Group #18075159 — subgroups

Subgroups — #18075159

Order 4864.

2486 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 2486 conjugacy classes of subgroups — too many to draw. Only its 163 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563556	C₂	1	2	yes	maximal, complemented
2	#14561962	C₂	1	4	yes	maximal, complemented
3	C₂²×C₁₉×#120	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597290	—	2	4	no	—
5	#11926508	C₂²	1	4	yes	complemented
6	#11926268	—	2	8	no	—
7	C₂⁶×C₁₉	C₄	1	1	yes	characteristic
8	C₂³×D₄×C₁₉	C₄	1	2	yes	—
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#120	—	2	4	no	—
11	C₂×C₁₉×#120	—	2	8	no	—
12	C₂²×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic
13	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂⁵×C₁₉	—	2	2	no	—
15	C₂⁵×C₁₉	—	2	4	no	—
16	C₂⁵×C₁₉	—	4	4	no	—
17	C₂⁵×C₁₉	—	4	8	no	—
18	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂⁵×C₁₉	C₂×C₄	1	2	yes	—
20	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×D₄×C₁₉	—	2	4	no	—
22	C₂²×D₄×C₁₉	—	2	4	no	—
23	C₂²×D₄×C₁₉	—	2	4	no	—
24	C₂²×D₄×C₁₉	—	2	4	no	—
25	C₂²×D₄×C₁₉	—	4	4	no	—
26	C₂²×D₄×C₁₉	—	4	8	no	—
27	C₂²×D₄×C₁₉	D₄	1	4	yes	—
28	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₁₉×#120	—	2	32	no	—
31	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
32	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
33	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
34	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
35	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	—
36	C₂×#64520	—	2	4	no	—
37	#10597290	—	4	8	no	—
38	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
39	C₂⁴×C₁₉	—	2	4	no	—
40	C₂⁴×C₁₉	—	2	8	no	—
41	C₂⁴×C₁₉	—	2	2	no	—
42	C₂⁴×C₁₉	—	2	2	no	—
43	C₂⁴×C₁₉	—	2	2	no	—
44	C₂⁴×C₁₉	—	2	8	no	—
45	C₂⁴×C₁₉	—	2	2	no	—
46	C₂⁴×C₁₉	—	4	2	no	—
47	C₂⁴×C₁₉	—	4	4	no	—
48	C₂⁴×C₁₉	—	4	4	no	—
49	C₂⁴×C₁₉	—	4	4	no	—
50	C₂⁴×C₁₉	—	4	16	no	—
51	C₂⁴×C₁₉	—	4	16	no	—
52	C₂⁴×C₁₉	—	4	16	no	—
53	C₂⁴×C₁₉	—	4	4	no	—
54	C₂⁴×C₁₉	—	4	8	no	—
55	C₂⁴×C₁₉	—	4	4	no	—
56	C₂⁴×C₁₉	—	4	64	no	—
57	C₂⁴×C₁₉	—	4	4	no	—
58	C₂⁴×C₁₉	—	4	8	no	—
59	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
61	C₂⁴×C₁₉	C₂²⋊C₄	1	4	yes	—
62	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
63	C₂×D₄×C₁₉	—	2	16	no	—
64	C₂×D₄×C₁₉	—	2	8	no	—
65	C₂×D₄×C₁₉	—	2	8	no	—
66	C₂×D₄×C₁₉	—	4	4	no	—
67	C₂×D₄×C₁₉	—	4	16	no	—
68	C₂×D₄×C₁₉	—	4	16	no	—
69	C₂×D₄×C₁₉	—	4	8	no	—
70	C₂×D₄×C₁₉	—	4	16	no	—
71	C₂×D₄×C₁₉	—	4	8	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	4	2	no	—
75	C₂²×C₄×C₁₉	—	4	4	no	—
76	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
77	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
78	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
79	C₂²⋊C₄×C₁₉	—	2	8	no	—
80	C₂²⋊C₄×C₁₉	—	2	16	no	—
81	#64520	—	4	8	no	—
82	C₂×C₁₉⋊C₈	—	4	4	no	—
83	#8547	—	19	1	no	maximal, Sylow
84	C₂³×C₁₉	—	2	2	no	—
85	C₂³×C₁₉	—	2	4	no	—
86	C₂³×C₁₉	—	2	8	no	—
87	C₂³×C₁₉	—	2	8	no	—
88	C₂³×C₁₉	—	2	8	no	—
89	C₂³×C₁₉	—	2	2	no	—
90	C₂³×C₁₉	—	2	4	no	—
91	C₂³×C₁₉	—	2	2	no	—
92	C₂³×C₁₉	—	2	4	no	—
93	C₂³×C₁₉	—	2	2	no	—
94	C₂³×C₁₉	—	2	4	no	—
95	C₂³×C₁₉	—	4	4	no	—
96	C₂³×C₁₉	—	4	4	no	—
97	C₂³×C₁₉	—	4	4	no	—
98	C₂³×C₁₉	—	4	16	no	—
99	C₂³×C₁₉	—	4	32	no	—
100	C₂³×C₁₉	—	4	4	no	—
101	C₂³×C₁₉	—	4	4	no	—
102	C₂³×C₁₉	—	4	4	no	—
103	C₂³×C₁₉	—	4	16	no	—
104	C₂³×C₁₉	—	4	32	no	—
105	C₂³×C₁₉	—	4	4	no	—
106	C₂³×C₁₉	—	4	4	no	—
107	C₂³×C₁₉	—	4	4	no	—
108	C₂³×C₁₉	—	4	32	no	—
109	C₂³×C₁₉	—	4	64	no	—
110	C₂³×C₁₉	—	4	32	no	—
111	C₂³×C₁₉	—	4	64	no	—
112	C₂³×C₁₉	—	4	4	no	—
113	C₂³×C₁₉	—	4	4	no	—
114	C₂³×C₁₉	—	4	4	no	—
115	C₂³×C₁₉	—	4	4	no	—
116	C₂³×C₁₉	—	8	8	no	—
117	C₂³×C₁₉	#99	1	4	yes	—
118	C₂³×C₁₉	#100	1	8	yes	complemented
119	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
121	D₄×C₁₉	—	4	16	no	—
122	D₄×C₁₉	—	4	32	no	—
123	C₂×C₄×C₁₉	—	2	4	no	—
124	C₂×C₄×C₁₉	—	2	4	no	—
125	C₂×C₄×C₁₉	—	4	4	no	—
126	C₂×C₄×C₁₉	—	4	4	no	—
127	C₂×C₄×C₁₉	—	4	4	no	—
128	C₂×C₄×C₁₉	—	4	4	no	—
129	C₂×C₄×C₁₉	#120	1	4	yes	—
130	C₁₉⋊C₈	—	8	4	no	—
131	C₂²×#120	D₁₉	1	1	yes	characteristic
132	#1783	—	19	2	no	—
133	#1462	—	19	4	no	—
134	C₂²×C₁₉	—	2	8	no	—
135	C₂²×C₁₉	—	2	2	no	—
136	C₂²×C₁₉	—	2	2	no	—
137	C₂²×C₁₉	—	2	2	no	—
138	C₂²×C₁₉	—	2	4	no	—
139	C₂²×C₁₉	—	2	8	no	—
140	C₂²×C₁₉	—	4	4	no	—
141	C₂²×C₁₉	—	4	8	no	—
142	C₂²×C₁₉	—	4	16	no	—
143	C₂²×C₁₉	—	4	4	no	—
144	C₂²×C₁₉	—	4	16	no	—
145	C₂²×C₁₉	—	4	16	no	—
146	C₂²×C₁₉	—	4	8	no	—
147	C₂²×C₁₉	—	4	64	no	—
148	C₂²×C₁₉	—	4	4	no	—
149	C₂²×C₁₉	—	4	4	no	—
150	C₂²×C₁₉	—	4	4	no	—
151	C₂²×C₁₉	—	4	2	no	—
152	C₂²×C₁₉	—	4	4	no	—
153	C₂²×C₁₉	—	8	4	no	—
154	C₂²×C₁₉	—	8	8	no	—
155	C₂²×C₁₉	#379	1	1	yes	characteristic
156	C₂²×C₁₉	C₂×#99	1	2	yes	—
157	C₂²×C₁₉	C₂×#100	1	4	yes	—
158	C₄×C₁₉	—	2	4	no	—
159	C₄×C₁₉	—	4	4	no	—
160	C₂⁶	Dic₁₉	1	1	yes	characteristic
161	C₂³×D₄	Dic₁₉	1	2	yes	—
162	C₂³×D₄	C₂×D₁₉	1	1	yes	characteristic
163	C₂×#120	—	2	4	no	—
164	C₂×#120	—	2	8	no	—
165	C₂²×C₂²⋊C₄	Dic₁₉	1	1	yes	characteristic
166	C₂²×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
167	C₂×#100	—	38	4	no	—
168	#407	—	19	4	no	—
169	#323	—	38	8	no	—
170	C₂×C₁₉	—	2	2	no	—
171	C₂×C₁₉	—	2	4	no	—
172	C₂×C₁₉	—	4	4	no	—
173	C₂×C₁₉	—	4	8	no	—
174	C₂×C₁₉	—	8	2	no	—
175	C₂×C₁₉	#1781	1	1	yes	characteristic
176	C₂×C₁₉	#1783	1	2	yes	—
177	C₂⁵	—	2	4	no	—
178	C₂⁵	—	2	2	no	—
179	C₂⁵	—	4	8	no	—
180	C₂⁵	—	4	4	no	—
181	C₂⁵	C₂×Dic₁₉	1	1	yes	characteristic
182	C₂⁵	C₂×Dic₁₉	1	2	yes	—
183	C₂⁵	C₂×Dic₁₉	1	1	yes	characteristic
184	C₂²×D₄	—	2	4	no	—
185	C₂²×D₄	—	2	4	no	—
186	C₂²×D₄	—	2	4	no	—
187	C₂²×D₄	—	2	4	no	—
188	C₂²×D₄	—	4	4	no	—
189	C₂²×D₄	—	4	8	no	—
190	C₂²×D₄	C₂²⋊D₁₉	1	4	yes	—
191	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
192	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
193	C₂×M₁₆	—	38	4	no	—
194	#120	—	2	32	no	—
195	C₂×C₂²⋊C₄	—	2	2	no	—
196	C₂×C₂²⋊C₄	—	2	4	no	—
197	C₂×C₂²⋊C₄	—	2	4	no	—
198	C₂×C₂²⋊C₄	—	2	4	no	—
199	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	8	yes	—
200	#100	—	76	8	no	—
201	C₂²⋊C₈	—	38	8	no	—
202	C₁₉	#8547	1	1	yes	characteristic, complemented, Sylow
203	C₂⁴	—	2	2	no	—
204	C₂⁴	—	2	2	no	—
205	C₂⁴	—	2	2	no	—
206	C₂⁴	—	2	8	no	—
207	C₂⁴	—	2	4	no	—
208	C₂⁴	—	2	8	no	—
209	C₂⁴	—	2	2	no	—
210	C₂⁴	—	4	2	no	—
211	C₂⁴	—	4	4	no	—
212	C₂⁴	—	4	4	no	—
213	C₂⁴	—	4	4	no	—
214	C₂⁴	—	4	16	no	—
215	C₂⁴	—	4	16	no	—
216	C₂⁴	—	4	16	no	—
217	C₂⁴	—	4	4	no	—
218	C₂⁴	—	4	8	no	—
219	C₂⁴	—	4	4	no	—
220	C₂⁴	—	4	64	no	—
221	C₂⁴	—	4	8	no	—
222	C₂⁴	—	4	4	no	—
223	C₂⁴	C₂²⋊Dic₁₉	1	2	yes	—
224	C₂⁴	C₂²⋊Dic₁₉	1	4	yes	—
225	C₂⁴	C₂²⋊Dic₁₉	1	2	yes	—
226	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
227	C₂×D₄	—	2	16	no	—
228	C₂×D₄	—	2	8	no	—
229	C₂×D₄	—	2	8	no	—
230	C₂×D₄	—	4	4	no	—
231	C₂×D₄	—	4	16	no	—
232	C₂×D₄	—	4	16	no	—
233	C₂×D₄	—	4	8	no	—
234	C₂×D₄	—	4	16	no	—
235	C₂×D₄	—	4	8	no	—
236	C₂²×C₄	—	2	2	no	—
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	4	2	no	—
239	C₂²×C₄	—	4	4	no	—
240	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
241	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
242	C₂²×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
243	M₁₆	—	76	8	no	—
244	C₂×C₈	—	76	4	no	—
245	C₂²⋊C₄	—	2	8	no	—
246	C₂²⋊C₄	—	2	16	no	—
247	C₂³	—	2	2	no	—
248	C₂³	—	2	4	no	—
249	C₂³	—	2	8	no	—
250	C₂³	—	2	8	no	—
251	C₂³	—	2	8	no	—
252	C₂³	—	2	2	no	—
253	C₂³	—	2	4	no	—
254	C₂³	—	2	2	no	—
255	C₂³	—	2	4	no	—
256	C₂³	—	2	2	no	—
257	C₂³	—	2	4	no	—
258	C₂³	—	4	4	no	—
259	C₂³	—	4	4	no	—
260	C₂³	—	4	4	no	—
261	C₂³	—	4	32	no	—
262	C₂³	—	4	16	no	—
263	C₂³	—	4	4	no	—
264	C₂³	—	4	4	no	—
265	C₂³	—	4	4	no	—
266	C₂³	—	4	16	no	—
267	C₂³	—	4	32	no	—
268	C₂³	—	4	4	no	—
269	C₂³	—	4	4	no	—
270	C₂³	—	4	4	no	—
271	C₂³	—	4	64	no	—
272	C₂³	—	4	32	no	—
273	C₂³	—	4	32	no	—
274	C₂³	—	4	64	no	—
275	C₂³	—	4	4	no	—
276	C₂³	—	4	4	no	—
277	C₂³	—	4	4	no	—
278	C₂³	—	4	4	no	—
279	C₂³	—	8	8	no	—
280	C₂³	#10597290	1	8	yes	complemented
281	C₂³	#10597291	1	4	yes	—
282	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
283	C₂³	C₂×C₂²⋊Dic₁₉	1	2	yes	—
284	D₄	—	4	16	no	—
285	D₄	—	4	32	no	—
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	4	4	no	—
289	C₂×C₄	—	4	4	no	—
290	C₂×C₄	—	4	4	no	—
291	C₂×C₄	—	4	4	no	—
292	C₂×C₄	#10597399	1	4	yes	—
293	C₈	—	152	4	no	—
294	C₂²	—	2	8	no	—
295	C₂²	—	2	2	no	—
296	C₂²	—	2	2	no	—
297	C₂²	—	2	2	no	—
298	C₂²	—	2	4	no	—
299	C₂²	—	2	8	no	—
300	C₂²	—	4	8	no	—
301	C₂²	—	4	4	no	—
302	C₂²	—	4	16	no	—
303	C₂²	—	4	4	no	—
304	C₂²	—	4	16	no	—
305	C₂²	—	4	16	no	—
306	C₂²	—	4	8	no	—
307	C₂²	—	4	64	no	—
308	C₂²	—	4	4	no	—
309	C₂²	—	4	4	no	—
310	C₂²	—	4	4	no	—
311	C₂²	—	4	2	no	—
312	C₂²	—	4	4	no	—
313	C₂²	—	8	4	no	—
314	C₂²	—	8	8	no	—
315	C₂²	#11926400	1	1	yes	characteristic
316	C₂²	C₂×#10597291	1	2	yes	—
317	C₂²	C₂×#10597290	1	4	yes	—
318	C₄	—	2	4	no	—
319	C₄	—	4	4	no	—
320	C₂	—	2	2	no	—
321	C₂	—	2	4	no	—
322	C₂	—	4	4	no	—
323	C₂	—	4	8	no	—
324	C₂	—	8	2	no	—
325	C₂	#14563550	1	1	yes	characteristic
326	C₂	#14563556	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563556

C₂

yes

maximal, complemented

#14561962

C₂

yes

maximal, complemented

C₂²×C₁₉×#120

C₂

yes

maximal, characteristic

C₂×#10597290

—

#11926508

C₂²

yes

complemented

#11926268

—

C₂⁶×C₁₉

C₄

yes

characteristic

C₂³×D₄×C₁₉

C₄

yes

—

C₂³×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#120

—

C₂×C₁₉×#120

—

C₂²×C₂²⋊C₄×C₁₉

C₄

yes

characteristic

C₂²×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂⁵×C₁₉

—

C₂⁵×C₁₉

—

C₂⁵×C₁₉

—

C₂⁵×C₁₉

—

C₂⁵×C₁₉

C₂×C₄

yes

characteristic

C₂⁵×C₁₉

C₂×C₄

yes

—

C₂⁵×C₁₉

C₂×C₄

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₁₉×#120

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₂×#64520

—

#10597290

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

#8547

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

100

C₂³×C₁₉

—

101

C₂³×C₁₉

—

102

C₂³×C₁₉

—

103

C₂³×C₁₉

—

104

C₂³×C₁₉

—

105

C₂³×C₁₉

—

106

C₂³×C₁₉

—

107

C₂³×C₁₉

—

108

C₂³×C₁₉

—

109

C₂³×C₁₉

—

110

C₂³×C₁₉

—

111

C₂³×C₁₉

—

112

C₂³×C₁₉

—

113

C₂³×C₁₉

—

114

C₂³×C₁₉

—

115

C₂³×C₁₉

—

116

C₂³×C₁₉

—

117

C₂³×C₁₉

#99

yes

—

118

C₂³×C₁₉

#100

yes

complemented

119

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

120

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

—

121

D₄×C₁₉

—

122

D₄×C₁₉

—

123

C₂×C₄×C₁₉

—

124

C₂×C₄×C₁₉

—

125

C₂×C₄×C₁₉

—

126

C₂×C₄×C₁₉

—

127

C₂×C₄×C₁₉

—

128

C₂×C₄×C₁₉

—

129

C₂×C₄×C₁₉

#120

yes

—

130

C₁₉⋊C₈

—

131

C₂²×#120

D₁₉

yes

characteristic

132

#1783

—

133

#1462

—

134

C₂²×C₁₉

—

135

C₂²×C₁₉

—

136

C₂²×C₁₉

—

137

C₂²×C₁₉

—

138

C₂²×C₁₉

—

139

C₂²×C₁₉

—

140

C₂²×C₁₉

—

141

C₂²×C₁₉

—

142

C₂²×C₁₉

—

143

C₂²×C₁₉

—

144

C₂²×C₁₉

—

145

C₂²×C₁₉

—

146

C₂²×C₁₉

—

147

C₂²×C₁₉

—

148

C₂²×C₁₉

—

149

C₂²×C₁₉

—

150

C₂²×C₁₉

—

151

C₂²×C₁₉

—

152

C₂²×C₁₉

—

153

C₂²×C₁₉

—

154

C₂²×C₁₉

—

155

C₂²×C₁₉

#379

yes

characteristic

156

C₂²×C₁₉

C₂×#99

yes

—

157

C₂²×C₁₉

C₂×#100

yes

—

158

C₄×C₁₉

—

159

C₄×C₁₉

—

160

C₂⁶

Dic₁₉

yes

characteristic

161

C₂³×D₄

Dic₁₉

yes

—

162

C₂³×D₄

C₂×D₁₉

yes

characteristic

163

C₂×#120

—

164

C₂×#120

—

165

C₂²×C₂²⋊C₄

Dic₁₉

yes

characteristic

166

C₂²×C₂²⋊C₄

C₂×D₁₉

yes

—

167

C₂×#100

—

168

#407

—

169

#323

—

170

C₂×C₁₉

—

171

C₂×C₁₉

—

172

C₂×C₁₉

—

173

C₂×C₁₉

—

174

C₂×C₁₉

—

175

C₂×C₁₉

#1781

yes

characteristic

176

C₂×C₁₉

#1783

yes

—

177

C₂⁵

—

178

C₂⁵

—

179

C₂⁵

—

180

C₂⁵

—

181

C₂⁵

C₂×Dic₁₉

yes

characteristic

182

C₂⁵

C₂×Dic₁₉

yes

—

183

C₂⁵

C₂×Dic₁₉

yes

characteristic

184

C₂²×D₄

—

185

C₂²×D₄

—

186

C₂²×D₄

—

187

C₂²×D₄

—

188

C₂²×D₄

—

189

C₂²×D₄

—

190

C₂²×D₄

C₂²⋊D₁₉

yes

—

191

C₂³×C₄

C₂×Dic₁₉

yes

—

192

C₂³×C₄

C₂²×D₁₉

yes

characteristic

193

C₂×M₁₆

—

194

#120

—

195

C₂×C₂²⋊C₄

—

196

C₂×C₂²⋊C₄

—

197

C₂×C₂²⋊C₄

—

198

C₂×C₂²⋊C₄

—

199

C₂×C₂²⋊C₄

C₂²⋊D₁₉

yes

—

200

#100

—

201

C₂²⋊C₈

—

202

C₁₉

#8547

yes

characteristic, complemented, Sylow

203

C₂⁴

—

204

C₂⁴

—

205

C₂⁴

—

206

C₂⁴

—

207

C₂⁴

—

208

C₂⁴

—

209

C₂⁴

—

210

C₂⁴

—

211

C₂⁴

—

212

C₂⁴

—

213

C₂⁴

—

214

C₂⁴

—

215

C₂⁴

—

216

C₂⁴

—

217

C₂⁴

—

218

C₂⁴

—

219

C₂⁴

—

220

C₂⁴

—

221

C₂⁴

—

222

C₂⁴

—

223

C₂⁴

C₂²⋊Dic₁₉

yes

—

224

C₂⁴

C₂²⋊Dic₁₉

yes

—

225

C₂⁴

C₂²⋊Dic₁₉

yes

—

226

C₂⁴

C₂²×Dic₁₉

yes

characteristic

227

C₂×D₄

—

228

C₂×D₄

—

229

C₂×D₄

—

230

C₂×D₄

—

231

C₂×D₄

—

232

C₂×D₄

—

233

C₂×D₄

—

234

C₂×D₄

—

235

C₂×D₄

—

236

C₂²×C₄

—

237

C₂²×C₄

—

238

C₂²×C₄

—

239

C₂²×C₄

—

240

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

241

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

242

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

243

M₁₆

—

244

C₂×C₈

—

245

C₂²⋊C₄

—

246

C₂²⋊C₄

—

247

C₂³

—

248

C₂³

—

249

C₂³

—

250

C₂³

—

251

C₂³

—

252

C₂³

—

253

C₂³

—

254

C₂³

—

255

C₂³

—

256

C₂³

—

257

C₂³

—

258

C₂³

—

259

C₂³

—

260

C₂³

—

261

C₂³

—

262

C₂³

—

263

C₂³

—

264

C₂³

—

265

C₂³

—

266

C₂³

—

267

C₂³

—

268

C₂³

—

269

C₂³

—

270

C₂³

—

271

C₂³

—

272

C₂³

—

273

C₂³

—

274

C₂³

—

275

C₂³

—

276

C₂³

—

277

C₂³

—

278

C₂³

—

279

C₂³

—

280

C₂³

#10597290

yes

complemented

281

C₂³

#10597291

yes

—

282

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

283

C₂³

C₂×C₂²⋊Dic₁₉

yes

—

284

D₄

—

285

D₄

—

286

C₂×C₄

—

287

C₂×C₄

—

288

C₂×C₄

—

289

C₂×C₄

—

290

C₂×C₄

—

291

C₂×C₄

—

292

C₂×C₄

#10597399

yes

—

293

C₈

—

152

—

294

C₂²

—

295

C₂²

—

296

C₂²

—

297

C₂²

—

298

C₂²

—

299

C₂²

—

300

C₂²

—

301

C₂²

—

302

C₂²

—

303

C₂²

—

304

C₂²

—

305

C₂²

—

306

C₂²

—

307

C₂²

—

308

C₂²

—

309

C₂²

—

310

C₂²

—

311

C₂²

—

312

C₂²

—

313

C₂²

—

314

C₂²

—

315

C₂²

#11926400

yes

characteristic

316

C₂²

C₂×#10597291

yes

—

317

C₂²

C₂×#10597290

yes

—

318

C₄

—

319

C₄

—

320

C₂

—

321

C₂

—

322

C₂

—

323

C₂

—

324

C₂

—

325

C₂

#14563550

yes

characteristic

326

C₂

#14563556

yes

—

	subgroup	G/H
center	C₂²	#11926400
commutator	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting, prime radical	C₂²×C₁₉×#120	C₂
socle	C₂²×C₁₉	#379
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×#120	D₁₉
hypocenter	C₁₉	#8547
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×#120

subgroup

G/H

center

C₂²

#11926400

commutator

C₂⁴×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting, prime radical

C₂²×C₁₉×#120

C₂

socle

C₂²×C₁₉

#379

cosocle

C₂³×C₄×C₁₉

C₂³

hypercenter

C₂²×#120

D₁₉

hypocenter

C₁₉

#8547

LCS

G ▷ C₂⁴×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×#120

N	H ≅ G/N	type
1. #14563556	C₂	semidirect
2. #14561962	C₂	semidirect
5. #11926508	C₂²	semidirect
118. C₂³×C₁₉	#100	semidirect
202. C₁₉	#8547	semidirect
280. C₂³	#10597290	semidirect

H ≅ G/N

type

1. #14563556

C₂

semidirect

2. #14561962

C₂

semidirect

5. #11926508

C₂²

semidirect

118. C₂³×C₁₉

#100

semidirect

202. C₁₉

#8547

semidirect

280. C₂³

#10597290

semidirect

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

subgroup	index
#14563556	2
#14561962	2
C₂²×C₁₉×#120	2
#8547	19

subgroup

index

#14563556

#14561962

C₂²×C₁₉×#120

#8547

Subgroups — #18075159

Conjugacy classes of subgroups

Complements

Maximal subgroups