Subgroups — #14577322

Order 2432.

1328 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927225	C₂	1	4	yes	maximal, complemented
2	#11927220	C₂	1	4	yes	maximal, complemented
3	#11927188	C₂	1	4	yes	maximal, complemented
4	#11927181	C₂	1	4	yes	maximal, complemented
5	#11927170	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927129	C₂	1	4	yes	maximal, complemented
7	#11927103	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927050	C₂	1	4	yes	maximal, complemented
9	C₂×#10597399	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927019	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927017	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₂²⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₉×#120	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂⁵×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×D₄×C₁₉	C₂²	1	2	yes	complemented
17	C₂²×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
19	C₂³×Dic₁₉	C₂²	1	2	yes	complemented
20	C₂×#64543	C₂²	1	4	yes	complemented
21	C₁₉×#120	C₂²	1	4	yes	—
22	C₁₉×#120	C₂²	1	2	yes	complemented
23	C₁₉×#120	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	complemented
26	#10597399	C₂²	1	4	yes	—
27	#10597399	C₂²	1	2	yes	complemented
28	#10597399	C₂²	1	2	yes	complemented
29	#10597399	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	complemented
34	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	complemented
35	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	complemented
36	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	complemented
37	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	complemented
38	#10597385	C₂²	1	4	yes	complemented
39	#10597385	C₂²	1	4	yes	complemented
40	#10597385	C₂²	1	4	yes	complemented
41	#10597384	C₂²	1	4	yes	complemented
42	#10597383	C₂²	1	2	yes	complemented
43	#10597382	C₂²	1	4	yes	complemented
44	#10597381	C₂²	1	4	yes	complemented
45	#10597381	C₂²	1	4	yes	complemented
46	#10597381	C₂²	1	2	yes	complemented
47	D₄×Dic₁₉	C₂²	1	4	yes	complemented
48	D₄×Dic₁₉	C₂²	1	4	yes	complemented
49	D₄×Dic₁₉	C₂²	1	4	yes	complemented
50	#10597375	C₂²	1	2	yes	complemented
51	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
52	#10597372	C₂²	1	2	yes	complemented
53	#10597370	C₂²	1	4	yes	complemented
54	#10597332	C₂²	1	4	yes	complemented
55	#10597331	C₂²	1	4	yes	complemented
56	#10597329	C₂²	1	4	yes	complemented
57	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
58	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
59	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
60	#10597325	C₂²	1	4	yes	complemented
61	#10597325	C₂²	1	4	yes	complemented
62	#10597324	C₂²	1	4	yes	complemented
63	#10597324	C₂²	1	4	yes	complemented
64	#10597324	C₂²	1	4	yes	complemented
65	#10597323	C₂²	1	4	yes	complemented
66	#10597323	C₂²	1	2	yes	complemented
67	C₂⁴×C₁₉	—	2	4	no	—
68	C₂⁴×C₁₉	—	4	4	no	—
69	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
70	C₂⁴×C₁₉	C₂³	1	2	yes	—
71	C₂⁴×C₁₉	C₂³	1	2	yes	—
72	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
73	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
74	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
75	C₂³×D₁₉	C₂³	1	1	yes	characteristic
76	C₂×D₄×C₁₉	—	2	4	no	—
77	C₂×D₄×C₁₉	—	4	4	no	—
78	C₂×D₄×C₁₉	C₂³	1	2	yes	—
79	C₂×D₄×C₁₉	C₂³	1	2	yes	—
80	C₂×D₄×C₁₉	C₂³	1	4	yes	—
81	C₂×D₄×C₁₉	C₂³	1	4	yes	—
82	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
84	C₂×C₂²⋊D₁₉	—	2	4	no	—
85	C₂×C₂²⋊D₁₉	—	4	4	no	—
86	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
87	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
88	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	complemented
91	C₂²×Dic₁₉	—	4	4	no	—
92	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
93	C₂²×Dic₁₉	C₂³	1	4	yes	—
94	C₂²×Dic₁₉	C₂³	1	2	yes	—
95	C₂²×Dic₁₉	C₂³	1	2	yes	—
96	C₂²×Dic₁₉	C₂³	1	4	yes	—
97	C₂²×Dic₁₉	C₂³	1	2	yes	—
98	C₂²×Dic₁₉	C₂³	1	4	yes	complemented
99	#64543	—	4	8	no	—
100	C₂×C₄×D₁₉	C₂³	1	4	yes	complemented
101	C₂×Dic₃₈	C₂³	1	4	yes	complemented
102	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
103	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
104	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
105	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
106	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
107	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
108	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
109	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
110	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
111	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
112	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
113	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
114	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
115	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
116	C₂²⋊Dic₁₉	C₂³	1	4	yes	complemented
117	C₂²⋊Dic₁₉	C₂³	1	4	yes	complemented
118	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	complemented
119	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	complemented
120	C₄⋊Dic₁₉	C₂³	1	4	yes	complemented
121	C₄⋊Dic₁₉	C₂³	1	4	yes	complemented
122	Dic₁₉⋊C₄	C₂³	1	4	yes	complemented
123	Dic₁₉⋊C₄	C₂³	1	4	yes	complemented
124	Dic₁₉⋊C₄	C₂³	1	4	yes	complemented
125	Dic₁₉⋊C₄	C₂³	1	4	yes	complemented
126	C₄×Dic₁₉	C₂³	1	4	yes	complemented
127	C₄×Dic₁₉	C₂³	1	4	yes	complemented
128	C₂³×C₁₉	—	2	2	no	—
129	C₂³×C₁₉	—	2	4	no	—
130	C₂³×C₁₉	—	2	4	no	—
131	C₂³×C₁₉	—	2	4	no	—
132	C₂³×C₁₉	—	2	2	no	—
133	C₂³×C₁₉	—	2	4	no	—
134	C₂³×C₁₉	—	2	4	no	—
135	C₂³×C₁₉	—	2	2	no	—
136	C₂³×C₁₉	—	4	2	no	—
137	C₂³×C₁₉	—	4	2	no	—
138	C₂³×C₁₉	—	4	2	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	—	4	16	no	—
142	C₂³×C₁₉	#41	1	4	yes	complemented
143	C₂³×C₁₉	C₂⁴	1	2	yes	—
144	C₂³×C₁₉	C₂⁴	1	2	yes	—
145	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
146	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
147	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
148	C₂³×C₁₉	C₂⁴	1	2	yes	—
149	C₂²×D₁₉	—	2	2	no	—
150	C₂²×D₁₉	—	4	2	no	—
151	C₂²×D₁₉	C₂⁴	1	2	yes	—
152	D₄×C₁₉	—	2	4	no	—
153	D₄×C₁₉	—	2	4	no	—
154	D₄×C₁₉	—	2	8	no	—
155	D₄×C₁₉	—	4	4	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
159	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
160	C₂²⋊D₁₉	—	2	4	no	—
161	C₂²⋊D₁₉	—	2	4	no	—
162	C₂²⋊D₁₉	—	2	8	no	—
163	C₂²⋊D₁₉	—	4	4	no	—
164	C₂²⋊D₁₉	—	4	4	no	—
165	C₂×Dic₁₉	—	2	2	no	—
166	C₂×Dic₁₉	—	2	8	no	—
167	C₂×Dic₁₉	—	4	4	no	—
168	C₂×Dic₁₉	—	4	2	no	—
169	C₂×Dic₁₉	—	4	4	no	—
170	C₂×Dic₁₉	—	4	2	no	—
171	C₂×Dic₁₉	—	4	2	no	—
172	C₂×Dic₁₉	C₂⁴	1	2	yes	—
173	C₂×Dic₁₉	C₂⁴	1	4	yes	—
174	C₂×Dic₁₉	C₂⁴	1	4	yes	—
175	C₂×Dic₁₉	C₂⁴	1	4	yes	—
176	C₄×D₁₉	—	4	4	no	—
177	Dic₃₈	—	4	4	no	—
178	#3490	—	19	1	no	maximal, Sylow
179	C₂²×C₁₉	—	2	8	no	—
180	C₂²×C₁₉	—	2	2	no	—
181	C₂²×C₁₉	—	2	2	no	—
182	C₂²×C₁₉	—	2	2	no	—
183	C₂²×C₁₉	—	2	2	no	—
184	C₂²×C₁₉	—	2	2	no	—
185	C₂²×C₁₉	—	2	2	no	—
186	C₂²×C₁₉	—	2	2	no	—
187	C₂²×C₁₉	—	2	4	no	—
188	C₂²×C₁₉	—	2	2	no	—
189	C₂²×C₁₉	—	2	2	no	—
190	C₂²×C₁₉	—	4	4	no	—
191	C₂²×C₁₉	—	4	8	no	—
192	C₂²×C₁₉	—	4	8	no	—
193	C₂²×C₁₉	—	4	4	no	—
194	C₂²×C₁₉	—	8	2	no	—
195	C₂²×C₁₉	C₂×#41	1	2	yes	—
196	C₂²×C₁₉	C₂×#41	1	2	yes	—
197	C₂²×C₁₉	C₂×#41	1	2	yes	—
198	C₂²×C₁₉	H(5,𝔽₂)	1	4	yes	—
199	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
200	C₂×D₁₉	—	2	2	no	—
201	C₂×D₁₉	—	2	4	no	—
202	C₂×D₁₉	—	8	2	no	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	2	4	no	—
205	Dic₁₉	—	2	2	no	—
206	Dic₁₉	—	2	4	no	—
207	Dic₁₉	—	2	4	no	—
208	Dic₁₉	—	2	4	no	—
209	#551	—	19	4	no	—
210	#551	—	19	4	no	—
211	#546	—	19	4	no	—
212	#546	—	19	4	no	—
213	#543	—	19	1	no	—
214	#538	—	19	4	no	—
215	#534	—	19	1	no	—
216	#525	—	19	4	no	—
217	C₂×#120	—	19	1	no	—
218	C₂×#120	D₁₉	1	1	yes	characteristic, complemented
219	#518	—	19	1	no	—
220	#518	—	19	1	no	—
221	C₂²×C₂²⋊C₄	—	19	1	no	—
222	C₂×C₁₉	—	2	2	no	—
223	C₂×C₁₉	—	2	2	no	—
224	C₂×C₁₉	—	2	4	no	—
225	C₂×C₁₉	—	2	2	no	—
226	C₂×C₁₉	—	4	2	no	—
227	C₂×C₁₉	—	4	2	no	—
228	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
229	C₂×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
230	D₁₉	—	4	2	no	—
231	C₂⁵	C₂×D₁₉	1	1	yes	characteristic
232	C₂×#41	—	19	4	no	—
233	C₂²×D₄	—	19	1	no	—
234	C₂²×D₄	—	19	2	no	—
235	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
236	C₂²×D₄	C₂×D₁₉	1	2	yes	complemented
237	C₂³×C₄	—	19	2	no	—
238	#126	—	19	4	no	—
239	#126	—	19	4	no	—
240	#124	—	19	4	no	—
241	#124	—	19	4	no	—
242	#123	—	19	4	no	—
243	#123	—	19	2	no	—
244	#123	—	19	4	no	—
245	#123	—	19	2	no	—
246	#123	—	19	4	no	—
247	#123	—	19	4	no	—
248	C₂²⋊Q₈	—	19	4	no	—
249	C₂²⋊Q₈	—	19	4	no	—
250	C₂²⋊Q₈	—	19	4	no	—
251	C₂²⋊Q₈	—	19	4	no	—
252	#121	—	19	4	no	—
253	#121	—	19	4	no	—
254	#121	—	19	4	no	—
255	#121	—	19	4	no	—
256	#120	—	19	2	no	—
257	#120	—	19	4	no	—
258	#120	—	19	2	no	—
259	#120	—	19	2	no	—
260	#120	—	19	2	no	—
261	#120	C₂×D₁₉	1	4	yes	—
262	#120	C₂×D₁₉	1	2	yes	complemented
263	#120	C₂×D₁₉	1	2	yes	complemented
264	C₄×D₄	—	19	4	no	—
265	C₄×D₄	—	19	4	no	—
266	C₄×D₄	—	19	4	no	—
267	C₄×D₄	—	19	4	no	—
268	C₄×D₄	—	19	4	no	—
269	C₄×D₄	—	19	4	no	—
270	#117	—	19	2	no	—
271	#117	—	19	2	no	—
272	#117	—	19	4	no	—
273	C₂×C₂²⋊C₄	—	19	1	no	—
274	C₂×C₂²⋊C₄	—	19	1	no	—
275	C₂×C₂²⋊C₄	—	19	2	no	—
276	C₂×C₂²⋊C₄	—	19	4	no	—
277	C₂×C₂²⋊C₄	—	19	4	no	—
278	C₂×C₂²⋊C₄	—	19	1	no	—
279	C₂×C₂²⋊C₄	—	19	2	no	—
280	C₂×C₂²⋊C₄	—	19	2	no	—
281	C₂×C₂²⋊C₄	—	19	2	no	—
282	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	complemented
284	C₁₉	#3490	1	1	yes	characteristic, complemented, Sylow
285	C₂⁴	—	2	4	no	—
286	C₂⁴	—	4	4	no	—
287	C₂⁴	—	19	1	no	—
288	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
289	C₂⁴	C₂²×D₁₉	1	2	yes	—
290	C₂⁴	C₂²×D₁₉	1	2	yes	—
291	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
292	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
293	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
294	#41	—	76	8	no	—
295	C₂×Q₈	—	19	4	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	4	4	no	—
298	C₂×D₄	—	19	2	no	—
299	C₂×D₄	—	19	2	no	—
300	C₂×D₄	—	19	4	no	—
301	C₂×D₄	—	19	4	no	—
302	C₂×D₄	—	19	4	no	—
303	C₂×D₄	—	38	4	no	—
304	C₂×D₄	—	76	4	no	—
305	C₂×D₄	C₂²×D₁₉	1	2	yes	—
306	C₂×D₄	C₂²×D₁₉	1	2	yes	—
307	C₂×D₄	C₂²×D₁₉	1	4	yes	—
308	C₂×D₄	C₂²×D₁₉	1	4	yes	—
309	C₂²×C₄	—	19	1	no	—
310	C₂²×C₄	—	19	4	no	—
311	C₂²×C₄	—	19	2	no	—
312	C₂²×C₄	—	19	4	no	—
313	C₂²×C₄	—	19	2	no	—
314	C₂²×C₄	—	19	2	no	—
315	C₂²×C₄	—	19	4	no	—
316	C₂²×C₄	—	19	4	no	—
317	C₂²×C₄	—	76	4	no	—
318	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
320	C₄⋊C₄	—	19	4	no	—
321	C₄⋊C₄	—	19	4	no	—
322	C₄⋊C₄	—	19	4	no	—
323	C₄⋊C₄	—	19	4	no	—
324	C₄⋊C₄	—	19	4	no	—
325	C₄⋊C₄	—	19	4	no	—
326	C₂²⋊C₄	—	19	2	no	—
327	C₂²⋊C₄	—	19	2	no	—
328	C₂²⋊C₄	—	19	2	no	—
329	C₂²⋊C₄	—	19	2	no	—
330	C₂²⋊C₄	—	19	4	no	—
331	C₂²⋊C₄	—	19	4	no	—
332	C₂²⋊C₄	—	19	2	no	—
333	C₂²⋊C₄	—	19	4	no	—
334	C₂²⋊C₄	—	19	2	no	—
335	C₂²⋊C₄	—	19	4	no	—
336	C₂²⋊C₄	—	19	4	no	—
337	C₂²⋊C₄	—	19	4	no	—
338	C₂²⋊C₄	—	19	4	no	—
339	C₂²⋊C₄	—	19	4	no	—
340	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
341	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
342	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
343	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
344	C₄²	—	19	4	no	—
345	C₄²	—	19	4	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	4	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	16	no	—
360	C₂³	—	19	2	no	—
361	C₂³	—	38	2	no	—
362	C₂³	—	76	2	no	—
363	C₂³	#64543	1	4	yes	complemented
364	C₂³	C₂³×D₁₉	1	2	yes	—
365	C₂³	C₂³×D₁₉	1	2	yes	—
366	C₂³	C₂³×D₁₉	1	1	yes	characteristic
367	C₂³	C₂³×D₁₉	1	1	yes	characteristic
368	C₂³	C₂³×D₁₉	1	1	yes	characteristic
369	C₂³	C₂³×D₁₉	1	2	yes	—
370	Q₈	—	76	4	no	—
371	D₄	—	2	4	no	—
372	D₄	—	2	4	no	—
373	D₄	—	2	8	no	—
374	D₄	—	4	4	no	—
375	D₄	—	38	4	no	—
376	D₄	—	38	4	no	—
377	D₄	—	38	8	no	—
378	D₄	—	76	4	no	—
379	D₄	—	76	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	19	2	no	—
383	C₂×C₄	—	19	4	no	—
384	C₂×C₄	—	19	4	no	—
385	C₂×C₄	—	19	4	no	—
386	C₂×C₄	—	38	2	no	—
387	C₂×C₄	—	38	8	no	—
388	C₂×C₄	—	76	4	no	—
389	C₂×C₄	—	76	2	no	—
390	C₂×C₄	—	76	4	no	—
391	C₂×C₄	—	76	2	no	—
392	C₂×C₄	—	76	2	no	—
393	C₂×C₄	—	76	4	no	—
394	C₂×C₄	C₂³×D₁₉	1	2	yes	—
395	C₂×C₄	C₂³×D₁₉	1	4	yes	—
396	C₂²	—	2	8	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	8	no	—
409	C₂²	—	4	8	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	38	2	no	—
413	C₂²	—	38	4	no	—
414	C₂²	—	152	2	no	—
415	C₂²	C₂×#64543	1	2	yes	—
416	C₂²	C₂×#64543	1	2	yes	—
417	C₂²	C₂×#64543	1	2	yes	—
418	C₂²	#10597430	1	4	yes	—
419	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
420	C₄	—	2	2	no	—
421	C₄	—	2	4	no	—
422	C₄	—	38	2	no	—
423	C₄	—	38	4	no	—
424	C₄	—	38	4	no	—
425	C₄	—	38	4	no	—
426	C₂	—	2	2	no	—
427	C₂	—	2	4	no	—
428	C₂	—	2	2	no	—
429	C₂	—	2	2	no	—
430	C₂	—	4	2	no	—
431	C₂	—	4	2	no	—
432	C₂	—	76	2	no	—
433	C₂	C₂²×#64543	1	1	yes	characteristic
434	C₂	C₂×#10597430	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₂×C₁₉×#120	C₂
hypercenter	C₂×#120	D₁₉
hypocenter	C₁₉	#3490
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×#120

Complements

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

N	H ≅ G/N	type
1. #11927225	C₂	semidirect
2. #11927220	C₂	semidirect
3. #11927188	C₂	semidirect
4. #11927181	C₂	semidirect
5. #11927170	C₂	semidirect
6. #11927129	C₂	semidirect
7. #11927103	C₂	semidirect
8. #11927050	C₂	semidirect
9. C₂×#10597399	C₂	semidirect
10. #11927019	C₂	semidirect
11. #11927017	C₂	semidirect
12. C₂²×C₂²⋊Dic₁₉	C₂	semidirect
13. C₂×C₁₉×#120	C₂	semidirect
16. C₂²×D₄×C₁₉	C₂²	semidirect
18. C₂²×C₂²⋊D₁₉	C₂²	semidirect
19. C₂³×Dic₁₉	C₂²	semidirect
20. C₂×#64543	C₂²	semidirect
22. C₁₉×#120	C₂²	semidirect
23. C₁₉×#120	C₂²	semidirect
25. C₂×C₂²⋊C₄×C₁₉	C₂²	semidirect
27. #10597399	C₂²	semidirect
28. #10597399	C₂²	semidirect
29. #10597399	C₂²	semidirect
33. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
34. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
35. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
36. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
37. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
38. #10597385	C₂²	semidirect
39. #10597385	C₂²	semidirect
40. #10597385	C₂²	semidirect
41. #10597384	C₂²	semidirect
42. #10597383	C₂²	semidirect
43. #10597382	C₂²	semidirect
44. #10597381	C₂²	semidirect
45. #10597381	C₂²	semidirect
46. #10597381	C₂²	semidirect
47. D₄×Dic₁₉	C₂²	semidirect
48. D₄×Dic₁₉	C₂²	semidirect
49. D₄×Dic₁₉	C₂²	semidirect
50. #10597375	C₂²	semidirect
51. C₄×C₂²⋊D₁₉	C₂²	semidirect
52. #10597372	C₂²	semidirect
53. #10597370	C₂²	semidirect
54. #10597332	C₂²	semidirect
55. #10597331	C₂²	semidirect
56. #10597329	C₂²	semidirect
57. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
58. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
59. C₂²⋊C₄×D₁₉	C₂²	semidirect
60. #10597325	C₂²	semidirect
61. #10597325	C₂²	semidirect
62. #10597324	C₂²	semidirect
63. #10597324	C₂²	semidirect
64. #10597324	C₂²	semidirect
65. #10597323	C₂²	semidirect
66. #10597323	C₂²	semidirect
90. C₂×C₂²⋊D₁₉	C₂³	semidirect
98. C₂²×Dic₁₉	C₂³	semidirect
100. C₂×C₄×D₁₉	C₂³	semidirect
101. C₂×Dic₃₈	C₂³	semidirect
116. C₂²⋊Dic₁₉	C₂³	semidirect
117. C₂²⋊Dic₁₉	C₂³	semidirect
118. (C₂×D₁₉)⋊C₄	C₂³	semidirect
119. (C₂×D₁₉)⋊C₄	C₂³	semidirect
120. C₄⋊Dic₁₉	C₂³	semidirect
121. C₄⋊Dic₁₉	C₂³	semidirect
122. Dic₁₉⋊C₄	C₂³	semidirect
123. Dic₁₉⋊C₄	C₂³	semidirect
124. Dic₁₉⋊C₄	C₂³	semidirect
125. Dic₁₉⋊C₄	C₂³	semidirect
126. C₄×Dic₁₉	C₂³	semidirect
127. C₄×Dic₁₉	C₂³	semidirect
142. C₂³×C₁₉	#41	semidirect
218. C₂×#120	D₁₉	semidirect
236. C₂²×D₄	C₂×D₁₉	semidirect
262. #120	C₂×D₁₉	semidirect
263. #120	C₂×D₁₉	semidirect
283. C₂×C₂²⋊C₄	C₂×D₁₉	semidirect
284. C₁₉	#3490	semidirect
363. C₂³	#64543	semidirect

Maximal subgroups

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

subgroup	index
#11927225	2
#11927220	2
#11927188	2
#11927181	2
#11927170	2
#11927129	2
#11927103	2
#11927050	2
C₂×#10597399	2
#11927019	2
#11927017	2
C₂²×C₂²⋊Dic₁₉	2
C₂×C₁₉×#120	2
#3490	19