Subgroups — C₁₃₉×#37192 #48031788

Order 35584.

2200 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2860×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2858×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2733×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2732×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2730×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2683×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2682×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2681×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2677×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2676×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2674×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2673×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2662×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2610×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2603×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2601×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2540×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	#2295×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#542×C₁₃₉	—	2	16	no	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
37	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
38	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
39	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
42	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
43	#399×C₁₃₉	C₂²	1	2	yes	—
44	#399×C₁₃₉	C₂²	1	2	yes	—
45	#398×C₁₃₉	C₂²	1	2	yes	—
46	#398×C₁₃₉	C₂²	1	2	yes	—
47	#397×C₁₃₉	C₂²	1	2	yes	—
48	#396×C₁₃₉	C₂²	1	2	yes	—
49	#396×C₁₃₉	C₂²	1	2	yes	—
50	#396×C₁₃₉	C₂²	1	2	yes	—
51	#396×C₁₃₉	C₂²	1	2	yes	—
52	#395×C₁₃₉	C₂²	1	2	yes	—
53	#395×C₁₃₉	C₂²	1	2	yes	—
54	#394×C₁₃₉	C₂²	1	2	yes	—
55	#394×C₁₃₉	C₂²	1	2	yes	—
56	#394×C₁₃₉	C₂²	1	2	yes	—
57	#394×C₁₃₉	C₂²	1	2	yes	—
58	#394×C₁₃₉	C₂²	1	2	yes	—
59	#394×C₁₃₉	C₂²	1	2	yes	—
60	#393×C₁₃₉	C₂²	1	2	yes	—
61	#393×C₁₃₉	C₂²	1	2	yes	—
62	#392×C₁₃₉	C₂²	1	2	yes	—
63	#392×C₁₃₉	C₂²	1	2	yes	—
64	#392×C₁₃₉	C₂²	1	2	yes	—
65	#392×C₁₃₉	C₂²	1	2	yes	—
66	#392×C₁₃₉	C₂²	1	2	yes	—
67	#391×C₁₃₉	C₂²	1	1	yes	characteristic
68	#391×C₁₃₉	C₂²	1	1	yes	characteristic
69	#390×C₁₃₉	C₂²	1	1	yes	characteristic
70	#390×C₁₃₉	C₂²	1	2	yes	—
71	#390×C₁₃₉	C₂²	1	2	yes	—
72	#390×C₁₃₉	C₂²	1	2	yes	—
73	#390×C₁₃₉	C₂²	1	1	yes	characteristic
74	#390×C₁₃₉	C₂²	1	1	yes	characteristic
75	#390×C₁₃₉	C₂²	1	2	yes	—
76	#390×C₁₃₉	C₂²	1	1	yes	characteristic
77	#390×C₁₃₉	C₂²	1	1	yes	characteristic
78	#390×C₁₃₉	C₂²	1	1	yes	characteristic
79	#390×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	1	yes	characteristic
84	#389×C₁₃₉	C₂²	1	1	yes	characteristic
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	#386×C₁₃₉	C₂²	1	2	yes	—
97	#386×C₁₃₉	C₂²	1	2	yes	—
98	#386×C₁₃₉	C₂²	1	2	yes	—
99	#386×C₁₃₉	C₂²	1	2	yes	—
100	#386×C₁₃₉	C₂²	1	2	yes	—
101	#385×C₁₃₉	C₂²	1	2	yes	—
102	#385×C₁₃₉	C₂²	1	2	yes	—
103	#385×C₁₃₉	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
106	#376×C₁₃₉	C₂²	1	2	yes	—
107	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
109	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
110	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
121	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
122	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
124	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
125	#127×C₁₃₉	—	4	2	no	—
126	#126×C₁₃₉	—	2	8	no	—
127	#126×C₁₃₉	—	2	8	no	—
128	#124×C₁₃₉	—	2	8	no	—
129	#124×C₁₃₉	—	2	8	no	—
130	#124×C₁₃₉	—	2	8	no	—
131	#124×C₁₃₉	—	4	4	no	—
132	#123×C₁₃₉	—	2	8	no	—
133	#123×C₁₃₉	—	2	8	no	—
134	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
135	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
136	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
137	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
138	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
139	#121×C₁₃₉	—	2	8	no	—
140	#121×C₁₃₉	—	4	4	no	—
141	#121×C₁₃₉	—	4	4	no	—
142	C₄×Q₈×C₁₃₉	D₄	1	8	yes	complemented
143	C₄×D₄×C₁₃₉	—	2	8	no	—
144	#117×C₁₃₉	—	2	8	no	—
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	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	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
160	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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×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×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
193	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
194	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
201	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
202	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
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	#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	2	yes	—
213	#95×C₁₃₉	C₂³	1	2	yes	—
214	#95×C₁₃₉	C₂³	1	2	yes	—
215	#95×C₁₃₉	C₂³	1	2	yes	—
216	#95×C₁₃₉	C₂³	1	2	yes	—
217	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
218	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
219	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
220	C₂×Q₈×C₁₃₉	—	2	4	no	—
221	C₂×Q₈×C₁₃₉	—	2	4	no	—
222	C₂×Q₈×C₁₃₉	—	4	1	no	—
223	C₂×Q₈×C₁₃₉	—	4	1	no	—
224	C₂×Q₈×C₁₃₉	—	4	2	no	—
225	C₂×Q₈×C₁₃₉	—	4	2	no	—
226	C₂×Q₈×C₁₃₉	—	4	2	no	—
227	C₂×Q₈×C₁₃₉	—	4	2	no	—
228	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
229	C₂×D₄×C₁₃₉	—	2	4	no	—
230	C₂×D₄×C₁₃₉	—	2	4	no	—
231	C₂×D₄×C₁₃₉	—	2	4	no	—
232	C₂×D₄×C₁₃₉	—	2	2	no	—
233	C₂×D₄×C₁₃₉	—	2	4	no	—
234	C₂×D₄×C₁₃₉	—	2	2	no	—
235	C₂×D₄×C₁₃₉	—	2	2	no	—
236	C₂×D₄×C₁₃₉	—	4	2	no	—
237	C₂×D₄×C₁₃₉	—	4	2	no	—
238	C₂×D₄×C₁₃₉	—	4	2	no	—
239	C₂×D₄×C₁₃₉	—	4	2	no	—
240	C₂×D₄×C₁₃₉	—	4	2	no	—
241	C₂×D₄×C₁₃₉	—	4	2	no	—
242	C₂×D₄×C₁₃₉	—	4	2	no	—
243	C₂×D₄×C₁₃₉	—	4	1	no	—
244	C₂×D₄×C₁₃₉	—	4	1	no	—
245	C₂×D₄×C₁₃₉	—	4	2	no	—
246	C₂×D₄×C₁₃₉	—	4	1	no	—
247	C₂×D₄×C₁₃₉	—	4	1	no	—
248	C₂×D₄×C₁₃₉	—	4	2	no	—
249	C₂×D₄×C₁₃₉	—	4	2	no	—
250	C₂×D₄×C₁₃₉	—	4	1	no	—
251	C₂×D₄×C₁₃₉	—	4	1	no	—
252	C₂×D₄×C₁₃₉	—	4	2	no	—
253	C₂×D₄×C₁₃₉	—	4	2	no	—
254	C₂×D₄×C₁₃₉	—	4	2	no	—
255	C₂×D₄×C₁₃₉	—	4	2	no	—
256	C₂²×C₄×C₁₃₉	—	2	4	no	—
257	C₂²×C₄×C₁₃₉	—	2	4	no	—
258	C₂²×C₄×C₁₃₉	—	2	4	no	—
259	C₂²×C₄×C₁₃₉	—	4	2	no	—
260	C₂²×C₄×C₁₃₉	—	4	2	no	—
261	C₂²×C₄×C₁₃₉	—	4	2	no	—
262	C₂²×C₄×C₁₃₉	—	4	2	no	—
263	C₂²×C₄×C₁₃₉	—	4	2	no	—
264	C₂²×C₄×C₁₃₉	—	4	2	no	—
265	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
281	C₄⋊C₄×C₁₃₉	—	2	4	no	—
282	C₄⋊C₄×C₁₃₉	—	2	4	no	—
283	C₄⋊C₄×C₁₃₉	—	2	4	no	—
284	C₄⋊C₄×C₁₃₉	—	2	4	no	—
285	C₄⋊C₄×C₁₃₉	—	2	4	no	—
286	C₄⋊C₄×C₁₃₉	—	2	4	no	—
287	C₄⋊C₄×C₁₃₉	—	2	4	no	—
288	C₄⋊C₄×C₁₃₉	—	2	4	no	—
289	C₄⋊C₄×C₁₃₉	—	2	4	no	—
290	C₄⋊C₄×C₁₃₉	—	2	2	no	—
291	C₄⋊C₄×C₁₃₉	—	2	4	no	—
292	C₄⋊C₄×C₁₃₉	—	4	1	no	—
293	C₄⋊C₄×C₁₃₉	—	4	1	no	—
294	C₄⋊C₄×C₁₃₉	—	4	1	no	—
295	C₄⋊C₄×C₁₃₉	—	4	1	no	—
296	C₄⋊C₄×C₁₃₉	—	4	2	no	—
297	C₄⋊C₄×C₁₃₉	—	4	2	no	—
298	C₄⋊C₄×C₁₃₉	—	4	1	no	—
299	C₄⋊C₄×C₁₃₉	—	4	1	no	—
300	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
301	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
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	—	2	4	no	—
306	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
307	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
308	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
309	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
310	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
311	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
312	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
313	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
314	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
315	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
316	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
317	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
318	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
319	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
320	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
321	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
322	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
323	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
324	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
325	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
326	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
327	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
328	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
329	C₄²×C₁₃₉	—	2	4	no	—
330	C₄²×C₁₃₉	—	2	2	no	—
331	C₄²×C₁₃₉	—	2	2	no	—
332	C₄²×C₁₃₉	—	2	2	no	—
333	C₄²×C₁₃₉	—	4	1	no	—
334	C₄²×C₁₃₉	—	4	2	no	—
335	C₄²×C₁₃₉	—	4	1	no	—
336	C₄²×C₁₃₉	—	4	1	no	—
337	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
338	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
339	C₂³×C₁₃₉	—	2	2	no	—
340	C₂³×C₁₃₉	—	2	2	no	—
341	C₂³×C₁₃₉	—	2	2	no	—
342	C₂³×C₁₃₉	—	2	2	no	—
343	C₂³×C₁₃₉	—	2	2	no	—
344	C₂³×C₁₃₉	—	2	2	no	—
345	C₂³×C₁₃₉	—	2	2	no	—
346	C₂³×C₁₃₉	—	2	2	no	—
347	C₂³×C₁₃₉	—	2	2	no	—
348	C₂³×C₁₃₉	—	2	2	no	—
349	C₂³×C₁₃₉	—	2	2	no	—
350	C₂³×C₁₃₉	—	2	2	no	—
351	C₂³×C₁₃₉	—	2	2	no	—
352	C₂³×C₁₃₉	—	2	2	no	—
353	C₂³×C₁₃₉	—	2	2	no	—
354	C₂³×C₁₃₉	—	2	2	no	—
355	C₂³×C₁₃₉	—	2	2	no	—
356	C₂³×C₁₃₉	—	2	2	no	—
357	C₂³×C₁₃₉	—	2	2	no	—
358	C₂³×C₁₃₉	—	2	2	no	—
359	C₂³×C₁₃₉	—	2	2	no	—
360	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
361	Q₈×C₁₃₉	—	4	4	no	—
362	Q₈×C₁₃₉	—	8	4	no	—
363	Q₈×C₁₃₉	—	8	4	no	—
364	D₄×C₁₃₉	—	4	8	no	—
365	D₄×C₁₃₉	—	8	4	no	—
366	D₄×C₁₃₉	—	8	4	no	—
367	D₄×C₁₃₉	—	8	4	no	—
368	D₄×C₁₃₉	—	8	2	no	—
369	D₄×C₁₃₉	—	8	2	no	—
370	D₄×C₁₃₉	—	8	2	no	—
371	D₄×C₁₃₉	—	8	4	no	—
372	D₄×C₁₃₉	—	8	4	no	—
373	C₂×C₄×C₁₃₉	—	2	1	no	—
374	C₂×C₄×C₁₃₉	—	2	1	no	—
375	C₂×C₄×C₁₃₉	—	2	1	no	—
376	C₂×C₄×C₁₃₉	—	2	2	no	—
377	C₂×C₄×C₁₃₉	—	2	2	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	1	no	—
383	C₂×C₄×C₁₃₉	—	2	1	no	—
384	C₂×C₄×C₁₃₉	—	2	1	no	—
385	C₂×C₄×C₁₃₉	—	2	1	no	—
386	C₂×C₄×C₁₃₉	—	2	1	no	—
387	C₂×C₄×C₁₃₉	—	2	2	no	—
388	C₂×C₄×C₁₃₉	—	2	2	no	—
389	C₂×C₄×C₁₃₉	—	2	2	no	—
390	C₂×C₄×C₁₃₉	—	2	2	no	—
391	C₂×C₄×C₁₃₉	—	2	2	no	—
392	C₂×C₄×C₁₃₉	—	2	2	no	—
393	C₂×C₄×C₁₃₉	—	2	2	no	—
394	C₂×C₄×C₁₃₉	—	2	1	no	—
395	C₂×C₄×C₁₃₉	—	2	2	no	—
396	C₂×C₄×C₁₃₉	—	2	2	no	—
397	C₂×C₄×C₁₃₉	—	2	2	no	—
398	C₂×C₄×C₁₃₉	—	2	2	no	—
399	C₂×C₄×C₁₃₉	—	2	2	no	—
400	C₂×C₄×C₁₃₉	—	2	2	no	—
401	C₂×C₄×C₁₃₉	—	2	2	no	—
402	C₂×C₄×C₁₃₉	—	2	2	no	—
403	C₂×C₄×C₁₃₉	—	2	1	no	—
404	C₂×C₄×C₁₃₉	—	2	2	no	—
405	C₂×C₄×C₁₃₉	—	2	1	no	—
406	C₂×C₄×C₁₃₉	—	2	2	no	—
407	C₂×C₄×C₁₃₉	—	2	2	no	—
408	C₂×C₄×C₁₃₉	—	2	2	no	—
409	C₂×C₄×C₁₃₉	—	2	2	no	—
410	C₂×C₄×C₁₃₉	—	2	2	no	—
411	C₂×C₄×C₁₃₉	—	2	2	no	—
412	C₂×C₄×C₁₃₉	—	2	2	no	—
413	C₂×C₄×C₁₃₉	—	4	8	no	—
414	C₂×C₄×C₁₃₉	—	8	4	no	—
415	C₂×C₄×C₁₃₉	—	8	4	no	—
416	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
417	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
420	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
422	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
423	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
424	C₂²×C₁₃₉	—	4	2	no	—
425	C₂²×C₁₃₉	—	4	2	no	—
426	C₂²×C₁₃₉	—	4	2	no	—
427	C₂²×C₁₃₉	—	4	2	no	—
428	C₂²×C₁₃₉	—	4	2	no	—
429	C₂²×C₁₃₉	—	4	2	no	—
430	C₂²×C₁₃₉	—	4	2	no	—
431	C₂²×C₁₃₉	—	4	2	no	—
432	C₂²×C₁₃₉	—	4	2	no	—
433	C₂²×C₁₃₉	—	4	2	no	—
434	C₂²×C₁₃₉	—	4	2	no	—
435	C₂²×C₁₃₉	—	4	2	no	—
436	C₂²×C₁₃₉	—	4	2	no	—
437	C₂²×C₁₃₉	—	4	2	no	—
438	C₂²×C₁₃₉	—	4	2	no	—
439	C₂²×C₁₃₉	—	4	2	no	—
440	C₂²×C₁₃₉	—	4	2	no	—
441	C₂²×C₁₃₉	—	4	2	no	—
442	C₂²×C₁₃₉	—	4	2	no	—
443	C₂²×C₁₃₉	—	4	2	no	—
444	C₂²×C₁₃₉	—	4	2	no	—
445	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
446	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
447	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
449	C₂²×C₁₃₉	#585	1	1	yes	characteristic
450	C₂²×C₁₃₉	#585	1	1	yes	characteristic
451	C₂²×C₁₃₉	#585	1	1	yes	characteristic
452	C₄×C₁₃₉	—	2	4	no	—
453	C₄×C₁₃₉	—	2	2	no	—
454	C₄×C₁₃₉	—	2	2	no	—
455	C₄×C₁₃₉	—	2	4	no	—
456	C₄×C₁₃₉	—	2	2	no	—
457	C₄×C₁₃₉	—	2	2	no	—
458	C₄×C₁₃₉	—	2	2	no	—
459	C₄×C₁₃₉	—	2	2	no	—
460	C₄×C₁₃₉	—	4	2	no	—
461	C₄×C₁₃₉	—	4	2	no	—
462	C₄×C₁₃₉	—	4	2	no	—
463	C₄×C₁₃₉	—	4	2	no	—
464	C₄×C₁₃₉	—	4	2	no	—
465	C₄×C₁₃₉	—	4	2	no	—
466	C₄×C₁₃₉	—	4	1	no	—
467	C₄×C₁₃₉	—	4	2	no	—
468	C₂×C₁₃₉	—	8	2	no	—
469	C₂×C₁₃₉	—	8	2	no	—
470	C₂×C₁₃₉	—	8	2	no	—
471	C₂×C₁₃₉	#3449	1	1	yes	characteristic
472	C₂×C₁₃₉	#3497	1	1	yes	characteristic
473	C₂×C₁₃₉	#3498	1	1	yes	characteristic
474	C₂×C₁₃₉	#3545	1	1	yes	characteristic
475	C₂×C₁₃₉	#3547	1	1	yes	characteristic
476	C₂×C₁₃₉	#3560	1	1	yes	characteristic
477	C₂×C₁₃₉	#3561	1	1	yes	characteristic
478	#37192	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
479	C₁₃₉	#37192	1	1	yes	characteristic, direct product factor, Sylow
480	C₂×#542	C₂×C₁₃₉	1	2	yes	complemented
481	#2860	C₂×C₁₃₉	1	1	yes	characteristic, complemented
482	#2858	C₂×C₁₃₉	1	1	yes	characteristic, complemented
483	#2733	C₂×C₁₃₉	1	1	yes	characteristic, complemented
484	#2732	C₂×C₁₃₉	1	1	yes	characteristic, complemented
485	#2730	C₂×C₁₃₉	1	2	yes	complemented
486	#2683	C₂×C₁₃₉	1	1	yes	characteristic, complemented
487	#2682	C₂×C₁₃₉	1	1	yes	characteristic, complemented
488	#2681	C₂×C₁₃₉	1	2	yes	complemented
489	#2677	C₂×C₁₃₉	1	2	yes	complemented
490	#2676	C₂×C₁₃₉	1	2	yes	complemented
491	#2674	C₂×C₁₃₉	1	2	yes	complemented
492	#2673	C₂×C₁₃₉	1	2	yes	complemented
493	#2662	C₂×C₁₃₉	1	2	yes	complemented
494	#2610	C₂×C₁₃₉	1	2	yes	complemented
495	#2603	C₂×C₁₃₉	1	2	yes	complemented
496	#2601	C₂×C₁₃₉	1	2	yes	complemented
497	#2540	C₂×C₁₃₉	1	2	yes	complemented
498	#2295	C₂×C₁₃₉	1	1	yes	characteristic, complemented
499	#542	—	2	16	no	—
500	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
501	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
502	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
503	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
504	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
505	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
506	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
507	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
508	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
509	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
510	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
511	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
512	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
513	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
514	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
515	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
516	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
517	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
518	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
519	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
520	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
521	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
522	#399	C₂²×C₁₃₉	1	2	yes	—
523	#399	C₂²×C₁₃₉	1	2	yes	—
524	#398	C₂²×C₁₃₉	1	2	yes	—
525	#398	C₂²×C₁₃₉	1	2	yes	—
526	#397	C₂²×C₁₃₉	1	2	yes	—
527	#396	C₂²×C₁₃₉	1	2	yes	—
528	#396	C₂²×C₁₃₉	1	2	yes	—
529	#396	C₂²×C₁₃₉	1	2	yes	—
530	#396	C₂²×C₁₃₉	1	2	yes	—
531	#395	C₂²×C₁₃₉	1	2	yes	—
532	#395	C₂²×C₁₃₉	1	2	yes	—
533	#394	C₂²×C₁₃₉	1	2	yes	—
534	#394	C₂²×C₁₃₉	1	2	yes	—
535	#394	C₂²×C₁₃₉	1	2	yes	—
536	#394	C₂²×C₁₃₉	1	2	yes	—
537	#394	C₂²×C₁₃₉	1	2	yes	—
538	#394	C₂²×C₁₃₉	1	2	yes	—
539	#393	C₂²×C₁₃₉	1	2	yes	—
540	#393	C₂²×C₁₃₉	1	2	yes	—
541	#392	C₂²×C₁₃₉	1	2	yes	—
542	#392	C₂²×C₁₃₉	1	2	yes	—
543	#392	C₂²×C₁₃₉	1	2	yes	—
544	#392	C₂²×C₁₃₉	1	2	yes	—
545	#392	C₂²×C₁₃₉	1	2	yes	—
546	#391	C₂²×C₁₃₉	1	1	yes	characteristic
547	#391	C₂²×C₁₃₉	1	1	yes	characteristic
548	#390	C₂²×C₁₃₉	1	2	yes	—
549	#390	C₂²×C₁₃₉	1	1	yes	characteristic
550	#390	C₂²×C₁₃₉	1	1	yes	characteristic
551	#390	C₂²×C₁₃₉	1	2	yes	—
552	#390	C₂²×C₁₃₉	1	1	yes	characteristic
553	#390	C₂²×C₁₃₉	1	1	yes	characteristic
554	#390	C₂²×C₁₃₉	1	2	yes	—
555	#390	C₂²×C₁₃₉	1	1	yes	characteristic
556	#390	C₂²×C₁₃₉	1	1	yes	characteristic
557	#390	C₂²×C₁₃₉	1	1	yes	characteristic
558	#390	C₂²×C₁₃₉	1	2	yes	—
559	#389	C₂²×C₁₃₉	1	1	yes	characteristic
560	#389	C₂²×C₁₃₉	1	1	yes	characteristic
561	#389	C₂²×C₁₃₉	1	1	yes	characteristic
562	#389	C₂²×C₁₃₉	1	1	yes	characteristic
563	#389	C₂²×C₁₃₉	1	1	yes	characteristic
564	#388	C₂²×C₁₃₉	1	2	yes	—
565	#388	C₂²×C₁₃₉	1	2	yes	—
566	#388	C₂²×C₁₃₉	1	2	yes	—
567	#388	C₂²×C₁₃₉	1	2	yes	—
568	#388	C₂²×C₁₃₉	1	2	yes	—
569	#388	C₂²×C₁₃₉	1	2	yes	—
570	#388	C₂²×C₁₃₉	1	2	yes	—
571	#388	C₂²×C₁₃₉	1	2	yes	—
572	#387	C₂²×C₁₃₉	1	2	yes	—
573	#387	C₂²×C₁₃₉	1	2	yes	—
574	#387	C₂²×C₁₃₉	1	2	yes	—
575	#386	C₂²×C₁₃₉	1	2	yes	—
576	#386	C₂²×C₁₃₉	1	2	yes	—
577	#386	C₂²×C₁₃₉	1	2	yes	—
578	#386	C₂²×C₁₃₉	1	2	yes	—
579	#386	C₂²×C₁₃₉	1	2	yes	—
580	#385	C₂²×C₁₃₉	1	2	yes	—
581	#385	C₂²×C₁₃₉	1	2	yes	—
582	#385	C₂²×C₁₃₉	1	2	yes	—
583	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
584	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
585	#376	C₂²×C₁₃₉	1	2	yes	—
586	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
587	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
588	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
589	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
590	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
591	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
592	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
593	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
594	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
595	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
596	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
597	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
598	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
599	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
600	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
601	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
602	C₄⋊Q₈	—	2	8	no	—
603	C₄⋊Q₈	—	4	2	no	—
604	#127	—	4	2	no	—
605	#126	—	2	8	no	—
606	#126	—	2	8	no	—
607	#124	—	2	8	no	—
608	#124	—	2	8	no	—
609	#124	—	2	8	no	—
610	#124	—	4	4	no	—
611	#123	—	2	8	no	—
612	#123	—	2	8	no	—
613	C₂²⋊Q₈	—	2	8	no	—
614	C₂²⋊Q₈	—	2	8	no	—
615	C₂²⋊Q₈	—	2	8	no	—
616	C₂²⋊Q₈	—	4	4	no	—
617	C₂²⋊Q₈	—	4	4	no	—
618	#121	—	2	8	no	—
619	#121	—	4	4	no	—
620	#121	—	4	4	no	—
621	C₄×Q₈	D₄×C₁₃₉	1	8	yes	complemented
622	C₄×D₄	—	2	8	no	—
623	#117	—	2	8	no	—
624	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
672	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
673	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
678	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
680	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
681	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
682	#95	C₂³×C₁₃₉	1	2	yes	—
683	#95	C₂³×C₁₃₉	1	2	yes	—
684	#95	C₂³×C₁₃₉	1	2	yes	—
685	#95	C₂³×C₁₃₉	1	2	yes	—
686	#95	C₂³×C₁₃₉	1	2	yes	—
687	#95	C₂³×C₁₃₉	1	2	yes	—
688	#95	C₂³×C₁₃₉	1	2	yes	—
689	#95	C₂³×C₁₃₉	1	2	yes	—
690	#95	C₂³×C₁₃₉	1	2	yes	—
691	#95	C₂³×C₁₃₉	1	2	yes	—
692	#95	C₂³×C₁₃₉	1	2	yes	—
693	#95	C₂³×C₁₃₉	1	2	yes	—
694	#95	C₂³×C₁₃₉	1	2	yes	—
695	#95	C₂³×C₁₃₉	1	2	yes	—
696	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
697	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
698	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
699	C₂×Q₈	—	2	4	no	—
700	C₂×Q₈	—	2	4	no	—
701	C₂×Q₈	—	4	1	no	—
702	C₂×Q₈	—	4	1	no	—
703	C₂×Q₈	—	4	2	no	—
704	C₂×Q₈	—	4	2	no	—
705	C₂×Q₈	—	4	2	no	—
706	C₂×Q₈	—	4	2	no	—
707	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	2	4	no	—
710	C₂×D₄	—	2	4	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	4	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	4	2	no	—
716	C₂×D₄	—	4	2	no	—
717	C₂×D₄	—	4	2	no	—
718	C₂×D₄	—	4	2	no	—
719	C₂×D₄	—	4	2	no	—
720	C₂×D₄	—	4	2	no	—
721	C₂×D₄	—	4	2	no	—
722	C₂×D₄	—	4	1	no	—
723	C₂×D₄	—	4	1	no	—
724	C₂×D₄	—	4	2	no	—
725	C₂×D₄	—	4	1	no	—
726	C₂×D₄	—	4	1	no	—
727	C₂×D₄	—	4	2	no	—
728	C₂×D₄	—	4	2	no	—
729	C₂×D₄	—	4	1	no	—
730	C₂×D₄	—	4	1	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	2	no	—
734	C₂×D₄	—	4	2	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	2	4	no	—
737	C₂²×C₄	—	2	4	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	—	4	2	no	—
740	C₂²×C₄	—	4	2	no	—
741	C₂²×C₄	—	4	2	no	—
742	C₂²×C₄	—	4	2	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
760	C₄⋊C₄	—	2	4	no	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	—	2	4	no	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	4	no	—
771	C₄⋊C₄	—	4	1	no	—
772	C₄⋊C₄	—	4	1	no	—
773	C₄⋊C₄	—	4	1	no	—
774	C₄⋊C₄	—	4	1	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₄⋊C₄	—	4	2	no	—
777	C₄⋊C₄	—	4	1	no	—
778	C₄⋊C₄	—	4	1	no	—
779	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
780	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	2	4	no	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	4	2	no	—
798	C₂²⋊C₄	—	4	2	no	—
799	C₂²⋊C₄	—	4	2	no	—
800	C₂²⋊C₄	—	4	2	no	—
801	C₂²⋊C₄	—	4	2	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	—	4	2	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	—	4	2	no	—
808	C₄²	—	2	4	no	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	4	1	no	—
813	C₄²	—	4	2	no	—
814	C₄²	—	4	1	no	—
815	C₄²	—	4	1	no	—
816	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
817	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	2	no	—
839	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
840	Q₈	—	4	4	no	—
841	Q₈	—	8	4	no	—
842	Q₈	—	8	4	no	—
843	D₄	—	4	8	no	—
844	D₄	—	8	4	no	—
845	D₄	—	8	2	no	—
846	D₄	—	8	2	no	—
847	D₄	—	8	2	no	—
848	D₄	—	8	4	no	—
849	D₄	—	8	4	no	—
850	D₄	—	8	4	no	—
851	D₄	—	8	4	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	4	8	no	—
893	C₂×C₄	—	8	4	no	—
894	C₂×C₄	—	8	4	no	—
895	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
896	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
897	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
898	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
899	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
900	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
901	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
902	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	2	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
925	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
926	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
927	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
928	C₂²	#585×C₁₃₉	1	1	yes	characteristic
929	C₂²	#585×C₁₃₉	1	1	yes	characteristic
930	C₂²	#585×C₁₃₉	1	1	yes	characteristic
931	C₄	—	2	2	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	4	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	2	4	no	—
938	C₄	—	2	2	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	1	no	—
941	C₄	—	4	2	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	2	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₂	—	8	2	no	—
948	C₂	—	8	2	no	—
949	C₂	—	8	2	no	—
950	C₂	#3449×C₁₃₉	1	1	yes	characteristic
951	C₂	#3497×C₁₃₉	1	1	yes	characteristic
952	C₂	#3498×C₁₃₉	1	1	yes	characteristic
953	C₂	#3545×C₁₃₉	1	1	yes	characteristic
954	C₂	#3547×C₁₃₉	1	1	yes	characteristic
955	C₂	#3560×C₁₃₉	1	1	yes	characteristic
956	C₂	#3561×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#542×C₁₃₉	C₂	semidirect
2. #2860×C₁₃₉	C₂	semidirect
3. #2858×C₁₃₉	C₂	semidirect
4. #2733×C₁₃₉	C₂	semidirect
5. #2732×C₁₃₉	C₂	semidirect
6. #2730×C₁₃₉	C₂	semidirect
7. #2683×C₁₃₉	C₂	semidirect
8. #2682×C₁₃₉	C₂	semidirect
9. #2681×C₁₃₉	C₂	semidirect
10. #2677×C₁₃₉	C₂	semidirect
11. #2676×C₁₃₉	C₂	semidirect
12. #2674×C₁₃₉	C₂	semidirect
13. #2673×C₁₃₉	C₂	semidirect
14. #2662×C₁₃₉	C₂	semidirect
15. #2610×C₁₃₉	C₂	semidirect
16. #2603×C₁₃₉	C₂	semidirect
17. #2601×C₁₃₉	C₂	semidirect
18. #2540×C₁₃₉	C₂	semidirect
19. #2295×C₁₃₉	C₂	semidirect
142. C₄×Q₈×C₁₃₉	D₄	semidirect
478. #37192	C₁₃₉	direct (N × H)
479. C₁₃₉	#37192	direct (N × H)
480. C₂×#542	C₂×C₁₃₉	semidirect
481. #2860	C₂×C₁₃₉	semidirect
482. #2858	C₂×C₁₃₉	semidirect
483. #2733	C₂×C₁₃₉	semidirect
484. #2732	C₂×C₁₃₉	semidirect
485. #2730	C₂×C₁₃₉	semidirect
486. #2683	C₂×C₁₃₉	semidirect
487. #2682	C₂×C₁₃₉	semidirect
488. #2681	C₂×C₁₃₉	semidirect
489. #2677	C₂×C₁₃₉	semidirect
490. #2676	C₂×C₁₃₉	semidirect
491. #2674	C₂×C₁₃₉	semidirect
492. #2673	C₂×C₁₃₉	semidirect
493. #2662	C₂×C₁₃₉	semidirect
494. #2610	C₂×C₁₃₉	semidirect
495. #2603	C₂×C₁₃₉	semidirect
496. #2601	C₂×C₁₃₉	semidirect
497. #2540	C₂×C₁₃₉	semidirect
498. #2295	C₂×C₁₃₉	semidirect
621. C₄×Q₈	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#542×C₁₃₉	2
#2860×C₁₃₉	2
#2858×C₁₃₉	2
#2733×C₁₃₉	2
#2732×C₁₃₉	2
#2730×C₁₃₉	2
#2683×C₁₃₉	2
#2682×C₁₃₉	2
#2681×C₁₃₉	2
#2677×C₁₃₉	2
#2676×C₁₃₉	2
#2674×C₁₃₉	2
#2673×C₁₃₉	2
#2662×C₁₃₉	2
#2610×C₁₃₉	2
#2603×C₁₃₉	2
#2601×C₁₃₉	2
#2540×C₁₃₉	2
#2295×C₁₃₉	2
#37192	139

Subgroups — C139×#37192 #48031788

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37192 #48031788