Subgroups — C₁₃₉×#36134 #48030730

Order 35584.

2298 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2868×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2857×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2552×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2542×C₁₃₉	C₂	1	2	yes	maximal
6	#2538×C₁₃₉	C₂	1	2	yes	maximal
7	#2441×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2429×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2423×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2365×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2354×C₁₃₉	C₂	1	2	yes	maximal
12	Q₈×C₄⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
15	#533×C₁₃₉	—	2	16	no	—
16	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
19	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#125×C₁₃₉	C₂²	1	4	yes	—
21	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
24	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃₉	C₂²	1	4	yes	—
26	C₂×C₄×Q₈×C₁₃₉	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
31	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
32	#399×C₁₃₉	C₂²	1	8	yes	—
33	#398×C₁₃₉	C₂²	1	8	yes	—
34	#396×C₁₃₉	C₂²	1	8	yes	—
35	#391×C₁₃₉	C₂²	1	2	yes	—
36	#391×C₁₃₉	C₂²	1	4	yes	—
37	#390×C₁₃₉	C₂²	1	4	yes	—
38	#389×C₁₃₉	C₂²	1	4	yes	—
39	#389×C₁₃₉	C₂²	1	4	yes	—
40	#389×C₁₃₉	C₂²	1	2	yes	—
41	#389×C₁₃₉	C₂²	1	2	yes	—
42	#389×C₁₃₉	C₂²	1	4	yes	—
43	#389×C₁₃₉	C₂²	1	8	yes	—
44	#388×C₁₃₉	C₂²	1	8	yes	—
45	#387×C₁₃₉	C₂²	1	8	yes	—
46	#384×C₁₃₉	C₂²	1	2	yes	—
47	#384×C₁₃₉	C₂²	1	4	yes	—
48	#384×C₁₃₉	C₂²	1	2	yes	—
49	#384×C₁₃₉	C₂²	1	1	yes	characteristic
50	#384×C₁₃₉	C₂²	1	2	yes	—
51	#384×C₁₃₉	C₂²	1	2	yes	—
52	#380×C₁₃₉	C₂²	1	4	yes	—
53	#380×C₁₃₉	C₂²	1	4	yes	—
54	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
55	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
58	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
59	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
60	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
61	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
62	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
63	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
64	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
65	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
66	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
70	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
71	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
72	C₄⋊Q₈×C₁₃₉	—	4	4	no	—
73	C₄⋊Q₈×C₁₃₉	D₄	1	8	yes	complemented
74	#125×C₁₃₉	—	2	16	no	—
75	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
76	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
77	C₂²⋊Q₈×C₁₃₉	—	4	8	no	—
78	C₄×Q₈×C₁₃₉	—	2	16	no	—
79	C₄×Q₈×C₁₃₉	—	2	16	no	—
80	C₄×Q₈×C₁₃₉	—	2	8	no	—
81	C₄×D₄×C₁₃₉	—	2	4	no	—
82	C₄×D₄×C₁₃₉	—	2	4	no	—
83	C₄×D₄×C₁₃₉	Q₈	1	8	yes	complemented
84	#117×C₁₃₉	—	2	16	no	—
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
87	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
88	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
105	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
107	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂×C₄²×C₁₃₉	—	2	8	no	—
109	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
110	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
111	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
112	C₂×C₄²×C₁₃₉	C₂³	1	8	yes	—
113	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
114	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
121	#95×C₁₃₉	C₂³	1	8	yes	—
122	#95×C₁₃₉	C₂³	1	2	yes	—
123	#95×C₁₃₉	C₂³	1	4	yes	—
124	#95×C₁₃₉	C₂³	1	4	yes	—
125	#95×C₁₃₉	C₂³	1	2	yes	—
126	#95×C₁₃₉	C₂³	1	2	yes	—
127	#95×C₁₃₉	C₂³	1	8	yes	—
128	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
129	C₂×Q₈×C₁₃₉	—	2	8	no	—
130	C₂×Q₈×C₁₃₉	—	2	4	no	—
131	C₂×Q₈×C₁₃₉	—	2	8	no	—
132	C₂×Q₈×C₁₃₉	—	2	8	no	—
133	C₂×Q₈×C₁₃₉	—	2	4	no	—
134	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
135	C₂×D₄×C₁₃₉	—	2	2	no	—
136	C₂×D₄×C₁₃₉	—	2	2	no	—
137	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
138	C₂²×C₄×C₁₃₉	—	2	4	no	—
139	C₂²×C₄×C₁₃₉	—	2	4	no	—
140	C₂²×C₄×C₁₃₉	—	2	4	no	—
141	C₂²×C₄×C₁₃₉	—	2	4	no	—
142	C₂²×C₄×C₁₃₉	—	2	4	no	—
143	C₂²×C₄×C₁₃₉	—	2	4	no	—
144	C₂²×C₄×C₁₃₉	—	2	4	no	—
145	C₂²×C₄×C₁₃₉	—	2	4	no	—
146	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
147	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
151	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
154	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
157	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
158	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
160	C₄⋊C₄×C₁₃₉	—	2	8	no	—
161	C₄⋊C₄×C₁₃₉	—	2	16	no	—
162	C₄⋊C₄×C₁₃₉	—	2	16	no	—
163	C₄⋊C₄×C₁₃₉	—	2	8	no	—
164	C₄⋊C₄×C₁₃₉	—	2	2	no	—
165	C₄⋊C₄×C₁₃₉	—	2	2	no	—
166	C₄⋊C₄×C₁₃₉	—	2	8	no	—
167	C₄⋊C₄×C₁₃₉	—	2	4	no	—
168	C₄⋊C₄×C₁₃₉	—	2	8	no	—
169	C₄⋊C₄×C₁₃₉	—	2	8	no	—
170	C₄⋊C₄×C₁₃₉	—	2	4	no	—
171	C₄⋊C₄×C₁₃₉	—	2	4	no	—
172	C₄⋊C₄×C₁₃₉	—	4	8	no	—
173	C₄⋊C₄×C₁₃₉	—	4	4	no	—
174	C₄⋊C₄×C₁₃₉	—	4	4	no	—
175	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
176	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
177	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
178	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
179	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
180	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
181	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
182	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
183	C₄²×C₁₃₉	—	2	4	no	—
184	C₄²×C₁₃₉	—	2	4	no	—
185	C₄²×C₁₃₉	—	2	4	no	—
186	C₄²×C₁₃₉	—	2	16	no	—
187	C₄²×C₁₃₉	—	2	8	no	—
188	C₄²×C₁₃₉	—	2	2	no	—
189	C₄²×C₁₃₉	—	2	2	no	—
190	C₄²×C₁₃₉	—	2	2	no	—
191	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
192	C₄²×C₁₃₉	C₂×Q₈	1	4	yes	—
193	C₄²×C₁₃₉	#41	1	4	yes	—
194	C₄²×C₁₃₉	#41	1	4	yes	—
195	C₂³×C₁₃₉	—	2	2	no	—
196	C₂³×C₁₃₉	—	2	2	no	—
197	C₂³×C₁₃₉	—	2	2	no	—
198	C₂³×C₁₃₉	—	2	2	no	—
199	C₂³×C₁₃₉	—	2	2	no	—
200	C₂³×C₁₃₉	—	2	2	no	—
201	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
202	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
203	Q₈×C₁₃₉	—	2	16	no	—
204	Q₈×C₁₃₉	—	4	16	no	—
205	D₄×C₁₃₉	—	2	8	no	—
206	C₂×C₄×C₁₃₉	—	2	2	no	—
207	C₂×C₄×C₁₃₉	—	2	4	no	—
208	C₂×C₄×C₁₃₉	—	2	1	no	—
209	C₂×C₄×C₁₃₉	—	2	1	no	—
210	C₂×C₄×C₁₃₉	—	2	1	no	—
211	C₂×C₄×C₁₃₉	—	2	1	no	—
212	C₂×C₄×C₁₃₉	—	2	1	no	—
213	C₂×C₄×C₁₃₉	—	2	1	no	—
214	C₂×C₄×C₁₃₉	—	2	2	no	—
215	C₂×C₄×C₁₃₉	—	2	4	no	—
216	C₂×C₄×C₁₃₉	—	2	16	no	—
217	C₂×C₄×C₁₃₉	—	2	2	no	—
218	C₂×C₄×C₁₃₉	—	2	2	no	—
219	C₂×C₄×C₁₃₉	—	2	8	no	—
220	C₂×C₄×C₁₃₉	—	2	4	no	—
221	C₂×C₄×C₁₃₉	—	2	2	no	—
222	C₂×C₄×C₁₃₉	—	2	2	no	—
223	C₂×C₄×C₁₃₉	—	2	8	no	—
224	C₂×C₄×C₁₃₉	—	2	4	no	—
225	C₂×C₄×C₁₃₉	—	2	8	no	—
226	C₂×C₄×C₁₃₉	—	2	2	no	—
227	C₂×C₄×C₁₃₉	—	2	4	no	—
228	C₂×C₄×C₁₃₉	—	2	2	no	—
229	C₂×C₄×C₁₃₉	—	4	8	no	—
230	C₂×C₄×C₁₃₉	—	4	8	no	—
231	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
232	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
236	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
237	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
238	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
239	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
240	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
241	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
242	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
243	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
244	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
245	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
246	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
247	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
248	C₂²×C₁₃₉	—	2	4	no	—
249	C₂²×C₁₃₉	—	2	4	no	—
250	C₂²×C₁₃₉	—	2	4	no	—
251	C₂²×C₁₃₉	—	4	2	no	—
252	C₂²×C₁₃₉	—	4	2	no	—
253	C₂²×C₁₃₉	—	4	2	no	—
254	C₂²×C₁₃₉	—	4	2	no	—
255	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
256	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
257	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
258	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
259	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
260	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
261	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
262	C₄×C₁₃₉	—	2	8	no	—
263	C₄×C₁₃₉	—	2	4	no	—
264	C₄×C₁₃₉	—	2	2	no	—
265	C₄×C₁₃₉	—	2	2	no	—
266	C₄×C₁₃₉	—	2	2	no	—
267	C₄×C₁₃₉	—	4	2	no	—
268	C₄×C₁₃₉	—	4	2	no	—
269	C₄×C₁₃₉	—	4	8	no	—
270	C₄×C₁₃₉	—	4	4	no	—
271	C₄×C₁₃₉	#533	1	4	yes	complemented
272	C₄×C₁₃₉	#547	1	4	yes	—
273	C₄×C₁₃₉	D₄×Q₈	1	4	yes	—
274	C₄×C₁₃₉	#550	1	4	yes	—
275	C₂×C₁₃₉	—	4	4	no	—
276	C₂×C₁₃₉	C₂×#533	1	1	yes	characteristic
277	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
278	C₂×C₁₃₉	C₂×D₄×Q₈	1	1	yes	characteristic
279	C₂×C₁₃₉	C₂×#550	1	1	yes	characteristic
280	C₂×C₁₃₉	#3503	1	1	yes	characteristic
281	C₂×C₁₃₉	#3509	1	1	yes	characteristic
282	C₂×C₁₃₉	#3511	1	1	yes	characteristic
283	#36134	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₁₃₉	#36134	1	1	yes	characteristic, direct product factor, Sylow
285	C₂×#533	C₂×C₁₃₉	1	2	yes	complemented
286	#2868	C₂×C₁₃₉	1	1	yes	characteristic, complemented
287	#2857	C₂×C₁₃₉	1	2	yes	complemented
288	#2552	C₂×C₁₃₉	1	2	yes	complemented
289	#2542	C₂×C₁₃₉	1	2	yes	—
290	#2538	C₂×C₁₃₉	1	2	yes	—
291	#2441	C₂×C₁₃₉	1	4	yes	complemented
292	#2429	C₂×C₁₃₉	1	4	yes	complemented
293	#2423	C₂×C₁₃₉	1	4	yes	complemented
294	#2365	C₂×C₁₃₉	1	2	yes	complemented
295	#2354	C₂×C₁₃₉	1	2	yes	—
296	Q₈×C₄⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
297	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
298	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic
299	#533	—	2	16	no	—
300	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
301	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
302	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
303	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
304	C₂×#125	C₂²×C₁₃₉	1	4	yes	—
305	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
306	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
307	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
308	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
309	C₂×C₄×Q₈	C₂²×C₁₃₉	1	4	yes	—
310	C₂×C₄×Q₈	C₂²×C₁₃₉	1	4	yes	—
311	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
312	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
313	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
314	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
315	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
316	#399	C₂²×C₁₃₉	1	8	yes	—
317	#398	C₂²×C₁₃₉	1	8	yes	—
318	#396	C₂²×C₁₃₉	1	8	yes	—
319	#391	C₂²×C₁₃₉	1	2	yes	—
320	#391	C₂²×C₁₃₉	1	4	yes	—
321	#390	C₂²×C₁₃₉	1	4	yes	—
322	#389	C₂²×C₁₃₉	1	2	yes	—
323	#389	C₂²×C₁₃₉	1	2	yes	—
324	#389	C₂²×C₁₃₉	1	4	yes	—
325	#389	C₂²×C₁₃₉	1	4	yes	—
326	#389	C₂²×C₁₃₉	1	8	yes	—
327	#389	C₂²×C₁₃₉	1	4	yes	—
328	#388	C₂²×C₁₃₉	1	8	yes	—
329	#387	C₂²×C₁₃₉	1	8	yes	—
330	#384	C₂²×C₁₃₉	1	1	yes	characteristic
331	#384	C₂²×C₁₃₉	1	2	yes	—
332	#384	C₂²×C₁₃₉	1	4	yes	—
333	#384	C₂²×C₁₃₉	1	2	yes	—
334	#384	C₂²×C₁₃₉	1	2	yes	—
335	#384	C₂²×C₁₃₉	1	2	yes	—
336	#380	C₂²×C₁₃₉	1	4	yes	—
337	#380	C₂²×C₁₃₉	1	4	yes	—
338	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
339	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
340	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
341	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
342	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
343	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
344	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
345	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
346	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
347	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
348	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
349	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
350	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
351	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
352	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
353	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
354	C₄⋊Q₈	—	2	8	no	—
355	C₄⋊Q₈	—	2	8	no	—
356	C₄⋊Q₈	—	4	4	no	—
357	C₄⋊Q₈	D₄×C₁₃₉	1	8	yes	complemented
358	#125	—	2	16	no	—
359	C₂²⋊Q₈	—	2	16	no	—
360	C₂²⋊Q₈	—	2	16	no	—
361	C₂²⋊Q₈	—	4	8	no	—
362	C₄×Q₈	—	2	16	no	—
363	C₄×Q₈	—	2	16	no	—
364	C₄×Q₈	—	2	8	no	—
365	C₄×D₄	—	2	4	no	—
366	C₄×D₄	—	2	4	no	—
367	C₄×D₄	Q₈×C₁₃₉	1	8	yes	complemented
368	#117	—	2	16	no	—
369	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
373	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
380	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
381	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
392	C₂×C₄²	—	2	8	no	—
393	C₂×C₄²	C₂³×C₁₃₉	1	8	yes	—
394	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
395	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
396	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
397	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
398	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
399	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
404	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
405	#95	C₂³×C₁₃₉	1	2	yes	—
406	#95	C₂³×C₁₃₉	1	2	yes	—
407	#95	C₂³×C₁₃₉	1	2	yes	—
408	#95	C₂³×C₁₃₉	1	8	yes	—
409	#95	C₂³×C₁₃₉	1	4	yes	—
410	#95	C₂³×C₁₃₉	1	4	yes	—
411	#95	C₂³×C₁₃₉	1	8	yes	—
412	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
413	C₂×Q₈	—	2	8	no	—
414	C₂×Q₈	—	2	4	no	—
415	C₂×Q₈	—	2	8	no	—
416	C₂×Q₈	—	2	8	no	—
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
431	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
432	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
433	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
435	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
436	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
437	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
438	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
440	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
441	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
442	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
443	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
444	C₄⋊C₄	—	2	8	no	—
445	C₄⋊C₄	—	2	16	no	—
446	C₄⋊C₄	—	2	16	no	—
447	C₄⋊C₄	—	2	8	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	8	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	8	no	—
453	C₄⋊C₄	—	2	8	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	4	8	no	—
457	C₄⋊C₄	—	4	4	no	—
458	C₄⋊C₄	—	4	4	no	—
459	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
460	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
461	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
462	C₂²⋊C₄	—	2	16	no	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	4	8	no	—
466	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
467	C₄²	—	2	4	no	—
468	C₄²	—	2	4	no	—
469	C₄²	—	2	4	no	—
470	C₄²	—	2	16	no	—
471	C₄²	—	2	8	no	—
472	C₄²	—	2	2	no	—
473	C₄²	—	2	2	no	—
474	C₄²	—	2	2	no	—
475	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
476	C₄²	C₂×Q₈×C₁₃₉	1	4	yes	—
477	C₄²	#41×C₁₃₉	1	4	yes	—
478	C₄²	#41×C₁₃₉	1	4	yes	—
479	C₂³	—	2	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	2	no	—
485	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
486	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
487	Q₈	—	2	16	no	—
488	Q₈	—	4	16	no	—
489	D₄	—	2	8	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	16	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	8	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	4	8	no	—
514	C₂×C₄	—	4	8	no	—
515	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
516	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
517	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
518	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
519	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
520	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
521	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
522	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
523	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
524	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
525	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
526	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
527	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
528	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
529	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
530	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
531	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
532	C₂²	—	2	4	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
540	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
541	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
542	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
543	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
544	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
545	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
546	C₄	—	2	8	no	—
547	C₄	—	2	4	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	2	no	—
551	C₄	—	4	2	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	8	no	—
554	C₄	—	4	4	no	—
555	C₄	#533×C₁₃₉	1	4	yes	complemented
556	C₄	#547×C₁₃₉	1	4	yes	—
557	C₄	D₄×Q₈×C₁₃₉	1	4	yes	—
558	C₄	#550×C₁₃₉	1	4	yes	—
559	C₂	—	4	4	no	—
560	C₂	C₂×#533×C₁₃₉	1	1	yes	characteristic
561	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
562	C₂	C₂×D₄×Q₈×C₁₃₉	1	1	yes	characteristic
563	C₂	C₂×#550×C₁₃₉	1	1	yes	characteristic
564	C₂	#3503×C₁₃₉	1	1	yes	characteristic
565	C₂	#3509×C₁₃₉	1	1	yes	characteristic
566	C₂	#3511×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₁₃₉	C₂	semidirect
2. #2868×C₁₃₉	C₂	semidirect
3. #2857×C₁₃₉	C₂	semidirect
4. #2552×C₁₃₉	C₂	semidirect
7. #2441×C₁₃₉	C₂	semidirect
8. #2429×C₁₃₉	C₂	semidirect
9. #2423×C₁₃₉	C₂	semidirect
10. #2365×C₁₃₉	C₂	semidirect
12. Q₈×C₄⋊C₄×C₁₃₉	C₂	semidirect
13. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
73. C₄⋊Q₈×C₁₃₉	D₄	semidirect
83. C₄×D₄×C₁₃₉	Q₈	semidirect
271. C₄×C₁₃₉	#533	semidirect
283. #36134	C₁₃₉	direct (N × H)
284. C₁₃₉	#36134	direct (N × H)
285. C₂×#533	C₂×C₁₃₉	semidirect
286. #2868	C₂×C₁₃₉	semidirect
287. #2857	C₂×C₁₃₉	semidirect
288. #2552	C₂×C₁₃₉	semidirect
291. #2441	C₂×C₁₃₉	semidirect
292. #2429	C₂×C₁₃₉	semidirect
293. #2423	C₂×C₁₃₉	semidirect
294. #2365	C₂×C₁₃₉	semidirect
296. Q₈×C₄⋊C₄	C₂×C₁₃₉	semidirect
297. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
357. C₄⋊Q₈	D₄×C₁₃₉	semidirect
367. C₄×D₄	Q₈×C₁₃₉	semidirect
555. C₄	#533×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₁₃₉	2
#2868×C₁₃₉	2
#2857×C₁₃₉	2
#2552×C₁₃₉	2
#2542×C₁₃₉	2
#2538×C₁₃₉	2
#2441×C₁₃₉	2
#2429×C₁₃₉	2
#2423×C₁₃₉	2
#2365×C₁₃₉	2
#2354×C₁₃₉	2
Q₈×C₄⋊C₄×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36134	139

Subgroups — C139×#36134 #48030730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36134 #48030730