Subgroups — C₁₃₉×#37254 #48031850

Order 35584.

1752 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2864×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2792×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2761×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	#2727×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2724×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2723×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2709×C₁₃₉	C₂	1	2	yes	maximal
8	#2683×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2638×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2466×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2449×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2322×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	C₄×#127×C₁₃₉	C₂	1	1	yes	maximal, characteristic
14	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
16	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
18	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
19	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
22	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
23	#399×C₁₃₉	C₂²	1	4	yes	—
24	#398×C₁₃₉	C₂²	1	2	yes	—
25	#398×C₁₃₉	C₂²	1	4	yes	—
26	#397×C₁₃₉	C₂²	1	4	yes	—
27	#397×C₁₃₉	C₂²	1	2	yes	—
28	#397×C₁₃₉	C₂²	1	4	yes	—
29	#396×C₁₃₉	C₂²	1	4	yes	—
30	#396×C₁₃₉	C₂²	1	4	yes	—
31	#395×C₁₃₉	C₂²	1	2	yes	—
32	#395×C₁₃₉	C₂²	1	4	yes	—
33	#394×C₁₃₉	C₂²	1	4	yes	—
34	#394×C₁₃₉	C₂²	1	4	yes	—
35	#394×C₁₃₉	C₂²	1	4	yes	—
36	#393×C₁₃₉	C₂²	1	2	yes	—
37	#390×C₁₃₉	C₂²	1	1	yes	characteristic
38	#390×C₁₃₉	C₂²	1	4	yes	—
39	#390×C₁₃₉	C₂²	1	1	yes	characteristic
40	#389×C₁₃₉	C₂²	1	4	yes	—
41	#389×C₁₃₉	C₂²	1	4	yes	—
42	#389×C₁₃₉	C₂²	1	2	yes	—
43	#389×C₁₃₉	C₂²	1	2	yes	—
44	#389×C₁₃₉	C₂²	1	2	yes	—
45	#389×C₁₃₉	C₂²	1	2	yes	—
46	#388×C₁₃₉	C₂²	1	4	yes	—
47	#388×C₁₃₉	C₂²	1	4	yes	—
48	#387×C₁₃₉	C₂²	1	4	yes	—
49	#387×C₁₃₉	C₂²	1	4	yes	—
50	#387×C₁₃₉	C₂²	1	4	yes	—
51	#387×C₁₃₉	C₂²	1	4	yes	—
52	#387×C₁₃₉	C₂²	1	4	yes	—
53	#386×C₁₃₉	C₂²	1	2	yes	—
54	#386×C₁₃₉	C₂²	1	4	yes	—
55	#386×C₁₃₉	C₂²	1	4	yes	—
56	#385×C₁₃₉	C₂²	1	4	yes	—
57	#385×C₁₃₉	C₂²	1	2	yes	—
58	#385×C₁₃₉	C₂²	1	4	yes	—
59	#385×C₁₃₉	C₂²	1	4	yes	—
60	#384×C₁₃₉	C₂²	1	1	yes	characteristic
61	#382×C₁₃₉	C₂²	1	2	yes	—
62	#382×C₁₃₉	C₂²	1	2	yes	—
63	#381×C₁₃₉	C₂²	1	2	yes	—
64	#381×C₁₃₉	C₂²	1	2	yes	—
65	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
66	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
67	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
69	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
75	#127×C₁₃₉	—	2	4	no	—
76	#126×C₁₃₉	—	4	8	no	—
77	#123×C₁₃₉	—	2	8	no	—
78	C₂²⋊Q₈×C₁₃₉	—	4	8	no	—
79	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
80	C₄×D₄×C₁₃₉	—	4	8	no	—
81	C₄×D₄×C₁₃₉	—	4	2	no	—
82	C₄×D₄×C₁₃₉	—	4	2	no	—
83	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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	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	2	yes	—
96	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
113	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
117	#95×C₁₃₉	C₂³	1	2	yes	—
118	#95×C₁₃₉	C₂³	1	4	yes	—
119	#95×C₁₃₉	C₂³	1	4	yes	—
120	#95×C₁₃₉	C₂³	1	4	yes	—
121	#95×C₁₃₉	C₂³	1	4	yes	—
122	#95×C₁₃₉	C₂³	1	4	yes	—
123	#95×C₁₃₉	C₂³	1	2	yes	—
124	#95×C₁₃₉	C₂³	1	4	yes	—
125	#95×C₁₃₉	C₂³	1	4	yes	—
126	#95×C₁₃₉	C₂³	1	4	yes	—
127	#95×C₁₃₉	C₂³	1	4	yes	—
128	#95×C₁₃₉	C₂³	1	4	yes	—
129	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
130	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
131	C₂×Q₈×C₁₃₉	—	4	4	no	—
132	C₂×Q₈×C₁₃₉	—	4	2	no	—
133	C₂×D₄×C₁₃₉	—	2	8	no	—
134	C₂×D₄×C₁₃₉	—	2	2	no	—
135	C₂×D₄×C₁₃₉	—	2	8	no	—
136	C₂×D₄×C₁₃₉	—	4	1	no	—
137	C₂×D₄×C₁₃₉	—	4	4	no	—
138	C₂×D₄×C₁₃₉	—	4	1	no	—
139	C₂×D₄×C₁₃₉	—	4	1	no	—
140	C₂×D₄×C₁₃₉	—	4	1	no	—
141	C₂×D₄×C₁₃₉	#41	1	4	yes	—
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	—	4	2	no	—
146	C₂²×C₄×C₁₃₉	—	4	2	no	—
147	C₂²×C₄×C₁₃₉	—	4	2	no	—
148	C₂²×C₄×C₁₃₉	—	4	4	no	—
149	C₂²×C₄×C₁₃₉	—	4	4	no	—
150	C₂²×C₄×C₁₃₉	—	4	4	no	—
151	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
152	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
162	C₄⋊C₄×C₁₃₉	—	2	8	no	—
163	C₄⋊C₄×C₁₃₉	—	2	8	no	—
164	C₄⋊C₄×C₁₃₉	—	2	4	no	—
165	C₄⋊C₄×C₁₃₉	—	2	8	no	—
166	C₄⋊C₄×C₁₃₉	—	2	4	no	—
167	C₄⋊C₄×C₁₃₉	—	2	8	no	—
168	C₄⋊C₄×C₁₃₉	—	4	4	no	—
169	C₄⋊C₄×C₁₃₉	—	4	2	no	—
170	C₄⋊C₄×C₁₃₉	—	4	2	no	—
171	C₄⋊C₄×C₁₃₉	—	4	4	no	—
172	C₄⋊C₄×C₁₃₉	—	4	1	no	—
173	C₄⋊C₄×C₁₃₉	—	4	1	no	—
174	C₄⋊C₄×C₁₃₉	—	4	4	no	—
175	C₄⋊C₄×C₁₃₉	—	4	2	no	—
176	C₄⋊C₄×C₁₃₉	—	4	4	no	—
177	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
178	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
179	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
180	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
181	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
182	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
183	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
184	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
185	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
186	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
187	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
188	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
189	C₄²×C₁₃₉	—	2	2	no	—
190	C₄²×C₁₃₉	—	2	4	no	—
191	C₄²×C₁₃₉	—	2	2	no	—
192	C₄²×C₁₃₉	—	2	4	no	—
193	C₄²×C₁₃₉	—	4	1	no	—
194	C₄²×C₁₃₉	—	4	4	no	—
195	C₂³×C₁₃₉	—	2	4	no	—
196	C₂³×C₁₃₉	—	2	2	no	—
197	C₂³×C₁₃₉	—	2	4	no	—
198	C₂³×C₁₃₉	—	2	2	no	—
199	C₂³×C₁₃₉	—	2	2	no	—
200	C₂³×C₁₃₉	—	2	4	no	—
201	C₂³×C₁₃₉	—	2	2	no	—
202	C₂³×C₁₃₉	—	2	4	no	—
203	C₂³×C₁₃₉	—	2	2	no	—
204	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
205	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
206	Q₈×C₁₃₉	—	8	4	no	—
207	D₄×C₁₃₉	—	4	4	no	—
208	D₄×C₁₃₉	—	4	16	no	—
209	D₄×C₁₃₉	—	4	4	no	—
210	C₂×C₄×C₁₃₉	—	2	2	no	—
211	C₂×C₄×C₁₃₉	—	2	1	no	—
212	C₂×C₄×C₁₃₉	—	2	2	no	—
213	C₂×C₄×C₁₃₉	—	2	2	no	—
214	C₂×C₄×C₁₃₉	—	2	2	no	—
215	C₂×C₄×C₁₃₉	—	2	2	no	—
216	C₂×C₄×C₁₃₉	—	2	1	no	—
217	C₂×C₄×C₁₃₉	—	2	4	no	—
218	C₂×C₄×C₁₃₉	—	2	4	no	—
219	C₂×C₄×C₁₃₉	—	2	1	no	—
220	C₂×C₄×C₁₃₉	—	2	4	no	—
221	C₂×C₄×C₁₃₉	—	2	4	no	—
222	C₂×C₄×C₁₃₉	—	2	4	no	—
223	C₂×C₄×C₁₃₉	—	2	4	no	—
224	C₂×C₄×C₁₃₉	—	2	4	no	—
225	C₂×C₄×C₁₃₉	—	2	4	no	—
226	C₂×C₄×C₁₃₉	—	2	4	no	—
227	C₂×C₄×C₁₃₉	—	2	4	no	—
228	C₂×C₄×C₁₃₉	—	2	2	no	—
229	C₂×C₄×C₁₃₉	—	2	2	no	—
230	C₂×C₄×C₁₃₉	—	2	2	no	—
231	C₂×C₄×C₁₃₉	—	2	4	no	—
232	C₂×C₄×C₁₃₉	—	2	4	no	—
233	C₂×C₄×C₁₃₉	—	2	4	no	—
234	C₂×C₄×C₁₃₉	—	2	4	no	—
235	C₂×C₄×C₁₃₉	—	4	8	no	—
236	C₂×C₄×C₁₃₉	—	8	4	no	—
237	C₂×C₄×C₁₃₉	—	8	4	no	—
238	C₂×C₄×C₁₃₉	—	8	4	no	—
239	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
240	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
241	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
242	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
243	C₂²×C₁₃₉	—	2	4	no	—
244	C₂²×C₁₃₉	—	2	8	no	—
245	C₂²×C₁₃₉	—	4	2	no	—
246	C₂²×C₁₃₉	—	4	2	no	—
247	C₂²×C₁₃₉	—	4	4	no	—
248	C₂²×C₁₃₉	—	4	2	no	—
249	C₂²×C₁₃₉	—	4	4	no	—
250	C₂²×C₁₃₉	—	4	2	no	—
251	C₂²×C₁₃₉	—	4	2	no	—
252	C₂²×C₁₃₉	—	4	4	no	—
253	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
254	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
255	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
256	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
257	C₂²×C₁₃₉	#585	1	1	yes	characteristic
258	C₄×C₁₃₉	—	2	2	no	—
259	C₄×C₁₃₉	—	2	4	no	—
260	C₄×C₁₃₉	—	2	2	no	—
261	C₄×C₁₃₉	—	2	4	no	—
262	C₄×C₁₃₉	—	4	4	no	—
263	C₄×C₁₃₉	—	4	4	no	—
264	C₄×C₁₃₉	—	4	2	no	—
265	C₄×C₁₃₉	—	4	2	no	—
266	C₄×C₁₃₉	—	4	4	no	—
267	C₄×C₁₃₉	—	4	1	no	—
268	C₄×C₁₃₉	—	4	4	no	—
269	C₂×C₁₃₉	—	4	4	no	—
270	C₂×C₁₃₉	—	8	2	no	—
271	C₂×C₁₃₉	#3459	1	1	yes	characteristic
272	C₂×C₁₃₉	#3520	1	2	yes	—
273	C₂×C₁₃₉	#3543	1	1	yes	characteristic
274	C₂×C₁₃₉	#3550	1	1	yes	characteristic
275	C₂×C₁₃₉	#3559	1	2	yes	—
276	#37254	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₁₃₉	#37254	1	1	yes	characteristic, direct product factor, Sylow
278	#2864	C₂×C₁₃₉	1	2	yes	complemented
279	#2792	C₂×C₁₃₉	1	2	yes	complemented
280	#2761	C₂×C₁₃₉	1	4	yes	complemented
281	#2727	C₂×C₁₃₉	1	2	yes	complemented
282	#2724	C₂×C₁₃₉	1	1	yes	characteristic, complemented
283	#2723	C₂×C₁₃₉	1	4	yes	complemented
284	#2709	C₂×C₁₃₉	1	2	yes	—
285	#2683	C₂×C₁₃₉	1	1	yes	characteristic, complemented
286	#2638	C₂×C₁₃₉	1	2	yes	complemented
287	#2466	C₂×C₁₃₉	1	4	yes	complemented
288	#2449	C₂×C₁₃₉	1	4	yes	complemented
289	#2322	C₂×C₁₃₉	1	2	yes	complemented
290	C₄×#127	C₂×C₁₃₉	1	1	yes	characteristic
291	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
292	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
293	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
294	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
295	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
296	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
297	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
298	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
299	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
300	#399	C₂²×C₁₃₉	1	4	yes	—
301	#398	C₂²×C₁₃₉	1	2	yes	—
302	#398	C₂²×C₁₃₉	1	4	yes	—
303	#397	C₂²×C₁₃₉	1	4	yes	—
304	#397	C₂²×C₁₃₉	1	2	yes	—
305	#397	C₂²×C₁₃₉	1	4	yes	—
306	#396	C₂²×C₁₃₉	1	4	yes	—
307	#396	C₂²×C₁₃₉	1	4	yes	—
308	#395	C₂²×C₁₃₉	1	2	yes	—
309	#395	C₂²×C₁₃₉	1	4	yes	—
310	#394	C₂²×C₁₃₉	1	4	yes	—
311	#394	C₂²×C₁₃₉	1	4	yes	—
312	#394	C₂²×C₁₃₉	1	4	yes	—
313	#393	C₂²×C₁₃₉	1	2	yes	—
314	#390	C₂²×C₁₃₉	1	1	yes	characteristic
315	#390	C₂²×C₁₃₉	1	4	yes	—
316	#390	C₂²×C₁₃₉	1	1	yes	characteristic
317	#389	C₂²×C₁₃₉	1	4	yes	—
318	#389	C₂²×C₁₃₉	1	2	yes	—
319	#389	C₂²×C₁₃₉	1	2	yes	—
320	#389	C₂²×C₁₃₉	1	2	yes	—
321	#389	C₂²×C₁₃₉	1	2	yes	—
322	#389	C₂²×C₁₃₉	1	4	yes	—
323	#388	C₂²×C₁₃₉	1	4	yes	—
324	#388	C₂²×C₁₃₉	1	4	yes	—
325	#387	C₂²×C₁₃₉	1	4	yes	—
326	#387	C₂²×C₁₃₉	1	4	yes	—
327	#387	C₂²×C₁₃₉	1	4	yes	—
328	#387	C₂²×C₁₃₉	1	4	yes	—
329	#387	C₂²×C₁₃₉	1	4	yes	—
330	#386	C₂²×C₁₃₉	1	2	yes	—
331	#386	C₂²×C₁₃₉	1	4	yes	—
332	#386	C₂²×C₁₃₉	1	4	yes	—
333	#385	C₂²×C₁₃₉	1	4	yes	—
334	#385	C₂²×C₁₃₉	1	2	yes	—
335	#385	C₂²×C₁₃₉	1	4	yes	—
336	#385	C₂²×C₁₃₉	1	4	yes	—
337	#384	C₂²×C₁₃₉	1	1	yes	characteristic
338	#382	C₂²×C₁₃₉	1	2	yes	—
339	#382	C₂²×C₁₃₉	1	2	yes	—
340	#381	C₂²×C₁₃₉	1	2	yes	—
341	#381	C₂²×C₁₃₉	1	2	yes	—
342	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
343	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
344	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
345	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
346	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
347	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
348	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
349	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
350	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
351	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
352	#127	—	2	4	no	—
353	#126	—	4	8	no	—
354	#123	—	2	8	no	—
355	C₂²⋊Q₈	—	4	8	no	—
356	C₂²⋊Q₈	—	4	4	no	—
357	C₄×D₄	—	4	8	no	—
358	C₄×D₄	—	4	2	no	—
359	C₄×D₄	—	4	2	no	—
360	C₂×C₄⋊C₄	—	4	4	no	—
361	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
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	4	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	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
373	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	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	4	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
388	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
390	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
392	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
393	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
394	#95	C₂³×C₁₃₉	1	4	yes	—
395	#95	C₂³×C₁₃₉	1	4	yes	—
396	#95	C₂³×C₁₃₉	1	4	yes	—
397	#95	C₂³×C₁₃₉	1	2	yes	—
398	#95	C₂³×C₁₃₉	1	2	yes	—
399	#95	C₂³×C₁₃₉	1	4	yes	—
400	#95	C₂³×C₁₃₉	1	4	yes	—
401	#95	C₂³×C₁₃₉	1	4	yes	—
402	#95	C₂³×C₁₃₉	1	4	yes	—
403	#95	C₂³×C₁₃₉	1	4	yes	—
404	#95	C₂³×C₁₃₉	1	4	yes	—
405	#95	C₂³×C₁₃₉	1	4	yes	—
406	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
407	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
408	C₂×Q₈	—	4	4	no	—
409	C₂×Q₈	—	4	2	no	—
410	C₂×D₄	—	2	8	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	8	no	—
413	C₂×D₄	—	4	1	no	—
414	C₂×D₄	—	4	4	no	—
415	C₂×D₄	—	4	1	no	—
416	C₂×D₄	—	4	1	no	—
417	C₂×D₄	—	4	1	no	—
418	C₂×D₄	#41×C₁₃₉	1	4	yes	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	—	4	4	no	—
426	C₂²×C₄	—	4	4	no	—
427	C₂²×C₄	—	4	4	no	—
428	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
430	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
431	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
432	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
433	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
434	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
435	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
437	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
438	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
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	4	no	—
444	C₄⋊C₄	—	2	8	no	—
445	C₄⋊C₄	—	4	4	no	—
446	C₄⋊C₄	—	4	2	no	—
447	C₄⋊C₄	—	4	2	no	—
448	C₄⋊C₄	—	4	4	no	—
449	C₄⋊C₄	—	4	1	no	—
450	C₄⋊C₄	—	4	1	no	—
451	C₄⋊C₄	—	4	4	no	—
452	C₄⋊C₄	—	4	2	no	—
453	C₄⋊C₄	—	4	4	no	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	8	no	—
456	C₂²⋊C₄	—	2	8	no	—
457	C₂²⋊C₄	—	2	8	no	—
458	C₂²⋊C₄	—	4	2	no	—
459	C₂²⋊C₄	—	4	4	no	—
460	C₂²⋊C₄	—	4	2	no	—
461	C₂²⋊C₄	—	4	2	no	—
462	C₂²⋊C₄	—	4	4	no	—
463	C₂²⋊C₄	—	4	4	no	—
464	C₂²⋊C₄	—	4	4	no	—
465	C₂²⋊C₄	—	4	4	no	—
466	C₄²	—	2	2	no	—
467	C₄²	—	2	4	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	4	no	—
470	C₄²	—	4	1	no	—
471	C₄²	—	4	4	no	—
472	C₂³	—	2	4	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	2	no	—
481	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
482	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
483	Q₈	—	8	4	no	—
484	D₄	—	4	4	no	—
485	D₄	—	4	16	no	—
486	D₄	—	4	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	4	8	no	—
513	C₂×C₄	—	8	4	no	—
514	C₂×C₄	—	8	4	no	—
515	C₂×C₄	—	8	4	no	—
516	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
517	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
518	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
519	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	8	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	4	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	4	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	4	no	—
530	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
531	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
532	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
533	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
534	C₂²	#585×C₁₃₉	1	1	yes	characteristic
535	C₄	—	2	2	no	—
536	C₄	—	2	4	no	—
537	C₄	—	2	2	no	—
538	C₄	—	2	4	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	4	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	4	no	—
544	C₄	—	4	4	no	—
545	C₄	—	4	4	no	—
546	C₂	—	4	4	no	—
547	C₂	—	8	2	no	—
548	C₂	#3459×C₁₃₉	1	1	yes	characteristic
549	C₂	#3520×C₁₃₉	1	2	yes	—
550	C₂	#3543×C₁₃₉	1	1	yes	characteristic
551	C₂	#3550×C₁₃₉	1	1	yes	characteristic
552	C₂	#3559×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#127×C₁₃₉	C₂²
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. #2864×C₁₃₉	C₂	semidirect
2. #2792×C₁₃₉	C₂	semidirect
3. #2761×C₁₃₉	C₂	semidirect
4. #2727×C₁₃₉	C₂	semidirect
5. #2724×C₁₃₉	C₂	semidirect
6. #2723×C₁₃₉	C₂	semidirect
8. #2683×C₁₃₉	C₂	semidirect
9. #2638×C₁₃₉	C₂	semidirect
10. #2466×C₁₃₉	C₂	semidirect
11. #2449×C₁₃₉	C₂	semidirect
12. #2322×C₁₃₉	C₂	semidirect
276. #37254	C₁₃₉	direct (N × H)
277. C₁₃₉	#37254	direct (N × H)
278. #2864	C₂×C₁₃₉	semidirect
279. #2792	C₂×C₁₃₉	semidirect
280. #2761	C₂×C₁₃₉	semidirect
281. #2727	C₂×C₁₃₉	semidirect
282. #2724	C₂×C₁₃₉	semidirect
283. #2723	C₂×C₁₃₉	semidirect
285. #2683	C₂×C₁₃₉	semidirect
286. #2638	C₂×C₁₃₉	semidirect
287. #2466	C₂×C₁₃₉	semidirect
288. #2449	C₂×C₁₃₉	semidirect
289. #2322	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2864×C₁₃₉	2
#2792×C₁₃₉	2
#2761×C₁₃₉	2
#2727×C₁₃₉	2
#2724×C₁₃₉	2
#2723×C₁₃₉	2
#2709×C₁₃₉	2
#2683×C₁₃₉	2
#2638×C₁₃₉	2
#2466×C₁₃₉	2
#2449×C₁₃₉	2
#2322×C₁₃₉	2
C₄×#127×C₁₃₉	2
#37254	139

Subgroups — C139×#37254 #48031850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37254 #48031850