Subgroups — #14577683

Order 2432.

1124 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927254	C₂	1	2	yes	maximal, complemented
2	#11927233	C₂	1	2	yes	maximal, complemented
3	#11927219	C₂	1	4	yes	maximal, complemented
4	Q₈×D₇₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927204	C₂	1	2	yes	maximal, complemented
6	#11927199	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927197	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927187	C₂	1	2	yes	maximal, complemented
9	#11927163	C₂	1	2	yes	maximal, complemented
10	#11927135	C₂	1	4	yes	maximal, complemented
11	#11927099	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927081	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927056	C₂	1	2	yes	maximal, complemented
14	C₂²⋊Q₈×D₁₉	C₂	1	2	yes	maximal, complemented
15	#11927026	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#556	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#64545	C₂²	1	2	yes	—
19	C₂×Q₈×D₁₉	C₂²	1	2	yes	complemented
20	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
21	C₂×#64541	C₂²	1	2	yes	complemented
22	C₂²×C₄×D₁₉	C₂²	1	2	yes	—
23	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#126	C₂²	1	4	yes	complemented
25	C₁₉×#124	C₂²	1	2	yes	—
26	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
28	C₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
29	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#117	C₂²	1	2	yes	complemented
31	#10597393	C₂²	1	1	yes	characteristic, complemented
32	#10597392	C₂²	1	1	yes	characteristic
33	#10597392	C₂²	1	2	yes	—
34	#10597392	C₂²	1	2	yes	complemented
35	Q₈×Dic₁₉	C₂²	1	2	yes	complemented
36	#10597384	C₂²	1	2	yes	—
37	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
39	#10597370	C₂²	1	2	yes	complemented
40	#10597344	C₂²	1	2	yes	complemented
41	#10597343	C₂²	1	2	yes	—
42	#10597343	C₂²	1	2	yes	complemented
43	#10597343	C₂²	1	4	yes	complemented
44	#10597342	C₂²	1	4	yes	—
45	#10597342	C₂²	1	4	yes	complemented
46	#10597341	C₂²	1	1	yes	characteristic
47	#10597341	C₂²	1	2	yes	complemented
48	#10597340	C₂²	1	2	yes	—
49	#10597340	C₂²	1	4	yes	complemented
50	#10597339	C₂²	1	1	yes	characteristic
51	#10597339	C₂²	1	4	yes	complemented
52	#10597338	C₂²	1	2	yes	—
53	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
54	C₄⋊C₄×D₁₉	C₂²	1	4	yes	complemented
55	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
56	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
57	#10597336	C₂²	1	1	yes	characteristic, complemented
58	#10597336	C₂²	1	2	yes	complemented
59	#10597333	C₂²	1	2	yes	complemented
60	#10597332	C₂²	1	4	yes	complemented
61	#10597331	C₂²	1	4	yes	complemented
62	#10597330	C₂²	1	4	yes	—
63	#10597329	C₂²	1	4	yes	—
64	#10597329	C₂²	1	4	yes	complemented
65	#10597328	C₂²	1	4	yes	—
66	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
67	C₂²⋊C₄×D₁₉	C₂²	1	4	yes	—
68	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
69	#10597325	C₂²	1	4	yes	complemented
70	#10597324	C₂²	1	4	yes	complemented
71	C₄×D₇₆	C₂²	1	4	yes	—
72	C₄×D₇₆	C₂²	1	2	yes	—
73	C₄×D₇₆	C₂²	1	2	yes	—
74	C₄×D₇₆	C₂²	1	1	yes	characteristic
75	C₄×D₇₆	C₂²	1	4	yes	complemented
76	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
77	#10597318	C₂²	1	2	yes	complemented
78	#10597318	C₂²	1	4	yes	complemented
79	C₄²×D₁₉	C₂²	1	1	yes	characteristic
80	#10597316	C₂²	1	4	yes	complemented
81	#10597315	C₂²	1	1	yes	characteristic, complemented
82	#10597315	C₂²	1	2	yes	complemented
83	C₂³×D₁₉	C₂³	1	2	yes	—
84	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
85	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
88	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
90	C₂²×Dic₁₉	C₂³	1	2	yes	—
91	#64545	—	2	8	no	—
92	Q₈×D₁₉	—	4	4	no	—
93	D₄×D₁₉	—	2	4	no	—
94	#64541	—	4	4	no	—
95	C₂×D₇₆	C₂³	1	1	yes	characteristic
96	C₂×D₇₆	C₂³	1	4	yes	—
97	C₂×D₇₆	C₂³	1	2	yes	—
98	C₂×D₇₆	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₁₉	—	4	4	no	—
100	C₂×C₄×D₁₉	C₂³	1	2	yes	—
101	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₁₉	C₂³	1	2	yes	—
104	C₂×C₄×D₁₉	C₂³	1	4	yes	—
105	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₁₉	C₂³	1	2	yes	—
107	C₂×C₄×D₁₉	C₂³	1	2	yes	—
108	C₂×C₄×D₁₉	C₂³	1	4	yes	—
109	C₂×C₄×D₁₉	C₂³	1	4	yes	—
110	C₂×Dic₃₈	C₂³	1	2	yes	—
111	C₂×Dic₃₈	C₂³	1	4	yes	—
112	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
113	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
114	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
120	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
121	C₄²×C₁₉	C₂³	1	4	yes	—
122	C₄²×C₁₉	C₂³	1	1	yes	characteristic
123	C₄²×C₁₉	C₂³	1	2	yes	—
124	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
125	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
126	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
127	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
130	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
131	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
132	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
133	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
134	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
135	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
136	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
137	C₄⋊Dic₁₉	C₂³	1	2	yes	—
138	C₄⋊Dic₁₉	C₂³	1	4	yes	—
139	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₁₉	C₂³	1	4	yes	—
141	C₄⋊Dic₁₉	C₂³	1	2	yes	—
142	C₄⋊Dic₁₉	C₂³	1	2	yes	—
143	Dic₁₉⋊C₄	C₂³	1	4	yes	—
144	Dic₁₉⋊C₄	C₂³	1	2	yes	—
145	Dic₁₉⋊C₄	C₂³	1	4	yes	—
146	Dic₁₉⋊C₄	C₂³	1	2	yes	—
147	Dic₁₉⋊C₄	C₂³	1	4	yes	—
148	Dic₁₉⋊C₄	C₂³	1	2	yes	—
149	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
150	C₄×Dic₁₉	C₂³	1	4	yes	—
151	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
152	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
153	C₂³×C₁₉	C₂⁴	1	2	yes	—
154	C₂²×D₁₉	—	2	4	no	—
155	C₂²×D₁₉	—	2	4	no	—
156	C₂²×D₁₉	—	4	2	no	—
157	C₂²×D₁₉	C₂⁴	1	2	yes	—
158	C₂²×D₁₉	C₂⁴	1	2	yes	—
159	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
160	Q₈×C₁₉	—	2	4	no	—
161	Q₈×C₁₉	—	2	2	no	—
162	D₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
165	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
167	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
168	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
169	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
171	C₂²⋊D₁₉	—	2	4	no	—
172	C₂²⋊D₁₉	—	4	4	no	—
173	C₂×Dic₁₉	—	4	2	no	—
174	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
175	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
176	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
177	C₂×Dic₁₉	C₂⁴	1	4	yes	—
178	C₂×Dic₁₉	C₂⁴	1	2	yes	—
179	C₂×Dic₁₉	C₂⁴	1	2	yes	—
180	D₇₆	—	2	8	no	—
181	D₇₆	—	2	4	no	—
182	D₇₆	—	2	2	no	—
183	D₇₆	#41	1	4	yes	complemented
184	C₄×D₁₉	—	2	8	no	—
185	C₄×D₁₉	—	2	2	no	—
186	C₄×D₁₉	—	2	2	no	—
187	C₄×D₁₉	—	2	4	no	—
188	C₄×D₁₉	—	2	2	no	—
189	C₄×D₁₉	—	2	4	no	—
190	C₄×D₁₉	—	4	2	no	—
191	C₄×D₁₉	—	4	2	no	—
192	C₄×D₁₉	—	4	4	no	—
193	C₄×D₁₉	—	4	4	no	—
194	Dic₃₈	—	2	4	no	—
195	Dic₃₈	—	4	4	no	—
196	#3520	—	19	1	no	maximal, Sylow
197	C₂²×C₁₉	—	2	2	no	—
198	C₂²×C₁₉	—	2	2	no	—
199	C₂²×C₁₉	—	2	2	no	—
200	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
201	C₂×D₁₉	—	2	1	no	—
202	C₂×D₁₉	—	2	2	no	—
203	C₂×D₁₉	—	2	1	no	—
204	C₂×D₁₉	—	2	2	no	—
205	C₂×D₁₉	—	2	2	no	—
206	C₂×D₁₉	—	2	2	no	—
207	C₂×D₁₉	—	2	2	no	—
208	C₂×D₁₉	—	4	8	no	—
209	C₂×D₁₉	C₂×#41	1	4	yes	—
210	C₂×D₁₉	2₋¹⁺⁴	1	2	yes	—
211	C₄×C₁₉	—	2	4	no	—
212	C₄×C₁₉	—	2	2	no	—
213	C₄×C₁₉	—	2	2	no	—
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	2	2	no	—
216	C₄×C₁₉	C₂×#41	1	2	yes	—
217	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
218	Dic₁₉	—	2	2	no	—
219	Dic₁₉	—	2	1	no	—
220	Dic₁₉	—	2	4	no	—
221	Dic₁₉	—	2	2	no	—
222	Dic₁₉	—	2	1	no	—
223	Dic₁₉	—	2	1	no	—
224	#556	D₁₉	1	1	yes	characteristic, complemented
225	#554	—	19	2	no	—
226	#552	—	19	2	no	—
227	#551	—	19	4	no	—
228	D₄×Q₈	—	19	1	no	—
229	#548	—	19	2	no	—
230	#547	—	19	1	no	—
231	#547	—	19	1	no	—
232	#546	—	19	2	no	—
233	#542	—	19	2	no	—
234	#539	—	19	4	no	—
235	#533	—	19	1	no	—
236	#529	—	19	1	no	—
237	#525	—	19	2	no	—
238	C₂×C₂²⋊Q₈	—	19	2	no	—
239	#520	—	19	2	no	—
240	C₂×C₄×D₄	—	19	1	no	—
241	C₂×C₁₉	—	4	2	no	—
242	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
243	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
244	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
245	D₁₉	—	2	2	no	—
246	D₁₉	—	2	4	no	—
247	D₁₉	—	4	2	no	—
248	C₂×#41	—	19	2	no	—
249	C₂×#41	—	19	2	no	—
250	C₂²×Q₈	—	19	2	no	—
251	C₂²×D₄	—	19	1	no	—
252	C₂³×C₄	—	19	2	no	—
253	C₄⋊Q₈	—	19	1	no	—
254	C₄⋊Q₈	—	19	2	no	—
255	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
256	#126	—	19	2	no	—
257	#126	—	19	4	no	—
258	#126	C₂×D₁₉	1	4	yes	complemented
259	#125	—	19	1	no	—
260	#125	—	19	2	no	—
261	#125	—	19	4	no	—
262	#124	—	19	1	no	—
263	#124	—	19	4	no	—
264	#124	C₂×D₁₉	1	2	yes	—
265	#123	—	19	2	no	—
266	#123	—	19	4	no	—
267	#123	—	19	4	no	—
268	#123	—	19	4	no	—
269	#123	—	19	4	no	—
270	C₂²⋊Q₈	—	19	1	no	—
271	C₂²⋊Q₈	—	19	2	no	—
272	C₂²⋊Q₈	—	19	2	no	—
273	C₂²⋊Q₈	—	19	2	no	—
274	C₂²⋊Q₈	—	19	2	no	—
275	C₂²⋊Q₈	—	19	4	no	—
276	C₂²⋊Q₈	—	19	2	no	—
277	C₂²⋊Q₈	—	19	4	no	—
278	C₂²⋊Q₈	—	19	4	no	—
279	C₂²⋊Q₈	—	19	4	no	—
280	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
281	#121	—	19	2	no	—
282	#121	—	19	1	no	—
283	#121	—	19	2	no	—
284	#121	—	19	4	no	—
285	#120	—	19	4	no	—
286	C₄×Q₈	—	19	2	no	—
287	C₄×Q₈	—	19	2	no	—
288	C₄×Q₈	C₂×D₁₉	1	2	yes	complemented
289	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
290	C₄×D₄	—	19	1	no	—
291	C₄×D₄	—	19	2	no	—
292	C₄×D₄	—	19	1	no	—
293	C₄×D₄	—	19	4	no	—
294	C₄×D₄	—	19	2	no	—
295	C₄×D₄	—	19	1	no	—
296	C₄×D₄	—	19	4	no	—
297	C₄×D₄	—	19	2	no	—
298	C₄×D₄	—	19	4	no	—
299	C₄×D₄	—	19	2	no	—
300	C₄×D₄	—	19	1	no	—
301	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
302	#117	—	19	2	no	—
303	#117	—	19	2	no	—
304	#117	—	19	4	no	—
305	#117	C₂×D₁₉	1	2	yes	complemented
306	C₂×C₄⋊C₄	—	19	1	no	—
307	C₂×C₄⋊C₄	—	19	4	no	—
308	C₂×C₄⋊C₄	—	19	2	no	—
309	C₂×C₄⋊C₄	—	19	2	no	—
310	C₂×C₂²⋊C₄	—	19	2	no	—
311	C₂×C₂²⋊C₄	—	19	4	no	—
312	C₂×C₄²	—	19	1	no	—
313	C₁₉	#3520	1	1	yes	characteristic, complemented, Sylow
314	C₂⁴	—	19	2	no	—
315	#41	—	38	8	no	—
316	#41	—	76	4	no	—
317	C₂×Q₈	—	19	2	no	—
318	C₂×Q₈	—	19	4	no	—
319	C₂×Q₈	—	76	4	no	—
320	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
321	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
322	C₂×D₄	—	19	2	no	—
323	C₂×D₄	—	19	4	no	—
324	C₂×D₄	—	19	1	no	—
325	C₂×D₄	—	19	2	no	—
326	C₂×D₄	—	19	4	no	—
327	C₂×D₄	—	19	1	no	—
328	C₂×D₄	—	38	4	no	—
329	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
330	C₂²×C₄	—	19	2	no	—
331	C₂²×C₄	—	19	1	no	—
332	C₂²×C₄	—	19	1	no	—
333	C₂²×C₄	—	19	1	no	—
334	C₂²×C₄	—	19	4	no	—
335	C₂²×C₄	—	19	2	no	—
336	C₂²×C₄	—	19	2	no	—
337	C₂²×C₄	—	19	4	no	—
338	C₂²×C₄	—	19	2	no	—
339	C₂²×C₄	—	19	2	no	—
340	C₂²×C₄	—	19	4	no	—
341	C₂²×C₄	—	76	4	no	—
342	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
343	C₄⋊C₄	—	19	2	no	—
344	C₄⋊C₄	—	19	4	no	—
345	C₄⋊C₄	—	19	2	no	—
346	C₄⋊C₄	—	19	4	no	—
347	C₄⋊C₄	—	19	2	no	—
348	C₄⋊C₄	—	19	4	no	—
349	C₄⋊C₄	—	19	1	no	—
350	C₄⋊C₄	—	19	1	no	—
351	C₄⋊C₄	—	19	2	no	—
352	C₄⋊C₄	—	19	4	no	—
353	C₄⋊C₄	—	19	2	no	—
354	C₄⋊C₄	—	19	4	no	—
355	C₄⋊C₄	—	19	2	no	—
356	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
357	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
358	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
359	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
360	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
361	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
362	C₂²⋊C₄	—	19	2	no	—
363	C₂²⋊C₄	—	19	4	no	—
364	C₂²⋊C₄	—	19	2	no	—
365	C₂²⋊C₄	—	19	2	no	—
366	C₂²⋊C₄	—	19	4	no	—
367	C₂²⋊C₄	—	19	2	no	—
368	C₂²⋊C₄	—	19	4	no	—
369	C₂²⋊C₄	—	19	2	no	—
370	C₂²⋊C₄	—	19	2	no	—
371	C₂²⋊C₄	—	19	2	no	—
372	C₂²⋊C₄	—	19	4	no	—
373	C₂²⋊C₄	—	19	2	no	—
374	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
375	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
376	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
377	C₄²	—	19	1	no	—
378	C₄²	—	19	1	no	—
379	C₄²	—	19	1	no	—
380	C₄²	—	19	4	no	—
381	C₄²	C₂²×D₁₉	1	1	yes	characteristic
382	C₄²	C₂²×D₁₉	1	4	yes	—
383	C₄²	C₂²×D₁₉	1	2	yes	—
384	C₂³	—	19	1	no	—
385	C₂³	—	19	2	no	—
386	C₂³	—	19	2	no	—
387	C₂³	—	38	4	no	—
388	C₂³	—	38	4	no	—
389	C₂³	—	76	2	no	—
390	C₂³	C₂³×D₁₉	1	2	yes	—
391	Q₈	—	2	4	no	—
392	Q₈	—	2	2	no	—
393	Q₈	—	38	4	no	—
394	Q₈	—	76	4	no	—
395	D₄	—	2	2	no	—
396	D₄	—	19	4	no	—
397	D₄	—	38	8	no	—
398	D₄	—	38	4	no	—
399	D₄	—	38	4	no	—
400	D₄	—	38	2	no	—
401	D₄	—	76	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	19	1	no	—
404	C₂×C₄	—	19	1	no	—
405	C₂×C₄	—	19	1	no	—
406	C₂×C₄	—	19	4	no	—
407	C₂×C₄	—	19	2	no	—
408	C₂×C₄	—	19	2	no	—
409	C₂×C₄	—	38	8	no	—
410	C₂×C₄	—	38	2	no	—
411	C₂×C₄	—	38	2	no	—
412	C₂×C₄	—	38	4	no	—
413	C₂×C₄	—	38	2	no	—
414	C₂×C₄	—	38	4	no	—
415	C₂×C₄	—	76	2	no	—
416	C₂×C₄	—	76	2	no	—
417	C₂×C₄	—	76	4	no	—
418	C₂×C₄	—	76	4	no	—
419	C₂×C₄	—	76	2	no	—
420	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
421	C₂×C₄	C₂³×D₁₉	1	4	yes	—
422	C₂×C₄	C₂³×D₁₉	1	2	yes	—
423	C₂×C₄	C₂³×D₁₉	1	2	yes	—
424	C₂×C₄	C₂³×D₁₉	1	2	yes	—
425	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
426	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	19	4	no	—
431	C₂²	—	19	2	no	—
432	C₂²	—	38	1	no	—
433	C₂²	—	38	2	no	—
434	C₂²	—	38	1	no	—
435	C₂²	—	38	2	no	—
436	C₂²	—	38	2	no	—
437	C₂²	—	38	2	no	—
438	C₂²	—	38	2	no	—
439	C₂²	—	76	8	no	—
440	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
441	C₄	—	2	4	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	2	no	—
446	C₄	—	38	2	no	—
447	C₄	—	38	1	no	—
448	C₄	—	38	1	no	—
449	C₄	—	38	2	no	—
450	C₄	—	38	4	no	—
451	C₄	—	38	1	no	—
452	C₄	#41×D₁₉	1	2	yes	—
453	C₄	#10597435	1	2	yes	—
454	C₂	—	4	2	no	—
455	C₂	—	38	2	no	—
456	C₂	—	38	4	no	—
457	C₂	—	76	2	no	—
458	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
459	C₂	C₂×#10597435	1	1	yes	characteristic
460	C₂	2₋¹⁺⁴×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#556	C₂
hypercenter	#556	D₁₉
hypocenter	C₁₉	#3520
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #11927254	C₂	semidirect
2. #11927233	C₂	semidirect
3. #11927219	C₂	semidirect
4. Q₈×D₇₆	C₂	semidirect
5. #11927204	C₂	semidirect
6. #11927199	C₂	semidirect
7. #11927197	C₂	semidirect
8. #11927187	C₂	semidirect
9. #11927163	C₂	semidirect
10. #11927135	C₂	semidirect
11. #11927099	C₂	semidirect
12. #11927081	C₂	semidirect
13. #11927056	C₂	semidirect
14. C₂²⋊Q₈×D₁₉	C₂	semidirect
15. #11927026	C₂	semidirect
16. C₄×D₄×D₁₉	C₂	semidirect
17. C₁₉×#556	C₂	semidirect
19. C₂×Q₈×D₁₉	C₂²	semidirect
21. C₂×#64541	C₂²	semidirect
23. C₁₉×C₄⋊Q₈	C₂²	semidirect
24. C₁₉×#126	C₂²	semidirect
26. C₁₉×C₂²⋊Q₈	C₂²	semidirect
27. C₄×Q₈×C₁₉	C₂²	semidirect
28. C₄×Q₈×C₁₉	C₂²	semidirect
30. C₁₉×#117	C₂²	semidirect
31. #10597393	C₂²	semidirect
34. #10597392	C₂²	semidirect
35. Q₈×Dic₁₉	C₂²	semidirect
39. #10597370	C₂²	semidirect
40. #10597344	C₂²	semidirect
42. #10597343	C₂²	semidirect
43. #10597343	C₂²	semidirect
45. #10597342	C₂²	semidirect
47. #10597341	C₂²	semidirect
49. #10597340	C₂²	semidirect
51. #10597339	C₂²	semidirect
54. C₄⋊C₄×D₁₉	C₂²	semidirect
55. C₄⋊C₄×D₁₉	C₂²	semidirect
56. C₄⋊C₄×D₁₉	C₂²	semidirect
57. #10597336	C₂²	semidirect
58. #10597336	C₂²	semidirect
59. #10597333	C₂²	semidirect
60. #10597332	C₂²	semidirect
61. #10597331	C₂²	semidirect
64. #10597329	C₂²	semidirect
69. #10597325	C₂²	semidirect
70. #10597324	C₂²	semidirect
75. C₄×D₇₆	C₂²	semidirect
76. C₄×D₇₆	C₂²	semidirect
77. #10597318	C₂²	semidirect
78. #10597318	C₂²	semidirect
80. #10597316	C₂²	semidirect
81. #10597315	C₂²	semidirect
82. #10597315	C₂²	semidirect
183. D₇₆	#41	semidirect
224. #556	D₁₉	semidirect
255. C₄⋊Q₈	C₂×D₁₉	semidirect
258. #126	C₂×D₁₉	semidirect
280. C₂²⋊Q₈	C₂×D₁₉	semidirect
288. C₄×Q₈	C₂×D₁₉	semidirect
289. C₄×Q₈	C₂×D₁₉	semidirect
305. #117	C₂×D₁₉	semidirect
313. C₁₉	#3520	semidirect

Maximal subgroups

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

subgroup	index
#11927254	2
#11927233	2
#11927219	2
Q₈×D₇₆	2
#11927204	2
#11927199	2
#11927197	2
#11927187	2
#11927163	2
#11927135	2
#11927099	2
#11927081	2
#11927056	2
C₂²⋊Q₈×D₁₉	2
#11927026	2
C₄×D₄×D₁₉	2
C₁₉×#556	2
#3520	19