19	1	no	—
262	#577	—	19	4	no	—
263	#577	—	19	4	no	—
264	#576	—	19	4	no	—
265	#576	—	19	4	no	—
266	#575	—	19	1	no	—
267	#575	—	19	4	no	—
268	#575	—	19	1	no	—
269	C₂×AGL(1,ℤ/8)	—	19	1	no	—
270	C₂×AGL(1,ℤ/8)	—	19	4	no	—
271	C₂×AGL(1,ℤ/8)	D₁₉	1	1	yes	characteristic, complemented
272	#568	—	19	1	no	—
273	C₂×C₁₉	—	2	1	no	—
274	C₂×C₁₉	—	2	1	no	—
275	C₂×C₁₉	—	2	1	no	—
276	C₂×C₁₉	—	4	4	no	—
277	C₂×C₁₉	—	4	2	no	—
278	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
279	D₁₉	—	2	4	no	—
280	D₁₉	—	4	2	no	—
281	D₁₉	—	4	2	no	—
282	2₋¹⁺⁴	—	19	2	no	—
283	2₋¹⁺⁴	—	19	2	no	—
284	2₋¹⁺⁴	—	38	1	no	—
285	H(5,𝔽₂)	—	19	2	no	—
286	H(5,𝔽₂)	—	19	4	no	—
287	H(5,𝔽₂)	—	19	4	no	—
288	H(5,𝔽₂)	—	19	2	no	—
289	H(5,𝔽₂)	—	38	2	no	—
290	H(5,𝔽₂)	—	38	2	no	—
291	H(5,𝔽₂)	—	38	2	no	—
292	H(5,𝔽₂)	—	38	1	no	—
293	C₂×#41	—	19	1	no	—
294	C₂×#41	—	19	4	no	—
295	C₂×#41	—	19	2	no	—
296	C₂×#41	—	19	1	no	—
297	C₂×#41	—	19	1	no	—
298	C₂×#41	—	38	2	no	—
299	C₂×#41	—	38	1	no	—
300	C₂×#41	—	38	2	no	—
301	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
302	C₂²×D₄	—	19	2	no	—
303	C₂²×D₄	—	38	1	no	—
304	C₂²×D₄	—	38	2	no	—
305	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
306	#137	—	19	2	no	—
307	#137	—	19	2	no	—
308	#137	—	19	8	no	—
309	#137	—	19	2	no	—
310	#137	—	19	2	no	—
311	AGL(1,ℤ/8)	—	19	2	no	—
312	AGL(1,ℤ/8)	—	19	4	no	—
313	AGL(1,ℤ/8)	—	19	4	no	—
314	AGL(1,ℤ/8)	—	19	2	no	—
315	AGL(1,ℤ/8)	—	19	8	no	—
316	AGL(1,ℤ/8)	—	19	8	no	—
317	AGL(1,ℤ/8)	—	19	8	no	—
318	AGL(1,ℤ/8)	—	19	2	no	—
319	AGL(1,ℤ/8)	—	19	2	no	—
320	AGL(1,ℤ/8)	C₂×D₁₉	1	4	yes	complemented
321	AGL(1,ℤ/8)	C₂×D₁₉	1	4	yes	complemented
322	#135	—	19	4	no	—
323	#135	—	19	8	no	—
324	#135	—	19	8	no	—
325	#135	—	19	4	no	—
326	C₂×SD₁₆	—	19	2	no	—
327	C₂×SD₁₆	—	19	8	no	—
328	C₂×SD₁₆	C₂×D₁₉	1	2	yes	complemented
329	C₂×D₈	—	19	2	no	—
330	C₂×D₈	—	19	8	no	—
331	C₂×D₈	C₂×D₁₉	1	2	yes	complemented
332	#131	—	19	4	no	—
333	#131	—	19	4	no	—
334	C₂×M₁₆	—	19	1	no	—
335	C₂×M₁₆	—	19	4	no	—
336	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
337	C₁₉	#3585	1	1	yes	characteristic, complemented, Sylow
338	C₂⁴	—	2	1	no	—
339	C₂⁴	—	38	2	no	—
340	#41	—	2	1	no	—
341	#41	—	2	1	no	—
342	#41	—	19	2	no	—
343	#41	—	19	2	no	—
344	#41	—	19	2	no	—
345	#41	—	19	2	no	—
346	#41	—	19	4	no	—
347	#41	—	19	8	no	—
348	#41	—	19	4	no	—
349	#41	—	19	2	no	—
350	#41	—	19	2	no	—
351	#41	—	19	2	no	—
352	#41	—	19	2	no	—
353	#41	—	38	4	no	—
354	#41	—	38	4	no	—
355	#41	—	38	2	no	—
356	#41	—	38	2	no	—
357	#41	—	38	4	no	—
358	#41	—	38	4	no	—
359	#41	—	38	4	no	—
360	#41	—	38	4	no	—
361	#41	—	38	4	no	—
362	#41	—	38	2	no	—
363	#41	—	38	2	no	—
364	#41	—	38	1	no	—
365	#41	—	38	1	no	—
366	#41	—	38	1	no	—
367	#41	—	38	1	no	—
368	#41	C₂²×D₁₉	1	2	yes	—
369	#41	C₂²×D₁₉	1	2	yes	complemented
370	C₂×Q₈	—	19	1	no	—
371	C₂×Q₈	—	19	4	no	—
372	C₂×Q₈	—	19	1	no	—
373	C₂×Q₈	—	19	1	no	—
374	C₂×Q₈	—	38	2	no	—
375	C₂×Q₈	—	38	2	no	—
376	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic, complemented
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	19	2	no	—
382	C₂×D₄	—	19	8	no	—
383	C₂×D₄	—	19	4	no	—
384	C₂×D₄	—	19	1	no	—
385	C₂×D₄	—	19	1	no	—
386	C₂×D₄	—	19	1	no	—
387	C₂×D₄	—	38	2	no	—
388	C₂×D₄	—	38	4	no	—
389	C₂×D₄	—	38	2	no	—
390	C₂×D₄	—	38	4	no	—
391	C₂×D₄	—	38	4	no	—
392	C₂×D₄	—	38	4	no	—
393	C₂×D₄	—	38	2	no	—
394	C₂×D₄	—	38	4	no	—
395	C₂×D₄	—	38	8	no	—
396	C₂×D₄	—	38	8	no	—
397	C₂×D₄	—	38	4	no	—
398	C₂×D₄	—	38	2	no	—
399	C₂×D₄	—	38	1	no	—
400	C₂×D₄	—	38	1	no	—
401	C₂×D₄	C₂²×D₁₉	1	2	yes	—
402	C₂×D₄	C₂²×D₁₉	1	2	yes	—
403	C₂×D₄	C₂²×D₁₉	1	2	yes	—
404	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic, complemented
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	19	2	no	—
407	C₂²×C₄	—	38	4	no	—
408	C₂²×C₄	—	38	2	no	—
409	C₂²×C₄	—	38	1	no	—
410	C₂²×C₄	—	38	1	no	—
411	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
412	Q₁₆	—	19	4	no	—
413	Q₁₆	—	19	4	no	—
414	SD₁₆	—	19	4	no	—
415	SD₁₆	—	19	8	no	—
416	SD₁₆	—	19	4	no	—
417	SD₁₆	—	19	4	no	—
418	SD₁₆	—	19	4	no	—
419	SD₁₆	C₂²×D₁₉	1	8	yes	complemented
420	D₈	—	19	8	no	—
421	D₈	—	19	4	no	—
422	D₈	—	19	4	no	—
423	D₈	C₂²×D₁₉	1	8	yes	complemented
424	M₁₆	—	19	2	no	—
425	M₁₆	—	19	2	no	—
426	M₁₆	—	19	8	no	—
427	M₁₆	C₂²×D₁₉	1	2	yes	—
428	M₁₆	C₂²×D₁₉	1	2	yes	complemented
429	C₂×C₈	—	19	2	no	—
430	C₂×C₈	—	19	8	no	—
431	C₂×C₈	C₂²×D₁₉	1	2	yes	complemented
432	C₂³	—	2	2	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	8	2	no	—
437	C₂³	—	19	2	no	—
438	C₂³	—	38	4	no	—
439	C₂³	—	38	8	no	—
440	C₂³	—	38	1	no	—
441	C₂³	—	38	1	no	—
442	C₂³	—	152	4	no	—
443	C₂³	D₄×D₁₉	1	1	yes	characteristic
444	Q₈	—	2	1	no	—
445	Q₈	—	19	2	no	—
446	Q₈	—	19	2	no	—
447	Q₈	—	19	2	no	—
448	Q₈	—	19	2	no	—
449	Q₈	—	38	4	no	—
450	Q₈	—	38	1	no	—
451	Q₈	—	38	1	no	—
452	Q₈	C₂³×D₁₉	1	2	yes	—
453	D₄	—	2	2	no	—
454	D₄	—	2	2	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	2	no	—
457	D₄	—	2	2	no	—
458	D₄	—	2	1	no	—
459	D₄	—	19	4	no	—
460	D₄	—	19	4	no	—
461	D₄	—	19	2	no	—
462	D₄	—	19	2	no	—
463	D₄	—	19	2	no	—
464	D₄	—	19	2	no	—
465	D₄	—	38	4	no	—
466	D₄	—	38	8	no	—
467	D₄	—	38	4	no	—
468	D₄	—	38	8	no	—
469	D₄	—	38	4	no	—
470	D₄	—	38	2	no	—
471	D₄	—	38	2	no	—
472	D₄	—	38	2	no	—
473	D₄	—	38	2	no	—
474	D₄	—	38	1	no	—
475	D₄	—	38	1	no	—
476	D₄	C₂³×D₁₉	1	2	yes	—
477	D₄	C₂³×D₁₉	1	4	yes	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	19	2	no	—
482	C₂×C₄	—	19	4	no	—
483	C₂×C₄	—	19	4	no	—
484	C₂×C₄	—	38	4	no	—
485	C₂×C₄	—	38	4	no	—
486	C₂×C₄	—	38	8	no	—
487	C₂×C₄	—	38	4	no	—
488	C₂×C₄	—	38	1	no	—
489	C₂×C₄	—	38	1	no	—
490	C₂×C₄	—	38	2	no	—
491	C₂×C₄	—	38	2	no	—
492	C₂×C₄	—	38	2	no	—
493	C₂×C₄	—	38	2	no	—
494	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
495	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
496	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
497	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
498	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
499	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
500	C₈	—	19	4	no	—
501	C₈	C₂³×D₁₉	1	4	yes	—
502	C₂²	—	2	2	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	8	2	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	1	no	—
509	C₂²	—	19	4	no	—
510	C₂²	—	38	2	no	—
511	C₂²	—	38	2	no	—
512	C₂²	—	76	2	no	—
513	C₂²	—	76	2	no	—
514	C₂²	—	152	1	no	—
515	C₂²	—	152	8	no	—
516	C₂²	—	152	4	no	—
517	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
518	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
519	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
520	C₄	—	2	2	no	—
521	C₄	—	19	4	no	—
522	C₄	—	38	2	no	—
523	C₄	—	38	2	no	—
524	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
525	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
526	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
527	C₄	C₂⁴×D₁₉	1	1	yes	characteristic
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	2	1	no	—
531	C₂	—	4	4	no	—
532	C₂	—	4	2	no	—
533	C₂	—	38	4	no	—
534	C₂	—	76	2	no	—
535	C₂	—	76	2	no	—
536	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	C₂×C₁₉×AGL(1,ℤ/8)	C₂
socle	C₂×C₁₉	C₂³×D₄
hypercenter	C₂×AGL(1,ℤ/8)	D₁₉
hypocenter	C₁₉	#3585
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. #11927380	C₂	semidirect
2. C₂×#10597430	C₂	semidirect
3. #11927354	C₂	semidirect
4. #11927350	C₂	semidirect
5. #11927348	C₂	semidirect
6. #11927345	C₂	semidirect
7. #11927344	C₂	semidirect
8. #11927342	C₂	semidirect
9. #11927340	C₂	semidirect
10. C₂×#10597378	C₂	semidirect
11. AGL(1,ℤ/8)×D₁₉	C₂	semidirect
12. #11927310	C₂	semidirect
13. C₂×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
14. C₂×#41×C₁₉	C₂²	semidirect
15. C₂²×D₄×C₁₉	C₂²	semidirect
18. #10597436	C₂²	semidirect
20. #10597435	C₂²	semidirect
22. #41×D₁₉	C₂²	semidirect
23. #10597433	C₂²	semidirect
27. #10597430	C₂²	semidirect
28. #10597430	C₂²	semidirect
29. #10597430	C₂²	semidirect
31. C₂×#64543	C₂²	semidirect
33. C₂×D₄×D₁₉	C₂²	semidirect
36. C₂×#64541	C₂²	semidirect
37. C₂×#64541	C₂²	semidirect
38. C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
39. C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
40. C₂×SD₁₆×C₁₉	C₂²	semidirect
41. C₂×D₈×C₁₉	C₂²	semidirect
42. C₂×M₁₆×C₁₉	C₂²	semidirect
43. #10597397	C₂²	semidirect
44. #10597396	C₂²	semidirect
45. #10597395	C₂²	semidirect
46. #10597388	C₂²	semidirect
47. C₂×#64526	C₂²	semidirect
48. #10597378	C₂²	semidirect
49. #10597378	C₂²	semidirect
50. #10597378	C₂²	semidirect
51. C₂×#64525	C₂²	semidirect
52. C₂×#64520	C₂²	semidirect
53. #10597362	C₂²	semidirect
54. #10597361	C₂²	semidirect
55. #10597360	C₂²	semidirect
56. SD₁₆×D₁₉	C₂²	semidirect
57. #10597358	C₂²	semidirect
58. #10597357	C₂²	semidirect
59. #10597357	C₂²	semidirect
60. D₈×D₁₉	C₂²	semidirect
61. #10597355	C₂²	semidirect
62. #10597355	C₂²	semidirect
63. #10597354	C₂²	semidirect
64. #10597354	C₂²	semidirect
65. #10597353	C₂²	semidirect
66. M₁₆×D₁₉	C₂²	semidirect
67. #10597350	C₂²	semidirect
68. #10597347	C₂²	semidirect
74. #41×C₁₉	C₂³	semidirect
75. C₂×Q₈×C₁₉	C₂³	semidirect
83. C₂×D₄×C₁₉	C₂³	semidirect
96. #64545	C₂³	semidirect
98. Q₈×D₁₉	C₂³	semidirect
106. #64543	C₂³	semidirect
114. D₄×D₁₉	C₂³	semidirect
130. #64541	C₂³	semidirect
134. C₂×D₇₆	C₂³	semidirect
142. C₂×Dic₃₈	C₂³	semidirect
143. SD₁₆×C₁₉	C₂³	semidirect
144. D₈×C₁₉	C₂³	semidirect
146. M₁₆×C₁₉	C₂³	semidirect
147. C₂×C₈×C₁₉	C₂³	semidirect
148. #64528	C₂³	semidirect
149. #64527	C₂³	semidirect
150. #64526	C₂³	semidirect
151. #64526	C₂³	semidirect
152. #64525	C₂³	semidirect
153. #64525	C₂³	semidirect
155. #64520	C₂³	semidirect
156. C₂×C₁₉⋊C₈	C₂³	semidirect
157. Dic₇₆	C₂³	semidirect
158. D₁₅₂	C₂³	semidirect
159. #64516	C₂³	semidirect
160. #64516	C₂³	semidirect
161. #64515	C₂³	semidirect
162. C₈×D₁₉	C₂³	semidirect
271. C₂×AGL(1,ℤ/8)	D₁₉	semidirect
301. C₂×#41	C₂×D₁₉	semidirect
305. C₂²×D₄	C₂×D₁₉	semidirect
320. AGL(1,ℤ/8)	C₂×D₁₉	semidirect
321. AGL(1,ℤ/8)	C₂×D₁₉	semidirect
328. C₂×SD₁₆	C₂×D₁₉	semidirect
331. C₂×D₈	C₂×D₁₉	semidirect
336. C₂×M₁₆	C₂×D₁₉	semidirect
337. C₁₉	#3585	semidirect
369. #41	C₂²×D₁₉	semidirect
376. C₂×Q₈	C₂²×D₁₉	semidirect
404. C₂×D₄	C₂²×D₁₉	semidirect
419. SD₁₆	C₂²×D₁₉	semidirect
423. D₈	C₂²×D₁₉	semidirect
428. M₁₆	C₂²×D₁₉	semidirect
431. C₂×C₈	C₂²×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
#11927380	2
C₂×#10597430	2
#11927354	2
#11927350	2
#11927348	2
#11927345	2
#11927344	2
#11927342	2
#11927340	2
C₂×#10597378	2
AGL(1,ℤ/8)×D₁₉	2
#11927310	2
C₂×C₁₉×AGL(1,ℤ/8)	2
#3585	19