Subgroups — C₁₃₉×#37324 #48031920

Order 35584.

1758 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2808×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2806×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2805×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2741×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2727×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2702×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2616×C₁₃₉	C₂	1	2	yes	maximal
10	#2496×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2492×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2429×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2423×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2323×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic
16	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
20	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
27	#400×C₁₃₉	C₂²	1	4	yes	—
28	#400×C₁₃₉	C₂²	1	4	yes	—
29	#399×C₁₃₉	C₂²	1	4	yes	—
30	#398×C₁₃₉	C₂²	1	4	yes	—
31	#398×C₁₃₉	C₂²	1	4	yes	—
32	#397×C₁₃₉	C₂²	1	4	yes	—
33	#396×C₁₃₉	C₂²	1	4	yes	—
34	#395×C₁₃₉	C₂²	1	4	yes	—
35	#394×C₁₃₉	C₂²	1	4	yes	—
36	#394×C₁₃₉	C₂²	1	4	yes	—
37	#394×C₁₃₉	C₂²	1	4	yes	—
38	#393×C₁₃₉	C₂²	1	4	yes	—
39	#391×C₁₃₉	C₂²	1	1	yes	characteristic
40	#391×C₁₃₉	C₂²	1	1	yes	characteristic
41	#391×C₁₃₉	C₂²	1	2	yes	—
42	#391×C₁₃₉	C₂²	1	4	yes	—
43	#391×C₁₃₉	C₂²	1	2	yes	—
44	#391×C₁₃₉	C₂²	1	2	yes	—
45	#390×C₁₃₉	C₂²	1	1	yes	characteristic
46	#390×C₁₃₉	C₂²	1	1	yes	characteristic
47	#389×C₁₃₉	C₂²	1	2	yes	—
48	#389×C₁₃₉	C₂²	1	2	yes	—
49	#389×C₁₃₉	C₂²	1	4	yes	—
50	#389×C₁₃₉	C₂²	1	2	yes	—
51	#389×C₁₃₉	C₂²	1	4	yes	—
52	#389×C₁₃₉	C₂²	1	2	yes	—
53	#389×C₁₃₉	C₂²	1	2	yes	—
54	#388×C₁₃₉	C₂²	1	4	yes	—
55	#388×C₁₃₉	C₂²	1	4	yes	—
56	#388×C₁₃₉	C₂²	1	4	yes	—
57	#388×C₁₃₉	C₂²	1	4	yes	—
58	#388×C₁₃₉	C₂²	1	4	yes	—
59	#387×C₁₃₉	C₂²	1	4	yes	—
60	#387×C₁₃₉	C₂²	1	4	yes	—
61	#387×C₁₃₉	C₂²	1	4	yes	—
62	#386×C₁₃₉	C₂²	1	2	yes	—
63	#386×C₁₃₉	C₂²	1	2	yes	—
64	#384×C₁₃₉	C₂²	1	1	yes	characteristic
65	#384×C₁₃₉	C₂²	1	1	yes	characteristic
66	#380×C₁₃₉	C₂²	1	2	yes	—
67	#380×C₁₃₉	C₂²	1	2	yes	—
68	#380×C₁₃₉	C₂²	1	2	yes	—
69	#380×C₁₃₉	C₂²	1	2	yes	—
70	#380×C₁₃₉	C₂²	1	2	yes	—
71	#380×C₁₃₉	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
73	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
74	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
75	C₂×#41×C₁₃₉	—	2	4	no	—
76	C₂×#41×C₁₃₉	—	4	2	no	—
77	C₂×#41×C₁₃₉	—	4	2	no	—
78	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
79	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
81	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
82	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
88	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
89	#126×C₁₃₉	—	4	8	no	—
90	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
91	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
92	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
93	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
94	C₄×Q₈×C₁₃₉	—	4	4	no	—
95	#117×C₁₃₉	—	4	2	no	—
96	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	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	2	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	2	yes	—
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
125	C₂×C₄²×C₁₃₉	—	4	2	no	—
126	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
132	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
133	#95×C₁₃₉	C₂³	1	4	yes	—
134	#95×C₁₃₉	C₂³	1	4	yes	—
135	#95×C₁₃₉	C₂³	1	4	yes	—
136	#95×C₁₃₉	C₂³	1	4	yes	—
137	#95×C₁₃₉	C₂³	1	4	yes	—
138	#95×C₁₃₉	C₂³	1	4	yes	—
139	#95×C₁₃₉	C₂³	1	4	yes	—
140	#95×C₁₃₉	C₂³	1	2	yes	—
141	#95×C₁₃₉	C₂³	1	2	yes	—
142	#95×C₁₃₉	C₂³	1	4	yes	—
143	#95×C₁₃₉	C₂³	1	4	yes	—
144	#95×C₁₃₉	C₂³	1	2	yes	—
145	#95×C₁₃₉	C₂³	1	2	yes	—
146	#95×C₁₃₉	C₂³	1	4	yes	—
147	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
148	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
149	#41×C₁₃₉	—	4	16	no	—
150	C₂×Q₈×C₁₃₉	—	2	4	no	—
151	C₂×Q₈×C₁₃₉	—	2	2	no	—
152	C₂×Q₈×C₁₃₉	—	2	4	no	—
153	C₂×Q₈×C₁₃₉	—	2	4	no	—
154	C₂×Q₈×C₁₃₉	—	2	4	no	—
155	C₂×Q₈×C₁₃₉	—	4	1	no	—
156	C₂×Q₈×C₁₃₉	—	4	1	no	—
157	C₂×Q₈×C₁₃₉	—	4	2	no	—
158	C₂×Q₈×C₁₃₉	—	4	2	no	—
159	C₂×D₄×C₁₃₉	—	2	4	no	—
160	C₂×D₄×C₁₃₉	—	2	2	no	—
161	C₂×D₄×C₁₃₉	—	4	1	no	—
162	C₂×D₄×C₁₃₉	—	4	1	no	—
163	C₂×D₄×C₁₃₉	—	4	2	no	—
164	C₂×D₄×C₁₃₉	—	4	2	no	—
165	C₂²×C₄×C₁₃₉	—	2	2	no	—
166	C₂²×C₄×C₁₃₉	—	2	2	no	—
167	C₂²×C₄×C₁₃₉	—	2	4	no	—
168	C₂²×C₄×C₁₃₉	—	2	2	no	—
169	C₂²×C₄×C₁₃₉	—	2	4	no	—
170	C₂²×C₄×C₁₃₉	—	2	4	no	—
171	C₂²×C₄×C₁₃₉	—	2	2	no	—
172	C₂²×C₄×C₁₃₉	—	2	2	no	—
173	C₂²×C₄×C₁₃₉	—	2	2	no	—
174	C₂²×C₄×C₁₃₉	—	4	1	no	—
175	C₂²×C₄×C₁₃₉	—	4	1	no	—
176	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
177	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
190	C₄⋊C₄×C₁₃₉	—	2	4	no	—
191	C₄⋊C₄×C₁₃₉	—	2	8	no	—
192	C₄⋊C₄×C₁₃₉	—	2	4	no	—
193	C₄⋊C₄×C₁₃₉	—	2	8	no	—
194	C₄⋊C₄×C₁₃₉	—	2	4	no	—
195	C₄⋊C₄×C₁₃₉	—	2	4	no	—
196	C₄⋊C₄×C₁₃₉	—	2	4	no	—
197	C₄⋊C₄×C₁₃₉	—	2	4	no	—
198	C₄⋊C₄×C₁₃₉	—	4	1	no	—
199	C₄⋊C₄×C₁₃₉	—	4	1	no	—
200	C₄⋊C₄×C₁₃₉	—	4	4	no	—
201	C₄⋊C₄×C₁₃₉	—	4	2	no	—
202	C₄⋊C₄×C₁₃₉	—	4	4	no	—
203	C₄⋊C₄×C₁₃₉	—	4	4	no	—
204	C₄⋊C₄×C₁₃₉	—	4	4	no	—
205	C₄⋊C₄×C₁₃₉	—	4	2	no	—
206	C₄⋊C₄×C₁₃₉	—	4	2	no	—
207	C₄⋊C₄×C₁₃₉	—	4	2	no	—
208	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
209	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
210	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
211	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
212	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
213	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
214	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
215	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
216	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
217	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
218	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
219	C₄²×C₁₃₉	—	2	2	no	—
220	C₄²×C₁₃₉	—	2	2	no	—
221	C₄²×C₁₃₉	—	2	4	no	—
222	C₄²×C₁₃₉	—	4	1	no	—
223	C₄²×C₁₃₉	—	4	1	no	—
224	C₄²×C₁₃₉	—	4	4	no	—
225	C₄²×C₁₃₉	—	4	4	no	—
226	C₂³×C₁₃₉	—	2	1	no	—
227	C₂³×C₁₃₉	—	2	1	no	—
228	C₂³×C₁₃₉	—	2	1	no	—
229	C₂³×C₁₃₉	—	2	1	no	—
230	C₂³×C₁₃₉	—	2	1	no	—
231	C₂³×C₁₃₉	—	2	1	no	—
232	C₂³×C₁₃₉	—	2	2	no	—
233	C₂³×C₁₃₉	—	2	2	no	—
234	C₂³×C₁₃₉	—	2	2	no	—
235	C₂³×C₁₃₉	—	2	2	no	—
236	C₂³×C₁₃₉	—	2	2	no	—
237	C₂³×C₁₃₉	—	2	2	no	—
238	C₂³×C₁₃₉	—	2	2	no	—
239	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
240	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
241	Q₈×C₁₃₉	—	4	4	no	—
242	Q₈×C₁₃₉	—	4	8	no	—
243	Q₈×C₁₃₉	—	8	4	no	—
244	D₄×C₁₃₉	—	4	4	no	—
245	D₄×C₁₃₉	—	4	8	no	—
246	C₂×C₄×C₁₃₉	—	2	1	no	—
247	C₂×C₄×C₁₃₉	—	2	1	no	—
248	C₂×C₄×C₁₃₉	—	2	1	no	—
249	C₂×C₄×C₁₃₉	—	2	1	no	—
250	C₂×C₄×C₁₃₉	—	2	1	no	—
251	C₂×C₄×C₁₃₉	—	2	1	no	—
252	C₂×C₄×C₁₃₉	—	2	1	no	—
253	C₂×C₄×C₁₃₉	—	2	1	no	—
254	C₂×C₄×C₁₃₉	—	2	1	no	—
255	C₂×C₄×C₁₃₉	—	2	1	no	—
256	C₂×C₄×C₁₃₉	—	2	8	no	—
257	C₂×C₄×C₁₃₉	—	2	4	no	—
258	C₂×C₄×C₁₃₉	—	2	4	no	—
259	C₂×C₄×C₁₃₉	—	2	2	no	—
260	C₂×C₄×C₁₃₉	—	2	2	no	—
261	C₂×C₄×C₁₃₉	—	2	2	no	—
262	C₂×C₄×C₁₃₉	—	2	2	no	—
263	C₂×C₄×C₁₃₉	—	2	4	no	—
264	C₂×C₄×C₁₃₉	—	2	4	no	—
265	C₂×C₄×C₁₃₉	—	2	4	no	—
266	C₂×C₄×C₁₃₉	—	2	4	no	—
267	C₂×C₄×C₁₃₉	—	2	4	no	—
268	C₂×C₄×C₁₃₉	—	2	4	no	—
269	C₂×C₄×C₁₃₉	—	2	4	no	—
270	C₂×C₄×C₁₃₉	—	2	2	no	—
271	C₂×C₄×C₁₃₉	—	2	2	no	—
272	C₂×C₄×C₁₃₉	—	2	2	no	—
273	C₂×C₄×C₁₃₉	—	2	2	no	—
274	C₂×C₄×C₁₃₉	—	2	2	no	—
275	C₂×C₄×C₁₃₉	—	2	4	no	—
276	C₂×C₄×C₁₃₉	—	2	4	no	—
277	C₂×C₄×C₁₃₉	—	2	4	no	—
278	C₂×C₄×C₁₃₉	—	4	4	no	—
279	C₂×C₄×C₁₃₉	—	4	4	no	—
280	C₂×C₄×C₁₃₉	—	4	8	no	—
281	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
282	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
283	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
284	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
285	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
286	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
287	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
288	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
289	C₂²×C₁₃₉	—	2	2	no	—
290	C₂²×C₁₃₉	—	2	2	no	—
291	C₂²×C₁₃₉	—	2	2	no	—
292	C₂²×C₁₃₉	—	4	1	no	—
293	C₂²×C₁₃₉	—	4	1	no	—
294	C₂²×C₁₃₉	—	4	1	no	—
295	C₂²×C₁₃₉	—	4	1	no	—
296	C₂²×C₁₃₉	—	4	2	no	—
297	C₂²×C₁₃₉	—	4	2	no	—
298	C₂²×C₁₃₉	—	4	2	no	—
299	C₂²×C₁₃₉	—	4	2	no	—
300	C₂²×C₁₃₉	—	4	2	no	—
301	C₂²×C₁₃₉	—	4	2	no	—
302	C₂²×C₁₃₉	—	4	2	no	—
303	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
304	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
305	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
306	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
307	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
308	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
309	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
310	C₄×C₁₃₉	—	2	2	no	—
311	C₄×C₁₃₉	—	2	2	no	—
312	C₄×C₁₃₉	—	2	2	no	—
313	C₄×C₁₃₉	—	2	2	no	—
314	C₄×C₁₃₉	—	2	2	no	—
315	C₄×C₁₃₉	—	4	2	no	—
316	C₄×C₁₃₉	—	4	4	no	—
317	C₄×C₁₃₉	—	4	4	no	—
318	C₄×C₁₃₉	—	4	4	no	—
319	C₄×C₁₃₉	—	4	2	no	—
320	C₄×C₁₃₉	—	4	4	no	—
321	C₄×C₁₃₉	—	4	2	no	—
322	C₄×C₁₃₉	#538	1	4	yes	—
323	C₂×C₁₃₉	—	4	2	no	—
324	C₂×C₁₃₉	—	8	2	no	—
325	C₂×C₁₃₉	C₂×#538	1	1	yes	characteristic
326	C₂×C₁₃₉	#3509	1	1	yes	characteristic
327	C₂×C₁₃₉	#3511	1	1	yes	characteristic
328	C₂×C₁₃₉	#3536	1	1	yes	characteristic
329	C₂×C₁₃₉	#3538	1	1	yes	characteristic
330	C₂×C₁₃₉	#3548	1	1	yes	characteristic
331	C₂×C₁₃₉	#3550	1	1	yes	characteristic
332	#37324	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
333	C₁₃₉	#37324	1	1	yes	characteristic, direct product factor, Sylow
334	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
335	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
336	#2808	C₂×C₁₃₉	1	2	yes	complemented
337	#2806	C₂×C₁₃₉	1	2	yes	complemented
338	#2805	C₂×C₁₃₉	1	2	yes	complemented
339	#2741	C₂×C₁₃₉	1	4	yes	complemented
340	#2727	C₂×C₁₃₉	1	2	yes	complemented
341	#2702	C₂×C₁₃₉	1	4	yes	complemented
342	#2616	C₂×C₁₃₉	1	2	yes	—
343	#2496	C₂×C₁₃₉	1	2	yes	complemented
344	#2492	C₂×C₁₃₉	1	2	yes	complemented
345	#2429	C₂×C₁₃₉	1	2	yes	complemented
346	#2423	C₂×C₁₃₉	1	2	yes	complemented
347	#2323	C₂×C₁₃₉	1	2	yes	complemented
348	#2297	C₂×C₁₃₉	1	1	yes	characteristic
349	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
350	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
351	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
352	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
353	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
354	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
355	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
356	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
357	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
358	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
359	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
360	#400	C₂²×C₁₃₉	1	4	yes	—
361	#400	C₂²×C₁₃₉	1	4	yes	—
362	#399	C₂²×C₁₃₉	1	4	yes	—
363	#398	C₂²×C₁₃₉	1	4	yes	—
364	#398	C₂²×C₁₃₉	1	4	yes	—
365	#397	C₂²×C₁₃₉	1	4	yes	—
366	#396	C₂²×C₁₃₉	1	4	yes	—
367	#395	C₂²×C₁₃₉	1	4	yes	—
368	#394	C₂²×C₁₃₉	1	4	yes	—
369	#394	C₂²×C₁₃₉	1	4	yes	—
370	#394	C₂²×C₁₃₉	1	4	yes	—
371	#393	C₂²×C₁₃₉	1	4	yes	—
372	#391	C₂²×C₁₃₉	1	2	yes	—
373	#391	C₂²×C₁₃₉	1	2	yes	—
374	#391	C₂²×C₁₃₉	1	2	yes	—
375	#391	C₂²×C₁₃₉	1	4	yes	—
376	#391	C₂²×C₁₃₉	1	1	yes	characteristic
377	#391	C₂²×C₁₃₉	1	1	yes	characteristic
378	#390	C₂²×C₁₃₉	1	1	yes	characteristic
379	#390	C₂²×C₁₃₉	1	1	yes	characteristic
380	#389	C₂²×C₁₃₉	1	2	yes	—
381	#389	C₂²×C₁₃₉	1	4	yes	—
382	#389	C₂²×C₁₃₉	1	2	yes	—
383	#389	C₂²×C₁₃₉	1	2	yes	—
384	#389	C₂²×C₁₃₉	1	2	yes	—
385	#389	C₂²×C₁₃₉	1	2	yes	—
386	#389	C₂²×C₁₃₉	1	4	yes	—
387	#388	C₂²×C₁₃₉	1	4	yes	—
388	#388	C₂²×C₁₃₉	1	4	yes	—
389	#388	C₂²×C₁₃₉	1	4	yes	—
390	#388	C₂²×C₁₃₉	1	4	yes	—
391	#388	C₂²×C₁₃₉	1	4	yes	—
392	#387	C₂²×C₁₃₉	1	4	yes	—
393	#387	C₂²×C₁₃₉	1	4	yes	—
394	#387	C₂²×C₁₃₉	1	4	yes	—
395	#386	C₂²×C₁₃₉	1	2	yes	—
396	#386	C₂²×C₁₃₉	1	2	yes	—
397	#384	C₂²×C₁₃₉	1	1	yes	characteristic
398	#384	C₂²×C₁₃₉	1	1	yes	characteristic
399	#380	C₂²×C₁₃₉	1	2	yes	—
400	#380	C₂²×C₁₃₉	1	2	yes	—
401	#380	C₂²×C₁₃₉	1	2	yes	—
402	#380	C₂²×C₁₃₉	1	2	yes	—
403	#380	C₂²×C₁₃₉	1	2	yes	—
404	#380	C₂²×C₁₃₉	1	2	yes	—
405	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
406	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
407	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
408	C₂×#41	—	2	4	no	—
409	C₂×#41	—	4	2	no	—
410	C₂×#41	—	4	2	no	—
411	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
412	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
413	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
414	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
415	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
416	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
417	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
418	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
419	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
420	C₄⋊Q₈	—	4	2	no	—
421	C₄⋊Q₈	—	4	2	no	—
422	#126	—	4	8	no	—
423	C₂²⋊Q₈	—	2	8	no	—
424	C₂²⋊Q₈	—	4	4	no	—
425	C₂²⋊Q₈	—	4	4	no	—
426	C₂²⋊Q₈	—	4	4	no	—
427	C₄×Q₈	—	4	4	no	—
428	#117	—	4	2	no	—
429	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
431	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
432	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
433	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
434	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
435	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
436	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
437	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
440	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
443	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
458	C₂×C₄²	—	4	2	no	—
459	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
460	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
461	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
463	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
464	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
465	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
466	#95	C₂³×C₁₃₉	1	2	yes	—
467	#95	C₂³×C₁₃₉	1	2	yes	—
468	#95	C₂³×C₁₃₉	1	2	yes	—
469	#95	C₂³×C₁₃₉	1	2	yes	—
470	#95	C₂³×C₁₃₉	1	4	yes	—
471	#95	C₂³×C₁₃₉	1	4	yes	—
472	#95	C₂³×C₁₃₉	1	4	yes	—
473	#95	C₂³×C₁₃₉	1	4	yes	—
474	#95	C₂³×C₁₃₉	1	4	yes	—
475	#95	C₂³×C₁₃₉	1	4	yes	—
476	#95	C₂³×C₁₃₉	1	4	yes	—
477	#95	C₂³×C₁₃₉	1	4	yes	—
478	#95	C₂³×C₁₃₉	1	4	yes	—
479	#95	C₂³×C₁₃₉	1	4	yes	—
480	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
481	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
482	#41	—	4	16	no	—
483	C₂×Q₈	—	2	4	no	—
484	C₂×Q₈	—	2	2	no	—
485	C₂×Q₈	—	2	4	no	—
486	C₂×Q₈	—	2	4	no	—
487	C₂×Q₈	—	2	4	no	—
488	C₂×Q₈	—	4	1	no	—
489	C₂×Q₈	—	4	1	no	—
490	C₂×Q₈	—	4	2	no	—
491	C₂×Q₈	—	4	2	no	—
492	C₂×D₄	—	2	4	no	—
493	C₂×D₄	—	2	2	no	—
494	C₂×D₄	—	4	1	no	—
495	C₂×D₄	—	4	1	no	—
496	C₂×D₄	—	4	2	no	—
497	C₂×D₄	—	4	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	4	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	4	no	—
503	C₂²×C₄	—	2	4	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	4	1	no	—
508	C₂²×C₄	—	4	1	no	—
509	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
510	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
511	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
512	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
513	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
514	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
515	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
516	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
517	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
518	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
519	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
520	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
521	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
522	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	2	8	no	—
525	C₄⋊C₄	—	2	4	no	—
526	C₄⋊C₄	—	2	8	no	—
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	2	4	no	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	2	4	no	—
531	C₄⋊C₄	—	4	1	no	—
532	C₄⋊C₄	—	4	1	no	—
533	C₄⋊C₄	—	4	4	no	—
534	C₄⋊C₄	—	4	2	no	—
535	C₄⋊C₄	—	4	4	no	—
536	C₄⋊C₄	—	4	4	no	—
537	C₄⋊C₄	—	4	4	no	—
538	C₄⋊C₄	—	4	2	no	—
539	C₄⋊C₄	—	4	2	no	—
540	C₄⋊C₄	—	4	2	no	—
541	C₂²⋊C₄	—	2	8	no	—
542	C₂²⋊C₄	—	2	4	no	—
543	C₂²⋊C₄	—	2	4	no	—
544	C₂²⋊C₄	—	2	4	no	—
545	C₂²⋊C₄	—	2	4	no	—
546	C₂²⋊C₄	—	4	2	no	—
547	C₂²⋊C₄	—	4	4	no	—
548	C₂²⋊C₄	—	4	4	no	—
549	C₂²⋊C₄	—	4	4	no	—
550	C₂²⋊C₄	—	4	4	no	—
551	C₂²⋊C₄	—	4	4	no	—
552	C₄²	—	2	2	no	—
553	C₄²	—	2	2	no	—
554	C₄²	—	2	4	no	—
555	C₄²	—	4	1	no	—
556	C₄²	—	4	1	no	—
557	C₄²	—	4	4	no	—
558	C₄²	—	4	4	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	2	no	—
566	C₂³	—	2	2	no	—
567	C₂³	—	2	2	no	—
568	C₂³	—	2	2	no	—
569	C₂³	—	2	2	no	—
570	C₂³	—	2	2	no	—
571	C₂³	—	2	2	no	—
572	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
573	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
574	Q₈	—	4	4	no	—
575	Q₈	—	4	8	no	—
576	Q₈	—	8	4	no	—
577	D₄	—	4	4	no	—
578	D₄	—	4	8	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	8	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	4	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	4	4	no	—
612	C₂×C₄	—	4	4	no	—
613	C₂×C₄	—	4	8	no	—
614	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
615	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
616	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
617	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
618	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
619	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
620	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
621	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	4	1	no	—
627	C₂²	—	4	1	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	2	no	—
630	C₂²	—	4	2	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	2	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	2	no	—
636	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
637	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
638	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
639	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
640	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
641	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
642	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
643	C₄	—	2	2	no	—
644	C₄	—	2	2	no	—
645	C₄	—	2	2	no	—
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	4	4	no	—
649	C₄	—	4	2	no	—
650	C₄	—	4	4	no	—
651	C₄	—	4	2	no	—
652	C₄	—	4	2	no	—
653	C₄	—	4	4	no	—
654	C₄	—	4	4	no	—
655	C₄	#538×C₁₃₉	1	4	yes	—
656	C₂	—	4	2	no	—
657	C₂	—	8	2	no	—
658	C₂	C₂×#538×C₁₃₉	1	1	yes	characteristic
659	C₂	#3509×C₁₃₉	1	1	yes	characteristic
660	C₂	#3511×C₁₃₉	1	1	yes	characteristic
661	C₂	#3536×C₁₃₉	1	1	yes	characteristic
662	C₂	#3538×C₁₃₉	1	1	yes	characteristic
663	C₂	#3548×C₁₃₉	1	1	yes	characteristic
664	C₂	#3550×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×#41×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. #2857×C₁₃₉	C₂	semidirect
2. #2857×C₁₃₉	C₂	semidirect
3. #2808×C₁₃₉	C₂	semidirect
4. #2806×C₁₃₉	C₂	semidirect
5. #2805×C₁₃₉	C₂	semidirect
6. #2741×C₁₃₉	C₂	semidirect
7. #2727×C₁₃₉	C₂	semidirect
8. #2702×C₁₃₉	C₂	semidirect
10. #2496×C₁₃₉	C₂	semidirect
11. #2492×C₁₃₉	C₂	semidirect
12. #2429×C₁₃₉	C₂	semidirect
13. #2423×C₁₃₉	C₂	semidirect
14. #2323×C₁₃₉	C₂	semidirect
332. #37324	C₁₃₉	direct (N × H)
333. C₁₃₉	#37324	direct (N × H)
334. #2857	C₂×C₁₃₉	semidirect
335. #2857	C₂×C₁₃₉	semidirect
336. #2808	C₂×C₁₃₉	semidirect
337. #2806	C₂×C₁₃₉	semidirect
338. #2805	C₂×C₁₃₉	semidirect
339. #2741	C₂×C₁₃₉	semidirect
340. #2727	C₂×C₁₃₉	semidirect
341. #2702	C₂×C₁₃₉	semidirect
343. #2496	C₂×C₁₃₉	semidirect
344. #2492	C₂×C₁₃₉	semidirect
345. #2429	C₂×C₁₃₉	semidirect
346. #2423	C₂×C₁₃₉	semidirect
347. #2323	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2857×C₁₃₉	2
#2808×C₁₃₉	2
#2806×C₁₃₉	2
#2805×C₁₃₉	2
#2741×C₁₃₉	2
#2727×C₁₃₉	2
#2702×C₁₃₉	2
#2616×C₁₃₉	2
#2496×C₁₃₉	2
#2492×C₁₃₉	2
#2429×C₁₃₉	2
#2423×C₁₃₉	2
#2323×C₁₃₉	2
#2297×C₁₃₉	2
#37324	139

Subgroups — C139×#37324 #48031920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37324 #48031920