Subgroups — C₁₃₉×#36562 #48031158

Order 35584.

2182 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#557×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#554×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2862×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2859×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2567×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2566×C₁₃₉	C₂	1	2	yes	maximal
7	#2565×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2556×C₁₃₉	C₂	1	8	yes	maximal, complemented
9	#2542×C₁₃₉	C₂	1	1	yes	maximal, characteristic
10	#2429×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2360×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	C₄×#124×C₁₃₉	C₂	1	2	yes	maximal
14	C₄²×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#557×C₁₃₉	—	2	8	no	—
16	#554×C₁₃₉	—	2	8	no	—
17	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#125×C₁₃₉	C₂²	1	4	yes	—
21	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
35	#399×C₁₃₉	C₂²	1	4	yes	—
36	#398×C₁₃₉	C₂²	1	8	yes	—
37	#396×C₁₃₉	C₂²	1	8	yes	—
38	#395×C₁₃₉	C₂²	1	4	yes	—
39	#391×C₁₃₉	C₂²	1	4	yes	—
40	#391×C₁₃₉	C₂²	1	1	yes	characteristic
41	#391×C₁₃₉	C₂²	1	2	yes	—
42	#391×C₁₃₉	C₂²	1	4	yes	—
43	#390×C₁₃₉	C₂²	1	2	yes	—
44	#390×C₁₃₉	C₂²	1	1	yes	characteristic
45	#389×C₁₃₉	C₂²	1	8	yes	—
46	#389×C₁₃₉	C₂²	1	8	yes	—
47	#389×C₁₃₉	C₂²	1	4	yes	—
48	#388×C₁₃₉	C₂²	1	4	yes	—
49	#388×C₁₃₉	C₂²	1	8	yes	—
50	#387×C₁₃₉	C₂²	1	8	yes	—
51	#385×C₁₃₉	C₂²	1	8	yes	—
52	#384×C₁₃₉	C₂²	1	2	yes	—
53	#384×C₁₃₉	C₂²	1	2	yes	—
54	#382×C₁₃₉	C₂²	1	1	yes	characteristic
55	#382×C₁₃₉	C₂²	1	2	yes	—
56	#382×C₁₃₉	C₂²	1	2	yes	—
57	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
59	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
60	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
61	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	8	yes	—
62	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
63	C₄³×C₁₃₉	C₂²	1	2	yes	—
64	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
65	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
66	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
71	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
72	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
73	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
74	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
75	#125×C₁₃₉	—	2	16	no	—
76	#125×C₁₃₉	—	2	8	no	—
77	#125×C₁₃₉	—	2	8	no	—
78	#124×C₁₃₉	Q₈	1	8	yes	complemented
79	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
80	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
81	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
82	C₄×Q₈×C₁₃₉	—	2	8	no	—
83	C₄×Q₈×C₁₃₉	—	2	8	no	—
84	C₄×Q₈×C₁₃₉	—	2	8	no	—
85	C₄×Q₈×C₁₃₉	—	2	4	no	—
86	C₄×Q₈×C₁₃₉	D₄	1	8	yes	—
87	C₄×D₄×C₁₃₉	—	2	8	no	—
88	C₄×D₄×C₁₃₉	—	2	4	no	—
89	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
90	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	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	2	yes	—
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
110	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
113	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
114	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
120	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
124	#95×C₁₃₉	C₂³	1	2	yes	—
125	#95×C₁₃₉	C₂³	1	8	yes	—
126	#95×C₁₃₉	C₂³	1	8	yes	—
127	#95×C₁₃₉	C₂³	1	4	yes	—
128	#95×C₁₃₉	C₂³	1	4	yes	—
129	#95×C₁₃₉	C₂³	1	8	yes	—
130	#95×C₁₃₉	C₂³	1	4	yes	—
131	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
132	C₂×Q₈×C₁₃₉	—	2	2	no	—
133	C₂×Q₈×C₁₃₉	—	2	4	no	—
134	C₂×Q₈×C₁₃₉	—	2	4	no	—
135	C₂×Q₈×C₁₃₉	—	2	4	no	—
136	C₂×Q₈×C₁₃₉	—	2	8	no	—
137	C₂×Q₈×C₁₃₉	—	2	2	no	—
138	C₂×Q₈×C₁₃₉	—	4	4	no	—
139	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
140	C₂×Q₈×C₁₃₉	C₂×Q₈	1	4	yes	—
141	C₂×D₄×C₁₃₉	—	2	2	no	—
142	C₂×D₄×C₁₃₉	—	2	2	no	—
143	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
144	C₂²×C₄×C₁₃₉	—	2	4	no	—
145	C₂²×C₄×C₁₃₉	—	2	8	no	—
146	C₂²×C₄×C₁₃₉	—	2	8	no	—
147	C₂²×C₄×C₁₃₉	—	4	8	no	—
148	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
161	C₄⋊C₄×C₁₃₉	—	2	8	no	—
162	C₄⋊C₄×C₁₃₉	—	2	4	no	—
163	C₄⋊C₄×C₁₃₉	—	2	2	no	—
164	C₄⋊C₄×C₁₃₉	—	2	4	no	—
165	C₄⋊C₄×C₁₃₉	—	2	4	no	—
166	C₄⋊C₄×C₁₃₉	—	2	2	no	—
167	C₄⋊C₄×C₁₃₉	—	2	8	no	—
168	C₄⋊C₄×C₁₃₉	—	2	8	no	—
169	C₄⋊C₄×C₁₃₉	—	2	4	no	—
170	C₄⋊C₄×C₁₃₉	—	2	8	no	—
171	C₄⋊C₄×C₁₃₉	—	2	8	no	—
172	C₄⋊C₄×C₁₃₉	—	2	4	no	—
173	C₄⋊C₄×C₁₃₉	—	2	8	no	—
174	C₄⋊C₄×C₁₃₉	—	2	16	no	—
175	C₄⋊C₄×C₁₃₉	—	4	8	no	—
176	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
177	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
178	C₄⋊C₄×C₁₃₉	#41	1	8	yes	—
179	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
180	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
181	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
182	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
183	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	16	yes	—
184	C₄²×C₁₃₉	—	2	8	no	—
185	C₄²×C₁₃₉	—	2	4	no	—
186	C₄²×C₁₃₉	—	2	8	no	—
187	C₄²×C₁₃₉	—	2	4	no	—
188	C₄²×C₁₃₉	—	2	4	no	—
189	C₄²×C₁₃₉	—	2	2	no	—
190	C₄²×C₁₃₉	—	4	4	no	—
191	C₄²×C₁₃₉	—	4	2	no	—
192	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
193	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
194	C₄²×C₁₃₉	C₂×Q₈	1	4	yes	—
195	C₂³×C₁₃₉	—	2	2	no	—
196	C₂³×C₁₃₉	—	2	4	no	—
197	C₂³×C₁₃₉	—	2	2	no	—
198	C₂³×C₁₃₉	—	2	4	no	—
199	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
200	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
201	Q₈×C₁₃₉	—	2	8	no	—
202	Q₈×C₁₃₉	—	2	8	no	—
203	Q₈×C₁₃₉	—	4	8	no	—
204	Q₈×C₁₃₉	—	8	4	no	—
205	D₄×C₁₃₉	—	2	8	no	—
206	C₂×C₄×C₁₃₉	—	2	2	no	—
207	C₂×C₄×C₁₃₉	—	2	2	no	—
208	C₂×C₄×C₁₃₉	—	2	4	no	—
209	C₂×C₄×C₁₃₉	—	2	4	no	—
210	C₂×C₄×C₁₃₉	—	2	2	no	—
211	C₂×C₄×C₁₃₉	—	2	2	no	—
212	C₂×C₄×C₁₃₉	—	2	4	no	—
213	C₂×C₄×C₁₃₉	—	2	4	no	—
214	C₂×C₄×C₁₃₉	—	2	2	no	—
215	C₂×C₄×C₁₃₉	—	2	2	no	—
216	C₂×C₄×C₁₃₉	—	2	4	no	—
217	C₂×C₄×C₁₃₉	—	2	2	no	—
218	C₂×C₄×C₁₃₉	—	2	4	no	—
219	C₂×C₄×C₁₃₉	—	2	2	no	—
220	C₂×C₄×C₁₃₉	—	2	8	no	—
221	C₂×C₄×C₁₃₉	—	2	4	no	—
222	C₂×C₄×C₁₃₉	—	2	2	no	—
223	C₂×C₄×C₁₃₉	—	2	2	no	—
224	C₂×C₄×C₁₃₉	—	2	4	no	—
225	C₂×C₄×C₁₃₉	—	2	8	no	—
226	C₂×C₄×C₁₃₉	—	4	8	no	—
227	C₂×C₄×C₁₃₉	—	8	8	no	—
228	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
229	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
230	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
231	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
234	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
235	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
236	C₂×C₄×C₁₃₉	C₂×#41	1	8	yes	—
237	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
238	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
239	C₂²×C₁₃₉	—	2	4	no	—
240	C₂²×C₁₃₉	—	2	8	no	—
241	C₂²×C₁₃₉	—	4	2	no	—
242	C₂²×C₁₃₉	—	4	2	no	—
243	C₂²×C₁₃₉	—	4	4	no	—
244	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
245	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
246	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
247	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
248	C₂²×C₁₃₉	#585	1	2	yes	—
249	C₄×C₁₃₉	—	2	4	no	—
250	C₄×C₁₃₉	—	2	4	no	—
251	C₄×C₁₃₉	—	2	4	no	—
252	C₄×C₁₃₉	—	2	4	no	—
253	C₄×C₁₃₉	—	2	2	no	—
254	C₄×C₁₃₉	—	2	8	no	—
255	C₄×C₁₃₉	—	4	2	no	—
256	C₄×C₁₃₉	—	4	4	no	—
257	C₄×C₁₃₉	—	4	2	no	—
258	C₄×C₁₃₉	—	4	4	no	—
259	C₄×C₁₃₉	—	4	2	no	—
260	C₄×C₁₃₉	#532	1	4	yes	—
261	C₄×C₁₃₉	D₄×Q₈	1	4	yes	—
262	C₂×C₁₃₉	—	4	4	no	—
263	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
264	C₂×C₁₃₉	C₂×D₄×Q₈	1	1	yes	characteristic
265	C₂×C₁₃₉	Q₈×#41	1	2	yes	—
266	C₂×C₁₃₉	#3500	1	1	yes	characteristic
267	C₂×C₁₃₉	#3515	1	2	yes	—
268	#36562	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₁₃₉	#36562	1	1	yes	characteristic, direct product factor, Sylow
270	C₂×#557	C₂×C₁₃₉	1	1	yes	characteristic, complemented
271	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic
272	#2862	C₂×C₁₃₉	1	1	yes	characteristic, complemented
273	#2859	C₂×C₁₃₉	1	2	yes	complemented
274	#2567	C₂×C₁₃₉	1	1	yes	characteristic, complemented
275	#2566	C₂×C₁₃₉	1	2	yes	—
276	#2565	C₂×C₁₃₉	1	2	yes	complemented
277	#2556	C₂×C₁₃₉	1	8	yes	complemented
278	#2542	C₂×C₁₃₉	1	1	yes	characteristic
279	#2429	C₂×C₁₃₉	1	4	yes	complemented
280	#2360	C₂×C₁₃₉	1	4	yes	complemented
281	C₄×#124	C₂×C₁₃₉	1	2	yes	—
282	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic
283	C₄²×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
284	#557	—	2	8	no	—
285	#554	—	2	8	no	—
286	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
287	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
288	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
289	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
290	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
291	C₂×#125	C₂²×C₁₃₉	1	4	yes	—
292	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
293	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
294	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
295	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
296	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
297	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
298	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
299	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
300	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
301	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
302	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
303	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
304	#399	C₂²×C₁₃₉	1	4	yes	—
305	#398	C₂²×C₁₃₉	1	8	yes	—
306	#396	C₂²×C₁₃₉	1	8	yes	—
307	#395	C₂²×C₁₃₉	1	4	yes	—
308	#391	C₂²×C₁₃₉	1	1	yes	characteristic
309	#391	C₂²×C₁₃₉	1	2	yes	—
310	#391	C₂²×C₁₃₉	1	4	yes	—
311	#391	C₂²×C₁₃₉	1	4	yes	—
312	#390	C₂²×C₁₃₉	1	1	yes	characteristic
313	#390	C₂²×C₁₃₉	1	2	yes	—
314	#389	C₂²×C₁₃₉	1	4	yes	—
315	#389	C₂²×C₁₃₉	1	8	yes	—
316	#389	C₂²×C₁₃₉	1	8	yes	—
317	#388	C₂²×C₁₃₉	1	8	yes	—
318	#388	C₂²×C₁₃₉	1	4	yes	—
319	#387	C₂²×C₁₃₉	1	8	yes	—
320	#385	C₂²×C₁₃₉	1	8	yes	—
321	#384	C₂²×C₁₃₉	1	2	yes	—
322	#384	C₂²×C₁₃₉	1	2	yes	—
323	#382	C₂²×C₁₃₉	1	2	yes	—
324	#382	C₂²×C₁₃₉	1	1	yes	characteristic
325	#382	C₂²×C₁₃₉	1	2	yes	—
326	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
327	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
328	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
329	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
330	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
331	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	8	yes	—
332	C₄³	C₂²×C₁₃₉	1	2	yes	—
333	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
334	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
335	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
336	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
337	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
338	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
339	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
340	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
341	C₄⋊Q₈	—	2	8	no	—
342	C₄⋊Q₈	—	2	4	no	—
343	C₄⋊Q₈	—	2	4	no	—
344	#125	—	2	16	no	—
345	#125	—	2	8	no	—
346	#125	—	2	8	no	—
347	#124	Q₈×C₁₃₉	1	8	yes	complemented
348	C₂²⋊Q₈	—	2	8	no	—
349	C₂²⋊Q₈	—	2	16	no	—
350	C₂²⋊Q₈	—	2	16	no	—
351	C₄×Q₈	—	2	8	no	—
352	C₄×Q₈	—	2	8	no	—
353	C₄×Q₈	—	2	8	no	—
354	C₄×Q₈	—	2	4	no	—
355	C₄×Q₈	D₄×C₁₃₉	1	8	yes	—
356	C₄×D₄	—	2	8	no	—
357	C₄×D₄	—	2	4	no	—
358	C₂×C₄⋊C₄	—	2	8	no	—
359	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
360	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
382	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
383	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
384	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
385	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
386	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
388	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
389	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
390	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
391	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
393	#95	C₂³×C₁₃₉	1	4	yes	—
394	#95	C₂³×C₁₃₉	1	8	yes	—
395	#95	C₂³×C₁₃₉	1	4	yes	—
396	#95	C₂³×C₁₃₉	1	8	yes	—
397	#95	C₂³×C₁₃₉	1	4	yes	—
398	#95	C₂³×C₁₃₉	1	2	yes	—
399	#95	C₂³×C₁₃₉	1	8	yes	—
400	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	4	no	—
403	C₂×Q₈	—	2	4	no	—
404	C₂×Q₈	—	2	4	no	—
405	C₂×Q₈	—	2	8	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	4	4	no	—
408	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
409	C₂×Q₈	C₂×Q₈×C₁₃₉	1	4	yes	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	—	4	8	no	—
417	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
419	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
420	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
421	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
422	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
423	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
424	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
426	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
427	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
428	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
430	C₄⋊C₄	—	2	8	no	—
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	8	no	—
437	C₄⋊C₄	—	2	8	no	—
438	C₄⋊C₄	—	2	4	no	—
439	C₄⋊C₄	—	2	8	no	—
440	C₄⋊C₄	—	2	8	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	8	no	—
443	C₄⋊C₄	—	2	16	no	—
444	C₄⋊C₄	—	4	8	no	—
445	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
446	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
447	C₄⋊C₄	#41×C₁₃₉	1	8	yes	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	8	no	—
450	C₂²⋊C₄	—	2	16	no	—
451	C₂²⋊C₄	—	4	4	no	—
452	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	16	yes	—
453	C₄²	—	2	8	no	—
454	C₄²	—	2	4	no	—
455	C₄²	—	2	8	no	—
456	C₄²	—	2	4	no	—
457	C₄²	—	2	4	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	4	4	no	—
460	C₄²	—	4	2	no	—
461	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
462	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
463	C₄²	C₂×Q₈×C₁₃₉	1	4	yes	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	4	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	4	no	—
468	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
469	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
470	Q₈	—	2	8	no	—
471	Q₈	—	2	8	no	—
472	Q₈	—	4	8	no	—
473	Q₈	—	8	4	no	—
474	D₄	—	2	8	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	8	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	8	no	—
495	C₂×C₄	—	4	8	no	—
496	C₂×C₄	—	8	8	no	—
497	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
498	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
499	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
500	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
501	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
502	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
503	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
504	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
505	C₂×C₄	C₂×#41×C₁₃₉	1	8	yes	—
506	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
507	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
508	C₂²	—	2	4	no	—
509	C₂²	—	2	8	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	4	no	—
513	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
514	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
515	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
516	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
517	C₂²	#585×C₁₃₉	1	2	yes	—
518	C₄	—	2	4	no	—
519	C₄	—	2	4	no	—
520	C₄	—	2	4	no	—
521	C₄	—	2	4	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	8	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	4	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	2	no	—
529	C₄	#532×C₁₃₉	1	4	yes	—
530	C₄	D₄×Q₈×C₁₃₉	1	4	yes	—
531	C₂	—	4	4	no	—
532	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
533	C₂	C₂×D₄×Q₈×C₁₃₉	1	1	yes	characteristic
534	C₂	Q₈×#41×C₁₃₉	1	2	yes	—
535	C₂	#3500×C₁₃₉	1	1	yes	characteristic
536	C₂	#3515×C₁₃₉	1	2	yes	—

	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×#557×C₁₃₉	C₂	semidirect
3. #2862×C₁₃₉	C₂	semidirect
4. #2859×C₁₃₉	C₂	semidirect
5. #2567×C₁₃₉	C₂	semidirect
7. #2565×C₁₃₉	C₂	semidirect
8. #2556×C₁₃₉	C₂	semidirect
10. #2429×C₁₃₉	C₂	semidirect
11. #2360×C₁₃₉	C₂	semidirect
14. C₄²×Q₈×C₁₃₉	C₂	semidirect
78. #124×C₁₃₉	Q₈	semidirect
268. #36562	C₁₃₉	direct (N × H)
269. C₁₃₉	#36562	direct (N × H)
270. C₂×#557	C₂×C₁₃₉	semidirect
272. #2862	C₂×C₁₃₉	semidirect
273. #2859	C₂×C₁₃₉	semidirect
274. #2567	C₂×C₁₃₉	semidirect
276. #2565	C₂×C₁₃₉	semidirect
277. #2556	C₂×C₁₃₉	semidirect
279. #2429	C₂×C₁₃₉	semidirect
280. #2360	C₂×C₁₃₉	semidirect
283. C₄²×Q₈	C₂×C₁₃₉	semidirect
347. #124	Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#557×C₁₃₉	2
C₂×#554×C₁₃₉	2
#2862×C₁₃₉	2
#2859×C₁₃₉	2
#2567×C₁₃₉	2
#2566×C₁₃₉	2
#2565×C₁₃₉	2
#2556×C₁₃₉	2
#2542×C₁₃₉	2
#2429×C₁₃₉	2
#2360×C₁₃₉	2
C₄×#124×C₁₃₉	2
C₄²×Q₈×C₁₃₉	2
#36562	139

Subgroups — C139×#36562 #48031158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36562 #48031158