Subgroups — C₁₃₉×#37337 #48031933

Order 35584.

1544 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2860×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2859×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2798×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2754×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2721×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2721×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2704×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2698×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2690×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2689×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2647×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2644×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	#2580×C₁₃₉	C₂	1	1	yes	maximal, characteristic
14	#2570×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2567×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2542×C₁₃₉	C₂	1	1	yes	maximal, characteristic
17	#2513×C₁₃₉	C₂	1	1	yes	maximal, characteristic
18	#2512×C₁₃₉	C₂	1	1	yes	maximal, characteristic
19	#2507×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#2506×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2331×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#2319×C₁₃₉	C₂	1	1	yes	maximal, characteristic
23	#2295×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₂²⋊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	#400×C₁₃₉	C₂²	1	2	yes	—
34	#400×C₁₃₉	C₂²	1	2	yes	—
35	#400×C₁₃₉	C₂²	1	2	yes	—
36	#400×C₁₃₉	C₂²	1	2	yes	—
37	#399×C₁₃₉	C₂²	1	2	yes	—
38	#399×C₁₃₉	C₂²	1	2	yes	—
39	#399×C₁₃₉	C₂²	1	2	yes	—
40	#398×C₁₃₉	C₂²	1	2	yes	—
41	#398×C₁₃₉	C₂²	1	2	yes	—
42	#398×C₁₃₉	C₂²	1	2	yes	—
43	#398×C₁₃₉	C₂²	1	2	yes	—
44	#398×C₁₃₉	C₂²	1	2	yes	—
45	#398×C₁₃₉	C₂²	1	2	yes	—
46	#397×C₁₃₉	C₂²	1	2	yes	—
47	#397×C₁₃₉	C₂²	1	2	yes	—
48	#397×C₁₃₉	C₂²	1	2	yes	—
49	#397×C₁₃₉	C₂²	1	2	yes	—
50	#397×C₁₃₉	C₂²	1	2	yes	—
51	#397×C₁₃₉	C₂²	1	2	yes	—
52	#396×C₁₃₉	C₂²	1	2	yes	—
53	#396×C₁₃₉	C₂²	1	2	yes	—
54	#395×C₁₃₉	C₂²	1	2	yes	—
55	#395×C₁₃₉	C₂²	1	2	yes	—
56	#393×C₁₃₉	C₂²	1	2	yes	—
57	#391×C₁₃₉	C₂²	1	1	yes	characteristic
58	#391×C₁₃₉	C₂²	1	2	yes	—
59	#391×C₁₃₉	C₂²	1	1	yes	characteristic
60	#391×C₁₃₉	C₂²	1	2	yes	—
61	#391×C₁₃₉	C₂²	1	2	yes	—
62	#390×C₁₃₉	C₂²	1	1	yes	characteristic
63	#390×C₁₃₉	C₂²	1	1	yes	characteristic
64	#390×C₁₃₉	C₂²	1	1	yes	characteristic
65	#390×C₁₃₉	C₂²	1	1	yes	characteristic
66	#390×C₁₃₉	C₂²	1	1	yes	characteristic
67	#390×C₁₃₉	C₂²	1	1	yes	characteristic
68	#389×C₁₃₉	C₂²	1	1	yes	characteristic
69	#389×C₁₃₉	C₂²	1	1	yes	characteristic
70	#389×C₁₃₉	C₂²	1	2	yes	—
71	#389×C₁₃₉	C₂²	1	1	yes	characteristic
72	#389×C₁₃₉	C₂²	1	1	yes	characteristic
73	#389×C₁₃₉	C₂²	1	1	yes	characteristic
74	#389×C₁₃₉	C₂²	1	1	yes	characteristic
75	#389×C₁₃₉	C₂²	1	1	yes	characteristic
76	#389×C₁₃₉	C₂²	1	1	yes	characteristic
77	#389×C₁₃₉	C₂²	1	1	yes	characteristic
78	#389×C₁₃₉	C₂²	1	1	yes	characteristic
79	#389×C₁₃₉	C₂²	1	1	yes	characteristic
80	#389×C₁₃₉	C₂²	1	1	yes	characteristic
81	#389×C₁₃₉	C₂²	1	1	yes	characteristic
82	#389×C₁₃₉	C₂²	1	1	yes	characteristic
83	#389×C₁₃₉	C₂²	1	2	yes	—
84	#389×C₁₃₉	C₂²	1	2	yes	—
85	#388×C₁₃₉	C₂²	1	2	yes	—
86	#388×C₁₃₉	C₂²	1	2	yes	—
87	#388×C₁₃₉	C₂²	1	2	yes	—
88	#388×C₁₃₉	C₂²	1	2	yes	—
89	#388×C₁₃₉	C₂²	1	2	yes	—
90	#388×C₁₃₉	C₂²	1	2	yes	—
91	#388×C₁₃₉	C₂²	1	2	yes	—
92	#388×C₁₃₉	C₂²	1	2	yes	—
93	#387×C₁₃₉	C₂²	1	2	yes	—
94	#387×C₁₃₉	C₂²	1	2	yes	—
95	#387×C₁₃₉	C₂²	1	2	yes	—
96	#387×C₁₃₉	C₂²	1	1	yes	characteristic
97	#387×C₁₃₉	C₂²	1	1	yes	characteristic
98	#387×C₁₃₉	C₂²	1	1	yes	characteristic
99	#387×C₁₃₉	C₂²	1	1	yes	characteristic
100	#387×C₁₃₉	C₂²	1	2	yes	—
101	#387×C₁₃₉	C₂²	1	2	yes	—
102	#387×C₁₃₉	C₂²	1	2	yes	—
103	#385×C₁₃₉	C₂²	1	2	yes	—
104	#385×C₁₃₉	C₂²	1	2	yes	—
105	#384×C₁₃₉	C₂²	1	1	yes	characteristic
106	#384×C₁₃₉	C₂²	1	1	yes	characteristic
107	#384×C₁₃₉	C₂²	1	1	yes	characteristic
108	#384×C₁₃₉	C₂²	1	2	yes	—
109	#382×C₁₃₉	C₂²	1	1	yes	characteristic
110	#382×C₁₃₉	C₂²	1	1	yes	characteristic
111	#382×C₁₃₉	C₂²	1	2	yes	—
112	#381×C₁₃₉	C₂²	1	2	yes	—
113	#380×C₁₃₉	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
119	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
120	#376×C₁₃₉	C₂²	1	1	yes	characteristic
121	#376×C₁₃₉	C₂²	1	1	yes	characteristic
122	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
125	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
128	#126×C₁₃₉	—	4	4	no	—
129	#126×C₁₃₉	—	4	4	no	—
130	#125×C₁₃₉	—	4	4	no	—
131	#125×C₁₃₉	—	4	4	no	—
132	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
133	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
134	C₄×Q₈×C₁₃₉	—	2	4	no	—
135	C₄×D₄×C₁₃₉	—	2	4	no	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
194	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
195	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
197	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
198	#95×C₁₃₉	C₂³	1	2	yes	—
199	#95×C₁₃₉	C₂³	1	2	yes	—
200	#95×C₁₃₉	C₂³	1	2	yes	—
201	#95×C₁₃₉	C₂³	1	2	yes	—
202	#95×C₁₃₉	C₂³	1	2	yes	—
203	#95×C₁₃₉	C₂³	1	1	yes	characteristic
204	#95×C₁₃₉	C₂³	1	2	yes	—
205	#95×C₁₃₉	C₂³	1	1	yes	characteristic
206	#95×C₁₃₉	C₂³	1	2	yes	—
207	#95×C₁₃₉	C₂³	1	2	yes	—
208	#95×C₁₃₉	C₂³	1	1	yes	characteristic
209	#95×C₁₃₉	C₂³	1	1	yes	characteristic
210	#95×C₁₃₉	C₂³	1	1	yes	characteristic
211	#95×C₁₃₉	C₂³	1	1	yes	characteristic
212	#95×C₁₃₉	C₂³	1	2	yes	—
213	#95×C₁₃₉	C₂³	1	2	yes	—
214	#95×C₁₃₉	C₂³	1	2	yes	—
215	#95×C₁₃₉	C₂³	1	1	yes	characteristic
216	#95×C₁₃₉	C₂³	1	2	yes	—
217	#95×C₁₃₉	C₂³	1	2	yes	—
218	#95×C₁₃₉	C₂³	1	2	yes	—
219	#95×C₁₃₉	C₂³	1	2	yes	—
220	#95×C₁₃₉	C₂³	1	2	yes	—
221	#95×C₁₃₉	C₂³	1	2	yes	—
222	#95×C₁₃₉	C₂³	1	1	yes	characteristic
223	#95×C₁₃₉	C₂³	1	1	yes	characteristic
224	#95×C₁₃₉	C₂³	1	2	yes	—
225	#95×C₁₃₉	C₂³	1	2	yes	—
226	#95×C₁₃₉	C₂³	1	1	yes	characteristic
227	#95×C₁₃₉	C₂³	1	1	yes	characteristic
228	#95×C₁₃₉	C₂³	1	1	yes	characteristic
229	#95×C₁₃₉	C₂³	1	1	yes	characteristic
230	#95×C₁₃₉	C₂³	1	1	yes	characteristic
231	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
232	C₂×Q₈×C₁₃₉	—	2	2	no	—
233	C₂×Q₈×C₁₃₉	—	2	4	no	—
234	C₂×Q₈×C₁₃₉	—	2	2	no	—
235	C₂×Q₈×C₁₃₉	—	4	1	no	—
236	C₂×Q₈×C₁₃₉	—	4	2	no	—
237	C₂×Q₈×C₁₃₉	—	4	2	no	—
238	C₂×D₄×C₁₃₉	—	2	2	no	—
239	C₂×D₄×C₁₃₉	—	2	2	no	—
240	C₂×D₄×C₁₃₉	—	2	2	no	—
241	C₂²×C₄×C₁₃₉	—	2	4	no	—
242	C₂²×C₄×C₁₃₉	—	4	2	no	—
243	C₂²×C₄×C₁₃₉	—	4	2	no	—
244	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
266	C₄⋊C₄×C₁₃₉	—	2	2	no	—
267	C₄⋊C₄×C₁₃₉	—	2	2	no	—
268	C₄⋊C₄×C₁₃₉	—	2	2	no	—
269	C₄⋊C₄×C₁₃₉	—	2	2	no	—
270	C₄⋊C₄×C₁₃₉	—	2	4	no	—
271	C₄⋊C₄×C₁₃₉	—	2	2	no	—
272	C₄⋊C₄×C₁₃₉	—	2	2	no	—
273	C₄⋊C₄×C₁₃₉	—	2	2	no	—
274	C₄⋊C₄×C₁₃₉	—	2	2	no	—
275	C₄⋊C₄×C₁₃₉	—	2	4	no	—
276	C₄⋊C₄×C₁₃₉	—	2	4	no	—
277	C₄⋊C₄×C₁₃₉	—	2	2	no	—
278	C₄⋊C₄×C₁₃₉	—	2	4	no	—
279	C₄⋊C₄×C₁₃₉	—	2	4	no	—
280	C₄⋊C₄×C₁₃₉	—	2	2	no	—
281	C₄⋊C₄×C₁₃₉	—	2	2	no	—
282	C₄⋊C₄×C₁₃₉	—	2	2	no	—
283	C₄⋊C₄×C₁₃₉	—	2	2	no	—
284	C₄⋊C₄×C₁₃₉	—	2	2	no	—
285	C₄⋊C₄×C₁₃₉	—	2	2	no	—
286	C₄⋊C₄×C₁₃₉	—	4	2	no	—
287	C₄⋊C₄×C₁₃₉	—	4	1	no	—
288	C₄⋊C₄×C₁₃₉	—	4	2	no	—
289	C₄⋊C₄×C₁₃₉	—	4	2	no	—
290	C₄⋊C₄×C₁₃₉	—	4	2	no	—
291	C₄⋊C₄×C₁₃₉	—	4	2	no	—
292	C₄⋊C₄×C₁₃₉	—	4	2	no	—
293	C₄⋊C₄×C₁₃₉	—	4	2	no	—
294	C₄⋊C₄×C₁₃₉	—	4	2	no	—
295	C₄⋊C₄×C₁₃₉	—	4	2	no	—
296	C₄⋊C₄×C₁₃₉	—	4	2	no	—
297	C₄⋊C₄×C₁₃₉	—	4	2	no	—
298	C₄⋊C₄×C₁₃₉	—	4	2	no	—
299	C₄⋊C₄×C₁₃₉	—	4	2	no	—
300	C₄⋊C₄×C₁₃₉	—	4	2	no	—
301	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
302	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
303	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
304	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
305	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
306	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
307	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
308	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
309	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
310	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
311	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
312	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
313	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
314	C₄²×C₁₃₉	—	2	2	no	—
315	C₄²×C₁₃₉	—	2	2	no	—
316	C₄²×C₁₃₉	—	2	2	no	—
317	C₄²×C₁₃₉	—	2	2	no	—
318	C₄²×C₁₃₉	—	2	2	no	—
319	C₄²×C₁₃₉	—	2	2	no	—
320	C₄²×C₁₃₉	—	2	2	no	—
321	C₄²×C₁₃₉	—	2	2	no	—
322	C₄²×C₁₃₉	—	2	2	no	—
323	C₄²×C₁₃₉	—	4	2	no	—
324	C₄²×C₁₃₉	—	4	1	no	—
325	C₄²×C₁₃₉	—	4	2	no	—
326	C₄²×C₁₃₉	—	4	2	no	—
327	C₄²×C₁₃₉	#41	1	4	yes	—
328	C₂³×C₁₃₉	—	2	2	no	—
329	C₂³×C₁₃₉	—	2	2	no	—
330	C₂³×C₁₃₉	—	2	2	no	—
331	C₂³×C₁₃₉	—	2	2	no	—
332	C₂³×C₁₃₉	—	2	2	no	—
333	C₂³×C₁₃₉	—	2	2	no	—
334	C₂³×C₁₃₉	—	2	2	no	—
335	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
336	Q₈×C₁₃₉	—	4	4	no	—
337	Q₈×C₁₃₉	—	8	4	no	—
338	D₄×C₁₃₉	—	4	4	no	—
339	C₂×C₄×C₁₃₉	—	2	1	no	—
340	C₂×C₄×C₁₃₉	—	2	1	no	—
341	C₂×C₄×C₁₃₉	—	2	1	no	—
342	C₂×C₄×C₁₃₉	—	2	1	no	—
343	C₂×C₄×C₁₃₉	—	2	1	no	—
344	C₂×C₄×C₁₃₉	—	2	1	no	—
345	C₂×C₄×C₁₃₉	—	2	1	no	—
346	C₂×C₄×C₁₃₉	—	2	1	no	—
347	C₂×C₄×C₁₃₉	—	2	1	no	—
348	C₂×C₄×C₁₃₉	—	2	1	no	—
349	C₂×C₄×C₁₃₉	—	2	1	no	—
350	C₂×C₄×C₁₃₉	—	2	1	no	—
351	C₂×C₄×C₁₃₉	—	2	1	no	—
352	C₂×C₄×C₁₃₉	—	2	2	no	—
353	C₂×C₄×C₁₃₉	—	2	2	no	—
354	C₂×C₄×C₁₃₉	—	2	2	no	—
355	C₂×C₄×C₁₃₉	—	2	1	no	—
356	C₂×C₄×C₁₃₉	—	2	1	no	—
357	C₂×C₄×C₁₃₉	—	2	1	no	—
358	C₂×C₄×C₁₃₉	—	2	1	no	—
359	C₂×C₄×C₁₃₉	—	2	1	no	—
360	C₂×C₄×C₁₃₉	—	2	1	no	—
361	C₂×C₄×C₁₃₉	—	2	2	no	—
362	C₂×C₄×C₁₃₉	—	2	2	no	—
363	C₂×C₄×C₁₃₉	—	2	2	no	—
364	C₂×C₄×C₁₃₉	—	2	2	no	—
365	C₂×C₄×C₁₃₉	—	2	2	no	—
366	C₂×C₄×C₁₃₉	—	2	1	no	—
367	C₂×C₄×C₁₃₉	—	2	1	no	—
368	C₂×C₄×C₁₃₉	—	2	1	no	—
369	C₂×C₄×C₁₃₉	—	2	2	no	—
370	C₂×C₄×C₁₃₉	—	2	2	no	—
371	C₂×C₄×C₁₃₉	—	2	2	no	—
372	C₂×C₄×C₁₃₉	—	2	1	no	—
373	C₂×C₄×C₁₃₉	—	2	2	no	—
374	C₂×C₄×C₁₃₉	—	2	2	no	—
375	C₂×C₄×C₁₃₉	—	2	1	no	—
376	C₂×C₄×C₁₃₉	—	2	1	no	—
377	C₂×C₄×C₁₃₉	—	2	1	no	—
378	C₂×C₄×C₁₃₉	—	2	1	no	—
379	C₂×C₄×C₁₃₉	—	2	1	no	—
380	C₂×C₄×C₁₃₉	—	2	1	no	—
381	C₂×C₄×C₁₃₉	—	2	1	no	—
382	C₂×C₄×C₁₃₉	—	2	2	no	—
383	C₂×C₄×C₁₃₉	—	2	1	no	—
384	C₂×C₄×C₁₃₉	—	2	1	no	—
385	C₂×C₄×C₁₃₉	—	2	2	no	—
386	C₂×C₄×C₁₃₉	—	2	2	no	—
387	C₂×C₄×C₁₃₉	—	2	2	no	—
388	C₂×C₄×C₁₃₉	—	2	2	no	—
389	C₂×C₄×C₁₃₉	—	2	1	no	—
390	C₂×C₄×C₁₃₉	—	2	1	no	—
391	C₂×C₄×C₁₃₉	—	2	2	no	—
392	C₂×C₄×C₁₃₉	—	2	2	no	—
393	C₂×C₄×C₁₃₉	—	2	1	no	—
394	C₂×C₄×C₁₃₉	—	2	1	no	—
395	C₂×C₄×C₁₃₉	—	2	2	no	—
396	C₂×C₄×C₁₃₉	—	2	1	no	—
397	C₂×C₄×C₁₃₉	—	8	4	no	—
398	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
399	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
400	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
401	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
402	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
403	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
404	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
405	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
406	C₂²×C₁₃₉	—	4	2	no	—
407	C₂²×C₁₃₉	—	4	2	no	—
408	C₂²×C₁₃₉	—	4	2	no	—
409	C₂²×C₁₃₉	—	4	2	no	—
410	C₂²×C₁₃₉	—	4	2	no	—
411	C₂²×C₁₃₉	—	4	2	no	—
412	C₂²×C₁₃₉	—	4	2	no	—
413	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
414	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
415	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
416	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
417	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
418	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
419	C₂²×C₁₃₉	#585	1	1	yes	characteristic
420	C₄×C₁₃₉	—	2	2	no	—
421	C₄×C₁₃₉	—	2	2	no	—
422	C₄×C₁₃₉	—	2	2	no	—
423	C₄×C₁₃₉	—	2	2	no	—
424	C₄×C₁₃₉	—	2	2	no	—
425	C₄×C₁₃₉	—	4	1	no	—
426	C₄×C₁₃₉	—	4	1	no	—
427	C₄×C₁₃₉	—	4	1	no	—
428	C₄×C₁₃₉	—	4	2	no	—
429	C₄×C₁₃₉	—	4	2	no	—
430	C₄×C₁₃₉	—	4	2	no	—
431	C₄×C₁₃₉	—	4	1	no	—
432	C₄×C₁₃₉	—	4	1	no	—
433	C₄×C₁₃₉	—	4	1	no	—
434	C₄×C₁₃₉	—	4	2	no	—
435	C₄×C₁₃₉	—	4	1	no	—
436	C₄×C₁₃₉	—	4	2	no	—
437	C₄×C₁₃₉	—	4	2	no	—
438	C₄×C₁₃₉	—	4	1	no	—
439	C₄×C₁₃₉	—	4	1	no	—
440	C₄×C₁₃₉	—	4	2	no	—
441	C₄×C₁₃₉	#541	1	4	yes	—
442	C₂×C₁₃₉	—	8	2	no	—
443	C₂×C₁₃₉	C₂×#541	1	1	yes	characteristic
444	C₂×C₁₃₉	#3495	1	1	yes	characteristic
445	C₂×C₁₃₉	#3508	1	1	yes	characteristic
446	C₂×C₁₃₉	#3544	1	1	yes	characteristic
447	C₂×C₁₃₉	#3550	1	1	yes	characteristic
448	C₂×C₁₃₉	#3554	1	1	yes	characteristic
449	C₂×C₁₃₉	#3559	1	1	yes	characteristic
450	#37337	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
451	C₁₃₉	#37337	1	1	yes	characteristic, direct product factor, Sylow
452	#2860	C₂×C₁₃₉	1	1	yes	characteristic
453	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
454	#2798	C₂×C₁₃₉	1	2	yes	complemented
455	#2754	C₂×C₁₃₉	1	2	yes	complemented
456	#2721	C₂×C₁₃₉	1	2	yes	complemented
457	#2721	C₂×C₁₃₉	1	2	yes	complemented
458	#2704	C₂×C₁₃₉	1	2	yes	complemented
459	#2698	C₂×C₁₃₉	1	2	yes	complemented
460	#2690	C₂×C₁₃₉	1	2	yes	complemented
461	#2689	C₂×C₁₃₉	1	2	yes	complemented
462	#2647	C₂×C₁₃₉	1	1	yes	characteristic, complemented
463	#2644	C₂×C₁₃₉	1	1	yes	characteristic
464	#2580	C₂×C₁₃₉	1	1	yes	characteristic
465	#2570	C₂×C₁₃₉	1	1	yes	characteristic, complemented
466	#2567	C₂×C₁₃₉	1	1	yes	characteristic, complemented
467	#2542	C₂×C₁₃₉	1	1	yes	characteristic
468	#2513	C₂×C₁₃₉	1	1	yes	characteristic
469	#2512	C₂×C₁₃₉	1	1	yes	characteristic
470	#2507	C₂×C₁₃₉	1	1	yes	characteristic, complemented
471	#2506	C₂×C₁₃₉	1	1	yes	characteristic, complemented
472	#2331	C₂×C₁₃₉	1	1	yes	characteristic, complemented
473	#2319	C₂×C₁₃₉	1	1	yes	characteristic
474	#2295	C₂×C₁₃₉	1	1	yes	characteristic, complemented
475	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
476	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
477	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
478	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
479	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
480	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
481	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
482	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
483	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
484	#400	C₂²×C₁₃₉	1	2	yes	—
485	#400	C₂²×C₁₃₉	1	2	yes	—
486	#400	C₂²×C₁₃₉	1	2	yes	—
487	#400	C₂²×C₁₃₉	1	2	yes	—
488	#399	C₂²×C₁₃₉	1	2	yes	—
489	#399	C₂²×C₁₃₉	1	2	yes	—
490	#399	C₂²×C₁₃₉	1	2	yes	—
491	#398	C₂²×C₁₃₉	1	2	yes	—
492	#398	C₂²×C₁₃₉	1	2	yes	—
493	#398	C₂²×C₁₃₉	1	2	yes	—
494	#398	C₂²×C₁₃₉	1	2	yes	—
495	#398	C₂²×C₁₃₉	1	2	yes	—
496	#398	C₂²×C₁₃₉	1	2	yes	—
497	#397	C₂²×C₁₃₉	1	2	yes	—
498	#397	C₂²×C₁₃₉	1	2	yes	—
499	#397	C₂²×C₁₃₉	1	2	yes	—
500	#397	C₂²×C₁₃₉	1	2	yes	—
501	#397	C₂²×C₁₃₉	1	2	yes	—
502	#397	C₂²×C₁₃₉	1	2	yes	—
503	#396	C₂²×C₁₃₉	1	2	yes	—
504	#396	C₂²×C₁₃₉	1	2	yes	—
505	#395	C₂²×C₁₃₉	1	2	yes	—
506	#395	C₂²×C₁₃₉	1	2	yes	—
507	#393	C₂²×C₁₃₉	1	2	yes	—
508	#391	C₂²×C₁₃₉	1	2	yes	—
509	#391	C₂²×C₁₃₉	1	2	yes	—
510	#391	C₂²×C₁₃₉	1	2	yes	—
511	#391	C₂²×C₁₃₉	1	1	yes	characteristic
512	#391	C₂²×C₁₃₉	1	1	yes	characteristic
513	#390	C₂²×C₁₃₉	1	1	yes	characteristic
514	#390	C₂²×C₁₃₉	1	1	yes	characteristic
515	#390	C₂²×C₁₃₉	1	1	yes	characteristic
516	#390	C₂²×C₁₃₉	1	1	yes	characteristic
517	#390	C₂²×C₁₃₉	1	1	yes	characteristic
518	#390	C₂²×C₁₃₉	1	1	yes	characteristic
519	#389	C₂²×C₁₃₉	1	1	yes	characteristic
520	#389	C₂²×C₁₃₉	1	1	yes	characteristic
521	#389	C₂²×C₁₃₉	1	1	yes	characteristic
522	#389	C₂²×C₁₃₉	1	1	yes	characteristic
523	#389	C₂²×C₁₃₉	1	1	yes	characteristic
524	#389	C₂²×C₁₃₉	1	1	yes	characteristic
525	#389	C₂²×C₁₃₉	1	1	yes	characteristic
526	#389	C₂²×C₁₃₉	1	1	yes	characteristic
527	#389	C₂²×C₁₃₉	1	1	yes	characteristic
528	#389	C₂²×C₁₃₉	1	1	yes	characteristic
529	#389	C₂²×C₁₃₉	1	1	yes	characteristic
530	#389	C₂²×C₁₃₉	1	1	yes	characteristic
531	#389	C₂²×C₁₃₉	1	2	yes	—
532	#389	C₂²×C₁₃₉	1	2	yes	—
533	#389	C₂²×C₁₃₉	1	2	yes	—
534	#389	C₂²×C₁₃₉	1	1	yes	characteristic
535	#389	C₂²×C₁₃₉	1	1	yes	characteristic
536	#388	C₂²×C₁₃₉	1	2	yes	—
537	#388	C₂²×C₁₃₉	1	2	yes	—
538	#388	C₂²×C₁₃₉	1	2	yes	—
539	#388	C₂²×C₁₃₉	1	2	yes	—
540	#388	C₂²×C₁₃₉	1	2	yes	—
541	#388	C₂²×C₁₃₉	1	2	yes	—
542	#388	C₂²×C₁₃₉	1	2	yes	—
543	#388	C₂²×C₁₃₉	1	2	yes	—
544	#387	C₂²×C₁₃₉	1	2	yes	—
545	#387	C₂²×C₁₃₉	1	2	yes	—
546	#387	C₂²×C₁₃₉	1	2	yes	—
547	#387	C₂²×C₁₃₉	1	2	yes	—
548	#387	C₂²×C₁₃₉	1	1	yes	characteristic
549	#387	C₂²×C₁₃₉	1	1	yes	characteristic
550	#387	C₂²×C₁₃₉	1	2	yes	—
551	#387	C₂²×C₁₃₉	1	2	yes	—
552	#387	C₂²×C₁₃₉	1	1	yes	characteristic
553	#387	C₂²×C₁₃₉	1	1	yes	characteristic
554	#385	C₂²×C₁₃₉	1	2	yes	—
555	#385	C₂²×C₁₃₉	1	2	yes	—
556	#384	C₂²×C₁₃₉	1	2	yes	—
557	#384	C₂²×C₁₃₉	1	1	yes	characteristic
558	#384	C₂²×C₁₃₉	1	1	yes	characteristic
559	#384	C₂²×C₁₃₉	1	1	yes	characteristic
560	#382	C₂²×C₁₃₉	1	1	yes	characteristic
561	#382	C₂²×C₁₃₉	1	1	yes	characteristic
562	#382	C₂²×C₁₃₉	1	2	yes	—
563	#381	C₂²×C₁₃₉	1	2	yes	—
564	#380	C₂²×C₁₃₉	1	2	yes	—
565	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
566	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
567	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
568	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
569	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
570	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
571	#376	C₂²×C₁₃₉	1	1	yes	characteristic
572	#376	C₂²×C₁₃₉	1	1	yes	characteristic
573	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
574	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
575	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
576	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
578	C₄⋊Q₈	—	2	4	no	—
579	#126	—	4	4	no	—
580	#126	—	4	4	no	—
581	#125	—	4	4	no	—
582	#125	—	4	4	no	—
583	C₂²⋊Q₈	—	4	4	no	—
584	C₂²⋊Q₈	—	4	4	no	—
585	C₄×Q₈	—	2	4	no	—
586	C₄×D₄	—	2	4	no	—
587	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
635	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
645	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
646	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
648	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
649	#95	C₂³×C₁₃₉	1	1	yes	characteristic
650	#95	C₂³×C₁₃₉	1	1	yes	characteristic
651	#95	C₂³×C₁₃₉	1	1	yes	characteristic
652	#95	C₂³×C₁₃₉	1	1	yes	characteristic
653	#95	C₂³×C₁₃₉	1	1	yes	characteristic
654	#95	C₂³×C₁₃₉	1	1	yes	characteristic
655	#95	C₂³×C₁₃₉	1	1	yes	characteristic
656	#95	C₂³×C₁₃₉	1	1	yes	characteristic
657	#95	C₂³×C₁₃₉	1	2	yes	—
658	#95	C₂³×C₁₃₉	1	1	yes	characteristic
659	#95	C₂³×C₁₃₉	1	1	yes	characteristic
660	#95	C₂³×C₁₃₉	1	1	yes	characteristic
661	#95	C₂³×C₁₃₉	1	1	yes	characteristic
662	#95	C₂³×C₁₃₉	1	1	yes	characteristic
663	#95	C₂³×C₁₃₉	1	1	yes	characteristic
664	#95	C₂³×C₁₃₉	1	2	yes	—
665	#95	C₂³×C₁₃₉	1	2	yes	—
666	#95	C₂³×C₁₃₉	1	2	yes	—
667	#95	C₂³×C₁₃₉	1	2	yes	—
668	#95	C₂³×C₁₃₉	1	2	yes	—
669	#95	C₂³×C₁₃₉	1	2	yes	—
670	#95	C₂³×C₁₃₉	1	2	yes	—
671	#95	C₂³×C₁₃₉	1	2	yes	—
672	#95	C₂³×C₁₃₉	1	2	yes	—
673	#95	C₂³×C₁₃₉	1	2	yes	—
674	#95	C₂³×C₁₃₉	1	2	yes	—
675	#95	C₂³×C₁₃₉	1	2	yes	—
676	#95	C₂³×C₁₃₉	1	2	yes	—
677	#95	C₂³×C₁₃₉	1	2	yes	—
678	#95	C₂³×C₁₃₉	1	2	yes	—
679	#95	C₂³×C₁₃₉	1	2	yes	—
680	#95	C₂³×C₁₃₉	1	2	yes	—
681	#95	C₂³×C₁₃₉	1	2	yes	—
682	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	4	no	—
685	C₂×Q₈	—	2	2	no	—
686	C₂×Q₈	—	4	1	no	—
687	C₂×Q₈	—	4	2	no	—
688	C₂×Q₈	—	4	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	1	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	—	4	2	no	—
749	C₄⋊C₄	—	4	2	no	—
750	C₄⋊C₄	—	4	2	no	—
751	C₄⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	2	no	—
774	C₄²	—	4	2	no	—
775	C₄²	—	4	1	no	—
776	C₄²	—	4	2	no	—
777	C₄²	—	4	2	no	—
778	C₄²	#41×C₁₃₉	1	4	yes	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
787	Q₈	—	4	4	no	—
788	Q₈	—	8	4	no	—
789	D₄	—	4	4	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	8	4	no	—
849	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
850	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
851	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
852	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
853	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
854	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
855	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
856	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
865	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
866	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
867	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
868	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
869	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
870	C₂²	#585×C₁₃₉	1	1	yes	characteristic
871	C₄	—	2	2	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	2	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	2	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	1	no	—
884	C₄	—	4	1	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	2	no	—
888	C₄	—	4	2	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	1	no	—
891	C₄	—	4	1	no	—
892	C₄	#541×C₁₃₉	1	4	yes	—
893	C₂	—	8	2	no	—
894	C₂	C₂×#541×C₁₃₉	1	1	yes	characteristic
895	C₂	#3495×C₁₃₉	1	1	yes	characteristic
896	C₂	#3508×C₁₃₉	1	1	yes	characteristic
897	C₂	#3544×C₁₃₉	1	1	yes	characteristic
898	C₂	#3550×C₁₃₉	1	1	yes	characteristic
899	C₂	#3554×C₁₃₉	1	1	yes	characteristic
900	C₂	#3559×C₁₃₉	1	1	yes	characteristic

	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
2. #2859×C₁₃₉	C₂	semidirect
3. #2798×C₁₃₉	C₂	semidirect
4. #2754×C₁₃₉	C₂	semidirect
5. #2721×C₁₃₉	C₂	semidirect
6. #2721×C₁₃₉	C₂	semidirect
7. #2704×C₁₃₉	C₂	semidirect
8. #2698×C₁₃₉	C₂	semidirect
9. #2690×C₁₃₉	C₂	semidirect
10. #2689×C₁₃₉	C₂	semidirect
11. #2647×C₁₃₉	C₂	semidirect
14. #2570×C₁₃₉	C₂	semidirect
15. #2567×C₁₃₉	C₂	semidirect
19. #2507×C₁₃₉	C₂	semidirect
20. #2506×C₁₃₉	C₂	semidirect
21. #2331×C₁₃₉	C₂	semidirect
23. #2295×C₁₃₉	C₂	semidirect
450. #37337	C₁₃₉	direct (N × H)
451. C₁₃₉	#37337	direct (N × H)
453. #2859	C₂×C₁₃₉	semidirect
454. #2798	C₂×C₁₃₉	semidirect
455. #2754	C₂×C₁₃₉	semidirect
456. #2721	C₂×C₁₃₉	semidirect
457. #2721	C₂×C₁₃₉	semidirect
458. #2704	C₂×C₁₃₉	semidirect
459. #2698	C₂×C₁₃₉	semidirect
460. #2690	C₂×C₁₃₉	semidirect
461. #2689	C₂×C₁₃₉	semidirect
462. #2647	C₂×C₁₃₉	semidirect
465. #2570	C₂×C₁₃₉	semidirect
466. #2567	C₂×C₁₃₉	semidirect
470. #2507	C₂×C₁₃₉	semidirect
471. #2506	C₂×C₁₃₉	semidirect
472. #2331	C₂×C₁₃₉	semidirect
474. #2295	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2860×C₁₃₉	2
#2859×C₁₃₉	2
#2798×C₁₃₉	2
#2754×C₁₃₉	2
#2721×C₁₃₉	2
#2704×C₁₃₉	2
#2698×C₁₃₉	2
#2690×C₁₃₉	2
#2689×C₁₃₉	2
#2647×C₁₃₉	2
#2644×C₁₃₉	2
#2580×C₁₃₉	2
#2570×C₁₃₉	2
#2567×C₁₃₉	2
#2542×C₁₃₉	2
#2513×C₁₃₉	2
#2512×C₁₃₉	2
#2507×C₁₃₉	2
#2506×C₁₃₉	2
#2331×C₁₃₉	2
#2319×C₁₃₉	2
#2295×C₁₃₉	2
#37337	139

Subgroups — C139×#37337 #48031933

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37337 #48031933