Subgroups — #14578412

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×#10597435	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927353	C₂	1	4	yes	maximal, complemented
4	#11927351	C₂	1	4	yes	maximal, complemented
5	#11927348	C₂	1	4	yes	maximal, complemented
6	#11927346	C₂	1	4	yes	maximal, complemented
7	#11927343	C₂	1	4	yes	maximal, complemented
8	#11927342	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10597354	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10597395	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	C₁₉×#575	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
15	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
16	#10597436	—	2	1	no	—
17	#10597436	C₂²	1	2	yes	complemented
18	#10597435	—	2	2	no	—
19	#10597435	—	2	2	no	—
20	#10597435	—	2	1	no	—
21	#10597435	C₂²	1	4	yes	complemented
22	#10597435	C₂²	1	4	yes	complemented
23	#10597435	C₂²	1	2	yes	complemented
24	#41×D₁₉	—	2	2	no	—
25	#41×D₁₉	C₂²	1	4	yes	complemented
26	#10597433	C₂²	1	2	yes	complemented
27	C₂×#64545	C₂²	1	2	yes	complemented
28	#10597430	—	2	2	no	—
29	#10597430	C₂²	1	2	yes	complemented
30	C₂×D₄×D₁₉	—	2	2	no	—
31	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
32	C₂×#64541	—	2	2	no	—
33	C₂×#64541	—	2	1	no	—
34	C₂×#64541	C₂²	1	1	yes	characteristic
35	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
36	C₂²×D₇₆	—	2	1	no	—
37	C₂²×D₇₆	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#137	C₂²	1	2	yes	complemented
39	C₁₉×#137	C₂²	1	2	yes	complemented
40	C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
41	C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
42	C₁₉×#135	C₂²	1	4	yes	complemented
43	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
44	#10597397	C₂²	1	2	yes	complemented
45	#10597396	C₂²	1	4	yes	complemented
46	#10597395	C₂²	1	4	yes	complemented
47	#10597395	C₂²	1	4	yes	complemented
48	#10597395	C₂²	1	2	yes	complemented
49	#10597388	C₂²	1	2	yes	complemented
50	C₂×#64527	C₂²	1	2	yes	complemented
51	#10597378	C₂²	1	2	yes	complemented
52	C₂×#64525	C₂²	1	2	yes	complemented
53	C₂×#64520	C₂²	1	1	yes	characteristic, complemented
54	#10597365	C₂²	1	8	yes	complemented
55	#10597364	C₂²	1	8	yes	complemented
56	#10597362	C₂²	1	8	yes	complemented
57	#10597360	C₂²	1	8	yes	complemented
58	#10597360	C₂²	1	8	yes	complemented
59	SD₁₆×D₁₉	C₂²	1	8	yes	complemented
60	#10597357	C₂²	1	8	yes	complemented
61	D₈×D₁₉	C₂²	1	8	yes	complemented
62	#10597354	C₂²	1	4	yes	complemented
63	#10597354	C₂²	1	4	yes	complemented
64	#10597353	C₂²	1	4	yes	complemented
65	M₁₆×D₁₉	C₂²	1	4	yes	complemented
66	C₂×D₁₅₂	C₂²	1	2	yes	complemented
67	C₂×#64516	C₂²	1	2	yes	complemented
68	#10597347	C₂²	1	4	yes	complemented
69	C₂³×D₁₉	—	2	1	no	—
70	C₂³×D₁₉	—	2	2	no	—
71	#41×C₁₉	—	2	1	no	—
72	#41×C₁₉	—	2	1	no	—
73	#41×C₁₉	—	2	1	no	—
74	#41×C₁₉	—	2	1	no	—
75	#41×C₁₉	C₂³	1	2	yes	—
76	#41×C₁₉	C₂³	1	2	yes	—
77	#41×C₁₉	C₂³	1	2	yes	—
78	#41×C₁₉	C₂³	1	2	yes	complemented
79	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic, complemented
81	C₂×D₄×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	—	2	1	no	—
83	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic, complemented
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊D₁₉	—	2	1	no	—
89	C₂×C₂²⋊D₁₉	—	2	4	no	—
90	C₂×C₂²⋊D₁₉	—	2	2	no	—
91	C₂×C₂²⋊D₁₉	D₄	1	2	yes	—
92	#64545	—	2	2	no	—
93	#64545	—	2	4	no	—
94	#64545	C₂³	1	8	yes	—
95	#64545	C₂³	1	4	yes	complemented
96	Q₈×D₁₉	—	2	2	no	—
97	Q₈×D₁₉	C₂³	1	4	yes	complemented
98	#64543	—	2	4	no	—
99	#64543	—	2	4	no	—
100	#64543	—	2	2	no	—
101	#64543	C₂³	1	4	yes	complemented
102	D₄×D₁₉	—	2	4	no	—
103	D₄×D₁₉	—	2	8	no	—
104	D₄×D₁₉	—	2	8	no	—
105	D₄×D₁₉	—	2	4	no	—
106	D₄×D₁₉	—	2	2	no	—
107	D₄×D₁₉	—	2	4	no	—
108	D₄×D₁₉	C₂³	1	8	yes	—
109	D₄×D₁₉	C₂³	1	4	yes	complemented
110	#64541	—	2	1	no	—
111	#64541	—	2	1	no	—
112	#64541	—	2	4	no	—
113	#64541	—	2	2	no	—
114	#64541	—	2	4	no	—
115	#64541	—	2	4	no	—
116	#64541	—	2	4	no	—
117	#64541	—	2	2	no	—
118	#64541	D₄	1	2	yes	—
119	#64541	D₄	1	2	yes	—
120	#64541	C₂³	1	2	yes	—
121	#64541	C₂³	1	2	yes	—
122	#64541	C₂³	1	2	yes	—
123	#64541	C₂³	1	2	yes	complemented
124	C₂×D₇₆	—	2	2	no	—
125	C₂×D₇₆	—	2	1	no	—
126	C₂×D₇₆	—	2	1	no	—
127	C₂×D₇₆	—	2	1	no	—
128	C₂×D₇₆	—	2	4	no	—
129	C₂×D₇₆	—	2	4	no	—
130	C₂×D₇₆	—	2	2	no	—
131	C₂×D₇₆	D₄	1	1	yes	characteristic
132	C₂×D₇₆	C₂³	1	2	yes	—
133	C₂×D₇₆	C₂³	1	2	yes	—
134	C₂×D₇₆	C₂³	1	2	yes	—
135	C₂×D₇₆	C₂³	1	1	yes	characteristic, complemented
136	C₂×C₄×D₁₉	—	2	1	no	—
137	C₂×C₄×D₁₉	—	2	2	no	—
138	C₂×C₄×D₁₉	—	2	4	no	—
139	C₂×C₄×D₁₉	C₂³	1	2	yes	—
140	C₂×Dic₃₈	—	2	2	no	—
141	C₂×Dic₃₈	D₄	1	1	yes	characteristic
142	C₂×Dic₃₈	C₂³	1	1	yes	characteristic, complemented
143	Q₁₆×C₁₉	C₂³	1	4	yes	complemented
144	SD₁₆×C₁₉	C₂³	1	4	yes	complemented
145	SD₁₆×C₁₉	C₂³	1	4	yes	complemented
146	D₈×C₁₉	C₂³	1	4	yes	complemented
147	M₁₆×C₁₉	C₂³	1	2	yes	—
148	M₁₆×C₁₉	C₂³	1	2	yes	complemented
149	C₂×C₈×C₁₉	C₂³	1	2	yes	complemented
150	#64528	C₂³	1	4	yes	complemented
151	#64527	C₂³	1	8	yes	complemented
152	#64527	C₂³	1	4	yes	complemented
153	#64526	C₂³	1	4	yes	complemented
154	#64525	C₂³	1	8	yes	complemented
155	#64525	C₂³	1	4	yes	complemented
156	#64520	C₂³	1	2	yes	—
157	#64520	C₂³	1	2	yes	complemented
158	C₂×C₁₉⋊C₈	C₂³	1	2	yes	complemented
159	D₁₅₂	C₂³	1	8	yes	complemented
160	#64516	C₂³	1	8	yes	complemented
161	#64515	C₂³	1	8	yes	complemented
162	C₈×D₁₉	C₂³	1	8	yes	complemented
163	C₂³×C₁₉	—	2	1	no	—
164	C₂³×C₁₉	—	2	1	no	—
165	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×D₁₉	—	2	2	no	—
167	C₂²×D₁₉	—	2	1	no	—
168	C₂²×D₁₉	—	2	2	no	—
169	C₂²×D₁₉	—	2	2	no	—
170	C₂²×D₁₉	—	2	4	no	—
171	C₂²×D₁₉	—	2	8	no	—
172	C₂²×D₁₉	—	8	4	no	—
173	C₂²×D₁₉	—	8	2	no	—
174	C₂²×D₁₉	C₂×D₄	1	2	yes	—
175	Q₈×C₁₉	—	2	1	no	—
176	Q₈×C₁₉	—	2	1	no	—
177	Q₈×C₁₉	C₂⁴	1	2	yes	—
178	Q₈×C₁₉	C₂⁴	1	2	yes	—
179	D₄×C₁₉	—	2	2	no	—
180	D₄×C₁₉	—	2	2	no	—
181	D₄×C₁₉	—	2	2	no	—
182	D₄×C₁₉	—	2	2	no	—
183	D₄×C₁₉	—	2	1	no	—
184	D₄×C₁₉	—	2	1	no	—
185	D₄×C₁₉	C₂⁴	1	2	yes	—
186	D₄×C₁₉	C₂⁴	1	2	yes	—
187	C₂×C₄×C₁₉	—	2	1	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	2	no	—
193	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
199	C₂²⋊D₁₉	—	2	2	no	—
200	C₂²⋊D₁₉	—	2	2	no	—
201	C₂²⋊D₁₉	—	2	4	no	—
202	C₂²⋊D₁₉	—	2	8	no	—
203	C₂²⋊D₁₉	—	2	4	no	—
204	C₂²⋊D₁₉	C₂×D₄	1	4	yes	—
205	C₂²⋊D₁₉	C₂×D₄	1	4	yes	—
206	C₂×Dic₁₉	—	2	1	no	—
207	C₂×Dic₁₉	—	2	4	no	—
208	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
209	D₇₆	—	2	8	no	—
210	D₇₆	—	2	4	no	—
211	D₇₆	—	2	2	no	—
212	D₇₆	—	2	2	no	—
213	D₇₆	—	2	2	no	—
214	D₇₆	—	2	1	no	—
215	D₇₆	C₂×D₄	1	2	yes	—
216	D₇₆	C₂×D₄	1	2	yes	—
217	D₇₆	C₂⁴	1	4	yes	—
218	D₇₆	C₂⁴	1	2	yes	—
219	C₄×D₁₉	—	2	4	no	—
220	C₄×D₁₉	—	2	2	no	—
221	C₄×D₁₉	—	2	2	no	—
222	C₄×D₁₉	—	2	8	no	—
223	C₄×D₁₉	—	2	4	no	—
224	C₄×D₁₉	C₂×D₄	1	4	yes	—
225	C₄×D₁₉	C₂⁴	1	4	yes	—
226	Dic₃₈	—	2	1	no	—
227	Dic₃₈	—	2	4	no	—
228	Dic₃₈	C₂×D₄	1	2	yes	—
229	Dic₃₈	C₂×D₄	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	2	no	—
236	C₂²×C₁₉	—	4	1	no	—
237	C₂²×C₁₉	—	4	2	no	—
238	C₂²×C₁₉	—	8	1	no	—
239	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
240	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
241	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
242	C₂×D₁₉	—	2	2	no	—
243	C₂×D₁₉	—	2	4	no	—
244	C₂×D₁₉	—	4	2	no	—
245	C₂×D₁₉	—	4	4	no	—
246	C₂×D₁₉	—	8	4	no	—
247	C₂×D₁₉	—	8	8	no	—
248	C₂×D₁₉	—	8	1	no	—
249	C₂×D₁₉	—	8	2	no	—
250	C₂×D₁₉	—	8	2	no	—
251	C₂×D₁₉	C₂²×D₄	1	4	yes	—
252	C₄×C₁₉	—	2	2	no	—
253	C₄×C₁₉	—	2	2	no	—
254	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
255	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
256	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
257	C₄×C₁₉	C₂⁵	1	1	yes	characteristic
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	D₁₉	1	1	yes	characteristic, complemented
269	C₂×AGL(1,ℤ/8)	—	19	1	no	—
270	C₂×AGL(1,ℤ/8)	—	19	4	no	—
271	C₂×AGL(1,ℤ/8)	—	19	1	no	—
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	2	no	—
277	C₂×C₁₉	—	4	2	no	—
278	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
279	D₁₉	—	2	4	no	—
280	D₁₉	—	4	4	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	4	no	—
286	H(5,𝔽₂)	—	19	4	no	—
287	H(5,𝔽₂)	—	19	2	no	—
288	H(5,𝔽₂)	—	19	2	no	—
289	H(5,𝔽₂)	—	38	2	no	—
290	H(5,𝔽₂)	—	38	1	no	—
291	H(5,𝔽₂)	—	38	2	no	—
292	H(5,𝔽₂)	—	38	2	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	—	38	1	no	—
298	C₂×#41	—	38	2	no	—
299	C₂×#41	—	38	2	no	—
300	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
301	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
302	C₂²×D₄	—	19	2	no	—
303	C₂²×D₄	—	19	1	no	—
304	C₂²×D₄	—	38	1	no	—
305	C₂²×D₄	—	38	2	no	—
306	#137	—	19	2	no	—
307	#137	—	19	2	no	—
308	#137	—	19	8	no	—
309	#137	C₂×D₁₉	1	2	yes	complemented
310	#137	C₂×D₁₉	1	2	yes	complemented
311	AGL(1,ℤ/8)	—	19	4	no	—
312	AGL(1,ℤ/8)	—	19	2	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	4	no	—
319	AGL(1,ℤ/8)	—	19	4	no	—
320	AGL(1,ℤ/8)	C₂×D₁₉	1	2	yes	complemented
321	AGL(1,ℤ/8)	C₂×D₁₉	1	2	yes	complemented
322	#135	—	19	4	no	—
323	#135	—	19	8	no	—
324	#135	—	19	8	no	—
325	#135	C₂×D₁₉	1	4	yes	complemented
326	C₂×SD₁₆	—	19	2	no	—
327	C₂×SD₁₆	—	19	8	no	—
328	C₂×SD₁₆	—	19	2	no	—
329	C₂×D₈	—	19	2	no	—
330	C₂×D₈	—	19	8	no	—
331	C₂×D₈	—	19	2	no	—
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	—	38	2	no	—
339	C₂⁴	—	38	1	no	—
340	#41	—	2	1	no	—
341	#41	—	2	1	no	—
342	#41	—	2	1	no	—
343	#41	—	2	1	no	—
344	#41	—	19	2	no	—
345	#41	—	19	2	no	—
346	#41	—	19	2	no	—
347	#41	—	19	2	no	—
348	#41	—	19	8	no	—
349	#41	—	19	4	no	—
350	#41	—	19	4	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	4	no	—
357	#41	—	38	4	no	—
358	#41	—	38	2	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	C₂²×D₁₉	1	2	yes	—
367	#41	C₂²×D₁₉	1	2	yes	—
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	—	38	2	no	—
374	C₂×Q₈	—	38	2	no	—
375	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
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	—	19	2	no	—
380	C₂×D₄	—	19	8	no	—
381	C₂×D₄	—	19	4	no	—
382	C₂×D₄	—	19	1	no	—
383	C₂×D₄	—	19	2	no	—
384	C₂×D₄	—	19	2	no	—
385	C₂×D₄	—	19	2	no	—
386	C₂×D₄	—	19	1	no	—
387	C₂×D₄	—	38	4	no	—
388	C₂×D₄	—	38	4	no	—
389	C₂×D₄	—	38	2	no	—
390	C₂×D₄	—	38	2	no	—
391	C₂×D₄	—	38	4	no	—
392	C₂×D₄	—	38	2	no	—
393	C₂×D₄	—	38	8	no	—
394	C₂×D₄	—	38	8	no	—
395	C₂×D₄	—	38	4	no	—
396	C₂×D₄	—	38	2	no	—
397	C₂×D₄	—	38	4	no	—
398	C₂×D₄	—	38	4	no	—
399	C₂×D₄	—	38	1	no	—
400	C₂×D₄	—	38	1	no	—
401	C₂×D₄	—	38	1	no	—
402	C₂×D₄	—	38	1	no	—
403	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
404	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic, complemented
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	19	2	no	—
408	C₂²×C₄	—	38	2	no	—
409	C₂²×C₄	—	38	4	no	—
410	C₂²×C₄	—	38	1	no	—
411	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
412	Q₁₆	—	19	4	no	—
413	Q₁₆	C₂²×D₁₉	1	4	yes	complemented
414	SD₁₆	—	19	8	no	—
415	SD₁₆	—	19	4	no	—
416	SD₁₆	—	19	4	no	—
417	SD₁₆	—	19	8	no	—
418	SD₁₆	C₂²×D₁₉	1	4	yes	complemented
419	SD₁₆	C₂²×D₁₉	1	4	yes	complemented
420	D₈	—	19	4	no	—
421	D₈	—	19	8	no	—
422	D₈	—	19	8	no	—
423	D₈	C₂²×D₁₉	1	4	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	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	19	2	no	—
435	C₂³	—	38	4	no	—
436	C₂³	—	38	8	no	—
437	C₂³	—	38	2	no	—
438	C₂³	—	38	1	no	—
439	C₂³	—	38	2	no	—
440	C₂³	—	38	2	no	—
441	C₂³	—	152	2	no	—
442	C₂³	—	152	4	no	—
443	C₂³	D₄×D₁₉	1	1	yes	characteristic
444	Q₈	—	2	1	no	—
445	Q₈	—	2	1	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	C₂³×D₁₉	1	2	yes	—
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	1	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	4	no	—
465	D₄	—	38	8	no	—
466	D₄	—	38	4	no	—
467	D₄	—	38	8	no	—
468	D₄	—	38	4	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	2	no	—
475	D₄	—	38	1	no	—
476	D₄	C₂³×D₁₉	1	2	yes	—
477	D₄	C₂³×D₁₉	1	2	yes	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	19	2	no	—
485	C₂×C₄	—	19	4	no	—
486	C₂×C₄	—	19	4	no	—
487	C₂×C₄	—	38	8	no	—
488	C₂×C₄	—	38	4	no	—
489	C₂×C₄	—	38	4	no	—
490	C₂×C₄	—	38	4	no	—
491	C₂×C₄	—	38	1	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	2	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	8	1	no	—
507	C₂²	—	19	4	no	—
508	C₂²	—	38	2	no	—
509	C₂²	—	38	4	no	—
510	C₂²	—	76	2	no	—
511	C₂²	—	76	4	no	—
512	C₂²	—	152	2	no	—
513	C₂²	—	152	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	—	2	2	no	—
522	C₄	—	19	4	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	2	no	—
532	C₂	—	4	2	no	—
533	C₂	—	38	4	no	—
534	C₂	—	76	4	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	C₁₉×#575	C₂
socle	C₂×C₁₉	C₂³×D₄
hypercenter	#575	D₁₉
hypocenter	C₁₉	#3585
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #575

Complements

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

N	H ≅ G/N	type
1. #11927380	C₂	semidirect
2. C₂×#10597435	C₂	semidirect
3. #11927353	C₂	semidirect
4. #11927351	C₂	semidirect
5. #11927348	C₂	semidirect
6. #11927346	C₂	semidirect
7. #11927343	C₂	semidirect
8. #11927342	C₂	semidirect
9. C₂×#10597354	C₂	semidirect
10. C₂×#10597395	C₂	semidirect
11. AGL(1,ℤ/8)×D₁₉	C₂	semidirect
12. #11927310	C₂	semidirect
13. C₁₉×#575	C₂	semidirect
14. C₂×#41×C₁₉	C₂²	semidirect
15. C₂×#41×C₁₉	C₂²	semidirect
17. #10597436	C₂²	semidirect
21. #10597435	C₂²	semidirect
22. #10597435	C₂²	semidirect
23. #10597435	C₂²	semidirect
25. #41×D₁₉	C₂²	semidirect
26. #10597433	C₂²	semidirect
27. C₂×#64545	C₂²	semidirect
29. #10597430	C₂²	semidirect
31. C₂×D₄×D₁₉	C₂²	semidirect
35. C₂×#64541	C₂²	semidirect
37. C₂²×D₇₆	C₂²	semidirect
38. C₁₉×#137	C₂²	semidirect
39. C₁₉×#137	C₂²	semidirect
40. C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
41. C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
42. C₁₉×#135	C₂²	semidirect
43. C₂×M₁₆×C₁₉	C₂²	semidirect
44. #10597397	C₂²	semidirect
45. #10597396	C₂²	semidirect
46. #10597395	C₂²	semidirect
47. #10597395	C₂²	semidirect
48. #10597395	C₂²	semidirect
49. #10597388	C₂²	semidirect
50. C₂×#64527	C₂²	semidirect
51. #10597378	C₂²	semidirect
52. C₂×#64525	C₂²	semidirect
53. C₂×#64520	C₂²	semidirect
54. #10597365	C₂²	semidirect
55. #10597364	C₂²	semidirect
56. #10597362	C₂²	semidirect
57. #10597360	C₂²	semidirect
58. #10597360	C₂²	semidirect
59. SD₁₆×D₁₉	C₂²	semidirect
60. #10597357	C₂²	semidirect
61. D₈×D₁₉	C₂²	semidirect
62. #10597354	C₂²	semidirect
63. #10597354	C₂²	semidirect
64. #10597353	C₂²	semidirect
65. M₁₆×D₁₉	C₂²	semidirect
66. C₂×D₁₅₂	C₂²	semidirect
67. C₂×#64516	C₂²	semidirect
68. #10597347	C₂²	semidirect
78. #41×C₁₉	C₂³	semidirect
80. C₂×Q₈×C₁₉	C₂³	semidirect
84. C₂×D₄×C₁₉	C₂³	semidirect
95. #64545	C₂³	semidirect
97. Q₈×D₁₉	C₂³	semidirect
101. #64543	C₂³	semidirect
109. D₄×D₁₉	C₂³	semidirect
123. #64541	C₂³	semidirect
135. C₂×D₇₆	C₂³	semidirect
142. C₂×Dic₃₈	C₂³	semidirect
143. Q₁₆×C₁₉	C₂³	semidirect
144. SD₁₆×C₁₉	C₂³	semidirect
145. SD₁₆×C₁₉	C₂³	semidirect
146. D₈×C₁₉	C₂³	semidirect
148. M₁₆×C₁₉	C₂³	semidirect
149. C₂×C₈×C₁₉	C₂³	semidirect
150. #64528	C₂³	semidirect
151. #64527	C₂³	semidirect
152. #64527	C₂³	semidirect
153. #64526	C₂³	semidirect
154. #64525	C₂³	semidirect
155. #64525	C₂³	semidirect
157. #64520	C₂³	semidirect
158. C₂×C₁₉⋊C₈	C₂³	semidirect
159. D₁₅₂	C₂³	semidirect
160. #64516	C₂³	semidirect
161. #64515	C₂³	semidirect
162. C₈×D₁₉	C₂³	semidirect
268. #575	D₁₉	semidirect
300. C₂×#41	C₂×D₁₉	semidirect
301. C₂×#41	C₂×D₁₉	semidirect
309. #137	C₂×D₁₉	semidirect
310. #137	C₂×D₁₉	semidirect
320. AGL(1,ℤ/8)	C₂×D₁₉	semidirect
321. AGL(1,ℤ/8)	C₂×D₁₉	semidirect
325. #135	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
413. Q₁₆	C₂²×D₁₉	semidirect
418. SD₁₆	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×#10597435	2
#11927353	2
#11927351	2
#11927348	2
#11927346	2
#11927343	2
#11927342	2
C₂×#10597354	2
C₂×#10597395	2
AGL(1,ℤ/8)×D₁₉	2
#11927310	2
C₁₉×#575	2
#3585	19