Group #18077828 — subgroups

Subgroups — #18077828

Order 4864.

654 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 155 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	C₂×#11926918	C₂	1	1	yes	maximal, characteristic
2	#14564562	C₂	1	2	yes	maximal
3	C₂×#11926293	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561476	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#64527	—	2	2	no	—
7	C₂×#10597320	C₂²	1	1	yes	characteristic
8	#11926918	—	2	2	no	—
9	#11926918	C₄	1	4	yes	complemented
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
11	C₂×#10597266	—	2	2	no	—
12	C₂×#10597266	—	2	2	no	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#11926293	—	2	2	no	—
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₁₉×#391	—	2	2	no	—
17	C₁₉×#389	—	2	2	no	—
18	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
21	C₂²×D₇₆	—	2	2	no	—
22	C₂²×D₇₆	—	2	1	no	—
23	C₁₉×C₄⋊Q₈	—	2	2	no	—
24	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
25	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
29	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
30	C₂×C₄²×C₁₉	—	2	2	no	—
31	C₂×C₄²×C₁₉	—	2	2	no	—
32	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	C₂×#64527	—	2	8	no	—
34	C₂×#64527	—	4	4	no	—
35	C₂×#64527	—	4	4	no	—
36	C₂²×C₁₉⋊C₈	—	2	1	no	—
37	C₂²×C₁₉⋊C₈	—	2	2	no	—
38	#10597320	—	2	1	no	—
39	#10597320	—	2	2	no	—
40	#10597320	C₂×C₄	1	2	yes	—
41	C₁₉×#95	—	2	4	no	—
42	C₁₉×#95	—	2	2	no	—
43	#10597266	—	4	4	no	—
44	#10597266	—	4	4	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
47	C₄×C₁₉⋊C₈	—	2	1	no	—
48	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
49	C₂³×D₁₉	—	4	1	no	—
50	C₂×Q₈×C₁₉	—	2	2	no	—
51	C₂×Q₈×C₁₉	—	4	2	no	—
52	C₂×Q₈×C₁₉	—	4	2	no	—
53	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
54	C₂²×C₄×C₁₉	—	2	2	no	—
55	C₂²×C₄×C₁₉	—	2	2	no	—
56	C₂²×C₄×C₁₉	—	2	2	no	—
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
59	C₂×D₇₆	—	2	2	no	—
60	C₂×D₇₆	—	2	4	no	—
61	C₂×D₇₆	—	4	2	no	—
62	C₂×D₇₆	—	4	2	no	—
63	C₂×D₇₆	—	4	2	no	—
64	C₂×D₇₆	—	4	2	no	—
65	C₂×D₇₆	—	4	2	no	—
66	C₂×D₇₆	—	4	2	no	—
67	C₂×D₇₆	—	4	2	no	—
68	C₂×D₇₆	—	4	1	no	—
69	C₄⋊C₄×C₁₉	—	2	4	no	—
70	C₄⋊C₄×C₁₉	—	2	4	no	—
71	C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₄⋊C₄×C₁₉	—	8	2	no	—
75	C₄⋊C₄×C₁₉	SD₁₆	1	4	yes	complemented
76	C₄²×C₁₉	—	4	2	no	—
77	C₄²×C₁₉	—	4	2	no	—
78	C₄²×C₁₉	—	8	2	no	—
79	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₄²×C₁₉	#41	1	2	yes	—
82	#64527	—	4	16	no	—
83	C₂×C₁₉⋊C₈	—	2	2	no	—
84	C₂×C₁₉⋊C₈	—	2	2	no	—
85	C₂×C₁₉⋊C₈	—	2	2	no	—
86	C₂×C₁₉⋊C₈	—	4	2	no	—
87	C₂×C₁₉⋊C₈	—	4	2	no	—
88	C₂×C₁₉⋊C₈	—	4	2	no	—
89	#9063	—	19	1	no	maximal, Sylow
90	C₂³×C₁₉	#120	1	1	yes	characteristic
91	C₂²×D₁₉	—	4	2	no	—
92	C₂²×D₁₉	—	8	2	no	—
93	C₂²×D₁₉	—	8	2	no	—
94	C₂²×D₁₉	—	8	1	no	—
95	C₂²×D₁₉	—	8	1	no	—
96	Q₈×C₁₉	—	4	4	no	—
97	Q₈×C₁₉	—	8	2	no	—
98	C₂×C₄×C₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	2	1	no	—
100	C₂×C₄×C₁₉	—	2	4	no	—
101	C₂×C₄×C₁₉	—	2	4	no	—
102	C₂×C₄×C₁₉	—	4	2	no	—
103	C₂×C₄×C₁₉	—	4	2	no	—
104	C₂×C₄×C₁₉	—	4	2	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	4	2	no	—
107	C₂×C₄×C₁₉	—	4	2	no	—
108	C₂×C₄×C₁₉	—	4	2	no	—
109	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
111	C₂×C₄×C₁₉	#121	1	2	yes	—
112	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
113	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
114	C₂×C₄×C₁₉	#135	1	2	yes	—
115	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
116	C₂×C₄×C₁₉	#137	1	2	yes	—
117	D₇₆	—	4	4	no	—
118	D₇₆	—	4	4	no	—
119	D₇₆	—	4	4	no	—
120	D₇₆	—	8	2	no	—
121	D₇₆	—	8	2	no	—
122	D₇₆	—	8	2	no	—
123	C₁₉⋊C₈	—	2	4	no	—
124	C₁₉⋊C₈	—	8	2	no	—
125	C₂×#492	—	19	1	no	—
126	#2369	D₁₉	1	1	yes	characteristic, complemented
127	#1982	—	19	2	no	—
128	C₂×#333	—	19	1	no	—
129	#1279	—	19	2	no	—
130	C₂²×C₁₉	#386	1	1	yes	characteristic
131	C₂²×C₁₉	#448	1	2	yes	—
132	C₂²×C₁₉	#449	1	2	yes	—
133	C₂²×C₁₉	#453	1	1	yes	characteristic
134	C₂²×C₁₉	#453	1	1	yes	characteristic
135	C₂×D₁₉	—	8	4	no	—
136	C₂×D₁₉	—	8	2	no	—
137	C₂×D₁₉	—	16	2	no	—
138	C₂×D₁₉	—	16	1	no	—
139	C₂×D₁₉	—	16	1	no	—
140	C₄×C₁₉	—	2	1	no	—
141	C₄×C₁₉	—	2	1	no	—
142	C₄×C₁₉	—	4	4	no	—
143	C₄×C₁₉	—	4	4	no	—
144	C₄×C₁₉	—	8	2	no	—
145	C₄×C₁₉	C₄×SD₁₆	1	2	yes	—
146	C₄×C₁₉	#440	1	2	yes	—
147	C₄×C₁₉	#460	1	2	yes	—
148	C₄×C₁₉	#464	1	2	yes	—
149	C₂²×SD₁₆	—	38	2	no	—
150	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
151	C₂×#127	—	19	1	no	—
152	#492	—	19	4	no	—
153	#492	—	38	2	no	—
154	C₂×C₄⋊C₈	—	19	2	no	—
155	C₂×#102	—	38	2	no	—
156	C₂×#102	—	38	2	no	—
157	C₂×C₄×C₈	—	19	1	no	—
158	#391	—	2	2	no	—
159	#389	—	2	2	no	—
160	C₄×C₄⋊C₄	—	2	2	no	—
161	C₄×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
162	#333	—	38	2	no	—
163	C₂×C₁₉	#1622	1	2	yes	—
164	C₂×C₁₉	#1623	1	1	yes	characteristic
165	C₂×C₁₉	#1624	1	1	yes	characteristic
166	C₂×C₁₉	#1880	1	2	yes	—
167	C₂×C₁₉	#1887	1	1	yes	characteristic
168	D₁₉	—	16	2	no	—
169	C₂²×Q₈	C₂²⋊D₁₉	1	2	yes	—
170	C₂²×D₄	—	38	1	no	—
171	C₂²×D₄	—	38	2	no	—
172	C₂×SD₁₆	—	38	8	no	—
173	C₂×SD₁₆	—	76	4	no	—
174	C₂×SD₁₆	—	76	4	no	—
175	C₂²×C₈	—	38	1	no	—
176	C₂²×C₈	—	38	2	no	—
177	C₄⋊Q₈	—	2	2	no	—
178	C₄⋊Q₈	C₄×D₁₉	1	2	yes	—
179	C₄⋊Q₈	D₇₆	1	2	yes	—
180	#127	—	19	2	no	—
181	#127	—	38	1	no	—
182	#127	—	38	2	no	—
183	C₂×C₄⋊C₄	—	2	2	no	—
184	C₂×C₄⋊C₄	—	2	2	no	—
185	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
186	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
187	C₂×C₄²	—	2	2	no	—
188	C₂×C₄²	—	2	2	no	—
189	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
190	C₄⋊C₈	—	38	2	no	—
191	C₄⋊C₈	—	38	2	no	—
192	#102	—	76	4	no	—
193	#102	—	76	4	no	—
194	C₄×C₈	—	19	2	no	—
195	C₄×C₈	—	38	1	no	—
196	#95	—	2	4	no	—
197	#95	—	2	2	no	—
198	C₁₉	#9063	1	1	yes	characteristic, complemented, Sylow
199	C₂⁴	—	76	1	no	—
200	C₂×Q₈	—	2	2	no	—
201	C₂×Q₈	—	4	2	no	—
202	C₂×Q₈	—	4	2	no	—
203	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
204	C₂×D₄	—	38	2	no	—
205	C₂×D₄	—	38	4	no	—
206	C₂×D₄	—	76	2	no	—
207	C₂×D₄	—	76	2	no	—
208	C₂×D₄	—	76	2	no	—
209	C₂×D₄	—	76	2	no	—
210	C₂×D₄	—	76	2	no	—
211	C₂×D₄	—	76	2	no	—
212	C₂×D₄	—	76	2	no	—
213	C₂×D₄	—	76	1	no	—
214	C₂²×C₄	—	2	2	no	—
215	C₂²×C₄	—	2	2	no	—
216	C₂²×C₄	—	2	2	no	—
217	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
218	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
219	SD₁₆	—	76	16	no	—
220	C₂×C₈	—	38	2	no	—
221	C₂×C₈	—	38	2	no	—
222	C₂×C₈	—	38	2	no	—
223	C₂×C₈	—	76	2	no	—
224	C₂×C₈	—	76	2	no	—
225	C₂×C₈	—	76	2	no	—
226	C₄⋊C₄	—	2	4	no	—
227	C₄⋊C₄	—	2	2	no	—
228	C₄⋊C₄	—	2	4	no	—
229	C₄⋊C₄	—	2	2	no	—
230	C₄⋊C₄	—	2	2	no	—
231	C₄⋊C₄	—	8	2	no	—
232	C₄⋊C₄	#64527	1	4	yes	complemented
233	C₄²	—	4	2	no	—
234	C₄²	—	4	2	no	—
235	C₄²	—	8	2	no	—
236	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
237	C₄²	C₂×D₇₆	1	1	yes	characteristic
238	C₄²	#64541	1	2	yes	—
239	C₂³	—	76	2	no	—
240	C₂³	—	152	2	no	—
241	C₂³	—	152	2	no	—
242	C₂³	—	152	1	no	—
243	C₂³	—	152	1	no	—
244	C₂³	#10597399	1	1	yes	characteristic
245	Q₈	—	4	4	no	—
246	Q₈	—	8	2	no	—
247	D₄	—	76	4	no	—
248	D₄	—	76	4	no	—
249	D₄	—	76	4	no	—
250	D₄	—	152	2	no	—
251	D₄	—	152	2	no	—
252	D₄	—	152	2	no	—
253	C₂×C₄	—	2	1	no	—
254	C₂×C₄	—	2	1	no	—
255	C₂×C₄	—	2	4	no	—
256	C₂×C₄	—	2	4	no	—
257	C₂×C₄	—	4	2	no	—
258	C₂×C₄	—	4	2	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	4	2	no	—
262	C₂×C₄	—	4	2	no	—
263	C₂×C₄	—	4	2	no	—
264	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
265	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
266	C₂×C₄	#10597375	1	1	yes	characteristic
267	C₂×C₄	#10597376	1	2	yes	—
268	C₂×C₄	C₂×#64527	1	2	yes	—
269	C₂×C₄	#10597388	1	2	yes	—
270	C₂×C₄	#10597395	1	2	yes	—
271	C₂×C₄	#10597396	1	2	yes	—
272	C₈	—	38	4	no	—
273	C₈	—	152	2	no	—
274	C₂²	—	304	2	no	—
275	C₂²	—	304	1	no	—
276	C₂²	—	304	1	no	—
277	C₂²	—	152	4	no	—
278	C₂²	—	152	2	no	—
279	C₂²	#11926423	1	1	yes	characteristic
280	C₂²	#11926683	1	2	yes	—
281	C₂²	#11926689	1	2	yes	—
282	C₂²	#11926712	1	1	yes	characteristic
283	C₂²	#11926712	1	1	yes	characteristic
284	C₄	—	2	1	no	—
285	C₄	—	2	1	no	—
286	C₄	—	4	4	no	—
287	C₄	—	4	4	no	—
288	C₄	—	8	2	no	—
289	C₄	C₄×#64527	1	2	yes	—
290	C₄	#11926642	1	2	yes	—
291	C₄	#11926744	1	2	yes	—
292	C₄	#11926766	1	2	yes	—
293	C₂	—	304	2	no	—
294	C₂	#14562707	1	2	yes	—
295	C₂	#14562713	1	1	yes	characteristic
296	C₂	#14562718	1	1	yes	characteristic
297	C₂	#14563990	1	2	yes	—
298	C₂	#14564033	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926918

C₂

yes

maximal, characteristic

#14564562

C₂

yes

maximal

C₂×#11926293

C₂

yes

maximal, characteristic, complemented

#14561476

C₂

yes

maximal, complemented

C₁₉×#2369

C₂

yes

maximal, characteristic, complemented

C₂²×#64527

—

C₂×#10597320

C₂²

yes

characteristic

#11926918

—

#11926918

C₄

yes

complemented

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×#10597266

—

C₂×#10597266

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926293

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#391

—

C₁₉×#389

—

C₄×C₄⋊C₄×C₁₉

—

C₄×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂²×Q₈×C₁₉

D₄

yes

—

C₂²×D₇₆

—

C₂²×D₇₆

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

#10597320

—

#10597320

—

#10597320

C₂×C₄

yes

—

C₁₉×#95

—

C₁₉×#95

—

#10597266

—

#10597266

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×D₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

SD₁₆

yes

complemented

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

#64527

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×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

—

108

C₂×C₄×C₁₉

—

109

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

110

C₂×C₄×C₁₉

C₄×D₄

yes

—

111

C₂×C₄×C₁₉

#121

yes

—

112

C₂×C₄×C₁₉

#123

yes

characteristic

113

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

114

C₂×C₄×C₁₉

#135

yes

—

115

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

116

C₂×C₄×C₁₉

#137

yes

—

117

D₇₆

—

118

D₇₆

—

119

D₇₆

—

120

D₇₆

—

121

D₇₆

—

122

D₇₆

—

123

C₁₉⋊C₈

—

124

C₁₉⋊C₈

—

125

C₂×#492

—

126

#2369

D₁₉

yes

characteristic, complemented

127

#1982

—

128

C₂×#333

—

129

#1279

—

130

C₂²×C₁₉

#386

yes

characteristic

131

C₂²×C₁₉

#448

yes

—

132

C₂²×C₁₉

#449

yes

—

133

C₂²×C₁₉

#453

yes

characteristic

134

C₂²×C₁₉

#453

yes

characteristic

135

C₂×D₁₉

—

136

C₂×D₁₉

—

137

C₂×D₁₉

—

138

C₂×D₁₉

—

139

C₂×D₁₉

—

140

C₄×C₁₉

—

141

C₄×C₁₉

—

142

C₄×C₁₉

—

143

C₄×C₁₉

—

144

C₄×C₁₉

—

145

C₄×C₁₉

C₄×SD₁₆

yes

—

146

C₄×C₁₉

#440

yes

—

147

C₄×C₁₉

#460

yes

—

148

C₄×C₁₉

#464

yes

—

149

C₂²×SD₁₆

—

150

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

151

C₂×#127

—

152

#492

—

153

#492

—

154

C₂×C₄⋊C₈

—

155

C₂×#102

—

156

C₂×#102

—

157

C₂×C₄×C₈

—

158

#391

—

159

#389

—

160

C₄×C₄⋊C₄

—

161

C₄×C₄⋊C₄

C₂×D₁₉

yes

—

162

#333

—

163

C₂×C₁₉

#1622

yes

—

164

C₂×C₁₉

#1623

yes

characteristic

165

C₂×C₁₉

#1624

yes

characteristic

166

C₂×C₁₉

#1880

yes

—

167

C₂×C₁₉

#1887

yes

characteristic

168

D₁₉

—

169

C₂²×Q₈

C₂²⋊D₁₉

yes

—

170

C₂²×D₄

—

171

C₂²×D₄

—

172

C₂×SD₁₆

—

173

C₂×SD₁₆

—

174

C₂×SD₁₆

—

175

C₂²×C₈

—

176

C₂²×C₈

—

177

C₄⋊Q₈

—

178

C₄⋊Q₈

C₄×D₁₉

yes

—

179

C₄⋊Q₈

D₇₆

yes

—

180

#127

—

181

#127

—

182

#127

—

183

C₂×C₄⋊C₄

—

184

C₂×C₄⋊C₄

—

185

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

186

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

187

C₂×C₄²

—

188

C₂×C₄²

—

189

C₂×C₄²

C₂²×D₁₉

yes

characteristic

190

C₄⋊C₈

—

191

C₄⋊C₈

—

192

#102

—

193

#102

—

194

C₄×C₈

—

195

C₄×C₈

—

196

#95

—

197

#95

—

198

C₁₉

#9063

yes

characteristic, complemented, Sylow

199

C₂⁴

—

200

C₂×Q₈

—

201

C₂×Q₈

—

202

C₂×Q₈

—

203

C₂×Q₈

(C₂×D₁₉)⋊C₄

yes

—

204

C₂×D₄

—

205

C₂×D₄

—

206

C₂×D₄

—

207

C₂×D₄

—

208

C₂×D₄

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂×D₄

—

212

C₂×D₄

—

213

C₂×D₄

—

214

C₂²×C₄

—

215

C₂²×C₄

—

216

C₂²×C₄

—

217

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

218

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

219

SD₁₆

—

220

C₂×C₈

—

221

C₂×C₈

—

222

C₂×C₈

—

223

C₂×C₈

—

224

C₂×C₈

—

225

C₂×C₈

—

226

C₄⋊C₄

—

227

C₄⋊C₄

—

228

C₄⋊C₄

—

229

C₄⋊C₄

—

230

C₄⋊C₄

—

231

C₄⋊C₄

—

232

C₄⋊C₄

#64527

yes

complemented

233

C₄²

—

234

C₄²

—

235

C₄²

—

236

C₄²

C₂×C₄×D₁₉

yes

characteristic

237

C₄²

C₂×D₇₆

yes

characteristic

238

C₄²

#64541

yes

—

239

C₂³

—

240

C₂³

—

152

—

241

C₂³

—

152

—

242

C₂³

—

152

—

243

C₂³

—

152

—

244

C₂³

#10597399

yes

characteristic

245

Q₈

—

246

Q₈

—

247

D₄

—

248

D₄

—

249

D₄

—

250

D₄

—

152

—

251

D₄

—

152

—

252

D₄

—

152

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

—

263

C₂×C₄

—

264

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

265

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

266

C₂×C₄

#10597375

yes

characteristic

267

C₂×C₄

#10597376

yes

—

268

C₂×C₄

C₂×#64527

yes

—

269

C₂×C₄

#10597388

yes

—

270

C₂×C₄

#10597395

yes

—

271

C₂×C₄

#10597396

yes

—

272

C₈

—

273

C₈

—

152

—

274

C₂²

—

304

—

275

C₂²

—

304

—

276

C₂²

—

304

—

277

C₂²

—

152

—

278

C₂²

—

152

—

279

C₂²

#11926423

yes

characteristic

280

C₂²

#11926683

yes

—

281

C₂²

#11926689

yes

—

282

C₂²

#11926712

yes

characteristic

283

C₂²

#11926712

yes

characteristic

284

C₄

—

285

C₄

—

286

C₄

—

287

C₄

—

288

C₄

—

289

C₄

C₄×#64527

yes

—

290

C₄

#11926642

yes

—

291

C₄

#11926744

yes

—

292

C₄

#11926766

yes

—

293

C₂

—

304

—

294

C₂

#14562707

yes

—

295

C₂

#14562713

yes

characteristic

296

C₂

#14562718

yes

characteristic

297

C₂

#14563990

yes

—

298

C₂

#14564033

yes

characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2369	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×#10597320	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2369	D₁₉
hypocenter	C₁₉	#9063
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2369

subgroup

G/H

center

C₂³

#10597399

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2369

C₂

C₂³×C₁₉

C₂²

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2369

N	H ≅ G/N	type
3. C₂×#11926293	C₂	semidirect
4. #14561476	C₂	semidirect
5. C₁₉×#2369	C₂	semidirect
9. #11926918	C₄	semidirect
75. C₄⋊C₄×C₁₉	SD₁₆	semidirect
126. #2369	D₁₉	semidirect
198. C₁₉	#9063	semidirect
232. C₄⋊C₄	#64527	semidirect

H ≅ G/N

type

3. C₂×#11926293

C₂

semidirect

4. #14561476

C₂

semidirect

5. C₁₉×#2369

C₂

semidirect

9. #11926918

C₄

semidirect

75. C₄⋊C₄×C₁₉

SD₁₆

semidirect

126. #2369

D₁₉

semidirect

198. C₁₉

#9063

semidirect

232. C₄⋊C₄

#64527

semidirect

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

subgroup	index
C₂×#11926918	2
#14564562	2
C₂×#11926293	2
#14561476	2
C₁₉×#2369	2
#9063	19

subgroup

index

C₁₉×#2369

Subgroups — #18077828

Conjugacy classes of subgroups

Complements

Maximal subgroups