Group #18069535 — subgroups

Subgroups — #18069535

Order 4864.

364 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 95 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	#14563928	C₂	1	1	yes	maximal, characteristic
2	#14561953	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉×#100	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₁₉⋊C₈	C₄	1	1	yes	characteristic
5	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
6	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
7	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	1	yes	characteristic
8	#11926299	—	2	1	no	—
9	#11926270	—	2	1	no	—
10	#11926268	C₄	1	2	yes	—
11	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#100	C₄	1	2	yes	—
13	C₄×M₁₆×C₁₉	—	2	1	no	—
14	C₁₉×#343	—	2	1	no	—
15	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
18	C₂×M₁₆×C₁₉	—	2	2	no	—
19	C₄×D₄×C₁₉	—	4	1	no	—
20	C₄×D₄×C₁₉	—	4	1	no	—
21	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₂²⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×C₁₉⋊C₈	—	2	1	no	—
26	C₂²×C₁₉⋊C₈	—	2	1	no	—
27	C₂²×C₁₉⋊C₈	—	4	2	no	—
28	C₂²×C₁₉⋊C₈	—	4	1	no	—
29	C₂²×C₁₉⋊C₈	—	4	1	no	—
30	C₁₉×#100	—	2	2	no	—
31	C₁₉×#100	C₈	1	4	yes	complemented
32	C₁₉×#97	—	4	1	no	—
33	C₄×C₈×C₁₉	—	4	1	no	—
34	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
35	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
36	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
37	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
38	C₂⁴×C₁₉	C₄²	1	1	yes	characteristic
39	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
40	C₂×D₄×C₁₉	—	4	1	no	—
41	C₂×D₄×C₁₉	—	4	1	no	—
42	C₂×D₄×C₁₉	C₂×C₈	1	2	yes	—
43	C₂×D₄×C₁₉	M₁₆	1	2	yes	—
44	C₂²×C₄×C₁₉	—	2	1	no	—
45	C₂²×C₄×C₁₉	—	2	1	no	—
46	C₂²×C₄×C₁₉	—	2	1	no	—
47	C₂²×C₄×C₁₉	—	2	1	no	—
48	C₂²×C₄×C₁₉	—	4	1	no	—
49	C₂²×C₄×C₁₉	—	4	1	no	—
50	C₂²×C₄×C₁₉	—	4	1	no	—
51	C₂²×C₄×C₁₉	—	4	1	no	—
52	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
57	M₁₆×C₁₉	—	2	4	no	—
58	M₁₆×C₁₉	—	4	2	no	—
59	C₂×C₈×C₁₉	—	4	2	no	—
60	C₄⋊C₄×C₁₉	—	4	1	no	—
61	C₂²⋊C₄×C₁₉	—	4	1	no	—
62	C₂²⋊C₄×C₁₉	—	4	1	no	—
63	C₄²×C₁₉	—	2	1	no	—
64	C₄²×C₁₉	—	2	1	no	—
65	C₂×C₁₉⋊C₈	—	2	2	no	—
66	C₂×C₁₉⋊C₈	—	4	1	no	—
67	C₂×C₁₉⋊C₈	—	4	2	no	—
68	C₂×C₁₉⋊C₈	—	4	1	no	—
69	C₂×C₁₉⋊C₈	—	4	2	no	—
70	C₂×C₁₉⋊C₈	—	4	2	no	—
71	C₂×C₁₉⋊C₈	—	4	1	no	—
72	C₂×C₁₉⋊C₈	—	4	1	no	—
73	C₂×C₁₉⋊C₈	—	4	1	no	—
74	C₂×C₁₉⋊C₈	—	8	1	no	—
75	C₂×C₁₉⋊C₈	—	8	1	no	—
76	#7203	—	19	1	no	maximal, Sylow
77	C₂³×C₁₉	—	2	1	no	—
78	C₂³×C₁₉	—	2	1	no	—
79	C₂³×C₁₉	—	2	1	no	—
80	C₂³×C₁₉	—	2	1	no	—
81	C₂³×C₁₉	—	4	1	no	—
82	C₂³×C₁₉	—	4	1	no	—
83	C₂³×C₁₉	—	4	1	no	—
84	C₂³×C₁₉	—	4	1	no	—
85	C₂³×C₁₉	#95	1	1	yes	characteristic
86	C₂³×C₁₉	C₄×C₈	1	1	yes	characteristic
87	C₂³×C₁₉	#97	1	1	yes	characteristic
88	C₂³×C₁₉	C₄⋊C₈	1	2	yes	—
89	D₄×C₁₉	—	4	2	no	—
90	D₄×C₁₉	—	4	2	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	2	1	no	—
96	C₂×C₄×C₁₉	—	2	1	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	4	2	no	—
99	C₂×C₄×C₁₉	—	4	1	no	—
100	C₂×C₄×C₁₉	—	4	1	no	—
101	C₂×C₄×C₁₉	—	4	1	no	—
102	C₂×C₄×C₁₉	—	4	1	no	—
103	C₂×C₄×C₁₉	—	4	1	no	—
104	C₂×C₄×C₁₉	—	4	1	no	—
105	C₂×C₄×C₁₉	—	4	1	no	—
106	C₂×C₄×C₁₉	—	8	1	no	—
107	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
108	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
109	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
110	C₈×C₁₉	—	4	4	no	—
111	C₁₉⋊C₈	—	4	2	no	—
112	C₁₉⋊C₈	—	8	1	no	—
113	C₁₉⋊C₈	—	8	2	no	—
114	#1869	—	19	1	no	—
115	C₄×#100	D₁₉	1	1	yes	characteristic
116	#1459	—	19	1	no	—
117	C₂²×C₁₉	—	2	1	no	—
118	C₂²×C₁₉	—	2	1	no	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	—	2	2	no	—
122	C₂²×C₁₉	—	4	1	no	—
123	C₂²×C₁₉	—	4	1	no	—
124	C₂²×C₁₉	—	4	2	no	—
125	C₂²×C₁₉	—	4	2	no	—
126	C₂²×C₁₉	—	4	1	no	—
127	C₂²×C₁₉	—	4	1	no	—
128	C₂²×C₁₉	—	4	1	no	—
129	C₂²×C₁₉	—	4	1	no	—
130	C₂²×C₁₉	—	8	1	no	—
131	C₂²×C₁₉	#336	1	1	yes	characteristic
132	C₂²×C₁₉	#342	1	1	yes	characteristic
133	C₂²×C₁₉	#344	1	1	yes	characteristic
134	C₄×C₁₉	—	2	2	no	—
135	C₄×C₁₉	—	2	1	no	—
136	C₄×C₁₉	—	4	1	no	—
137	C₄×C₁₉	—	4	1	no	—
138	C₄×C₁₉	—	4	1	no	—
139	C₄×C₁₉	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
140	C₄×C₁₉	#352	1	1	yes	characteristic
141	C₂³×C₈	—	19	1	no	—
142	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
143	C₂×#100	Dic₁₉	1	2	yes	—
144	C₂×C₂²⋊C₈	—	19	1	no	—
145	C₂×C₂²⋊C₈	—	38	1	no	—
146	C₂×C₂²⋊C₈	—	38	1	no	—
147	C₄×M₁₆	—	2	1	no	—
148	#343	—	2	1	no	—
149	#336	—	38	1	no	—
150	#324	—	38	1	no	—
151	#323	—	19	2	no	—
152	C₂×C₁₉	—	2	1	no	—
153	C₂×C₁₉	—	2	1	no	—
154	C₂×C₁₉	—	4	1	no	—
155	C₂×C₁₉	—	4	1	no	—
156	C₂×C₁₉	—	4	2	no	—
157	C₂×C₁₉	#1282	1	1	yes	characteristic
158	C₂×C₁₉	#1390	1	1	yes	characteristic
159	C₂×C₁₉	#1392	1	1	yes	characteristic
160	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
161	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
162	C₂³×C₄	D₇₆	1	1	yes	characteristic
163	C₂×M₁₆	—	2	2	no	—
164	C₂²×C₈	—	38	1	no	—
165	C₂²×C₈	—	38	1	no	—
166	C₂²×C₈	—	76	2	no	—
167	C₂²×C₈	—	76	1	no	—
168	C₂²×C₈	—	76	1	no	—
169	C₄×D₄	—	4	1	no	—
170	C₄×D₄	—	4	1	no	—
171	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
172	C₂×C₂²⋊C₄	Dic₃₈	1	1	yes	characteristic
173	C₂×C₂²⋊C₄	C₄×D₁₉	1	1	yes	characteristic
174	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
175	#100	—	2	2	no	—
176	#100	C₁₉⋊C₈	1	4	yes	complemented
177	C₂²⋊C₈	—	38	2	no	—
178	C₂²⋊C₈	—	76	2	no	—
179	C₂²⋊C₈	—	76	1	no	—
180	C₂²⋊C₈	—	76	1	no	—
181	#97	—	4	1	no	—
182	C₄×C₈	—	4	1	no	—
183	C₁₉	#7203	1	1	yes	characteristic, complemented, Sylow
184	C₂⁴	C₄×Dic₁₉	1	1	yes	characteristic
185	C₂⁴	C₄⋊Dic₁₉	1	1	yes	characteristic
186	C₂×D₄	—	4	1	no	—
187	C₂×D₄	—	4	1	no	—
188	C₂×D₄	C₂×C₁₉⋊C₈	1	2	yes	—
189	C₂×D₄	#64520	1	2	yes	—
190	C₂²×C₄	—	2	1	no	—
191	C₂²×C₄	—	2	1	no	—
192	C₂²×C₄	—	2	1	no	—
193	C₂²×C₄	—	2	1	no	—
194	C₂²×C₄	—	4	1	no	—
195	C₂²×C₄	—	4	1	no	—
196	C₂²×C₄	—	4	1	no	—
197	C₂²×C₄	—	4	1	no	—
198	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
199	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
200	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
201	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
202	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
203	M₁₆	—	2	4	no	—
204	M₁₆	—	4	2	no	—
205	C₂×C₈	—	4	2	no	—
206	C₂×C₈	—	38	2	no	—
207	C₂×C₈	—	76	1	no	—
208	C₂×C₈	—	76	2	no	—
209	C₂×C₈	—	76	1	no	—
210	C₂×C₈	—	76	2	no	—
211	C₂×C₈	—	76	2	no	—
212	C₂×C₈	—	76	1	no	—
213	C₂×C₈	—	76	1	no	—
214	C₂×C₈	—	76	1	no	—
215	C₂×C₈	—	152	1	no	—
216	C₂×C₈	—	152	1	no	—
217	C₄⋊C₄	—	4	1	no	—
218	C₂²⋊C₄	—	4	1	no	—
219	C₂²⋊C₄	—	4	1	no	—
220	C₄²	—	2	1	no	—
221	C₄²	—	2	1	no	—
222	C₂³	—	2	1	no	—
223	C₂³	—	2	1	no	—
224	C₂³	—	2	1	no	—
225	C₂³	—	2	1	no	—
226	C₂³	—	4	1	no	—
227	C₂³	—	4	1	no	—
228	C₂³	—	4	1	no	—
229	C₂³	—	4	1	no	—
230	C₂³	C₄×C₁₉⋊C₈	1	1	yes	characteristic
231	C₂³	#10597260	1	1	yes	characteristic
232	C₂³	C₄⋊(C₁₉⋊C₈)	1	2	yes	—
233	C₂³	C₁₉⋊#95	1	1	yes	characteristic
234	D₄	—	4	2	no	—
235	D₄	—	4	2	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	2	1	no	—
238	C₂×C₄	—	2	1	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	4	2	no	—
244	C₂×C₄	—	4	1	no	—
245	C₂×C₄	—	4	1	no	—
246	C₂×C₄	—	4	1	no	—
247	C₂×C₄	—	4	1	no	—
248	C₂×C₄	—	4	1	no	—
249	C₂×C₄	—	4	1	no	—
250	C₂×C₄	—	4	1	no	—
251	C₂×C₄	—	8	1	no	—
252	C₂×C₄	#10597263	1	1	yes	characteristic
253	C₂×C₄	#10597263	1	1	yes	characteristic
254	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
255	C₈	—	4	4	no	—
256	C₈	—	76	2	no	—
257	C₈	—	152	1	no	—
258	C₈	—	152	2	no	—
259	C₂²	—	2	1	no	—
260	C₂²	—	2	1	no	—
261	C₂²	—	2	1	no	—
262	C₂²	—	2	1	no	—
263	C₂²	—	2	2	no	—
264	C₂²	—	4	1	no	—
265	C₂²	—	4	1	no	—
266	C₂²	—	4	2	no	—
267	C₂²	—	4	2	no	—
268	C₂²	—	4	1	no	—
269	C₂²	—	4	1	no	—
270	C₂²	—	4	1	no	—
271	C₂²	—	4	1	no	—
272	C₂²	—	8	1	no	—
273	C₂²	#11926299	1	1	yes	characteristic
274	C₂²	#11926310	1	1	yes	characteristic
275	C₂²	#11926314	1	1	yes	characteristic
276	C₄	—	2	2	no	—
277	C₄	—	2	1	no	—
278	C₄	—	4	1	no	—
279	C₄	—	4	1	no	—
280	C₄	—	4	1	no	—
281	C₄	#11926332	1	1	yes	characteristic
282	C₄	#11926335	1	1	yes	characteristic
283	C₂	—	2	1	no	—
284	C₂	—	2	1	no	—
285	C₂	—	4	1	no	—
286	C₂	—	4	1	no	—
287	C₂	—	4	2	no	—
288	C₂	#14561483	1	1	yes	characteristic
289	C₂	#14561754	1	1	yes	characteristic
290	C₂	#14561757	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563928

C₂

yes

maximal, characteristic

#14561953

C₂

yes

maximal, characteristic

C₄×C₁₉×#100

C₂

yes

maximal, characteristic

C₂³×C₁₉⋊C₈

C₄

yes

characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×C₂²⋊(C₁₉⋊C₈)

C₄

yes

—

—

C₄

yes

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#100

C₄

yes

—

C₄×M₁₆×C₁₉

—

C₁₉×#343

—

C₂²×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×#100

—

C₁₉×#100

C₈

yes

complemented

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₄²

yes

characteristic

C₂⁴×C₁₉

C₄⋊C₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×C₈

yes

—

C₂×D₄×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7203

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#95

yes

characteristic

C₂³×C₁₉

C₄×C₈

yes

characteristic

C₂³×C₁₉

#97

yes

characteristic

C₂³×C₁₉

C₄⋊C₈

yes

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

—

106

C₂×C₄×C₁₉

—

107

C₂×C₄×C₁₉

C₂²⋊C₈

yes

—

108

C₂×C₄×C₁₉

#99

yes

characteristic

109

C₂×C₄×C₁₉

#99

yes

characteristic

110

C₈×C₁₉

—

111

C₁₉⋊C₈

—

112

C₁₉⋊C₈

—

113

C₁₉⋊C₈

—

114

#1869

—

115

C₄×#100

D₁₉

yes

characteristic

116

#1459

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

—

129

C₂²×C₁₉

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

#336

yes

characteristic

132

C₂²×C₁₉

#342

yes

characteristic

133

C₂²×C₁₉

#344

yes

characteristic

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

—

137

C₄×C₁₉

—

138

C₄×C₁₉

—

139

C₄×C₁₉

AΣL(1,𝔽₁₆)

yes

characteristic

140

C₄×C₁₉

#352

yes

characteristic

141

C₂³×C₈

—

142

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

143

C₂×#100

Dic₁₉

yes

—

144

C₂×C₂²⋊C₈

—

145

C₂×C₂²⋊C₈

—

146

C₂×C₂²⋊C₈

—

147

C₄×M₁₆

—

148

#343

—

149

#336

—

150

#324

—

151

#323

—

152

C₂×C₁₉

—

153

C₂×C₁₉

—

154

C₂×C₁₉

—

155

C₂×C₁₉

—

156

C₂×C₁₉

—

157

C₂×C₁₉

#1282

yes

characteristic

158

C₂×C₁₉

#1390

yes

characteristic

159

C₂×C₁₉

#1392

yes

characteristic

160

C₂²×D₄

C₂×Dic₁₉

yes

characteristic

161

C₂³×C₄

C₄×D₁₉

yes

characteristic

162

C₂³×C₄

D₇₆

yes

characteristic

163

C₂×M₁₆

—

164

C₂²×C₈

—

165

C₂²×C₈

—

166

C₂²×C₈

—

167

C₂²×C₈

—

168

C₂²×C₈

—

169

C₄×D₄

—

170

C₄×D₄

—

171

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

172

C₂×C₂²⋊C₄

Dic₃₈

yes

characteristic

173

C₂×C₂²⋊C₄

C₄×D₁₉

yes

characteristic

174

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

175

#100

—

176

#100

C₁₉⋊C₈

yes

complemented

177

C₂²⋊C₈

—

178

C₂²⋊C₈

—

179

C₂²⋊C₈

—

180

C₂²⋊C₈

—

181

#97

—

182

C₄×C₈

—

183

C₁₉

#7203

yes

characteristic, complemented, Sylow

184

C₂⁴

C₄×Dic₁₉

yes

characteristic

185

C₂⁴

C₄⋊Dic₁₉

yes

characteristic

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

C₂×C₁₉⋊C₈

yes

—

189

C₂×D₄

#64520

yes

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

—

197

C₂²×C₄

—

198

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

199

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

200

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

201

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

202

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

203

M₁₆

—

204

M₁₆

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

152

—

216

C₂×C₈

—

152

—

217

C₄⋊C₄

—

218

C₂²⋊C₄

—

219

C₂²⋊C₄

—

220

C₄²

—

221

C₄²

—

222

C₂³

—

223

C₂³

—

224

C₂³

—

225

C₂³

—

226

C₂³

—

227

C₂³

—

228

C₂³

—

229

C₂³

—

230

C₂³

C₄×C₁₉⋊C₈

yes

characteristic

231

C₂³

#10597260

yes

characteristic

232

C₂³

C₄⋊(C₁₉⋊C₈)

yes

—

233

C₂³

C₁₉⋊#95

yes

characteristic

234

D₄

—

235

D₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

—

248

C₂×C₄

—

249

C₂×C₄

—

250

C₂×C₄

—

251

C₂×C₄

—

252

C₂×C₄

#10597263

yes

characteristic

253

C₂×C₄

#10597263

yes

characteristic

254

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

—

255

C₈

—

256

C₈

—

257

C₈

—

152

—

258

C₈

—

152

—

259

C₂²

—

260

C₂²

—

261

C₂²

—

262

C₂²

—

263

C₂²

—

264

C₂²

—

265

C₂²

—

266

C₂²

—

267

C₂²

—

268

C₂²

—

269

C₂²

—

270

C₂²

—

271

C₂²

—

272

C₂²

—

273

C₂²

#11926299

yes

characteristic

274

C₂²

#11926310

yes

characteristic

275

C₂²

#11926314

yes

characteristic

276

C₄

—

277

C₄

—

278

C₄

—

279

C₄

—

280

C₄

—

281

C₄

#11926332

yes

characteristic

282

C₄

#11926335

yes

characteristic

283

C₂

—

284

C₂

—

285

C₂

—

286

C₂

—

287

C₂

—

288

C₂

#14561483

yes

characteristic

289

C₂

#14561754

yes

characteristic

290

C₂

#14561757

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597263
commutator	C₂³×C₁₉	C₄×C₈
Frattini	C₂×C₄×D₄	C₂×D₁₉
Fitting	C₄×C₁₉×#100	C₂
socle	C₂²×C₁₉	#342
prime radical	C₂²×D₄×C₁₉	C₂×C₄
cosocle	C₂×C₄×D₄×C₁₉	C₂²
hypercenter	C₄×#100	D₁₉
hypocenter	C₁₉	#7203
LCS	G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄×D₄ ◁ C₄×#100

subgroup

G/H

center

C₂×C₄

#10597263

commutator

C₂³×C₁₉

C₄×C₈

Frattini

C₂×C₄×D₄

C₂×D₁₉

Fitting

C₄×C₁₉×#100

C₂

socle

C₂²×C₁₉

#342

prime radical

C₂²×D₄×C₁₉

C₂×C₄

cosocle

C₂×C₄×D₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄×D₄ ◁ C₄×#100

N	H ≅ G/N	type
31. C₁₉×#100	C₈	semidirect
176. #100	C₁₉⋊C₈	semidirect
183. C₁₉	#7203	semidirect

H ≅ G/N

type

31. C₁₉×#100

C₈

semidirect

176. #100

C₁₉⋊C₈

semidirect

183. C₁₉

#7203

semidirect

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

subgroup	index
#14563928	2
#14561953	2
C₄×C₁₉×#100	2
#7203	19

subgroup

index

#14563928

#14561953

C₄×C₁₉×#100

#7203

Subgroups — #18069535

Conjugacy classes of subgroups

Complements

Maximal subgroups