Subgroups — C₁₃₉×#36209 #48030805

Order 35584.

1802 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2859×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2857×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2536×C₁₃₉	C₂	1	2	yes	maximal
4	#2508×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2495×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2489×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2485×C₁₃₉	C₂	1	4	yes	maximal
8	#2356×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2346×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2285×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
15	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
16	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
20	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
21	#400×C₁₃₉	C₂²	1	8	yes	—
22	#398×C₁₃₉	C₂²	1	4	yes	—
23	#397×C₁₃₉	C₂²	1	8	yes	—
24	#394×C₁₃₉	C₂²	1	4	yes	—
25	#391×C₁₃₉	C₂²	1	2	yes	—
26	#391×C₁₃₉	C₂²	1	4	yes	—
27	#389×C₁₃₉	C₂²	1	4	yes	—
28	#389×C₁₃₉	C₂²	1	4	yes	—
29	#389×C₁₃₉	C₂²	1	4	yes	—
30	#389×C₁₃₉	C₂²	1	4	yes	—
31	#389×C₁₃₉	C₂²	1	4	yes	—
32	#388×C₁₃₉	C₂²	1	8	yes	—
33	#388×C₁₃₉	C₂²	1	8	yes	—
34	#387×C₁₃₉	C₂²	1	8	yes	—
35	#384×C₁₃₉	C₂²	1	1	yes	characteristic
36	#384×C₁₃₉	C₂²	1	2	yes	—
37	#383×C₁₃₉	C₂²	1	4	yes	—
38	#382×C₁₃₉	C₂²	1	2	yes	—
39	#382×C₁₃₉	C₂²	1	4	yes	—
40	#382×C₁₃₉	C₂²	1	8	yes	—
41	#380×C₁₃₉	C₂²	1	4	yes	—
42	#380×C₁₃₉	C₂²	1	4	yes	—
43	#380×C₁₃₉	C₂²	1	4	yes	—
44	#380×C₁₃₉	C₂²	1	4	yes	—
45	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
47	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
48	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
49	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
50	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
51	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
52	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
53	#376×C₁₃₉	C₂²	1	4	yes	—
54	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
56	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
60	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
61	#125×C₁₃₉	—	4	4	no	—
62	C₂²⋊Q₈×C₁₃₉	—	4	8	no	—
63	C₄×Q₈×C₁₃₉	—	2	8	no	—
64	C₄×D₄×C₁₃₉	—	2	8	no	—
65	C₄×D₄×C₁₃₉	—	2	4	no	—
66	#117×C₁₃₉	—	2	16	no	—
67	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
71	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
76	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
77	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
78	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
80	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
81	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
82	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
83	C₂×C₄²×C₁₃₉	—	2	8	no	—
84	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
85	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
86	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
87	C₂×C₄²×C₁₃₉	C₂³	1	8	yes	—
88	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
89	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
90	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
94	#95×C₁₃₉	C₂³	1	8	yes	—
95	#95×C₁₃₉	C₂³	1	8	yes	—
96	#95×C₁₃₉	C₂³	1	8	yes	—
97	#95×C₁₃₉	C₂³	1	8	yes	—
98	#95×C₁₃₉	C₂³	1	4	yes	—
99	#95×C₁₃₉	C₂³	1	2	yes	—
100	#95×C₁₃₉	C₂³	1	1	yes	characteristic
101	#95×C₁₃₉	C₂³	1	8	yes	—
102	#95×C₁₃₉	C₂³	1	4	yes	—
103	#95×C₁₃₉	C₂³	1	2	yes	—
104	#95×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
106	C₂×Q₈×C₁₃₉	—	2	4	no	—
107	C₂×Q₈×C₁₃₉	—	2	4	no	—
108	C₂×Q₈×C₁₃₉	—	2	4	no	—
109	C₂×D₄×C₁₃₉	—	2	4	no	—
110	C₂×D₄×C₁₃₉	—	2	2	no	—
111	C₂²×C₄×C₁₃₉	—	2	4	no	—
112	C₂²×C₄×C₁₃₉	—	2	4	no	—
113	C₂²×C₄×C₁₃₉	—	2	4	no	—
114	C₂²×C₄×C₁₃₉	—	2	4	no	—
115	C₂²×C₄×C₁₃₉	—	2	4	no	—
116	C₂²×C₄×C₁₃₉	—	2	4	no	—
117	C₂²×C₄×C₁₃₉	—	2	4	no	—
118	C₂²×C₄×C₁₃₉	—	2	4	no	—
119	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
120	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
121	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
122	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
124	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
125	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
127	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
129	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
130	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
131	C₄⋊C₄×C₁₃₉	—	2	8	no	—
132	C₄⋊C₄×C₁₃₉	—	2	8	no	—
133	C₄⋊C₄×C₁₃₉	—	2	4	no	—
134	C₄⋊C₄×C₁₃₉	—	2	2	no	—
135	C₄⋊C₄×C₁₃₉	—	2	4	no	—
136	C₄⋊C₄×C₁₃₉	—	2	8	no	—
137	C₄⋊C₄×C₁₃₉	—	2	8	no	—
138	C₄⋊C₄×C₁₃₉	—	2	8	no	—
139	C₄⋊C₄×C₁₃₉	—	2	8	no	—
140	C₄⋊C₄×C₁₃₉	—	4	8	no	—
141	C₄⋊C₄×C₁₃₉	—	4	8	no	—
142	C₂²⋊C₄×C₁₃₉	—	2	16	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	—	4	8	no	—
147	C₄²×C₁₃₉	—	2	4	no	—
148	C₄²×C₁₃₉	—	2	4	no	—
149	C₄²×C₁₃₉	—	2	4	no	—
150	C₄²×C₁₃₉	—	2	16	no	—
151	C₄²×C₁₃₉	—	2	4	no	—
152	C₄²×C₁₃₉	—	2	8	no	—
153	C₄²×C₁₃₉	—	2	2	no	—
154	C₄²×C₁₃₉	—	2	4	no	—
155	C₄²×C₁₃₉	#41	1	4	yes	—
156	C₄²×C₁₃₉	#41	1	4	yes	—
157	C₂³×C₁₃₉	—	2	2	no	—
158	C₂³×C₁₃₉	—	2	2	no	—
159	C₂³×C₁₃₉	—	2	2	no	—
160	C₂³×C₁₃₉	—	2	2	no	—
161	C₂³×C₁₃₉	—	2	2	no	—
162	C₂³×C₁₃₉	—	2	2	no	—
163	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
164	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
165	Q₈×C₁₃₉	—	4	8	no	—
166	D₄×C₁₃₉	—	2	8	no	—
167	C₂×C₄×C₁₃₉	—	2	2	no	—
168	C₂×C₄×C₁₃₉	—	2	2	no	—
169	C₂×C₄×C₁₃₉	—	2	2	no	—
170	C₂×C₄×C₁₃₉	—	2	2	no	—
171	C₂×C₄×C₁₃₉	—	2	16	no	—
172	C₂×C₄×C₁₃₉	—	2	2	no	—
173	C₂×C₄×C₁₃₉	—	2	2	no	—
174	C₂×C₄×C₁₃₉	—	2	2	no	—
175	C₂×C₄×C₁₃₉	—	2	8	no	—
176	C₂×C₄×C₁₃₉	—	2	8	no	—
177	C₂×C₄×C₁₃₉	—	2	4	no	—
178	C₂×C₄×C₁₃₉	—	2	4	no	—
179	C₂×C₄×C₁₃₉	—	2	2	no	—
180	C₂×C₄×C₁₃₉	—	2	2	no	—
181	C₂×C₄×C₁₃₉	—	2	4	no	—
182	C₂×C₄×C₁₃₉	—	2	2	no	—
183	C₂×C₄×C₁₃₉	—	2	4	no	—
184	C₂×C₄×C₁₃₉	—	2	8	no	—
185	C₂×C₄×C₁₃₉	—	2	2	no	—
186	C₂×C₄×C₁₃₉	—	2	2	no	—
187	C₂×C₄×C₁₃₉	—	2	8	no	—
188	C₂×C₄×C₁₃₉	—	2	2	no	—
189	C₂×C₄×C₁₃₉	—	4	8	no	—
190	C₂×C₄×C₁₃₉	—	4	8	no	—
191	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
192	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
193	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
194	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
195	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
196	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
197	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
198	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
199	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
200	C₂²×C₁₃₉	—	2	4	no	—
201	C₂²×C₁₃₉	—	2	4	no	—
202	C₂²×C₁₃₉	—	2	4	no	—
203	C₂²×C₁₃₉	—	4	2	no	—
204	C₂²×C₁₃₉	—	4	2	no	—
205	C₂²×C₁₃₉	—	4	2	no	—
206	C₂²×C₁₃₉	—	4	2	no	—
207	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
208	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
209	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
210	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
211	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
212	C₄×C₁₃₉	—	2	2	no	—
213	C₄×C₁₃₉	—	2	4	no	—
214	C₄×C₁₃₉	—	2	2	no	—
215	C₄×C₁₃₉	—	4	4	no	—
216	C₄×C₁₃₉	—	4	2	no	—
217	C₄×C₁₃₉	—	4	2	no	—
218	C₄×C₁₃₉	—	4	4	no	—
219	C₄×C₁₃₉	—	4	2	no	—
220	C₄×C₁₃₉	—	4	8	no	—
221	C₄×C₁₃₉	#552	1	8	yes	—
222	C₄×C₁₃₉	#555	1	4	yes	—
223	C₂×C₁₃₉	—	4	4	no	—
224	C₂×C₁₃₉	#3444	1	1	yes	characteristic
225	C₂×C₁₃₉	C₂×#552	1	2	yes	—
226	C₂×C₁₃₉	C₂×#555	1	1	yes	characteristic
227	C₂×C₁₃₉	#3509	1	1	yes	characteristic
228	C₂×C₁₃₉	#3511	1	2	yes	—
229	#36209	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₁₃₉	#36209	1	1	yes	characteristic, direct product factor, Sylow
231	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
232	#2857	C₂×C₁₃₉	1	2	yes	complemented
233	#2536	C₂×C₁₃₉	1	2	yes	—
234	#2508	C₂×C₁₃₉	1	4	yes	complemented
235	#2495	C₂×C₁₃₉	1	4	yes	complemented
236	#2489	C₂×C₁₃₉	1	4	yes	complemented
237	#2485	C₂×C₁₃₉	1	4	yes	—
238	#2356	C₂×C₁₃₉	1	2	yes	complemented
239	#2346	C₂×C₁₃₉	1	4	yes	complemented
240	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
241	#2285	C₂×C₁₃₉	1	2	yes	complemented
242	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic
243	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
244	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
245	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
246	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
247	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
248	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
249	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
250	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
251	#400	C₂²×C₁₃₉	1	8	yes	—
252	#398	C₂²×C₁₃₉	1	4	yes	—
253	#397	C₂²×C₁₃₉	1	8	yes	—
254	#394	C₂²×C₁₃₉	1	4	yes	—
255	#391	C₂²×C₁₃₉	1	2	yes	—
256	#391	C₂²×C₁₃₉	1	4	yes	—
257	#389	C₂²×C₁₃₉	1	4	yes	—
258	#389	C₂²×C₁₃₉	1	4	yes	—
259	#389	C₂²×C₁₃₉	1	4	yes	—
260	#389	C₂²×C₁₃₉	1	4	yes	—
261	#389	C₂²×C₁₃₉	1	4	yes	—
262	#388	C₂²×C₁₃₉	1	8	yes	—
263	#388	C₂²×C₁₃₉	1	8	yes	—
264	#387	C₂²×C₁₃₉	1	8	yes	—
265	#384	C₂²×C₁₃₉	1	1	yes	characteristic
266	#384	C₂²×C₁₃₉	1	2	yes	—
267	#383	C₂²×C₁₃₉	1	4	yes	—
268	#382	C₂²×C₁₃₉	1	8	yes	—
269	#382	C₂²×C₁₃₉	1	2	yes	—
270	#382	C₂²×C₁₃₉	1	4	yes	—
271	#380	C₂²×C₁₃₉	1	4	yes	—
272	#380	C₂²×C₁₃₉	1	4	yes	—
273	#380	C₂²×C₁₃₉	1	4	yes	—
274	#380	C₂²×C₁₃₉	1	4	yes	—
275	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
276	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
277	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
278	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
279	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
280	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
281	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
282	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
283	#376	C₂²×C₁₃₉	1	4	yes	—
284	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
285	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
286	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
287	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
288	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
289	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
290	C₄⋊Q₈	—	2	4	no	—
291	#125	—	4	4	no	—
292	C₂²⋊Q₈	—	4	8	no	—
293	C₄×Q₈	—	2	8	no	—
294	C₄×D₄	—	2	8	no	—
295	C₄×D₄	—	2	4	no	—
296	#117	—	2	16	no	—
297	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
298	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
303	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
304	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
308	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
309	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
310	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
311	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
312	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
313	C₂×C₄²	—	2	8	no	—
314	C₂×C₄²	C₂³×C₁₃₉	1	8	yes	—
315	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
316	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
317	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
318	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
319	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
320	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
321	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
322	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
324	#95	C₂³×C₁₃₉	1	1	yes	characteristic
325	#95	C₂³×C₁₃₉	1	8	yes	—
326	#95	C₂³×C₁₃₉	1	4	yes	—
327	#95	C₂³×C₁₃₉	1	2	yes	—
328	#95	C₂³×C₁₃₉	1	1	yes	characteristic
329	#95	C₂³×C₁₃₉	1	2	yes	—
330	#95	C₂³×C₁₃₉	1	8	yes	—
331	#95	C₂³×C₁₃₉	1	8	yes	—
332	#95	C₂³×C₁₃₉	1	8	yes	—
333	#95	C₂³×C₁₃₉	1	8	yes	—
334	#95	C₂³×C₁₃₉	1	4	yes	—
335	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
350	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
351	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
352	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
353	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
354	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
355	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
356	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
360	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
361	C₄⋊C₄	—	2	8	no	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	8	no	—
367	C₄⋊C₄	—	2	8	no	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	4	8	no	—
371	C₄⋊C₄	—	4	8	no	—
372	C₂²⋊C₄	—	2	16	no	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	4	8	no	—
377	C₄²	—	2	4	no	—
378	C₄²	—	2	4	no	—
379	C₄²	—	2	4	no	—
380	C₄²	—	2	16	no	—
381	C₄²	—	2	4	no	—
382	C₄²	—	2	8	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	4	no	—
385	C₄²	#41×C₁₃₉	1	4	yes	—
386	C₄²	#41×C₁₃₉	1	4	yes	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
394	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
395	Q₈	—	4	8	no	—
396	D₄	—	2	8	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	16	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	4	8	no	—
420	C₂×C₄	—	4	8	no	—
421	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
422	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
423	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
424	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
425	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
426	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
427	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
428	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
429	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
438	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
439	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
440	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
441	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
442	C₄	—	2	2	no	—
443	C₄	—	2	4	no	—
444	C₄	—	2	2	no	—
445	C₄	—	4	4	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	4	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	8	no	—
451	C₄	#552×C₁₃₉	1	8	yes	—
452	C₄	#555×C₁₃₉	1	4	yes	—
453	C₂	—	4	4	no	—
454	C₂	#3444×C₁₃₉	1	1	yes	characteristic
455	C₂	C₂×#552×C₁₃₉	1	2	yes	—
456	C₂	C₂×#555×C₁₃₉	1	1	yes	characteristic
457	C₂	#3509×C₁₃₉	1	1	yes	characteristic
458	C₂	#3511×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. #2859×C₁₃₉	C₂	semidirect
2. #2857×C₁₃₉	C₂	semidirect
4. #2508×C₁₃₉	C₂	semidirect
5. #2495×C₁₃₉	C₂	semidirect
6. #2489×C₁₃₉	C₂	semidirect
8. #2356×C₁₃₉	C₂	semidirect
9. #2346×C₁₃₉	C₂	semidirect
10. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
11. #2285×C₁₃₉	C₂	semidirect
229. #36209	C₁₃₉	direct (N × H)
230. C₁₃₉	#36209	direct (N × H)
231. #2859	C₂×C₁₃₉	semidirect
232. #2857	C₂×C₁₃₉	semidirect
234. #2508	C₂×C₁₃₉	semidirect
235. #2495	C₂×C₁₃₉	semidirect
236. #2489	C₂×C₁₃₉	semidirect
238. #2356	C₂×C₁₃₉	semidirect
239. #2346	C₂×C₁₃₉	semidirect
240. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
241. #2285	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2859×C₁₃₉	2
#2857×C₁₃₉	2
#2536×C₁₃₉	2
#2508×C₁₃₉	2
#2495×C₁₃₉	2
#2489×C₁₃₉	2
#2485×C₁₃₉	2
#2356×C₁₃₉	2
#2346×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
#2285×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36209	139

Subgroups — C139×#36209 #48030805

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36209 #48030805