Subgroups — C₁₃₉×#37251 #48031847

Order 35584.

1708 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2861×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2861×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2808×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2806×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2732×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2725×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2718×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2712×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2704×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2682×C₁₃₉	C₂	1	1	yes	maximal, characteristic
11	#2674×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2672×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2651×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2589×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2554×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2465×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2426×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2335×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#123×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×#121×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
33	#400×C₁₃₉	C₂²	1	2	yes	—
34	#399×C₁₃₉	C₂²	1	2	yes	—
35	#399×C₁₃₉	C₂²	1	2	yes	—
36	#398×C₁₃₉	C₂²	1	2	yes	—
37	#398×C₁₃₉	C₂²	1	2	yes	—
38	#398×C₁₃₉	C₂²	1	2	yes	—
39	#398×C₁₃₉	C₂²	1	2	yes	—
40	#397×C₁₃₉	C₂²	1	2	yes	—
41	#397×C₁₃₉	C₂²	1	2	yes	—
42	#396×C₁₃₉	C₂²	1	2	yes	—
43	#396×C₁₃₉	C₂²	1	2	yes	—
44	#396×C₁₃₉	C₂²	1	2	yes	—
45	#396×C₁₃₉	C₂²	1	2	yes	—
46	#396×C₁₃₉	C₂²	1	2	yes	—
47	#395×C₁₃₉	C₂²	1	2	yes	—
48	#395×C₁₃₉	C₂²	1	2	yes	—
49	#394×C₁₃₉	C₂²	1	2	yes	—
50	#394×C₁₃₉	C₂²	1	2	yes	—
51	#394×C₁₃₉	C₂²	1	2	yes	—
52	#394×C₁₃₉	C₂²	1	2	yes	—
53	#394×C₁₃₉	C₂²	1	2	yes	—
54	#393×C₁₃₉	C₂²	1	2	yes	—
55	#393×C₁₃₉	C₂²	1	2	yes	—
56	#392×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	1	yes	characteristic
62	#391×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	2	yes	—
66	#390×C₁₃₉	C₂²	1	2	yes	—
67	#390×C₁₃₉	C₂²	1	1	yes	characteristic
68	#390×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	2	yes	—
73	#389×C₁₃₉	C₂²	1	2	yes	—
74	#389×C₁₃₉	C₂²	1	2	yes	—
75	#389×C₁₃₉	C₂²	1	2	yes	—
76	#388×C₁₃₉	C₂²	1	2	yes	—
77	#388×C₁₃₉	C₂²	1	2	yes	—
78	#388×C₁₃₉	C₂²	1	2	yes	—
79	#388×C₁₃₉	C₂²	1	2	yes	—
80	#388×C₁₃₉	C₂²	1	2	yes	—
81	#388×C₁₃₉	C₂²	1	2	yes	—
82	#388×C₁₃₉	C₂²	1	2	yes	—
83	#388×C₁₃₉	C₂²	1	2	yes	—
84	#388×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	#387×C₁₃₉	C₂²	1	2	yes	—
90	#387×C₁₃₉	C₂²	1	2	yes	—
91	#387×C₁₃₉	C₂²	1	2	yes	—
92	#387×C₁₃₉	C₂²	1	2	yes	—
93	#386×C₁₃₉	C₂²	1	2	yes	—
94	#386×C₁₃₉	C₂²	1	2	yes	—
95	#385×C₁₃₉	C₂²	1	2	yes	—
96	#385×C₁₃₉	C₂²	1	2	yes	—
97	#385×C₁₃₉	C₂²	1	2	yes	—
98	#385×C₁₃₉	C₂²	1	2	yes	—
99	#384×C₁₃₉	C₂²	1	1	yes	characteristic
100	#380×C₁₃₉	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
102	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
106	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
108	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
117	#126×C₁₃₉	—	4	4	no	—
118	#125×C₁₃₉	—	4	2	no	—
119	#125×C₁₃₉	—	4	2	no	—
120	#124×C₁₃₉	—	4	2	no	—
121	#124×C₁₃₉	—	4	2	no	—
122	#124×C₁₃₉	—	4	4	no	—
123	#123×C₁₃₉	—	2	8	no	—
124	#123×C₁₃₉	—	4	4	no	—
125	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
126	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
127	#121×C₁₃₉	—	4	4	no	—
128	C₄×Q₈×C₁₃₉	—	4	4	no	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
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	2	yes	—
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊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	2	yes	—
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊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×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	1	yes	characteristic
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	2	yes	—
186	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
187	#95×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
203	#95×C₁₃₉	C₂³	1	2	yes	—
204	#95×C₁₃₉	C₂³	1	2	yes	—
205	#95×C₁₃₉	C₂³	1	2	yes	—
206	#95×C₁₃₉	C₂³	1	2	yes	—
207	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
209	C₂×Q₈×C₁₃₉	—	2	4	no	—
210	C₂×Q₈×C₁₃₉	—	2	4	no	—
211	C₂×Q₈×C₁₃₉	—	2	2	no	—
212	C₂×Q₈×C₁₃₉	—	2	2	no	—
213	C₂×Q₈×C₁₃₉	—	4	2	no	—
214	C₂×Q₈×C₁₃₉	—	4	1	no	—
215	C₂×Q₈×C₁₃₉	—	4	1	no	—
216	C₂×Q₈×C₁₃₉	—	4	1	no	—
217	C₂×Q₈×C₁₃₉	—	4	1	no	—
218	C₂×D₄×C₁₃₉	—	2	4	no	—
219	C₂×D₄×C₁₃₉	—	2	2	no	—
220	C₂×D₄×C₁₃₉	—	2	2	no	—
221	C₂×D₄×C₁₃₉	—	4	2	no	—
222	C₂×D₄×C₁₃₉	—	4	2	no	—
223	C₂×D₄×C₁₃₉	—	4	2	no	—
224	C₂×D₄×C₁₃₉	—	4	1	no	—
225	C₂×D₄×C₁₃₉	—	4	1	no	—
226	C₂×D₄×C₁₃₉	—	4	2	no	—
227	C₂×D₄×C₁₃₉	—	4	1	no	—
228	C₂×D₄×C₁₃₉	—	4	1	no	—
229	C₂×D₄×C₁₃₉	—	4	2	no	—
230	C₂²×C₄×C₁₃₉	—	2	4	no	—
231	C₂²×C₄×C₁₃₉	—	4	2	no	—
232	C₂²×C₄×C₁₃₉	—	4	2	no	—
233	C₂²×C₄×C₁₃₉	—	4	2	no	—
234	C₂²×C₄×C₁₃₉	—	4	2	no	—
235	C₂²×C₄×C₁₃₉	—	4	2	no	—
236	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
252	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
253	C₄⋊C₄×C₁₃₉	—	2	4	no	—
254	C₄⋊C₄×C₁₃₉	—	2	4	no	—
255	C₄⋊C₄×C₁₃₉	—	2	2	no	—
256	C₄⋊C₄×C₁₃₉	—	2	4	no	—
257	C₄⋊C₄×C₁₃₉	—	2	4	no	—
258	C₄⋊C₄×C₁₃₉	—	2	4	no	—
259	C₄⋊C₄×C₁₃₉	—	2	4	no	—
260	C₄⋊C₄×C₁₃₉	—	2	4	no	—
261	C₄⋊C₄×C₁₃₉	—	4	1	no	—
262	C₄⋊C₄×C₁₃₉	—	4	1	no	—
263	C₄⋊C₄×C₁₃₉	—	4	2	no	—
264	C₄⋊C₄×C₁₃₉	—	4	2	no	—
265	C₄⋊C₄×C₁₃₉	—	4	2	no	—
266	C₄⋊C₄×C₁₃₉	—	4	2	no	—
267	C₄⋊C₄×C₁₃₉	—	4	2	no	—
268	C₄⋊C₄×C₁₃₉	—	4	2	no	—
269	C₄⋊C₄×C₁₃₉	—	4	2	no	—
270	C₄⋊C₄×C₁₃₉	—	4	1	no	—
271	C₄⋊C₄×C₁₃₉	—	4	1	no	—
272	C₄⋊C₄×C₁₃₉	—	4	1	no	—
273	C₄⋊C₄×C₁₃₉	—	4	1	no	—
274	C₄⋊C₄×C₁₃₉	—	4	2	no	—
275	C₄⋊C₄×C₁₃₉	—	4	2	no	—
276	C₄⋊C₄×C₁₃₉	—	4	2	no	—
277	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
278	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
279	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
280	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
281	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
282	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
283	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
284	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
285	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
286	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
287	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
288	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
289	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
290	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
291	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
292	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
293	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
294	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
295	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
296	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
297	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
298	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
299	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
300	C₄²×C₁₃₉	—	2	2	no	—
301	C₄²×C₁₃₉	—	2	2	no	—
302	C₄²×C₁₃₉	—	2	2	no	—
303	C₄²×C₁₃₉	—	2	2	no	—
304	C₄²×C₁₃₉	—	2	2	no	—
305	C₄²×C₁₃₉	—	2	2	no	—
306	C₄²×C₁₃₉	—	4	1	no	—
307	C₄²×C₁₃₉	—	4	2	no	—
308	C₄²×C₁₃₉	—	4	2	no	—
309	C₄²×C₁₃₉	—	4	2	no	—
310	C₄²×C₁₃₉	—	4	2	no	—
311	C₂³×C₁₃₉	—	2	2	no	—
312	C₂³×C₁₃₉	—	2	2	no	—
313	C₂³×C₁₃₉	—	2	2	no	—
314	C₂³×C₁₃₉	—	2	2	no	—
315	C₂³×C₁₃₉	—	2	2	no	—
316	C₂³×C₁₃₉	—	2	2	no	—
317	C₂³×C₁₃₉	—	2	2	no	—
318	C₂³×C₁₃₉	—	2	2	no	—
319	C₂³×C₁₃₉	—	2	2	no	—
320	C₂³×C₁₃₉	—	2	2	no	—
321	C₂³×C₁₃₉	—	2	2	no	—
322	C₂³×C₁₃₉	—	2	2	no	—
323	C₂³×C₁₃₉	—	2	2	no	—
324	C₂³×C₁₃₉	—	2	2	no	—
325	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
326	Q₈×C₁₃₉	—	4	8	no	—
327	Q₈×C₁₃₉	—	8	2	no	—
328	Q₈×C₁₃₉	—	8	2	no	—
329	D₄×C₁₃₉	—	8	4	no	—
330	D₄×C₁₃₉	—	8	2	no	—
331	D₄×C₁₃₉	—	8	2	no	—
332	D₄×C₁₃₉	—	8	4	no	—
333	C₂×C₄×C₁₃₉	—	2	1	no	—
334	C₂×C₄×C₁₃₉	—	2	1	no	—
335	C₂×C₄×C₁₃₉	—	2	1	no	—
336	C₂×C₄×C₁₃₉	—	2	1	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	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	2	no	—
348	C₂×C₄×C₁₃₉	—	2	2	no	—
349	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
356	C₂×C₄×C₁₃₉	—	2	2	no	—
357	C₂×C₄×C₁₃₉	—	2	2	no	—
358	C₂×C₄×C₁₃₉	—	2	2	no	—
359	C₂×C₄×C₁₃₉	—	2	2	no	—
360	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
367	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
373	C₂×C₄×C₁₃₉	—	2	2	no	—
374	C₂×C₄×C₁₃₉	—	2	2	no	—
375	C₂×C₄×C₁₃₉	—	2	2	no	—
376	C₂×C₄×C₁₃₉	—	2	2	no	—
377	C₂×C₄×C₁₃₉	—	8	4	no	—
378	C₂×C₄×C₁₃₉	—	8	4	no	—
379	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
380	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
381	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
382	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
383	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
384	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
385	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
386	C₂²×C₁₃₉	—	4	2	no	—
387	C₂²×C₁₃₉	—	4	2	no	—
388	C₂²×C₁₃₉	—	4	2	no	—
389	C₂²×C₁₃₉	—	4	2	no	—
390	C₂²×C₁₃₉	—	4	2	no	—
391	C₂²×C₁₃₉	—	4	2	no	—
392	C₂²×C₁₃₉	—	4	2	no	—
393	C₂²×C₁₃₉	—	4	2	no	—
394	C₂²×C₁₃₉	—	4	2	no	—
395	C₂²×C₁₃₉	—	4	2	no	—
396	C₂²×C₁₃₉	—	4	2	no	—
397	C₂²×C₁₃₉	—	4	2	no	—
398	C₂²×C₁₃₉	—	4	2	no	—
399	C₂²×C₁₃₉	—	4	2	no	—
400	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
401	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
402	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	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	C₄×C₁₃₉	—	2	2	no	—
408	C₄×C₁₃₉	—	2	4	no	—
409	C₄×C₁₃₉	—	2	2	no	—
410	C₄×C₁₃₉	—	2	2	no	—
411	C₄×C₁₃₉	—	2	2	no	—
412	C₄×C₁₃₉	—	2	2	no	—
413	C₄×C₁₃₉	—	2	2	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	2	no	—
420	C₄×C₁₃₉	—	4	2	no	—
421	C₄×C₁₃₉	—	4	2	no	—
422	C₄×C₁₃₉	—	4	2	no	—
423	C₄×C₁₃₉	—	4	2	no	—
424	C₂×C₁₃₉	—	8	2	no	—
425	C₂×C₁₃₉	—	8	2	no	—
426	C₂×C₁₃₉	#3461	1	1	yes	characteristic
427	C₂×C₁₃₉	#3519	1	1	yes	characteristic
428	C₂×C₁₃₉	#3522	1	1	yes	characteristic
429	C₂×C₁₃₉	#3548	1	1	yes	characteristic
430	C₂×C₁₃₉	#3552	1	1	yes	characteristic
431	C₂×C₁₃₉	#3558	1	1	yes	characteristic
432	C₂×C₁₃₉	#3561	1	1	yes	characteristic
433	#37251	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
434	C₁₃₉	#37251	1	1	yes	characteristic, direct product factor, Sylow
435	#2861	C₂×C₁₃₉	1	1	yes	characteristic, complemented
436	#2861	C₂×C₁₃₉	1	1	yes	characteristic, complemented
437	#2808	C₂×C₁₃₉	1	1	yes	characteristic, complemented
438	#2806	C₂×C₁₃₉	1	1	yes	characteristic, complemented
439	#2732	C₂×C₁₃₉	1	1	yes	characteristic, complemented
440	#2725	C₂×C₁₃₉	1	2	yes	complemented
441	#2718	C₂×C₁₃₉	1	2	yes	complemented
442	#2712	C₂×C₁₃₉	1	2	yes	complemented
443	#2704	C₂×C₁₃₉	1	2	yes	complemented
444	#2682	C₂×C₁₃₉	1	1	yes	characteristic
445	#2674	C₂×C₁₃₉	1	2	yes	complemented
446	#2672	C₂×C₁₃₉	1	2	yes	complemented
447	#2651	C₂×C₁₃₉	1	2	yes	complemented
448	#2589	C₂×C₁₃₉	1	2	yes	complemented
449	#2554	C₂×C₁₃₉	1	2	yes	complemented
450	#2465	C₂×C₁₃₉	1	2	yes	complemented
451	#2426	C₂×C₁₃₉	1	2	yes	complemented
452	#2335	C₂×C₁₃₉	1	2	yes	complemented
453	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
454	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
455	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
456	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
457	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
458	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
459	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
460	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
461	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
462	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
463	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
464	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
465	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
466	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
467	#400	C₂²×C₁₃₉	1	2	yes	—
468	#399	C₂²×C₁₃₉	1	2	yes	—
469	#399	C₂²×C₁₃₉	1	2	yes	—
470	#398	C₂²×C₁₃₉	1	2	yes	—
471	#398	C₂²×C₁₃₉	1	2	yes	—
472	#398	C₂²×C₁₃₉	1	2	yes	—
473	#398	C₂²×C₁₃₉	1	2	yes	—
474	#397	C₂²×C₁₃₉	1	2	yes	—
475	#397	C₂²×C₁₃₉	1	2	yes	—
476	#396	C₂²×C₁₃₉	1	2	yes	—
477	#396	C₂²×C₁₃₉	1	2	yes	—
478	#396	C₂²×C₁₃₉	1	2	yes	—
479	#396	C₂²×C₁₃₉	1	2	yes	—
480	#396	C₂²×C₁₃₉	1	2	yes	—
481	#395	C₂²×C₁₃₉	1	2	yes	—
482	#395	C₂²×C₁₃₉	1	2	yes	—
483	#394	C₂²×C₁₃₉	1	2	yes	—
484	#394	C₂²×C₁₃₉	1	2	yes	—
485	#394	C₂²×C₁₃₉	1	2	yes	—
486	#394	C₂²×C₁₃₉	1	2	yes	—
487	#394	C₂²×C₁₃₉	1	2	yes	—
488	#393	C₂²×C₁₃₉	1	2	yes	—
489	#393	C₂²×C₁₃₉	1	2	yes	—
490	#392	C₂²×C₁₃₉	1	2	yes	—
491	#391	C₂²×C₁₃₉	1	2	yes	—
492	#391	C₂²×C₁₃₉	1	1	yes	characteristic
493	#391	C₂²×C₁₃₉	1	2	yes	—
494	#391	C₂²×C₁₃₉	1	1	yes	characteristic
495	#391	C₂²×C₁₃₉	1	1	yes	characteristic
496	#391	C₂²×C₁₃₉	1	1	yes	characteristic
497	#390	C₂²×C₁₃₉	1	2	yes	—
498	#390	C₂²×C₁₃₉	1	1	yes	characteristic
499	#390	C₂²×C₁₃₉	1	1	yes	characteristic
500	#390	C₂²×C₁₃₉	1	1	yes	characteristic
501	#390	C₂²×C₁₃₉	1	1	yes	characteristic
502	#390	C₂²×C₁₃₉	1	2	yes	—
503	#389	C₂²×C₁₃₉	1	2	yes	—
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	2	yes	—
508	#389	C₂²×C₁₃₉	1	2	yes	—
509	#389	C₂²×C₁₃₉	1	2	yes	—
510	#388	C₂²×C₁₃₉	1	2	yes	—
511	#388	C₂²×C₁₃₉	1	2	yes	—
512	#388	C₂²×C₁₃₉	1	2	yes	—
513	#388	C₂²×C₁₃₉	1	2	yes	—
514	#388	C₂²×C₁₃₉	1	2	yes	—
515	#388	C₂²×C₁₃₉	1	2	yes	—
516	#388	C₂²×C₁₃₉	1	2	yes	—
517	#388	C₂²×C₁₃₉	1	2	yes	—
518	#388	C₂²×C₁₃₉	1	2	yes	—
519	#388	C₂²×C₁₃₉	1	2	yes	—
520	#388	C₂²×C₁₃₉	1	2	yes	—
521	#388	C₂²×C₁₃₉	1	2	yes	—
522	#388	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	#386	C₂²×C₁₃₉	1	2	yes	—
528	#386	C₂²×C₁₃₉	1	2	yes	—
529	#385	C₂²×C₁₃₉	1	2	yes	—
530	#385	C₂²×C₁₃₉	1	2	yes	—
531	#385	C₂²×C₁₃₉	1	2	yes	—
532	#385	C₂²×C₁₃₉	1	2	yes	—
533	#384	C₂²×C₁₃₉	1	1	yes	characteristic
534	#380	C₂²×C₁₃₉	1	2	yes	—
535	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
536	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
537	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
538	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
539	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
540	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
541	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
542	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
543	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
544	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
545	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
547	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
548	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
550	C₄⋊Q₈	—	2	4	no	—
551	#126	—	4	4	no	—
552	#125	—	4	2	no	—
553	#125	—	4	2	no	—
554	#124	—	4	2	no	—
555	#124	—	4	2	no	—
556	#124	—	4	4	no	—
557	#123	—	2	8	no	—
558	#123	—	4	4	no	—
559	C₂²⋊Q₈	—	4	4	no	—
560	C₂²⋊Q₈	—	4	4	no	—
561	#121	—	4	4	no	—
562	C₄×Q₈	—	4	4	no	—
563	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
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	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
588	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
603	C₂×C₂²⋊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	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
610	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
617	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
618	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
619	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
620	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
621	#95	C₂³×C₁₃₉	1	2	yes	—
622	#95	C₂³×C₁₃₉	1	2	yes	—
623	#95	C₂³×C₁₃₉	1	2	yes	—
624	#95	C₂³×C₁₃₉	1	2	yes	—
625	#95	C₂³×C₁₃₉	1	2	yes	—
626	#95	C₂³×C₁₃₉	1	2	yes	—
627	#95	C₂³×C₁₃₉	1	2	yes	—
628	#95	C₂³×C₁₃₉	1	2	yes	—
629	#95	C₂³×C₁₃₉	1	2	yes	—
630	#95	C₂³×C₁₃₉	1	2	yes	—
631	#95	C₂³×C₁₃₉	1	2	yes	—
632	#95	C₂³×C₁₃₉	1	2	yes	—
633	#95	C₂³×C₁₃₉	1	2	yes	—
634	#95	C₂³×C₁₃₉	1	2	yes	—
635	#95	C₂³×C₁₃₉	1	2	yes	—
636	#95	C₂³×C₁₃₉	1	2	yes	—
637	#95	C₂³×C₁₃₉	1	2	yes	—
638	#95	C₂³×C₁₃₉	1	2	yes	—
639	#95	C₂³×C₁₃₉	1	2	yes	—
640	#95	C₂³×C₁₃₉	1	2	yes	—
641	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
642	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
643	C₂×Q₈	—	2	4	no	—
644	C₂×Q₈	—	2	4	no	—
645	C₂×Q₈	—	2	2	no	—
646	C₂×Q₈	—	2	2	no	—
647	C₂×Q₈	—	4	2	no	—
648	C₂×Q₈	—	4	1	no	—
649	C₂×Q₈	—	4	1	no	—
650	C₂×Q₈	—	4	1	no	—
651	C₂×Q₈	—	4	1	no	—
652	C₂×D₄	—	2	4	no	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	—	4	2	no	—
657	C₂×D₄	—	4	2	no	—
658	C₂×D₄	—	4	1	no	—
659	C₂×D₄	—	4	1	no	—
660	C₂×D₄	—	4	2	no	—
661	C₂×D₄	—	4	1	no	—
662	C₂×D₄	—	4	1	no	—
663	C₂×D₄	—	4	2	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	4	1	no	—
696	C₄⋊C₄	—	4	1	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	1	no	—
705	C₄⋊C₄	—	4	1	no	—
706	C₄⋊C₄	—	4	1	no	—
707	C₄⋊C₄	—	4	1	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	4	2	no	—
725	C₂²⋊C₄	—	4	2	no	—
726	C₂²⋊C₄	—	4	2	no	—
727	C₂²⋊C₄	—	4	2	no	—
728	C₂²⋊C₄	—	4	2	no	—
729	C₂²⋊C₄	—	4	2	no	—
730	C₂²⋊C₄	—	4	2	no	—
731	C₂²⋊C₄	—	4	2	no	—
732	C₂²⋊C₄	—	4	2	no	—
733	C₂²⋊C₄	—	4	2	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	2	2	no	—
736	C₄²	—	2	2	no	—
737	C₄²	—	2	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	4	1	no	—
741	C₄²	—	4	2	no	—
742	C₄²	—	4	2	no	—
743	C₄²	—	4	2	no	—
744	C₄²	—	4	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
760	Q₈	—	4	8	no	—
761	Q₈	—	8	2	no	—
762	Q₈	—	8	2	no	—
763	D₄	—	8	2	no	—
764	D₄	—	8	2	no	—
765	D₄	—	8	4	no	—
766	D₄	—	8	4	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	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	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	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	8	4	no	—
812	C₂×C₄	—	8	4	no	—
813	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
814	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
815	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
816	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
817	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
818	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
819	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
835	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
836	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
837	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
838	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
839	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
840	C₂²	#585×C₁₃₉	1	1	yes	characteristic
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	4	no	—
846	C₄	—	2	2	no	—
847	C₄	—	2	2	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₂	—	8	2	no	—
859	C₂	—	8	2	no	—
860	C₂	#3461×C₁₃₉	1	1	yes	characteristic
861	C₂	#3519×C₁₃₉	1	1	yes	characteristic
862	C₂	#3522×C₁₃₉	1	1	yes	characteristic
863	C₂	#3548×C₁₃₉	1	1	yes	characteristic
864	C₂	#3552×C₁₃₉	1	1	yes	characteristic
865	C₂	#3558×C₁₃₉	1	1	yes	characteristic
866	C₂	#3561×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2682×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. #2861×C₁₃₉	C₂	semidirect
2. #2861×C₁₃₉	C₂	semidirect
3. #2808×C₁₃₉	C₂	semidirect
4. #2806×C₁₃₉	C₂	semidirect
5. #2732×C₁₃₉	C₂	semidirect
6. #2725×C₁₃₉	C₂	semidirect
7. #2718×C₁₃₉	C₂	semidirect
8. #2712×C₁₃₉	C₂	semidirect
9. #2704×C₁₃₉	C₂	semidirect
11. #2674×C₁₃₉	C₂	semidirect
12. #2672×C₁₃₉	C₂	semidirect
13. #2651×C₁₃₉	C₂	semidirect
14. #2589×C₁₃₉	C₂	semidirect
15. #2554×C₁₃₉	C₂	semidirect
16. #2465×C₁₃₉	C₂	semidirect
17. #2426×C₁₃₉	C₂	semidirect
18. #2335×C₁₃₉	C₂	semidirect
19. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
433. #37251	C₁₃₉	direct (N × H)
434. C₁₃₉	#37251	direct (N × H)
435. #2861	C₂×C₁₃₉	semidirect
436. #2861	C₂×C₁₃₉	semidirect
437. #2808	C₂×C₁₃₉	semidirect
438. #2806	C₂×C₁₃₉	semidirect
439. #2732	C₂×C₁₃₉	semidirect
440. #2725	C₂×C₁₃₉	semidirect
441. #2718	C₂×C₁₃₉	semidirect
442. #2712	C₂×C₁₃₉	semidirect
443. #2704	C₂×C₁₃₉	semidirect
445. #2674	C₂×C₁₃₉	semidirect
446. #2672	C₂×C₁₃₉	semidirect
447. #2651	C₂×C₁₃₉	semidirect
448. #2589	C₂×C₁₃₉	semidirect
449. #2554	C₂×C₁₃₉	semidirect
450. #2465	C₂×C₁₃₉	semidirect
451. #2426	C₂×C₁₃₉	semidirect
452. #2335	C₂×C₁₃₉	semidirect
453. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2861×C₁₃₉	2
#2808×C₁₃₉	2
#2806×C₁₃₉	2
#2732×C₁₃₉	2
#2725×C₁₃₉	2
#2718×C₁₃₉	2
#2712×C₁₃₉	2
#2704×C₁₃₉	2
#2682×C₁₃₉	2
#2674×C₁₃₉	2
#2672×C₁₃₉	2
#2651×C₁₃₉	2
#2589×C₁₃₉	2
#2554×C₁₃₉	2
#2465×C₁₃₉	2
#2426×C₁₃₉	2
#2335×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
#37251	139

Subgroups — C139×#37251 #48031847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37251 #48031847