Subgroups — #14577514

Order 2432.

992 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927271	C₂	1	2	yes	maximal, complemented
2	#11927270	C₂	1	2	yes	maximal, complemented
3	#11927265	C₂	1	2	yes	maximal, complemented
4	#11927262	C₂	1	2	yes	maximal, complemented
5	#11927235	C₂	1	2	yes	maximal, complemented
6	#11927233	C₂	1	2	yes	maximal, complemented
7	#11927232	C₂	1	2	yes	maximal, complemented
8	#11927228	C₂	1	2	yes	maximal, complemented
9	#11927154	C₂	1	2	yes	maximal, complemented
10	#11927152	C₂	1	2	yes	maximal, complemented
11	#11927117	C₂	1	2	yes	maximal
12	#11927101	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927099	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927099	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927099	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄⋊Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927020	C₂	1	2	yes	maximal, complemented
18	C₄×#64541	C₂	1	1	yes	maximal, characteristic
19	C₁₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×Q₈×D₁₉	C₂²	1	2	yes	—
21	C₂×#64541	C₂²	1	1	yes	characteristic
22	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₉×#125	C₂²	1	2	yes	—
25	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
28	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
29	C₁₉×#117	C₂²	1	2	yes	—
30	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
31	#10597392	C₂²	1	2	yes	—
32	#10597392	C₂²	1	2	yes	—
33	#10597392	C₂²	1	2	yes	—
34	Q₈×Dic₁₉	C₂²	1	2	yes	—
35	Q₈×Dic₁₉	C₂²	1	2	yes	—
36	Q₈×Dic₁₉	C₂²	1	2	yes	—
37	#10597390	C₂²	1	2	yes	—
38	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
42	#10597372	C₂²	1	2	yes	—
43	#10597372	C₂²	1	1	yes	characteristic
44	#10597370	C₂²	1	2	yes	—
45	#10597370	C₂²	1	2	yes	—
46	#10597344	C₂²	1	4	yes	—
47	#10597343	C₂²	1	2	yes	—
48	#10597343	C₂²	1	2	yes	—
49	#10597343	C₂²	1	2	yes	—
50	#10597340	C₂²	1	4	yes	—
51	#10597338	C₂²	1	2	yes	—
52	#10597338	C₂²	1	2	yes	—
53	#10597338	C₂²	1	2	yes	—
54	#10597338	C₂²	1	4	yes	—
55	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
56	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
57	#10597336	C₂²	1	2	yes	—
58	#10597336	C₂²	1	2	yes	—
59	#10597336	C₂²	1	2	yes	—
60	#10597336	C₂²	1	4	yes	—
61	#10597335	C₂²	1	4	yes	—
62	#10597335	C₂²	1	4	yes	—
63	#10597334	C₂²	1	2	yes	—
64	#10597334	C₂²	1	2	yes	—
65	#10597334	C₂²	1	4	yes	—
66	#10597333	C₂²	1	2	yes	—
67	#10597333	C₂²	1	2	yes	—
68	#10597333	C₂²	1	2	yes	—
69	#10597333	C₂²	1	4	yes	—
70	#10597331	C₂²	1	4	yes	—
71	#10597329	C₂²	1	4	yes	—
72	#10597325	C₂²	1	4	yes	—
73	#10597325	C₂²	1	4	yes	—
74	#10597322	C₂²	1	4	yes	—
75	C₄×D₇₆	C₂²	1	1	yes	characteristic
76	C₄×D₇₆	C₂²	1	1	yes	characteristic
77	#10597318	C₂²	1	1	yes	characteristic
78	#10597318	C₂²	1	4	yes	—
79	#10597318	C₂²	1	1	yes	characteristic
80	C₄²×D₁₉	C₂²	1	1	yes	characteristic
81	C₄²×D₁₉	C₂²	1	1	yes	characteristic
82	#10597316	C₂²	1	2	yes	—
83	#10597316	C₂²	1	4	yes	—
84	#10597315	C₂²	1	1	yes	characteristic
85	#10597315	C₂²	1	1	yes	characteristic
86	C₄×Dic₃₈	C₂²	1	2	yes	—
87	C₄×Dic₃₈	C₂²	1	2	yes	—
88	C₄×Dic₃₈	C₂²	1	4	yes	—
89	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
90	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
91	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
92	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
98	Q₈×D₁₉	—	2	8	no	—
99	#64541	—	2	4	no	—
100	C₂×D₇₆	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄×D₁₉	C₂³	1	4	yes	—
105	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
108	C₂×Dic₃₈	C₂³	1	2	yes	—
109	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
110	C₂×Dic₃₈	C₂³	1	4	yes	—
111	C₂×Dic₃₈	C₂³	1	2	yes	—
112	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
113	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
114	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
115	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
116	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
117	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
119	C₄²×C₁₉	C₂³	1	1	yes	characteristic
120	C₄²×C₁₉	C₂³	1	1	yes	characteristic
121	C₄²×C₁₉	C₂³	1	1	yes	characteristic
122	C₄²×C₁₉	C₂³	1	1	yes	characteristic
123	C₄²×C₁₉	C₂³	1	4	yes	—
124	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
125	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
126	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
127	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
130	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
131	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
132	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
133	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
134	C₄⋊Dic₁₉	C₂³	1	2	yes	—
135	C₄⋊Dic₁₉	C₂³	1	2	yes	—
136	C₄⋊Dic₁₉	C₂³	1	2	yes	—
137	C₄⋊Dic₁₉	C₂³	1	4	yes	—
138	C₄⋊Dic₁₉	C₂³	1	4	yes	—
139	C₄⋊Dic₁₉	C₂³	1	4	yes	—
140	C₄⋊Dic₁₉	C₂³	1	2	yes	—
141	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
143	Dic₁₉⋊C₄	C₂³	1	4	yes	—
144	Dic₁₉⋊C₄	C₂³	1	4	yes	—
145	Dic₁₉⋊C₄	C₂³	1	4	yes	—
146	Dic₁₉⋊C₄	C₂³	1	4	yes	—
147	Dic₁₉⋊C₄	C₂³	1	4	yes	—
148	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
149	Dic₁₉⋊C₄	C₂³	1	4	yes	—
150	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
151	Dic₁₉⋊C₄	C₂³	1	4	yes	—
152	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
153	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
154	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
155	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
156	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
157	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
158	C₄×Dic₁₉	C₂³	1	4	yes	—
159	C₄×Dic₁₉	C₂³	1	4	yes	—
160	C₄×Dic₁₉	C₂³	1	4	yes	—
161	C₄×Dic₁₉	C₂³	1	4	yes	—
162	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
163	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
164	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
165	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
166	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
167	Q₈×C₁₉	—	2	4	no	—
168	Q₈×C₁₉	—	2	4	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
174	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
175	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
180	C₂²⋊D₁₉	—	2	2	no	—
181	C₂²⋊D₁₉	—	2	2	no	—
182	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
183	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
184	C₂×Dic₁₉	C₂⁴	1	4	yes	—
185	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
186	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
187	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
188	C₂×Dic₁₉	C₂⁴	1	4	yes	—
189	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
190	D₇₆	—	2	2	no	—
191	C₄×D₁₉	—	2	8	no	—
192	C₄×D₁₉	—	2	2	no	—
193	C₄×D₁₉	—	2	2	no	—
194	C₄×D₁₉	—	2	2	no	—
195	C₄×D₁₉	—	2	2	no	—
196	C₄×D₁₉	—	2	2	no	—
197	C₄×D₁₉	#41	1	4	yes	—
198	Dic₃₈	—	2	4	no	—
199	Dic₃₈	—	2	4	no	—
200	Dic₃₈	—	2	2	no	—
201	Dic₃₈	—	2	8	no	—
202	#3509	—	19	1	no	maximal, Sylow
203	C₂²×C₁₉	—	2	1	no	—
204	C₂²×C₁₉	—	2	1	no	—
205	C₂²×C₁₉	—	2	1	no	—
206	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
207	C₂×D₁₉	—	2	1	no	—
208	C₂×D₁₉	—	2	1	no	—
209	C₂×D₁₉	—	2	1	no	—
210	C₂×D₁₉	—	2	1	no	—
211	C₂×D₁₉	—	2	1	no	—
212	C₂×D₁₉	C₂×#41	1	2	yes	—
213	C₄×C₁₉	—	2	4	no	—
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	2	1	no	—
217	C₄×C₁₉	—	2	4	no	—
218	C₄×C₁₉	C₂×#41	1	2	yes	—
219	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
220	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
221	Dic₁₉	—	2	4	no	—
222	Dic₁₉	—	2	1	no	—
223	Dic₁₉	—	2	4	no	—
224	Dic₁₉	—	2	1	no	—
225	Dic₁₉	—	2	1	no	—
226	Dic₁₉	—	2	1	no	—
227	Dic₁₉	—	2	1	no	—
228	Dic₁₉	C₂×#41	1	2	yes	—
229	#557	—	19	2	no	—
230	#557	—	19	2	no	—
231	#556	—	19	2	no	—
232	#556	—	19	2	no	—
233	#552	—	19	2	no	—
234	#552	—	19	2	no	—
235	#552	—	19	2	no	—
236	#552	—	19	2	no	—
237	#541	—	19	2	no	—
238	#541	—	19	2	no	—
239	#536	—	19	2	no	—
240	#533	—	19	1	no	—
241	#533	—	19	1	no	—
242	#533	—	19	1	no	—
243	#533	—	19	1	no	—
244	#533	D₁₉	1	1	yes	characteristic, complemented
245	C₂×C₄⋊Q₈	—	19	1	no	—
246	#519	—	19	2	no	—
247	C₄×#41	—	19	1	no	—
248	C₂×C₁₉	—	4	1	no	—
249	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
250	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
251	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
252	D₁₉	—	2	2	no	—
253	D₁₉	—	4	1	no	—
254	C₂×#41	—	19	1	no	—
255	C₂²×Q₈	—	19	2	no	—
256	C₄⋊Q₈	—	19	2	no	—
257	C₄⋊Q₈	—	19	2	no	—
258	C₄⋊Q₈	—	19	2	no	—
259	C₄⋊Q₈	—	19	4	no	—
260	C₄⋊Q₈	—	19	1	no	—
261	C₄⋊Q₈	—	19	1	no	—
262	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
263	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
264	#126	—	19	4	no	—
265	#126	—	19	4	no	—
266	#126	—	19	4	no	—
267	#126	—	19	4	no	—
268	#125	—	19	2	no	—
269	#125	—	19	2	no	—
270	#125	—	19	2	no	—
271	#125	—	19	4	no	—
272	#125	—	19	4	no	—
273	#125	—	19	4	no	—
274	#125	—	19	2	no	—
275	#125	—	19	4	no	—
276	#125	C₂×D₁₉	1	2	yes	—
277	#124	—	19	4	no	—
278	#123	—	19	4	no	—
279	#123	—	19	4	no	—
280	C₂²⋊Q₈	—	19	2	no	—
281	C₂²⋊Q₈	—	19	2	no	—
282	C₂²⋊Q₈	—	19	2	no	—
283	C₂²⋊Q₈	—	19	2	no	—
284	C₂²⋊Q₈	—	19	2	no	—
285	C₂²⋊Q₈	—	19	2	no	—
286	C₂²⋊Q₈	—	19	2	no	—
287	C₂²⋊Q₈	—	19	2	no	—
288	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	—
289	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	—
290	C₄×Q₈	—	19	2	no	—
291	C₄×Q₈	—	19	2	no	—
292	C₄×Q₈	—	19	2	no	—
293	C₄×Q₈	—	19	2	no	—
294	C₄×Q₈	—	19	4	no	—
295	C₄×Q₈	—	19	2	no	—
296	C₄×Q₈	—	19	2	no	—
297	C₄×Q₈	—	19	1	no	—
298	C₄×Q₈	—	19	1	no	—
299	C₄×Q₈	—	19	2	no	—
300	C₄×Q₈	—	19	4	no	—
301	C₄×Q₈	—	19	2	no	—
302	C₄×Q₈	C₂×D₁₉	1	2	yes	—
303	C₄×Q₈	C₂×D₁₉	1	2	yes	—
304	C₄×D₄	—	19	1	no	—
305	C₄×D₄	—	19	1	no	—
306	C₄×D₄	—	19	1	no	—
307	C₄×D₄	—	19	1	no	—
308	C₄×D₄	—	19	1	no	—
309	C₄×D₄	—	19	1	no	—
310	#117	—	19	1	no	—
311	#117	—	19	2	no	—
312	#117	—	19	2	no	—
313	#117	—	19	4	no	—
314	#117	—	19	2	no	—
315	#117	—	19	2	no	—
316	#117	—	19	1	no	—
317	#117	—	19	1	no	—
318	#117	—	19	4	no	—
319	#117	C₂×D₁₉	1	2	yes	—
320	C₂×C₄⋊C₄	—	19	2	no	—
321	C₂×C₄⋊C₄	—	19	2	no	—
322	C₂×C₄²	—	19	1	no	—
323	C₂×C₄²	—	19	1	no	—
324	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
325	C₁₉	#3509	1	1	yes	characteristic, complemented, Sylow
326	#41	—	38	4	no	—
327	C₂×Q₈	—	19	2	no	—
328	C₂×Q₈	—	19	2	no	—
329	C₂×Q₈	—	19	4	no	—
330	C₂×Q₈	—	19	1	no	—
331	C₂×Q₈	—	38	8	no	—
332	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
333	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
334	C₂×D₄	—	19	1	no	—
335	C₂×D₄	—	19	1	no	—
336	C₂×D₄	—	19	1	no	—
337	C₂²×C₄	—	19	1	no	—
338	C₂²×C₄	—	19	1	no	—
339	C₂²×C₄	—	19	1	no	—
340	C₂²×C₄	—	19	1	no	—
341	C₂²×C₄	—	19	1	no	—
342	C₂²×C₄	—	19	1	no	—
343	C₂²×C₄	—	19	4	no	—
344	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
345	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
346	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
347	C₄⋊C₄	—	19	4	no	—
348	C₄⋊C₄	—	19	4	no	—
349	C₄⋊C₄	—	19	1	no	—
350	C₄⋊C₄	—	19	1	no	—
351	C₄⋊C₄	—	19	1	no	—
352	C₄⋊C₄	—	19	1	no	—
353	C₄⋊C₄	—	19	4	no	—
354	C₄⋊C₄	—	19	4	no	—
355	C₄⋊C₄	—	19	4	no	—
356	C₄⋊C₄	—	19	4	no	—
357	C₄⋊C₄	—	19	4	no	—
358	C₄⋊C₄	—	19	2	no	—
359	C₄⋊C₄	—	19	2	no	—
360	C₄⋊C₄	—	19	2	no	—
361	C₄⋊C₄	—	19	1	no	—
362	C₄⋊C₄	—	19	1	no	—
363	C₄⋊C₄	—	19	2	no	—
364	C₄⋊C₄	—	19	4	no	—
365	C₄⋊C₄	—	19	4	no	—
366	C₄⋊C₄	—	19	4	no	—
367	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
368	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
369	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
370	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
371	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
372	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
373	C₂²⋊C₄	—	19	1	no	—
374	C₂²⋊C₄	—	19	1	no	—
375	C₂²⋊C₄	—	19	4	no	—
376	C₂²⋊C₄	—	19	1	no	—
377	C₂²⋊C₄	—	19	1	no	—
378	C₂²⋊C₄	—	19	4	no	—
379	C₂²⋊C₄	—	19	1	no	—
380	C₂²⋊C₄	—	19	1	no	—
381	C₂²⋊C₄	—	19	4	no	—
382	C₂²⋊C₄	—	19	4	no	—
383	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
384	C₄²	—	19	1	no	—
385	C₄²	—	19	1	no	—
386	C₄²	—	19	1	no	—
387	C₄²	—	19	1	no	—
388	C₄²	—	19	1	no	—
389	C₄²	—	19	1	no	—
390	C₄²	—	19	4	no	—
391	C₄²	—	19	4	no	—
392	C₄²	—	19	4	no	—
393	C₄²	—	19	4	no	—
394	C₄²	C₂²×D₁₉	1	1	yes	characteristic
395	C₄²	C₂²×D₁₉	1	1	yes	characteristic
396	C₄²	C₂²×D₁₉	1	1	yes	characteristic
397	C₄²	C₂²×D₁₉	1	1	yes	characteristic
398	C₄²	C₂²×D₁₉	1	4	yes	—
399	C₂³	—	19	1	no	—
400	C₂³	—	19	1	no	—
401	C₂³	C₂³×D₁₉	1	1	yes	characteristic
402	Q₈	—	2	4	no	—
403	Q₈	—	2	4	no	—
404	Q₈	—	38	8	no	—
405	Q₈	—	38	2	no	—
406	Q₈	—	38	4	no	—
407	Q₈	—	38	4	no	—
408	D₄	—	38	2	no	—
409	D₄	—	38	2	no	—
410	D₄	—	38	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	19	1	no	—
415	C₂×C₄	—	19	4	no	—
416	C₂×C₄	—	19	1	no	—
417	C₂×C₄	—	19	1	no	—
418	C₂×C₄	—	19	4	no	—
419	C₂×C₄	—	19	1	no	—
420	C₂×C₄	—	19	1	no	—
421	C₂×C₄	—	19	4	no	—
422	C₂×C₄	—	19	1	no	—
423	C₂×C₄	—	38	8	no	—
424	C₂×C₄	—	38	2	no	—
425	C₂×C₄	—	38	2	no	—
426	C₂×C₄	—	38	2	no	—
427	C₂×C₄	—	38	2	no	—
428	C₂×C₄	—	38	2	no	—
429	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
430	C₂×C₄	C₂³×D₁₉	1	4	yes	—
431	C₂×C₄	C₂³×D₁₉	1	4	yes	—
432	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
433	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
434	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
435	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
436	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	19	2	no	—
441	C₂²	—	38	1	no	—
442	C₂²	—	38	1	no	—
443	C₂²	—	38	1	no	—
444	C₂²	—	38	1	no	—
445	C₂²	—	38	1	no	—
446	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
447	C₄	—	2	1	no	—
448	C₄	—	2	4	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	4	no	—
451	C₄	—	2	1	no	—
452	C₄	—	19	2	no	—
453	C₄	—	38	1	no	—
454	C₄	—	38	4	no	—
455	C₄	—	38	1	no	—
456	C₄	—	38	1	no	—
457	C₄	—	38	1	no	—
458	C₄	—	38	1	no	—
459	C₄	—	38	4	no	—
460	C₄	#10597433	1	2	yes	—
461	C₄	#41×D₁₉	1	2	yes	—
462	C₄	#10597436	1	2	yes	—
463	C₂	—	4	1	no	—
464	C₂	—	38	2	no	—
465	C₂	—	76	1	no	—
466	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
467	C₂	C₂×#10597436	1	1	yes	characteristic
468	C₂	C₂×#10597433	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#533	C₂
prime radical	C₂×#64541	C₂²
hypercenter	#533	D₁₉
hypocenter	C₁₉	#3509
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #533

Complements

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

N	H ≅ G/N	type
1. #11927271	C₂	semidirect
2. #11927270	C₂	semidirect
3. #11927265	C₂	semidirect
4. #11927262	C₂	semidirect
5. #11927235	C₂	semidirect
6. #11927233	C₂	semidirect
7. #11927232	C₂	semidirect
8. #11927228	C₂	semidirect
9. #11927154	C₂	semidirect
10. #11927152	C₂	semidirect
12. #11927101	C₂	semidirect
13. #11927099	C₂	semidirect
14. #11927099	C₂	semidirect
15. #11927099	C₂	semidirect
16. C₄⋊Q₈×D₁₉	C₂	semidirect
17. #11927020	C₂	semidirect
19. C₁₉×#533	C₂	semidirect
244. #533	D₁₉	semidirect
325. C₁₉	#3509	semidirect

Maximal subgroups

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

subgroup	index
#11927271	2
#11927270	2
#11927265	2
#11927262	2
#11927235	2
#11927233	2
#11927232	2
#11927228	2
#11927154	2
#11927152	2
#11927117	2
#11927101	2
#11927099	2
C₄⋊Q₈×D₁₉	2
#11927020	2
C₄×#64541	2
C₁₉×#533	2
#3509	19