Subgroups — C₁₃₉×#37299 #48031895

Order 35584.

2258 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#2727×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2683×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2672×C₁₃₉	C₂	1	8	yes	maximal, complemented
7	#2620×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2567×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2545×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2544×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2542×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2296×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#542×C₁₃₉	—	2	16	no	—
14	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
15	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
18	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
20	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	8	yes	—
25	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
27	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
32	#399×C₁₃₉	C₂²	1	8	yes	—
33	#396×C₁₃₉	C₂²	1	8	yes	—
34	#396×C₁₃₉	C₂²	1	8	yes	—
35	#395×C₁₃₉	C₂²	1	8	yes	—
36	#394×C₁₃₉	C₂²	1	8	yes	—
37	#394×C₁₃₉	C₂²	1	8	yes	—
38	#391×C₁₃₉	C₂²	1	2	yes	—
39	#391×C₁₃₉	C₂²	1	2	yes	—
40	#390×C₁₃₉	C₂²	1	2	yes	—
41	#390×C₁₃₉	C₂²	1	2	yes	—
42	#390×C₁₃₉	C₂²	1	4	yes	—
43	#389×C₁₃₉	C₂²	1	2	yes	—
44	#389×C₁₃₉	C₂²	1	2	yes	—
45	#389×C₁₃₉	C₂²	1	8	yes	—
46	#389×C₁₃₉	C₂²	1	4	yes	—
47	#388×C₁₃₉	C₂²	1	8	yes	—
48	#386×C₁₃₉	C₂²	1	8	yes	—
49	#385×C₁₃₉	C₂²	1	4	yes	—
50	#384×C₁₃₉	C₂²	1	1	yes	characteristic
51	#384×C₁₃₉	C₂²	1	2	yes	—
52	#384×C₁₃₉	C₂²	1	1	yes	characteristic
53	#380×C₁₃₉	C₂²	1	4	yes	—
54	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
55	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
56	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
57	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
58	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
60	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
61	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
64	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
65	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
66	#127×C₁₃₉	—	4	2	no	—
67	#126×C₁₃₉	—	2	16	no	—
68	#124×C₁₃₉	—	2	16	no	—
69	#124×C₁₃₉	—	2	8	no	—
70	#124×C₁₃₉	—	4	4	no	—
71	#123×C₁₃₉	—	2	16	no	—
72	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
73	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
74	C₂²⋊Q₈×C₁₃₉	—	4	16	no	—
75	#121×C₁₃₉	—	2	8	no	—
76	#121×C₁₃₉	—	4	8	no	—
77	C₄×Q₈×C₁₃₉	—	2	8	no	—
78	C₄×D₄×C₁₃₉	—	2	8	no	—
79	#117×C₁₃₉	—	4	2	no	—
80	#117×C₁₃₉	D₄	1	8	yes	complemented
81	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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	8	yes	—
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
98	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
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	8	yes	—
102	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
103	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂×C₄²×C₁₃₉	—	4	2	no	—
106	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
109	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
110	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
111	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
112	#95×C₁₃₉	C₂³	1	4	yes	—
113	#95×C₁₃₉	C₂³	1	8	yes	—
114	#95×C₁₃₉	C₂³	1	8	yes	—
115	#95×C₁₃₉	C₂³	1	4	yes	—
116	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
117	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
118	C₂×Q₈×C₁₃₉	—	2	4	no	—
119	C₂×Q₈×C₁₃₉	—	2	8	no	—
120	C₂×Q₈×C₁₃₉	—	2	4	no	—
121	C₂×Q₈×C₁₃₉	—	2	4	no	—
122	C₂×Q₈×C₁₃₉	—	4	8	no	—
123	C₂×D₄×C₁₃₉	—	2	8	no	—
124	C₂×D₄×C₁₃₉	—	2	4	no	—
125	C₂×D₄×C₁₃₉	—	2	4	no	—
126	C₂×D₄×C₁₃₉	—	2	4	no	—
127	C₂×D₄×C₁₃₉	—	2	8	no	—
128	C₂×D₄×C₁₃₉	—	4	4	no	—
129	C₂×D₄×C₁₃₉	—	4	8	no	—
130	C₂×D₄×C₁₃₉	—	4	4	no	—
131	C₂²×C₄×C₁₃₉	—	2	2	no	—
132	C₂²×C₄×C₁₃₉	—	2	2	no	—
133	C₂²×C₄×C₁₃₉	—	2	4	no	—
134	C₂²×C₄×C₁₃₉	—	2	4	no	—
135	C₂²×C₄×C₁₃₉	—	2	8	no	—
136	C₂²×C₄×C₁₃₉	—	4	2	no	—
137	C₂²×C₄×C₁₃₉	—	4	8	no	—
138	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
149	C₄⋊C₄×C₁₃₉	—	2	4	no	—
150	C₄⋊C₄×C₁₃₉	—	2	4	no	—
151	C₄⋊C₄×C₁₃₉	—	2	8	no	—
152	C₄⋊C₄×C₁₃₉	—	2	8	no	—
153	C₄⋊C₄×C₁₃₉	—	2	8	no	—
154	C₄⋊C₄×C₁₃₉	—	2	8	no	—
155	C₄⋊C₄×C₁₃₉	—	2	8	no	—
156	C₄⋊C₄×C₁₃₉	—	2	8	no	—
157	C₄⋊C₄×C₁₃₉	—	4	2	no	—
158	C₄⋊C₄×C₁₃₉	—	4	4	no	—
159	C₄⋊C₄×C₁₃₉	—	4	8	no	—
160	C₄⋊C₄×C₁₃₉	—	4	4	no	—
161	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
162	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
163	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
164	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
165	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
166	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
167	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
168	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
169	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
170	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
171	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
172	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
173	C₄²×C₁₃₉	—	2	8	no	—
174	C₄²×C₁₃₉	—	2	2	no	—
175	C₄²×C₁₃₉	—	2	2	no	—
176	C₄²×C₁₃₉	—	2	4	no	—
177	C₄²×C₁₃₉	—	4	2	no	—
178	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
179	C₂³×C₁₃₉	—	2	1	no	—
180	C₂³×C₁₃₉	—	2	2	no	—
181	C₂³×C₁₃₉	—	2	1	no	—
182	C₂³×C₁₃₉	—	2	2	no	—
183	C₂³×C₁₃₉	—	2	4	no	—
184	C₂³×C₁₃₉	—	2	8	no	—
185	C₂³×C₁₃₉	—	2	4	no	—
186	C₂³×C₁₃₉	—	2	4	no	—
187	C₂³×C₁₃₉	—	2	8	no	—
188	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
189	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
190	Q₈×C₁₃₉	—	4	8	no	—
191	Q₈×C₁₃₉	—	8	8	no	—
192	D₄×C₁₃₉	—	4	8	no	—
193	D₄×C₁₃₉	—	8	8	no	—
194	D₄×C₁₃₉	—	8	8	no	—
195	C₂×C₄×C₁₃₉	—	2	2	no	—
196	C₂×C₄×C₁₃₉	—	2	2	no	—
197	C₂×C₄×C₁₃₉	—	2	1	no	—
198	C₂×C₄×C₁₃₉	—	2	4	no	—
199	C₂×C₄×C₁₃₉	—	2	2	no	—
200	C₂×C₄×C₁₃₉	—	2	4	no	—
201	C₂×C₄×C₁₃₉	—	2	1	no	—
202	C₂×C₄×C₁₃₉	—	2	2	no	—
203	C₂×C₄×C₁₃₉	—	2	8	no	—
204	C₂×C₄×C₁₃₉	—	2	4	no	—
205	C₂×C₄×C₁₃₉	—	2	4	no	—
206	C₂×C₄×C₁₃₉	—	2	4	no	—
207	C₂×C₄×C₁₃₉	—	2	4	no	—
208	C₂×C₄×C₁₃₉	—	2	8	no	—
209	C₂×C₄×C₁₃₉	—	2	4	no	—
210	C₂×C₄×C₁₃₉	—	2	4	no	—
211	C₂×C₄×C₁₃₉	—	2	8	no	—
212	C₂×C₄×C₁₃₉	—	2	4	no	—
213	C₂×C₄×C₁₃₉	—	2	4	no	—
214	C₂×C₄×C₁₃₉	—	4	8	no	—
215	C₂×C₄×C₁₃₉	—	8	8	no	—
216	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
217	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
218	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
221	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
222	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
223	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
224	C₂²×C₁₃₉	—	2	2	no	—
225	C₂²×C₁₃₉	—	2	2	no	—
226	C₂²×C₁₃₉	—	2	2	no	—
227	C₂²×C₁₃₉	—	4	2	no	—
228	C₂²×C₁₃₉	—	4	2	no	—
229	C₂²×C₁₃₉	—	4	4	no	—
230	C₂²×C₁₃₉	—	4	4	no	—
231	C₂²×C₁₃₉	—	4	4	no	—
232	C₂²×C₁₃₉	—	4	8	no	—
233	C₂²×C₁₃₉	—	4	8	no	—
234	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
235	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
236	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
237	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
238	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
239	C₄×C₁₃₉	—	2	2	no	—
240	C₄×C₁₃₉	—	2	4	no	—
241	C₄×C₁₃₉	—	2	4	no	—
242	C₄×C₁₃₉	—	2	4	no	—
243	C₄×C₁₃₉	—	2	4	no	—
244	C₄×C₁₃₉	—	4	4	no	—
245	C₄×C₁₃₉	—	4	4	no	—
246	C₄×C₁₃₉	—	4	4	no	—
247	C₄×C₁₃₉	—	4	4	no	—
248	C₄×C₁₃₉	#537	1	4	yes	—
249	C₂×C₁₃₉	—	4	2	no	—
250	C₂×C₁₃₉	—	8	4	no	—
251	C₂×C₁₃₉	C₂×#537	1	1	yes	characteristic
252	C₂×C₁₃₉	#3498	1	1	yes	characteristic
253	C₂×C₁₃₉	#3499	1	1	yes	characteristic
254	C₂×C₁₃₉	#3536	1	2	yes	—
255	C₂×C₁₃₉	#3550	1	2	yes	—
256	#37299	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
257	C₁₃₉	#37299	1	1	yes	characteristic, direct product factor, Sylow
258	C₂×#542	C₂×C₁₃₉	1	2	yes	complemented
259	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
260	#2856	C₂×C₁₃₉	1	1	yes	characteristic
261	#2727	C₂×C₁₃₉	1	4	yes	complemented
262	#2683	C₂×C₁₃₉	1	4	yes	complemented
263	#2672	C₂×C₁₃₉	1	8	yes	complemented
264	#2620	C₂×C₁₃₉	1	2	yes	complemented
265	#2567	C₂×C₁₃₉	1	2	yes	complemented
266	#2545	C₂×C₁₃₉	1	2	yes	complemented
267	#2544	C₂×C₁₃₉	1	2	yes	complemented
268	#2542	C₂×C₁₃₉	1	2	yes	complemented
269	#2296	C₂×C₁₃₉	1	1	yes	characteristic, complemented
270	#542	—	2	16	no	—
271	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
272	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
273	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
274	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
275	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
276	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
277	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
278	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
279	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
280	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
281	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	8	yes	—
282	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
283	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
284	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
285	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
286	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
287	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
288	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
289	#399	C₂²×C₁₃₉	1	8	yes	—
290	#396	C₂²×C₁₃₉	1	8	yes	—
291	#396	C₂²×C₁₃₉	1	8	yes	—
292	#395	C₂²×C₁₃₉	1	8	yes	—
293	#394	C₂²×C₁₃₉	1	8	yes	—
294	#394	C₂²×C₁₃₉	1	8	yes	—
295	#391	C₂²×C₁₃₉	1	2	yes	—
296	#391	C₂²×C₁₃₉	1	2	yes	—
297	#390	C₂²×C₁₃₉	1	4	yes	—
298	#390	C₂²×C₁₃₉	1	2	yes	—
299	#390	C₂²×C₁₃₉	1	2	yes	—
300	#389	C₂²×C₁₃₉	1	8	yes	—
301	#389	C₂²×C₁₃₉	1	4	yes	—
302	#389	C₂²×C₁₃₉	1	2	yes	—
303	#389	C₂²×C₁₃₉	1	2	yes	—
304	#388	C₂²×C₁₃₉	1	8	yes	—
305	#386	C₂²×C₁₃₉	1	8	yes	—
306	#385	C₂²×C₁₃₉	1	4	yes	—
307	#384	C₂²×C₁₃₉	1	1	yes	characteristic
308	#384	C₂²×C₁₃₉	1	2	yes	—
309	#384	C₂²×C₁₃₉	1	1	yes	characteristic
310	#380	C₂²×C₁₃₉	1	4	yes	—
311	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
312	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
313	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
314	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
315	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
316	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
317	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
318	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
319	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
321	C₄⋊Q₈	—	2	8	no	—
322	C₄⋊Q₈	—	4	2	no	—
323	#127	—	4	2	no	—
324	#126	—	2	16	no	—
325	#124	—	2	16	no	—
326	#124	—	2	8	no	—
327	#124	—	4	4	no	—
328	#123	—	2	16	no	—
329	C₂²⋊Q₈	—	2	8	no	—
330	C₂²⋊Q₈	—	2	16	no	—
331	C₂²⋊Q₈	—	4	16	no	—
332	#121	—	2	8	no	—
333	#121	—	4	8	no	—
334	C₄×Q₈	—	2	8	no	—
335	C₄×D₄	—	2	8	no	—
336	#117	—	4	2	no	—
337	#117	D₄×C₁₃₉	1	8	yes	complemented
338	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
339	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
342	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
343	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
344	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
346	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
348	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
349	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
350	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
362	C₂×C₄²	—	4	2	no	—
363	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
364	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
365	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
368	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
369	#95	C₂³×C₁₃₉	1	4	yes	—
370	#95	C₂³×C₁₃₉	1	4	yes	—
371	#95	C₂³×C₁₃₉	1	8	yes	—
372	#95	C₂³×C₁₃₉	1	8	yes	—
373	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
374	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	8	no	—
377	C₂×Q₈	—	2	4	no	—
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	—	4	8	no	—
380	C₂×D₄	—	2	8	no	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	4	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	8	no	—
385	C₂×D₄	—	4	4	no	—
386	C₂×D₄	—	4	8	no	—
387	C₂×D₄	—	4	4	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	8	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	—	4	8	no	—
395	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
396	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
397	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
398	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
399	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
400	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
401	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
403	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
404	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
405	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	8	no	—
409	C₄⋊C₄	—	2	8	no	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	2	8	no	—
412	C₄⋊C₄	—	2	8	no	—
413	C₄⋊C₄	—	2	8	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₄⋊C₄	—	4	4	no	—
416	C₄⋊C₄	—	4	8	no	—
417	C₄⋊C₄	—	4	4	no	—
418	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
419	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	8	no	—
423	C₂²⋊C₄	—	2	8	no	—
424	C₂²⋊C₄	—	2	8	no	—
425	C₂²⋊C₄	—	2	16	no	—
426	C₂²⋊C₄	—	4	2	no	—
427	C₂²⋊C₄	—	4	8	no	—
428	C₂²⋊C₄	—	4	8	no	—
429	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
430	C₄²	—	2	8	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	2	no	—
433	C₄²	—	2	4	no	—
434	C₄²	—	4	2	no	—
435	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	8	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	8	no	—
444	C₂³	—	2	4	no	—
445	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
446	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
447	Q₈	—	4	8	no	—
448	Q₈	—	8	8	no	—
449	D₄	—	4	8	no	—
450	D₄	—	8	8	no	—
451	D₄	—	8	8	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	8	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	8	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	4	8	no	—
472	C₂×C₄	—	8	8	no	—
473	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
474	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
475	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
476	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
477	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
478	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
479	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
480	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	8	no	—
487	C₂²	—	4	8	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	4	no	—
491	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
492	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
493	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
494	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
495	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
496	C₄	—	2	4	no	—
497	C₄	—	2	4	no	—
498	C₄	—	2	2	no	—
499	C₄	—	2	4	no	—
500	C₄	—	2	4	no	—
501	C₄	—	4	4	no	—
502	C₄	—	4	4	no	—
503	C₄	—	4	4	no	—
504	C₄	—	4	4	no	—
505	C₄	#537×C₁₃₉	1	4	yes	—
506	C₂	—	4	2	no	—
507	C₂	—	8	4	no	—
508	C₂	C₂×#537×C₁₃₉	1	1	yes	characteristic
509	C₂	#3498×C₁₃₉	1	1	yes	characteristic
510	C₂	#3499×C₁₃₉	1	1	yes	characteristic
511	C₂	#3536×C₁₃₉	1	2	yes	—
512	C₂	#3550×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2856×C₁₃₉	C₂
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×#542×C₁₃₉	C₂	semidirect
2. #2857×C₁₃₉	C₂	semidirect
4. #2727×C₁₃₉	C₂	semidirect
5. #2683×C₁₃₉	C₂	semidirect
6. #2672×C₁₃₉	C₂	semidirect
7. #2620×C₁₃₉	C₂	semidirect
8. #2567×C₁₃₉	C₂	semidirect
9. #2545×C₁₃₉	C₂	semidirect
10. #2544×C₁₃₉	C₂	semidirect
11. #2542×C₁₃₉	C₂	semidirect
12. #2296×C₁₃₉	C₂	semidirect
80. #117×C₁₃₉	D₄	semidirect
256. #37299	C₁₃₉	direct (N × H)
257. C₁₃₉	#37299	direct (N × H)
258. C₂×#542	C₂×C₁₃₉	semidirect
259. #2857	C₂×C₁₃₉	semidirect
261. #2727	C₂×C₁₃₉	semidirect
262. #2683	C₂×C₁₃₉	semidirect
263. #2672	C₂×C₁₃₉	semidirect
264. #2620	C₂×C₁₃₉	semidirect
265. #2567	C₂×C₁₃₉	semidirect
266. #2545	C₂×C₁₃₉	semidirect
267. #2544	C₂×C₁₃₉	semidirect
268. #2542	C₂×C₁₃₉	semidirect
269. #2296	C₂×C₁₃₉	semidirect
337. #117	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#542×C₁₃₉	2
#2857×C₁₃₉	2
#2856×C₁₃₉	2
#2727×C₁₃₉	2
#2683×C₁₃₉	2
#2672×C₁₃₉	2
#2620×C₁₃₉	2
#2567×C₁₃₉	2
#2545×C₁₃₉	2
#2544×C₁₃₉	2
#2542×C₁₃₉	2
#2296×C₁₃₉	2
#37299	139

Subgroups — C139×#37299 #48031895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37299 #48031895