Group #18070800 — subgroups

Subgroups — #18070800

Order 4864.

520 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 135 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	#14563488	C₂	1	2	yes	maximal, complemented
2	#14561461	C₂	1	2	yes	maximal, complemented
3	#14561456	C₂	1	2	yes	maximal
4	C₄×C₁₉×#124	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
6	C₂×#10597260	—	2	2	no	—
7	#11926299	C₂²	1	4	yes	—
8	C₂×C₁₉×#124	C₄	1	1	yes	characteristic
9	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
11	C₁₉×#391	C₂²	1	1	yes	characteristic
12	C₁₉×#390	C₂²	1	1	yes	characteristic
13	C₁₉×#388	—	2	2	no	—
14	C₁₉×#382	C₄	1	1	yes	characteristic
15	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
16	C₄³×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂³×C₄×C₁₉	—	2	1	no	—
20	C₁₉×#124	—	2	2	no	—
21	C₁₉×#124	—	2	2	no	—
22	C₄×Q₈×C₁₉	—	4	2	no	—
23	C₄×D₄×C₁₉	—	4	2	no	—
24	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
25	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₄²×C₁₉	—	2	1	no	—
31	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	D₄	1	2	yes	—
34	C₂×C₄²×C₁₉	D₄	1	2	yes	—
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	C₂²×C₁₉⋊C₈	—	2	4	no	—
37	C₁₉×#95	—	2	2	no	—
38	C₁₉×#95	—	2	2	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
40	#10597260	—	4	4	no	—
41	C₂⁴×C₁₉	—	2	1	no	—
42	C₂×Q₈×C₁₉	—	2	1	no	—
43	C₂×Q₈×C₁₉	—	4	1	no	—
44	C₂×Q₈×C₁₉	—	4	1	no	—
45	C₂×Q₈×C₁₉	M₁₆	1	2	yes	—
46	C₂×D₄×C₁₉	—	2	1	no	—
47	C₂×D₄×C₁₉	—	4	1	no	—
48	C₂×D₄×C₁₉	—	4	1	no	—
49	C₂×D₄×C₁₉	M₁₆	1	2	yes	—
50	C₂²×C₄×C₁₉	—	2	1	no	—
51	C₂²×C₄×C₁₉	—	2	1	no	—
52	C₂²×C₄×C₁₉	—	2	1	no	—
53	C₂²×C₄×C₁₉	—	4	2	no	—
54	C₂²×C₄×C₁₉	—	4	4	no	—
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
60	C₄⋊C₄×C₁₉	—	4	1	no	—
61	C₄⋊C₄×C₁₉	—	4	1	no	—
62	C₄⋊C₄×C₁₉	—	4	2	no	—
63	C₂²⋊C₄×C₁₉	—	2	8	no	—
64	C₂²⋊C₄×C₁₉	—	4	2	no	—
65	C₂²⋊C₄×C₁₉	—	4	2	no	—
66	C₂²⋊C₄×C₁₉	—	4	2	no	—
67	C₄²×C₁₉	—	2	2	no	—
68	C₄²×C₁₉	—	2	4	no	—
69	C₄²×C₁₉	—	2	1	no	—
70	C₄²×C₁₉	—	2	1	no	—
71	C₄²×C₁₉	—	2	2	no	—
72	C₄²×C₁₉	—	2	2	no	—
73	C₄²×C₁₉	—	4	1	no	—
74	C₄²×C₁₉	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	2	8	no	—
76	C₂×C₁₉⋊C₈	—	4	4	no	—
77	C₂×C₁₉⋊C₈	—	4	4	no	—
78	#7635	—	19	1	no	maximal, Sylow
79	C₂³×C₁₉	—	2	2	no	—
80	C₂³×C₁₉	—	4	1	no	—
81	C₂³×C₁₉	—	4	1	no	—
82	C₂³×C₁₉	—	4	2	no	—
83	C₂³×C₁₉	—	4	2	no	—
84	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	Q₈×C₁₉	—	4	2	no	—
86	Q₈×C₁₉	—	4	2	no	—
87	D₄×C₁₉	—	4	2	no	—
88	D₄×C₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	2	2	no	—
94	C₂×C₄×C₁₉	—	2	2	no	—
95	C₂×C₄×C₁₉	—	2	1	no	—
96	C₂×C₄×C₁₉	—	2	2	no	—
97	C₂×C₄×C₁₉	—	2	2	no	—
98	C₂×C₄×C₁₉	—	2	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	2	no	—
104	C₂×C₄×C₁₉	—	4	2	no	—
105	C₂×C₄×C₁₉	—	8	4	no	—
106	C₂×C₄×C₁₉	#100	1	2	yes	—
107	C₂×C₄×C₁₉	#104	1	4	yes	—
108	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
109	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
110	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
111	C₂×C₄×C₁₉	#137	1	2	yes	—
112	C₁₉⋊C₈	—	4	8	no	—
113	C₄×#124	D₁₉	1	1	yes	characteristic
114	#1767	—	19	2	no	—
115	#1272	—	19	2	no	—
116	#1270	—	19	2	no	—
117	C₂²×C₁₉	—	4	2	no	—
118	C₂²×C₁₉	—	4	4	no	—
119	C₂²×C₁₉	—	8	1	no	—
120	C₂²×C₁₉	—	8	2	no	—
121	C₂²×C₁₉	—	8	1	no	—
122	C₂²×C₁₉	#407	1	1	yes	characteristic
123	C₂²×C₁₉	#410	1	1	yes	characteristic
124	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
125	C₂²×C₁₉	#417	1	2	yes	—
126	C₂²×C₁₉	C₂×#104	1	2	yes	—
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	2	no	—
130	C₄×C₁₉	—	2	2	no	—
131	C₄×C₁₉	—	4	1	no	—
132	C₄×C₁₉	—	4	2	no	—
133	C₄×C₁₉	—	4	2	no	—
134	C₄×C₁₉	—	8	1	no	—
135	C₄×C₁₉	—	8	1	no	—
136	C₄×C₁₉	#329	1	4	yes	—
137	C₂×#124	Dic₁₉	1	1	yes	characteristic
138	C₂×C₄×Q₈	Dic₁₉	1	1	yes	characteristic
139	C₂×C₄×D₄	Dic₁₉	1	1	yes	characteristic
140	C₂×C₄⋊C₈	—	38	2	no	—
141	C₂×#97	—	38	2	no	—
142	#391	C₂×D₁₉	1	1	yes	characteristic
143	#390	C₂×D₁₉	1	1	yes	characteristic
144	#388	—	2	2	no	—
145	#382	Dic₁₉	1	1	yes	characteristic
146	C₄×C₂²⋊C₄	—	2	2	no	—
147	C₄³	C₂×D₁₉	1	1	yes	characteristic
148	#336	—	19	4	no	—
149	C₂×C₁₉	—	8	2	no	—
150	C₂×C₁₉	#1466	1	1	yes	characteristic
151	C₂×C₁₉	#1489	1	2	yes	—
152	C₂×C₁₉	#1509	1	2	yes	—
153	C₂×C₁₉	C₂×#329	1	1	yes	characteristic
154	C₂×C₁₉	#1560	1	1	yes	characteristic
155	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
156	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
157	C₂³×C₄	—	2	1	no	—
158	C₂²×C₈	—	38	4	no	—
159	#124	—	2	2	no	—
160	#124	—	2	2	no	—
161	C₄×Q₈	—	4	2	no	—
162	C₄×D₄	—	4	2	no	—
163	C₂×C₄⋊C₄	—	2	1	no	—
164	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
165	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
166	C₂×C₂²⋊C₄	—	2	2	no	—
167	C₂×C₂²⋊C₄	—	2	1	no	—
168	C₂×C₂²⋊C₄	—	2	2	no	—
169	C₂×C₄²	—	2	1	no	—
170	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
171	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
172	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
173	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
174	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
175	C₄⋊C₈	—	38	8	no	—
176	#97	—	76	4	no	—
177	#95	—	2	2	no	—
178	#95	—	2	2	no	—
179	C₁₉	#7635	1	1	yes	characteristic, complemented, Sylow
180	C₂⁴	—	2	1	no	—
181	C₂×Q₈	—	2	1	no	—
182	C₂×Q₈	—	4	1	no	—
183	C₂×Q₈	—	4	1	no	—
184	C₂×Q₈	#64520	1	2	yes	—
185	C₂×D₄	—	2	1	no	—
186	C₂×D₄	—	4	1	no	—
187	C₂×D₄	—	4	1	no	—
188	C₂×D₄	#64520	1	2	yes	—
189	C₂²×C₄	—	2	1	no	—
190	C₂²×C₄	—	2	1	no	—
191	C₂²×C₄	—	2	1	no	—
192	C₂²×C₄	—	4	2	no	—
193	C₂²×C₄	—	4	4	no	—
194	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
195	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
196	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
197	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
198	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
199	C₂×C₈	—	38	8	no	—
200	C₂×C₈	—	76	4	no	—
201	C₂×C₈	—	76	4	no	—
202	C₄⋊C₄	—	4	1	no	—
203	C₄⋊C₄	—	4	1	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₂²⋊C₄	—	2	8	no	—
206	C₂²⋊C₄	—	4	2	no	—
207	C₂²⋊C₄	—	4	2	no	—
208	C₂²⋊C₄	—	4	2	no	—
209	C₄²	—	2	2	no	—
210	C₄²	—	2	2	no	—
211	C₄²	—	2	2	no	—
212	C₄²	—	2	4	no	—
213	C₄²	—	2	1	no	—
214	C₄²	—	2	1	no	—
215	C₄²	—	4	1	no	—
216	C₄²	—	4	2	no	—
217	C₂³	—	2	2	no	—
218	C₂³	—	4	2	no	—
219	C₂³	—	4	2	no	—
220	C₂³	—	4	1	no	—
221	C₂³	—	4	1	no	—
222	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
223	Q₈	—	4	2	no	—
224	Q₈	—	4	2	no	—
225	D₄	—	4	2	no	—
226	D₄	—	4	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	2	1	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	4	1	no	—
238	C₂×C₄	—	4	1	no	—
239	C₂×C₄	—	4	2	no	—
240	C₂×C₄	—	4	2	no	—
241	C₂×C₄	—	4	1	no	—
242	C₂×C₄	—	4	1	no	—
243	C₂×C₄	—	8	4	no	—
244	C₂×C₄	#10597290	1	2	yes	—
245	C₂×C₄	#10597294	1	4	yes	—
246	C₂×C₄	C₂×#64520	1	1	yes	characteristic
247	C₂×C₄	C₂×#64520	1	1	yes	characteristic
248	C₂×C₄	#10597395	1	2	yes	—
249	C₂×C₄	#10597397	1	2	yes	—
250	C₈	—	76	8	no	—
251	C₂²	—	4	4	no	—
252	C₂²	—	4	2	no	—
253	C₂²	—	8	1	no	—
254	C₂²	—	8	2	no	—
255	C₂²	—	8	1	no	—
256	C₂²	#11926508	1	1	yes	characteristic
257	C₂²	#11926518	1	1	yes	characteristic
258	C₂²	C₂×#10597290	1	1	yes	characteristic
259	C₂²	#11926545	1	2	yes	—
260	C₂²	C₂×#10597294	1	2	yes	—
261	C₄	—	2	2	no	—
262	C₄	—	2	2	no	—
263	C₄	—	2	1	no	—
264	C₄	—	2	1	no	—
265	C₄	—	4	2	no	—
266	C₄	—	4	1	no	—
267	C₄	—	4	2	no	—
268	C₄	—	8	1	no	—
269	C₄	—	8	1	no	—
270	C₄	#11926284	1	4	yes	—
271	C₂	—	8	2	no	—
272	C₂	#14561976	1	1	yes	characteristic
273	C₂	#14562074	1	2	yes	—
274	C₂	#14562160	1	2	yes	—
275	C₂	C₂×#11926284	1	1	yes	characteristic
276	C₂	#14562370	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563488

C₂

yes

maximal, complemented

#14561461

C₂

yes

maximal, complemented

#14561456

C₂

yes

maximal

C₄×C₁₉×#124

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×#10597260

—

#11926299

C₂²

yes

—

C₂×C₁₉×#124

C₄

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₄

yes

characteristic

C₂×C₄×D₄×C₁₉

C₄

yes

characteristic

C₁₉×#391

C₂²

yes

characteristic

C₁₉×#390

C₂²

yes

characteristic

C₁₉×#388

—

C₁₉×#382

C₄

yes

characteristic

C₄×C₂²⋊C₄×C₁₉

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₁₉×#124

—

C₁₉×#124

—

C₄×Q₈×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

M₁₆

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

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

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7635

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

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

—

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

#100

yes

—

107

C₂×C₄×C₁₉

#104

yes

—

108

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

109

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

110

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

111

C₂×C₄×C₁₉

#137

yes

—

112

C₁₉⋊C₈

—

113

C₄×#124

D₁₉

yes

characteristic

114

#1767

—

115

#1272

—

116

#1270

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

#407

yes

characteristic

123

C₂²×C₁₉

#410

yes

characteristic

124

C₂²×C₁₉

C₂×#100

yes

characteristic

125

C₂²×C₁₉

#417

yes

—

126

C₂²×C₁₉

C₂×#104

yes

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

#329

yes

—

137

C₂×#124

Dic₁₉

yes

characteristic

138

C₂×C₄×Q₈

Dic₁₉

yes

characteristic

139

C₂×C₄×D₄

Dic₁₉

yes

characteristic

140

C₂×C₄⋊C₈

—

141

C₂×#97

—

142

#391

C₂×D₁₉

yes

characteristic

143

#390

C₂×D₁₉

yes

characteristic

144

#388

—

145

#382

Dic₁₉

yes

characteristic

146

C₄×C₂²⋊C₄

—

147

C₄³

C₂×D₁₉

yes

characteristic

148

#336

—

149

C₂×C₁₉

—

150

C₂×C₁₉

#1466

yes

characteristic

151

C₂×C₁₉

#1489

yes

—

152

C₂×C₁₉

#1509

yes

—

153

C₂×C₁₉

C₂×#329

yes

characteristic

154

C₂×C₁₉

#1560

yes

characteristic

155

C₂²×Q₈

C₂×Dic₁₉

yes

characteristic

156

C₂²×D₄

C₂×Dic₁₉

yes

characteristic

157

C₂³×C₄

—

158

C₂²×C₈

—

159

#124

—

160

#124

—

161

C₄×Q₈

—

162

C₄×D₄

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

165

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

166

C₂×C₂²⋊C₄

—

167

C₂×C₂²⋊C₄

—

168

C₂×C₂²⋊C₄

—

169

C₂×C₄²

—

170

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

171

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

172

C₂×C₄²

C₂²⋊D₁₉

yes

—

173

C₂×C₄²

C₂²⋊D₁₉

yes

—

174

C₂×C₄²

C₂²×D₁₉

yes

characteristic

175

C₄⋊C₈

—

176

#97

—

177

#95

—

178

#95

—

179

C₁₉

#7635

yes

characteristic, complemented, Sylow

180

C₂⁴

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

#64520

yes

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

#64520

yes

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

195

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

196

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

197

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

198

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₂²⋊C₄

—

206

C₂²⋊C₄

—

207

C₂²⋊C₄

—

208

C₂²⋊C₄

—

209

C₄²

—

210

C₄²

—

211

C₄²

—

212

C₄²

—

213

C₄²

—

214

C₄²

—

215

C₄²

—

216

C₄²

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

223

Q₈

—

224

Q₈

—

225

D₄

—

226

D₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

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

#10597290

yes

—

245

C₂×C₄

#10597294

yes

—

246

C₂×C₄

C₂×#64520

yes

characteristic

247

C₂×C₄

C₂×#64520

yes

characteristic

248

C₂×C₄

#10597395

yes

—

249

C₂×C₄

#10597397

yes

—

250

C₈

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

#11926508

yes

characteristic

257

C₂²

#11926518

yes

characteristic

258

C₂²

C₂×#10597290

yes

characteristic

259

C₂²

#11926545

yes

—

260

C₂²

C₂×#10597294

yes

—

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

—

265

C₄

—

266

C₄

—

267

C₄

—

268

C₄

—

269

C₄

—

270

C₄

#11926284

yes

—

271

C₂

—

272

C₂

#14561976

yes

characteristic

273

C₂

#14562074

yes

—

274

C₂

#14562160

yes

—

275

C₂

C₂×#11926284

yes

characteristic

276

C₂

#14562370

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#124	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₄×C₁₉	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#124	D₁₉
hypocenter	C₁₉	#7635
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#124

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×#124

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂²×D₄×C₁₉

C₂×C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#124

N	H ≅ G/N	type
1. #14563488	C₂	semidirect
2. #14561461	C₂	semidirect
179. C₁₉	#7635	semidirect

H ≅ G/N

type

1. #14563488

C₂

semidirect

2. #14561461

C₂

semidirect

179. C₁₉

#7635

semidirect

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

subgroup	index
#14563488	2
#14561461	2
#14561456	2
C₄×C₁₉×#124	2
#7635	19

subgroup

index

C₄×C₁₉×#124

Subgroups — #18070800

Conjugacy classes of subgroups

Complements

Maximal subgroups