Subgroups — C₂×#22581562 #31819769

Order 17792.

1004 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22581562	C₂	1	16	yes	maximal, direct product factor
2	C₂×#17984841	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#17984837	C₂	1	1	yes	maximal, characteristic
4	C₂×#17984837	C₂	1	1	yes	maximal, characteristic
5	C₂×#17984837	C₂	1	1	yes	maximal, characteristic
6	C₂×#17984836	C₂	1	1	yes	maximal, characteristic
7	C₂×#17984833	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#17984832	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#17984832	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#17984832	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#17984820	C₂	1	1	yes	maximal, characteristic
12	C₂×#17984820	C₂	1	1	yes	maximal, characteristic
13	C₂×C₄×Dic₂₇₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#17984807	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#17984800	C₂	1	1	yes	maximal, characteristic
16	C₂×#125×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Dic₂₇₈	C₂²	1	1	yes	characteristic
18	C₂²×Dic₂₇₈	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
20	#17984841	C₂²	1	8	yes	complemented
21	#17984837	C₂²	1	8	yes	—
22	#17984837	C₂²	1	8	yes	—
23	#17984837	C₂²	1	8	yes	—
24	#17984836	C₂²	1	8	yes	—
25	#17984833	C₂²	1	8	yes	complemented
26	#17984832	C₂²	1	8	yes	complemented
27	#17984832	C₂²	1	8	yes	complemented
28	#17984832	C₂²	1	8	yes	complemented
29	#17984820	C₂²	1	8	yes	—
30	#17984820	C₂²	1	8	yes	—
31	C₄×Dic₂₇₈	C₂²	1	8	yes	complemented
32	#17984807	C₂²	1	8	yes	complemented
33	#17984800	C₂²	1	8	yes	—
34	C₂×C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
50	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
51	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
52	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
53	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
54	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
55	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
56	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
57	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
58	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
59	#125×C₁₃₉	C₂²	1	8	yes	complemented
60	C₂×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
66	C₂×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
67	C₂³×D₁₃₉	C₂³	1	1	yes	characteristic
68	C₂×Dic₂₇₈	—	2	4	no	—
69	C₂×Dic₂₇₈	—	2	4	no	—
70	C₂×Dic₂₇₈	C₂³	1	4	yes	—
71	C₂×Dic₂₇₈	C₂³	1	4	yes	—
72	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
73	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
74	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
75	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
76	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
77	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
78	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
79	C₂×C₄×D₁₃₉	—	2	4	no	—
80	C₂×C₄×D₁₃₉	C₂³	1	4	yes	—
81	C₄⋊Dic₁₃₉	C₂³	1	4	yes	—
82	C₄⋊Dic₁₃₉	C₂³	1	4	yes	—
83	C₄⋊Dic₁₃₉	C₂³	1	4	yes	—
84	C₄⋊Dic₁₃₉	C₂³	1	4	yes	—
85	Dic₁₃₉⋊C₄	C₂³	1	4	yes	—
86	Dic₁₃₉⋊C₄	C₂³	1	4	yes	—
87	Dic₁₃₉⋊C₄	C₂³	1	4	yes	—
88	Dic₁₃₉⋊C₄	C₂³	1	4	yes	—
89	Dic₁₃₉⋊C₄	C₂³	1	4	yes	—
90	Dic₁₃₉⋊C₄	C₂³	1	4	yes	—
91	Dic₁₃₉⋊C₄	C₂³	1	4	yes	—
92	Dic₁₃₉⋊C₄	C₂³	1	4	yes	—
93	Dic₁₃₉⋊C₄	C₂³	1	4	yes	—
94	Dic₁₃₉⋊C₄	C₂³	1	4	yes	—
95	(C₂×D₁₃₉)⋊C₄	C₂³	1	4	yes	—
96	(C₂×D₁₃₉)⋊C₄	C₂³	1	4	yes	—
97	(C₂×D₁₃₉)⋊C₄	C₂³	1	4	yes	—
98	(C₂×D₁₃₉)⋊C₄	C₂³	1	4	yes	—
99	(C₂×D₁₃₉)⋊C₄	C₂³	1	4	yes	—
100	(C₂×D₁₃₉)⋊C₄	C₂³	1	4	yes	—
101	C₄×Dic₁₃₉	C₂³	1	4	yes	—
102	C₄×Dic₁₃₉	C₂³	1	4	yes	—
103	C₄×Dic₁₃₉	C₂³	1	4	yes	—
104	C₄×Dic₁₃₉	C₂³	1	4	yes	—
105	C₄×Dic₁₃₉	C₂³	1	4	yes	—
106	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
115	C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
116	C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
119	C₄²×C₁₃₉	C₂³	1	4	yes	—
120	C₂²×D₁₃₉	—	2	2	no	—
121	C₂²×D₁₃₉	—	2	2	no	—
122	C₂²×D₁₃₉	—	2	2	no	—
123	C₂²×D₁₃₉	C₂⁴	1	2	yes	—
124	Dic₂₇₈	—	2	8	no	—
125	Dic₂₇₈	—	2	8	no	—
126	C₂×Dic₁₃₉	—	2	2	no	—
127	C₂×Dic₁₃₉	—	2	2	no	—
128	C₂×Dic₁₃₉	—	2	2	no	—
129	C₂×Dic₁₃₉	—	2	2	no	—
130	C₂×Dic₁₃₉	—	2	2	no	—
131	C₂×Dic₁₃₉	—	2	2	no	—
132	C₂×Dic₁₃₉	#41	1	4	yes	—
133	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
134	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
135	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
136	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
137	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
138	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
139	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
140	C₄×D₁₃₉	—	2	8	no	—
141	C₂³×C₁₃₉	C₂⁴	1	1	yes	characteristic
142	C₂×C₄×C₁₃₉	—	2	2	no	—
143	C₂×C₄×C₁₃₉	—	2	2	no	—
144	C₂×C₄×C₁₃₉	—	2	2	no	—
145	C₂×C₄×C₁₃₉	—	2	2	no	—
146	C₂×C₄×C₁₃₉	—	2	2	no	—
147	C₂×C₄×C₁₃₉	—	2	2	no	—
148	C₂×C₄×C₁₃₉	—	2	2	no	—
149	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
150	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
151	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
152	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
153	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
154	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
155	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
156	C₂²×C₁₃₉	C₂×#41	1	2	yes	—
157	C₂²×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
158	C₂²×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
159	C₂²×C₁₃₉	C₂⁵	1	1	yes	characteristic
160	C₂×D₁₃₉	—	2	2	no	—
161	C₂×D₁₃₉	—	2	2	no	—
162	C₂×D₁₃₉	—	2	2	no	—
163	C₂×D₁₃₉	—	4	4	no	—
164	C₄×C₁₃₉	—	2	2	no	—
165	C₄×C₁₃₉	—	2	2	no	—
166	C₄×C₁₃₉	—	2	2	no	—
167	C₄×C₁₃₉	—	2	2	no	—
168	C₄×C₁₃₉	—	2	2	no	—
169	C₄×C₁₃₉	—	2	2	no	—
170	C₄×C₁₃₉	—	2	2	no	—
171	Dic₁₃₉	—	2	2	no	—
172	Dic₁₃₉	—	2	2	no	—
173	Dic₁₃₉	—	2	2	no	—
174	Dic₁₃₉	—	2	2	no	—
175	Dic₁₃₉	—	2	2	no	—
176	Dic₁₃₉	—	2	2	no	—
177	Dic₁₃₉	C₂×#41	1	4	yes	—
178	C₂×C₁₃₉	#541	1	4	yes	complemented
179	C₂×C₁₃₉	C₂²×#41	1	1	yes	characteristic
180	C₂×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
181	C₂×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
182	D₁₃₉	—	4	2	no	—
183	C₁₃₉	C₂×#541	1	1	yes	characteristic, complemented, Sylow
184	C₂×#541	—	139	1	no	maximal, Sylow
185	#541	—	139	16	no	—
186	C₂×C₄⋊Q₈	—	139	1	no	—
187	C₂×#126	—	139	1	no	—
188	C₂×#126	—	139	1	no	—
189	C₂×#126	—	139	1	no	—
190	C₂×#126	—	139	1	no	—
191	C₂×#125	—	139	1	no	—
192	C₂×#125	—	139	1	no	—
193	C₂×#125	—	139	1	no	—
194	C₂×#125	—	139	1	no	—
195	C₂×#125	D₁₃₉	1	1	yes	characteristic, complemented
196	C₂×C₂²⋊Q₈	—	139	1	no	—
197	C₂×C₂²⋊Q₈	—	139	1	no	—
198	C₂×C₄×Q₈	—	139	1	no	—
199	C₂×C₄×Q₈	—	139	1	no	—
200	C₂×#117	—	139	1	no	—
201	C₂²×Q₈	—	139	1	no	—
202	C₂²×Q₈	—	139	1	no	—
203	C₂³×C₄	—	139	1	no	—
204	C₄⋊Q₈	—	139	8	no	—
205	#126	—	139	8	no	—
206	#126	—	139	8	no	—
207	#126	—	139	8	no	—
208	#126	—	139	8	no	—
209	#125	—	139	8	no	—
210	#125	—	139	8	no	—
211	#125	—	139	8	no	—
212	#125	—	139	8	no	—
213	#125	C₂×D₁₃₉	1	8	yes	complemented
214	C₂²⋊Q₈	—	139	8	no	—
215	C₂²⋊Q₈	—	139	8	no	—
216	C₄×Q₈	—	139	8	no	—
217	C₄×Q₈	—	139	8	no	—
218	#117	—	139	8	no	—
219	C₂×C₄⋊C₄	—	139	1	no	—
220	C₂×C₄⋊C₄	—	139	1	no	—
221	C₂×C₄⋊C₄	—	139	1	no	—
222	C₂×C₄⋊C₄	—	139	1	no	—
223	C₂×C₄⋊C₄	—	139	1	no	—
224	C₂×C₄⋊C₄	—	139	1	no	—
225	C₂×C₄⋊C₄	—	139	1	no	—
226	C₂×C₄⋊C₄	—	139	1	no	—
227	C₂×C₄⋊C₄	—	139	1	no	—
228	C₂×C₄⋊C₄	—	139	1	no	—
229	C₂×C₄⋊C₄	—	139	1	no	—
230	C₂×C₄⋊C₄	—	139	1	no	—
231	C₂×C₄⋊C₄	—	139	1	no	—
232	C₂×C₄⋊C₄	—	139	1	no	—
233	C₂×C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	—	139	1	no	—
240	C₂×C₂²⋊C₄	—	139	1	no	—
241	C₂×C₂²⋊C₄	—	139	1	no	—
242	C₂×C₂²⋊C₄	—	139	1	no	—
243	C₂×C₂²⋊C₄	—	139	1	no	—
244	C₂×C₂²⋊C₄	—	139	1	no	—
245	C₂×C₄²	—	139	1	no	—
246	C₂×C₄²	—	139	1	no	—
247	C₂×C₄²	—	139	1	no	—
248	C₂×C₄²	—	139	1	no	—
249	C₂×C₄²	—	139	1	no	—
250	C₂×C₄²	C₂×D₁₃₉	1	1	yes	characteristic
251	C₂⁴	—	139	1	no	—
252	C₂×Q₈	—	278	4	no	—
253	C₂×Q₈	—	278	4	no	—
254	C₂×Q₈	—	139	4	no	—
255	C₂×Q₈	—	139	4	no	—
256	C₂²×C₄	—	278	4	no	—
257	C₂²×C₄	—	139	1	no	—
258	C₂²×C₄	—	139	1	no	—
259	C₂²×C₄	—	139	1	no	—
260	C₂²×C₄	—	139	1	no	—
261	C₂²×C₄	—	139	1	no	—
262	C₂²×C₄	—	139	1	no	—
263	C₂²×C₄	—	139	4	no	—
264	C₂²×C₄	—	139	1	no	—
265	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
266	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
267	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
268	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
269	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
270	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
271	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
272	C₄⋊C₄	—	139	4	no	—
273	C₄⋊C₄	—	139	4	no	—
274	C₄⋊C₄	—	139	4	no	—
275	C₄⋊C₄	—	139	4	no	—
276	C₄⋊C₄	—	139	4	no	—
277	C₄⋊C₄	—	139	4	no	—
278	C₄⋊C₄	—	139	4	no	—
279	C₄⋊C₄	—	139	4	no	—
280	C₄⋊C₄	—	139	4	no	—
281	C₄⋊C₄	—	139	4	no	—
282	C₄⋊C₄	—	139	4	no	—
283	C₄⋊C₄	—	139	4	no	—
284	C₄⋊C₄	—	139	4	no	—
285	C₄⋊C₄	—	139	4	no	—
286	C₄⋊C₄	C₂²×D₁₃₉	1	4	yes	—
287	C₄⋊C₄	C₂²×D₁₃₉	1	4	yes	—
288	C₄⋊C₄	C₂²×D₁₃₉	1	4	yes	—
289	C₄⋊C₄	C₂²×D₁₃₉	1	4	yes	—
290	C₄⋊C₄	C₂²×D₁₃₉	1	4	yes	—
291	C₄⋊C₄	C₂²×D₁₃₉	1	4	yes	—
292	C₂²⋊C₄	—	139	4	no	—
293	C₂²⋊C₄	—	139	4	no	—
294	C₂²⋊C₄	—	139	4	no	—
295	C₂²⋊C₄	—	139	4	no	—
296	C₂²⋊C₄	—	139	4	no	—
297	C₂²⋊C₄	—	139	4	no	—
298	C₄²	—	139	4	no	—
299	C₄²	—	139	4	no	—
300	C₄²	—	139	4	no	—
301	C₄²	—	139	4	no	—
302	C₄²	—	139	4	no	—
303	C₄²	C₂²×D₁₃₉	1	4	yes	—
304	C₂³	—	278	2	no	—
305	C₂³	—	278	2	no	—
306	C₂³	—	278	2	no	—
307	C₂³	—	139	2	no	—
308	C₂³	C₂³×D₁₃₉	1	1	yes	characteristic
309	Q₈	—	278	8	no	—
310	Q₈	—	278	8	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	278	8	no	—
319	C₂×C₄	—	278	2	no	—
320	C₂×C₄	—	278	2	no	—
321	C₂×C₄	—	278	2	no	—
322	C₂×C₄	—	278	2	no	—
323	C₂×C₄	—	278	2	no	—
324	C₂×C₄	—	278	2	no	—
325	C₂×C₄	—	139	2	no	—
326	C₂×C₄	—	139	2	no	—
327	C₂×C₄	—	139	2	no	—
328	C₂×C₄	—	139	2	no	—
329	C₂×C₄	—	139	2	no	—
330	C₂×C₄	—	139	2	no	—
331	C₂×C₄	—	139	4	no	—
332	C₂×C₄	—	139	2	no	—
333	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
334	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
335	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
336	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
337	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
338	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
339	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
340	C₂²	—	278	2	no	—
341	C₂²	—	278	2	no	—
342	C₂²	—	278	2	no	—
343	C₂²	—	556	4	no	—
344	C₂²	#41×D₁₃₉	1	2	yes	—
345	C₂²	#17984889	1	2	yes	—
346	C₂²	#17984890	1	2	yes	—
347	C₂²	C₂⁴×D₁₃₉	1	1	yes	characteristic
348	C₄	—	2	2	no	—
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	2	no	—
352	C₄	—	2	2	no	—
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	278	2	no	—
356	C₄	—	278	2	no	—
357	C₄	—	278	2	no	—
358	C₄	—	278	2	no	—
359	C₄	—	278	2	no	—
360	C₄	—	278	2	no	—
361	C₄	—	139	4	no	—
362	C₂	—	556	2	no	—
363	C₂	#22581562	1	4	yes	direct product factor
364	C₂	C₂×#41×D₁₃₉	1	1	yes	characteristic
365	C₂	C₂×#17984889	1	1	yes	characteristic
366	C₂	C₂×#17984890	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₃₉
commutator, cosocle	C₂²×C₁₃₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₃₉
Fitting	C₂×#125×C₁₃₉	C₂
socle	C₂³×C₁₃₉	C₂⁴
prime radical	C₂³×D₁₃₉	C₂³
hypercenter	C₂×#125	D₁₃₉
hypocenter	C₁₃₉	C₂×#541
LCS	G ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂³ ◁ C₂×#125

Complements

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

N	H ≅ G/N	type
1. #22581562	C₂	direct (N × H)
2. C₂×#17984841	C₂	semidirect
7. C₂×#17984833	C₂	semidirect
8. C₂×#17984832	C₂	semidirect
9. C₂×#17984832	C₂	semidirect
10. C₂×#17984832	C₂	semidirect
13. C₂×C₄×Dic₂₇₈	C₂	semidirect
14. C₂×#17984807	C₂	semidirect
16. C₂×#125×C₁₃₉	C₂	semidirect
20. #17984841	C₂²	semidirect
25. #17984833	C₂²	semidirect
26. #17984832	C₂²	semidirect
27. #17984832	C₂²	semidirect
28. #17984832	C₂²	semidirect
31. C₄×Dic₂₇₈	C₂²	semidirect
32. #17984807	C₂²	semidirect
59. #125×C₁₃₉	C₂²	semidirect
178. C₂×C₁₃₉	#541	semidirect
183. C₁₃₉	C₂×#541	semidirect
195. C₂×#125	D₁₃₉	semidirect
213. #125	C₂×D₁₃₉	semidirect
363. C₂	#22581562	direct (N × H)

Maximal subgroups

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

subgroup	index
#22581562	2
C₂×#17984841	2
C₂×#17984837	2
C₂×#17984836	2
C₂×#17984833	2
C₂×#17984832	2
C₂×#17984820	2
C₂×C₄×Dic₂₇₈	2
C₂×#17984807	2
C₂×#17984800	2
C₂×#125×C₁₃₉	2
C₂×#541	139

Subgroups — C2×#22581562 #31819769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22581562 #31819769