Subgroups — C₁₃₉×#37295 #48031891

Order 35584.

1446 conjugacy classes of subgroups.

The subgroup lattice has 878 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
2	#2851×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2776×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2769×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2762×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2755×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2747×C₁₃₉	C₂	1	2	yes	maximal
8	#2722×C₁₃₉	C₂	1	2	yes	maximal
9	#2698×C₁₃₉	C₂	1	2	yes	maximal
10	#2689×C₁₃₉	C₂	1	2	yes	maximal
11	#2660×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2647×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2509×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2508×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2507×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2507×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2496×C₁₃₉	C₂	1	1	yes	maximal, characteristic
18	#2496×C₁₃₉	C₂	1	1	yes	maximal, characteristic
19	#2495×C₁₃₉	C₂	1	1	yes	maximal, characteristic
20	#2494×C₁₃₉	C₂	1	1	yes	maximal, characteristic
21	#2331×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#2330×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#2283×C₁₃₉	C₂	1	1	yes	maximal, characteristic
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	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
29	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
30	#401×C₁₃₉	C₂²	1	2	yes	—
31	#400×C₁₃₉	C₂²	1	2	yes	—
32	#400×C₁₃₉	C₂²	1	2	yes	—
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	#400×C₁₃₉	C₂²	1	2	yes	—
38	#400×C₁₃₉	C₂²	1	2	yes	—
39	#398×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	#398×C₁₃₉	C₂²	1	2	yes	—
47	#398×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	#395×C₁₃₉	C₂²	1	2	yes	—
53	#395×C₁₃₉	C₂²	1	2	yes	—
54	#391×C₁₃₉	C₂²	1	2	yes	—
55	#391×C₁₃₉	C₂²	1	2	yes	—
56	#391×C₁₃₉	C₂²	1	2	yes	—
57	#389×C₁₃₉	C₂²	1	2	yes	—
58	#389×C₁₃₉	C₂²	1	2	yes	—
59	#389×C₁₃₉	C₂²	1	2	yes	—
60	#389×C₁₃₉	C₂²	1	2	yes	—
61	#389×C₁₃₉	C₂²	1	2	yes	—
62	#389×C₁₃₉	C₂²	1	1	yes	characteristic
63	#389×C₁₃₉	C₂²	1	1	yes	characteristic
64	#389×C₁₃₉	C₂²	1	1	yes	characteristic
65	#389×C₁₃₉	C₂²	1	1	yes	characteristic
66	#389×C₁₃₉	C₂²	1	1	yes	characteristic
67	#389×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	1	yes	characteristic
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	2	yes	—
75	#388×C₁₃₉	C₂²	1	2	yes	—
76	#388×C₁₃₉	C₂²	1	2	yes	—
77	#387×C₁₃₉	C₂²	1	2	yes	—
78	#387×C₁₃₉	C₂²	1	2	yes	—
79	#387×C₁₃₉	C₂²	1	2	yes	—
80	#387×C₁₃₉	C₂²	1	2	yes	—
81	#387×C₁₃₉	C₂²	1	2	yes	—
82	#387×C₁₃₉	C₂²	1	2	yes	—
83	#387×C₁₃₉	C₂²	1	2	yes	—
84	#387×C₁₃₉	C₂²	1	2	yes	—
85	#387×C₁₃₉	C₂²	1	2	yes	—
86	#387×C₁₃₉	C₂²	1	2	yes	—
87	#387×C₁₃₉	C₂²	1	2	yes	—
88	#387×C₁₃₉	C₂²	1	2	yes	—
89	#387×C₁₃₉	C₂²	1	2	yes	—
90	#385×C₁₃₉	C₂²	1	2	yes	—
91	#385×C₁₃₉	C₂²	1	2	yes	—
92	#384×C₁₃₉	C₂²	1	1	yes	characteristic
93	#384×C₁₃₉	C₂²	1	1	yes	characteristic
94	#384×C₁₃₉	C₂²	1	1	yes	characteristic
95	#383×C₁₃₉	C₂²	1	1	yes	characteristic
96	#383×C₁₃₉	C₂²	1	2	yes	—
97	#383×C₁₃₉	C₂²	1	1	yes	characteristic
98	#382×C₁₃₉	C₂²	1	2	yes	—
99	#382×C₁₃₉	C₂²	1	1	yes	characteristic
100	#382×C₁₃₉	C₂²	1	1	yes	characteristic
101	#382×C₁₃₉	C₂²	1	1	yes	characteristic
102	#382×C₁₃₉	C₂²	1	1	yes	characteristic
103	#382×C₁₃₉	C₂²	1	1	yes	characteristic
104	#381×C₁₃₉	C₂²	1	1	yes	characteristic
105	#381×C₁₃₉	C₂²	1	1	yes	characteristic
106	#380×C₁₃₉	C₂²	1	1	yes	characteristic
107	#380×C₁₃₉	C₂²	1	1	yes	characteristic
108	#380×C₁₃₉	C₂²	1	1	yes	characteristic
109	#380×C₁₃₉	C₂²	1	1	yes	characteristic
110	#380×C₁₃₉	C₂²	1	2	yes	—
111	#380×C₁₃₉	C₂²	1	1	yes	characteristic
112	#380×C₁₃₉	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
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×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
121	#376×C₁₃₉	C₂²	1	1	yes	characteristic
122	#376×C₁₃₉	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
124	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
128	#126×C₁₃₉	—	4	4	no	—
129	#126×C₁₃₉	—	4	4	no	—
130	#125×C₁₃₉	—	2	4	no	—
131	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃₉	—	2	4	no	—
174	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
183	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
185	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
186	#95×C₁₃₉	C₂³	1	1	yes	characteristic
187	#95×C₁₃₉	C₂³	1	1	yes	characteristic
188	#95×C₁₃₉	C₂³	1	2	yes	—
189	#95×C₁₃₉	C₂³	1	2	yes	—
190	#95×C₁₃₉	C₂³	1	2	yes	—
191	#95×C₁₃₉	C₂³	1	2	yes	—
192	#95×C₁₃₉	C₂³	1	2	yes	—
193	#95×C₁₃₉	C₂³	1	2	yes	—
194	#95×C₁₃₉	C₂³	1	2	yes	—
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	#95×C₁₃₉	C₂³	1	2	yes	—
197	#95×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
203	#95×C₁₃₉	C₂³	1	1	yes	characteristic
204	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
209	#95×C₁₃₉	C₂³	1	2	yes	—
210	#95×C₁₃₉	C₂³	1	2	yes	—
211	#95×C₁₃₉	C₂³	1	2	yes	—
212	#95×C₁₃₉	C₂³	1	1	yes	characteristic
213	#95×C₁₃₉	C₂³	1	1	yes	characteristic
214	#95×C₁₃₉	C₂³	1	1	yes	characteristic
215	#95×C₁₃₉	C₂³	1	1	yes	characteristic
216	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
223	#95×C₁₃₉	C₂³	1	1	yes	characteristic
224	#95×C₁₃₉	C₂³	1	1	yes	characteristic
225	#95×C₁₃₉	C₂³	1	1	yes	characteristic
226	#95×C₁₃₉	C₂³	1	1	yes	characteristic
227	#95×C₁₃₉	C₂³	1	1	yes	characteristic
228	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
229	C₂×Q₈×C₁₃₉	—	2	4	no	—
230	C₂×Q₈×C₁₃₉	—	4	2	no	—
231	C₂×Q₈×C₁₃₉	—	4	2	no	—
232	C₂²×C₄×C₁₃₉	—	2	2	no	—
233	C₂²×C₄×C₁₃₉	—	2	2	no	—
234	C₂²×C₄×C₁₃₉	—	2	2	no	—
235	C₂²×C₄×C₁₃₉	—	2	2	no	—
236	C₂²×C₄×C₁₃₉	—	2	2	no	—
237	C₂²×C₄×C₁₃₉	—	2	2	no	—
238	C₂²×C₄×C₁₃₉	—	2	2	no	—
239	C₂²×C₄×C₁₃₉	—	4	1	no	—
240	C₂²×C₄×C₁₃₉	—	4	1	no	—
241	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	2	yes	—
251	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
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	C₄⋊C₄×C₁₃₉	—	2	4	no	—
264	C₄⋊C₄×C₁₃₉	—	2	4	no	—
265	C₄⋊C₄×C₁₃₉	—	2	2	no	—
266	C₄⋊C₄×C₁₃₉	—	2	2	no	—
267	C₄⋊C₄×C₁₃₉	—	2	4	no	—
268	C₄⋊C₄×C₁₃₉	—	2	2	no	—
269	C₄⋊C₄×C₁₃₉	—	2	2	no	—
270	C₄⋊C₄×C₁₃₉	—	2	2	no	—
271	C₄⋊C₄×C₁₃₉	—	2	4	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	2	no	—
276	C₄⋊C₄×C₁₃₉	—	2	2	no	—
277	C₄⋊C₄×C₁₃₉	—	4	1	no	—
278	C₄⋊C₄×C₁₃₉	—	4	2	no	—
279	C₄⋊C₄×C₁₃₉	—	4	1	no	—
280	C₄⋊C₄×C₁₃₉	—	4	2	no	—
281	C₄⋊C₄×C₁₃₉	—	4	2	no	—
282	C₄⋊C₄×C₁₃₉	—	4	2	no	—
283	C₄⋊C₄×C₁₃₉	—	4	2	no	—
284	C₄⋊C₄×C₁₃₉	—	4	2	no	—
285	C₄⋊C₄×C₁₃₉	—	4	2	no	—
286	C₄⋊C₄×C₁₃₉	—	4	2	no	—
287	C₄⋊C₄×C₁₃₉	—	4	2	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	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
297	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
298	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
299	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
300	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
301	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
302	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
303	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
304	C₄²×C₁₃₉	—	2	2	no	—
305	C₄²×C₁₃₉	—	2	2	no	—
306	C₄²×C₁₃₉	—	2	2	no	—
307	C₄²×C₁₃₉	—	2	2	no	—
308	C₄²×C₁₃₉	—	2	2	no	—
309	C₄²×C₁₃₉	—	2	2	no	—
310	C₄²×C₁₃₉	—	2	2	no	—
311	C₄²×C₁₃₉	—	4	2	no	—
312	C₄²×C₁₃₉	—	4	2	no	—
313	C₄²×C₁₃₉	—	4	2	no	—
314	C₄²×C₁₃₉	—	4	2	no	—
315	C₄²×C₁₃₉	#41	1	4	yes	—
316	C₂³×C₁₃₉	—	2	1	no	—
317	C₂³×C₁₃₉	—	2	1	no	—
318	C₂³×C₁₃₉	—	2	1	no	—
319	C₂³×C₁₃₉	—	2	1	no	—
320	C₂³×C₁₃₉	—	2	1	no	—
321	C₂³×C₁₃₉	—	2	1	no	—
322	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
323	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
324	Q₈×C₁₃₉	—	8	4	no	—
325	C₂×C₄×C₁₃₉	—	2	1	no	—
326	C₂×C₄×C₁₃₉	—	2	1	no	—
327	C₂×C₄×C₁₃₉	—	2	1	no	—
328	C₂×C₄×C₁₃₉	—	2	1	no	—
329	C₂×C₄×C₁₃₉	—	2	1	no	—
330	C₂×C₄×C₁₃₉	—	2	1	no	—
331	C₂×C₄×C₁₃₉	—	2	1	no	—
332	C₂×C₄×C₁₃₉	—	2	1	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	2	1	no	—
338	C₂×C₄×C₁₃₉	—	2	1	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	2	no	—
341	C₂×C₄×C₁₃₉	—	2	2	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	2	1	no	—
344	C₂×C₄×C₁₃₉	—	2	2	no	—
345	C₂×C₄×C₁₃₉	—	2	1	no	—
346	C₂×C₄×C₁₃₉	—	2	2	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	1	no	—
353	C₂×C₄×C₁₃₉	—	2	1	no	—
354	C₂×C₄×C₁₃₉	—	2	1	no	—
355	C₂×C₄×C₁₃₉	—	2	1	no	—
356	C₂×C₄×C₁₃₉	—	2	2	no	—
357	C₂×C₄×C₁₃₉	—	2	2	no	—
358	C₂×C₄×C₁₃₉	—	2	1	no	—
359	C₂×C₄×C₁₃₉	—	2	2	no	—
360	C₂×C₄×C₁₃₉	—	2	1	no	—
361	C₂×C₄×C₁₃₉	—	2	1	no	—
362	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
370	C₂×C₄×C₁₃₉	—	2	2	no	—
371	C₂×C₄×C₁₃₉	—	2	2	no	—
372	C₂×C₄×C₁₃₉	—	2	2	no	—
373	C₂×C₄×C₁₃₉	—	2	2	no	—
374	C₂×C₄×C₁₃₉	—	2	1	no	—
375	C₂×C₄×C₁₃₉	—	2	1	no	—
376	C₂×C₄×C₁₃₉	—	2	1	no	—
377	C₂×C₄×C₁₃₉	—	2	2	no	—
378	C₂×C₄×C₁₃₉	—	2	2	no	—
379	C₂×C₄×C₁₃₉	—	2	1	no	—
380	C₂×C₄×C₁₃₉	—	2	2	no	—
381	C₂×C₄×C₁₃₉	—	2	1	no	—
382	C₂×C₄×C₁₃₉	—	2	1	no	—
383	C₂×C₄×C₁₃₉	—	2	1	no	—
384	C₂×C₄×C₁₃₉	—	2	2	no	—
385	C₂×C₄×C₁₃₉	—	4	4	no	—
386	C₂×C₄×C₁₃₉	—	4	4	no	—
387	C₂×C₄×C₁₃₉	—	4	4	no	—
388	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
389	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
390	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
391	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
392	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
393	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
394	C₂²×C₁₃₉	—	2	2	no	—
395	C₂²×C₁₃₉	—	2	2	no	—
396	C₂²×C₁₃₉	—	2	2	no	—
397	C₂²×C₁₃₉	—	4	1	no	—
398	C₂²×C₁₃₉	—	4	1	no	—
399	C₂²×C₁₃₉	—	4	1	no	—
400	C₂²×C₁₃₉	—	4	1	no	—
401	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
402	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
404	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
405	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
406	C₂²×C₁₃₉	#585	1	1	yes	characteristic
407	C₂²×C₁₃₉	#585	1	1	yes	characteristic
408	C₄×C₁₃₉	—	2	2	no	—
409	C₄×C₁₃₉	—	2	2	no	—
410	C₄×C₁₃₉	—	2	2	no	—
411	C₄×C₁₃₉	—	4	1	no	—
412	C₄×C₁₃₉	—	4	2	no	—
413	C₄×C₁₃₉	—	4	1	no	—
414	C₄×C₁₃₉	—	4	2	no	—
415	C₄×C₁₃₉	—	4	2	no	—
416	C₄×C₁₃₉	—	4	2	no	—
417	C₄×C₁₃₉	—	4	1	no	—
418	C₄×C₁₃₉	—	4	2	no	—
419	C₄×C₁₃₉	—	4	1	no	—
420	C₄×C₁₃₉	—	4	1	no	—
421	C₄×C₁₃₉	—	4	1	no	—
422	C₄×C₁₃₉	—	4	1	no	—
423	C₄×C₁₃₉	—	4	2	no	—
424	C₄×C₁₃₉	—	4	1	no	—
425	C₄×C₁₃₉	—	4	2	no	—
426	C₄×C₁₃₉	—	4	1	no	—
427	C₄×C₁₃₉	—	4	1	no	—
428	C₄×C₁₃₉	—	4	2	no	—
429	C₄×C₁₃₉	#541	1	4	yes	—
430	C₂×C₁₃₉	—	4	2	no	—
431	C₂×C₁₃₉	C₂×#541	1	1	yes	characteristic
432	C₂×C₁₃₉	#3494	1	1	yes	characteristic
433	C₂×C₁₃₉	#3495	1	1	yes	characteristic
434	C₂×C₁₃₉	#3544	1	1	yes	characteristic
435	C₂×C₁₃₉	#3555	1	1	yes	characteristic
436	C₂×C₁₃₉	#3559	1	1	yes	characteristic
437	C₂×C₁₃₉	#3565	1	1	yes	characteristic
438	#37295	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
439	C₁₃₉	#37295	1	1	yes	characteristic, direct product factor, Sylow
440	#2857	C₂×C₁₃₉	1	1	yes	characteristic
441	#2851	C₂×C₁₃₉	1	1	yes	characteristic
442	#2776	C₂×C₁₃₉	1	2	yes	complemented
443	#2769	C₂×C₁₃₉	1	2	yes	complemented
444	#2762	C₂×C₁₃₉	1	2	yes	complemented
445	#2755	C₂×C₁₃₉	1	2	yes	complemented
446	#2747	C₂×C₁₃₉	1	2	yes	—
447	#2722	C₂×C₁₃₉	1	2	yes	—
448	#2698	C₂×C₁₃₉	1	2	yes	—
449	#2689	C₂×C₁₃₉	1	2	yes	—
450	#2660	C₂×C₁₃₉	1	1	yes	characteristic, complemented
451	#2647	C₂×C₁₃₉	1	1	yes	characteristic, complemented
452	#2509	C₂×C₁₃₉	1	1	yes	characteristic, complemented
453	#2508	C₂×C₁₃₉	1	1	yes	characteristic, complemented
454	#2507	C₂×C₁₃₉	1	1	yes	characteristic, complemented
455	#2507	C₂×C₁₃₉	1	1	yes	characteristic, complemented
456	#2496	C₂×C₁₃₉	1	1	yes	characteristic
457	#2496	C₂×C₁₃₉	1	1	yes	characteristic
458	#2495	C₂×C₁₃₉	1	1	yes	characteristic
459	#2494	C₂×C₁₃₉	1	1	yes	characteristic
460	#2331	C₂×C₁₃₉	1	1	yes	characteristic, complemented
461	#2330	C₂×C₁₃₉	1	1	yes	characteristic, complemented
462	#2283	C₂×C₁₃₉	1	1	yes	characteristic
463	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
464	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
465	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
466	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
467	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
468	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
469	#401	C₂²×C₁₃₉	1	2	yes	—
470	#400	C₂²×C₁₃₉	1	2	yes	—
471	#400	C₂²×C₁₃₉	1	2	yes	—
472	#400	C₂²×C₁₃₉	1	2	yes	—
473	#400	C₂²×C₁₃₉	1	2	yes	—
474	#400	C₂²×C₁₃₉	1	2	yes	—
475	#400	C₂²×C₁₃₉	1	2	yes	—
476	#400	C₂²×C₁₃₉	1	2	yes	—
477	#400	C₂²×C₁₃₉	1	2	yes	—
478	#398	C₂²×C₁₃₉	1	2	yes	—
479	#398	C₂²×C₁₃₉	1	2	yes	—
480	#398	C₂²×C₁₃₉	1	2	yes	—
481	#398	C₂²×C₁₃₉	1	2	yes	—
482	#398	C₂²×C₁₃₉	1	2	yes	—
483	#398	C₂²×C₁₃₉	1	2	yes	—
484	#398	C₂²×C₁₃₉	1	2	yes	—
485	#398	C₂²×C₁₃₉	1	2	yes	—
486	#398	C₂²×C₁₃₉	1	2	yes	—
487	#397	C₂²×C₁₃₉	1	2	yes	—
488	#397	C₂²×C₁₃₉	1	2	yes	—
489	#397	C₂²×C₁₃₉	1	2	yes	—
490	#397	C₂²×C₁₃₉	1	2	yes	—
491	#395	C₂²×C₁₃₉	1	2	yes	—
492	#395	C₂²×C₁₃₉	1	2	yes	—
493	#391	C₂²×C₁₃₉	1	2	yes	—
494	#391	C₂²×C₁₃₉	1	2	yes	—
495	#391	C₂²×C₁₃₉	1	2	yes	—
496	#389	C₂²×C₁₃₉	1	2	yes	—
497	#389	C₂²×C₁₃₉	1	2	yes	—
498	#389	C₂²×C₁₃₉	1	1	yes	characteristic
499	#389	C₂²×C₁₃₉	1	1	yes	characteristic
500	#389	C₂²×C₁₃₉	1	1	yes	characteristic
501	#389	C₂²×C₁₃₉	1	1	yes	characteristic
502	#389	C₂²×C₁₃₉	1	1	yes	characteristic
503	#389	C₂²×C₁₃₉	1	1	yes	characteristic
504	#389	C₂²×C₁₃₉	1	1	yes	characteristic
505	#389	C₂²×C₁₃₉	1	1	yes	characteristic
506	#389	C₂²×C₁₃₉	1	2	yes	—
507	#389	C₂²×C₁₃₉	1	1	yes	characteristic
508	#389	C₂²×C₁₃₉	1	1	yes	characteristic
509	#389	C₂²×C₁₃₉	1	1	yes	characteristic
510	#389	C₂²×C₁₃₉	1	1	yes	characteristic
511	#389	C₂²×C₁₃₉	1	2	yes	—
512	#389	C₂²×C₁₃₉	1	2	yes	—
513	#389	C₂²×C₁₃₉	1	2	yes	—
514	#388	C₂²×C₁₃₉	1	2	yes	—
515	#388	C₂²×C₁₃₉	1	2	yes	—
516	#387	C₂²×C₁₃₉	1	2	yes	—
517	#387	C₂²×C₁₃₉	1	2	yes	—
518	#387	C₂²×C₁₃₉	1	2	yes	—
519	#387	C₂²×C₁₃₉	1	2	yes	—
520	#387	C₂²×C₁₃₉	1	2	yes	—
521	#387	C₂²×C₁₃₉	1	2	yes	—
522	#387	C₂²×C₁₃₉	1	2	yes	—
523	#387	C₂²×C₁₃₉	1	2	yes	—
524	#387	C₂²×C₁₃₉	1	2	yes	—
525	#387	C₂²×C₁₃₉	1	2	yes	—
526	#387	C₂²×C₁₃₉	1	2	yes	—
527	#387	C₂²×C₁₃₉	1	2	yes	—
528	#387	C₂²×C₁₃₉	1	2	yes	—
529	#385	C₂²×C₁₃₉	1	2	yes	—
530	#385	C₂²×C₁₃₉	1	2	yes	—
531	#384	C₂²×C₁₃₉	1	1	yes	characteristic
532	#384	C₂²×C₁₃₉	1	1	yes	characteristic
533	#384	C₂²×C₁₃₉	1	1	yes	characteristic
534	#383	C₂²×C₁₃₉	1	2	yes	—
535	#383	C₂²×C₁₃₉	1	1	yes	characteristic
536	#383	C₂²×C₁₃₉	1	1	yes	characteristic
537	#382	C₂²×C₁₃₉	1	1	yes	characteristic
538	#382	C₂²×C₁₃₉	1	1	yes	characteristic
539	#382	C₂²×C₁₃₉	1	1	yes	characteristic
540	#382	C₂²×C₁₃₉	1	2	yes	—
541	#382	C₂²×C₁₃₉	1	1	yes	characteristic
542	#382	C₂²×C₁₃₉	1	1	yes	characteristic
543	#381	C₂²×C₁₃₉	1	1	yes	characteristic
544	#381	C₂²×C₁₃₉	1	1	yes	characteristic
545	#380	C₂²×C₁₃₉	1	1	yes	characteristic
546	#380	C₂²×C₁₃₉	1	1	yes	characteristic
547	#380	C₂²×C₁₃₉	1	2	yes	—
548	#380	C₂²×C₁₃₉	1	1	yes	characteristic
549	#380	C₂²×C₁₃₉	1	1	yes	characteristic
550	#380	C₂²×C₁₃₉	1	1	yes	characteristic
551	#380	C₂²×C₁₃₉	1	1	yes	characteristic
552	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
553	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
554	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
555	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
556	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
557	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
558	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
559	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
560	#376	C₂²×C₁₃₉	1	1	yes	characteristic
561	#376	C₂²×C₁₃₉	1	1	yes	characteristic
562	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
563	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
564	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
566	C₄⋊Q₈	—	2	4	no	—
567	#126	—	4	4	no	—
568	#126	—	4	4	no	—
569	#125	—	2	4	no	—
570	C₂²⋊Q₈	—	4	4	no	—
571	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
607	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
610	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
612	C₂×C₄²	—	2	4	no	—
613	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
621	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
622	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
623	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
624	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
625	#95	C₂³×C₁₃₉	1	1	yes	characteristic
626	#95	C₂³×C₁₃₉	1	1	yes	characteristic
627	#95	C₂³×C₁₃₉	1	1	yes	characteristic
628	#95	C₂³×C₁₃₉	1	1	yes	characteristic
629	#95	C₂³×C₁₃₉	1	1	yes	characteristic
630	#95	C₂³×C₁₃₉	1	1	yes	characteristic
631	#95	C₂³×C₁₃₉	1	1	yes	characteristic
632	#95	C₂³×C₁₃₉	1	1	yes	characteristic
633	#95	C₂³×C₁₃₉	1	1	yes	characteristic
634	#95	C₂³×C₁₃₉	1	1	yes	characteristic
635	#95	C₂³×C₁₃₉	1	1	yes	characteristic
636	#95	C₂³×C₁₃₉	1	1	yes	characteristic
637	#95	C₂³×C₁₃₉	1	1	yes	characteristic
638	#95	C₂³×C₁₃₉	1	1	yes	characteristic
639	#95	C₂³×C₁₃₉	1	1	yes	characteristic
640	#95	C₂³×C₁₃₉	1	1	yes	characteristic
641	#95	C₂³×C₁₃₉	1	2	yes	—
642	#95	C₂³×C₁₃₉	1	2	yes	—
643	#95	C₂³×C₁₃₉	1	2	yes	—
644	#95	C₂³×C₁₃₉	1	2	yes	—
645	#95	C₂³×C₁₃₉	1	2	yes	—
646	#95	C₂³×C₁₃₉	1	2	yes	—
647	#95	C₂³×C₁₃₉	1	2	yes	—
648	#95	C₂³×C₁₃₉	1	2	yes	—
649	#95	C₂³×C₁₃₉	1	2	yes	—
650	#95	C₂³×C₁₃₉	1	2	yes	—
651	#95	C₂³×C₁₃₉	1	2	yes	—
652	#95	C₂³×C₁₃₉	1	2	yes	—
653	#95	C₂³×C₁₃₉	1	2	yes	—
654	#95	C₂³×C₁₃₉	1	2	yes	—
655	#95	C₂³×C₁₃₉	1	2	yes	—
656	#95	C₂³×C₁₃₉	1	2	yes	—
657	#95	C₂³×C₁₃₉	1	2	yes	—
658	#95	C₂³×C₁₃₉	1	2	yes	—
659	#95	C₂³×C₁₃₉	1	2	yes	—
660	#95	C₂³×C₁₃₉	1	2	yes	—
661	#95	C₂³×C₁₃₉	1	2	yes	—
662	#95	C₂³×C₁₃₉	1	2	yes	—
663	#95	C₂³×C₁₃₉	1	2	yes	—
664	#95	C₂³×C₁₃₉	1	2	yes	—
665	#95	C₂³×C₁₃₉	1	2	yes	—
666	#95	C₂³×C₁₃₉	1	2	yes	—
667	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
668	C₂×Q₈	—	2	4	no	—
669	C₂×Q₈	—	4	2	no	—
670	C₂×Q₈	—	4	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	4	1	no	—
679	C₂²×C₄	—	4	1	no	—
680	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
684	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
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	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	4	1	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	1	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	4	1	no	—
741	C₂²⋊C₄	—	4	2	no	—
742	C₂²⋊C₄	—	4	1	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	2	no	—
745	C₄²	—	2	2	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	4	2	no	—
751	C₄²	—	4	2	no	—
752	C₄²	—	4	2	no	—
753	C₄²	—	4	2	no	—
754	C₄²	#41×C₁₃₉	1	4	yes	—
755	C₂³	—	2	1	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	2	1	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
762	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
763	Q₈	—	8	4	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	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	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	4	4	no	—
825	C₂×C₄	—	4	4	no	—
826	C₂×C₄	—	4	4	no	—
827	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
828	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
829	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
830	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
831	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
832	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	1	no	—
840	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
841	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
842	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
843	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
844	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
845	C₂²	#585×C₁₃₉	1	1	yes	characteristic
846	C₂²	#585×C₁₃₉	1	1	yes	characteristic
847	C₄	—	2	2	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	2	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	1	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	1	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	2	no	—
868	C₄	#541×C₁₃₉	1	4	yes	—
869	C₂	—	4	2	no	—
870	C₂	C₂×#541×C₁₃₉	1	1	yes	characteristic
871	C₂	#3494×C₁₃₉	1	1	yes	characteristic
872	C₂	#3495×C₁₃₉	1	1	yes	characteristic
873	C₂	#3544×C₁₃₉	1	1	yes	characteristic
874	C₂	#3555×C₁₃₉	1	1	yes	characteristic
875	C₂	#3559×C₁₃₉	1	1	yes	characteristic
876	C₂	#3565×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂⁴×C₁₃₉	C₂⁴
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
3. #2776×C₁₃₉	C₂	semidirect
4. #2769×C₁₃₉	C₂	semidirect
5. #2762×C₁₃₉	C₂	semidirect
6. #2755×C₁₃₉	C₂	semidirect
11. #2660×C₁₃₉	C₂	semidirect
12. #2647×C₁₃₉	C₂	semidirect
13. #2509×C₁₃₉	C₂	semidirect
14. #2508×C₁₃₉	C₂	semidirect
15. #2507×C₁₃₉	C₂	semidirect
16. #2507×C₁₃₉	C₂	semidirect
21. #2331×C₁₃₉	C₂	semidirect
22. #2330×C₁₃₉	C₂	semidirect
438. #37295	C₁₃₉	direct (N × H)
439. C₁₃₉	#37295	direct (N × H)
442. #2776	C₂×C₁₃₉	semidirect
443. #2769	C₂×C₁₃₉	semidirect
444. #2762	C₂×C₁₃₉	semidirect
445. #2755	C₂×C₁₃₉	semidirect
450. #2660	C₂×C₁₃₉	semidirect
451. #2647	C₂×C₁₃₉	semidirect
452. #2509	C₂×C₁₃₉	semidirect
453. #2508	C₂×C₁₃₉	semidirect
454. #2507	C₂×C₁₃₉	semidirect
455. #2507	C₂×C₁₃₉	semidirect
460. #2331	C₂×C₁₃₉	semidirect
461. #2330	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
#2851×C₁₃₉	2
#2776×C₁₃₉	2
#2769×C₁₃₉	2
#2762×C₁₃₉	2
#2755×C₁₃₉	2
#2747×C₁₃₉	2
#2722×C₁₃₉	2
#2698×C₁₃₉	2
#2689×C₁₃₉	2
#2660×C₁₃₉	2
#2647×C₁₃₉	2
#2509×C₁₃₉	2
#2508×C₁₃₉	2
#2507×C₁₃₉	2
#2496×C₁₃₉	2
#2495×C₁₃₉	2
#2494×C₁₃₉	2
#2331×C₁₃₉	2
#2330×C₁₃₉	2
#2283×C₁₃₉	2
#37295	139

Subgroups — C139×#37295 #48031891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37295 #48031891