Subgroups — C₁₃₉×#37217 #48031813

Order 35584.

1958 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2854×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2850×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2805×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2801×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2778×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2733×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2703×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2682×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2682×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2673×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2673×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2672×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2635×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2576×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2555×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2457×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2428×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2335×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	C₄×#121×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
37	#401×C₁₃₉	C₂²	1	2	yes	—
38	#400×C₁₃₉	C₂²	1	2	yes	—
39	#400×C₁₃₉	C₂²	1	2	yes	—
40	#399×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	#395×C₁₃₉	C₂²	1	2	yes	—
45	#394×C₁₃₉	C₂²	1	2	yes	—
46	#394×C₁₃₉	C₂²	1	2	yes	—
47	#394×C₁₃₉	C₂²	1	2	yes	—
48	#394×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	#392×C₁₃₉	C₂²	1	2	yes	—
54	#392×C₁₃₉	C₂²	1	2	yes	—
55	#392×C₁₃₉	C₂²	1	2	yes	—
56	#392×C₁₃₉	C₂²	1	2	yes	—
57	#392×C₁₃₉	C₂²	1	2	yes	—
58	#392×C₁₃₉	C₂²	1	2	yes	—
59	#392×C₁₃₉	C₂²	1	2	yes	—
60	#392×C₁₃₉	C₂²	1	2	yes	—
61	#391×C₁₃₉	C₂²	1	1	yes	characteristic
62	#390×C₁₃₉	C₂²	1	2	yes	—
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	#389×C₁₃₉	C₂²	1	1	yes	characteristic
68	#389×C₁₃₉	C₂²	1	2	yes	—
69	#389×C₁₃₉	C₂²	1	2	yes	—
70	#389×C₁₃₉	C₂²	1	1	yes	characteristic
71	#389×C₁₃₉	C₂²	1	1	yes	characteristic
72	#388×C₁₃₉	C₂²	1	2	yes	—
73	#388×C₁₃₉	C₂²	1	2	yes	—
74	#388×C₁₃₉	C₂²	1	2	yes	—
75	#388×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	#387×C₁₃₉	C₂²	1	2	yes	—
84	#387×C₁₃₉	C₂²	1	2	yes	—
85	#387×C₁₃₉	C₂²	1	2	yes	—
86	#386×C₁₃₉	C₂²	1	2	yes	—
87	#386×C₁₃₉	C₂²	1	2	yes	—
88	#386×C₁₃₉	C₂²	1	2	yes	—
89	#386×C₁₃₉	C₂²	1	2	yes	—
90	#386×C₁₃₉	C₂²	1	2	yes	—
91	#386×C₁₃₉	C₂²	1	2	yes	—
92	#386×C₁₃₉	C₂²	1	2	yes	—
93	#386×C₁₃₉	C₂²	1	2	yes	—
94	#386×C₁₃₉	C₂²	1	2	yes	—
95	#386×C₁₃₉	C₂²	1	2	yes	—
96	#385×C₁₃₉	C₂²	1	2	yes	—
97	#385×C₁₃₉	C₂²	1	2	yes	—
98	#382×C₁₃₉	C₂²	1	1	yes	characteristic
99	#381×C₁₃₉	C₂²	1	2	yes	—
100	#380×C₁₃₉	C₂²	1	1	yes	characteristic
101	#380×C₁₃₉	C₂²	1	2	yes	—
102	#380×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	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
107	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
126	#127×C₁₃₉	—	4	4	no	—
127	#124×C₁₃₉	—	4	2	no	—
128	#124×C₁₃₉	—	4	4	no	—
129	#123×C₁₃₉	—	2	8	no	—
130	#123×C₁₃₉	—	4	4	no	—
131	#123×C₁₃₉	—	4	4	no	—
132	C₂²⋊Q₈×C₁₃₉	—	4	2	no	—
133	#121×C₁₃₉	—	2	4	no	—
134	#121×C₁₃₉	—	4	2	no	—
135	#121×C₁₃₉	—	4	4	no	—
136	#121×C₁₃₉	—	4	4	no	—
137	#121×C₁₃₉	—	4	4	no	—
138	#121×C₁₃₉	—	4	4	no	—
139	#121×C₁₃₉	—	4	2	no	—
140	C₄×D₄×C₁₃₉	—	4	2	no	—
141	C₄×D₄×C₁₃₉	—	4	4	no	—
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	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	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	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	1	yes	characteristic
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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×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×C₄²×C₁₃₉	—	4	2	no	—
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	2	yes	—
191	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
192	C₂×C₄²×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	#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	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
212	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
213	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
214	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
215	C₂×Q₈×C₁₃₉	—	2	2	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	4	no	—
220	C₂×D₄×C₁₃₉	—	2	4	no	—
221	C₂×D₄×C₁₃₉	—	2	2	no	—
222	C₂×D₄×C₁₃₉	—	2	4	no	—
223	C₂×D₄×C₁₃₉	—	2	4	no	—
224	C₂×D₄×C₁₃₉	—	2	2	no	—
225	C₂×D₄×C₁₃₉	—	2	2	no	—
226	C₂×D₄×C₁₃₉	—	4	1	no	—
227	C₂×D₄×C₁₃₉	—	4	2	no	—
228	C₂×D₄×C₁₃₉	—	4	1	no	—
229	C₂×D₄×C₁₃₉	—	4	1	no	—
230	C₂×D₄×C₁₃₉	—	4	2	no	—
231	C₂×D₄×C₁₃₉	—	4	1	no	—
232	C₂×D₄×C₁₃₉	—	4	2	no	—
233	C₂×D₄×C₁₃₉	—	4	2	no	—
234	C₂×D₄×C₁₃₉	—	4	2	no	—
235	C₂×D₄×C₁₃₉	—	4	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	1	no	—
243	C₂×D₄×C₁₃₉	—	4	2	no	—
244	C₂×D₄×C₁₃₉	—	4	2	no	—
245	C₂×D₄×C₁₃₉	—	4	2	no	—
246	C₂×D₄×C₁₃₉	—	4	2	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	2	no	—
251	C₂×D₄×C₁₃₉	—	4	2	no	—
252	C₂×D₄×C₁₃₉	—	4	2	no	—
253	C₂×D₄×C₁₃₉	—	4	2	no	—
254	C₂²×C₄×C₁₃₉	—	2	2	no	—
255	C₂²×C₄×C₁₃₉	—	2	2	no	—
256	C₂²×C₄×C₁₃₉	—	2	2	no	—
257	C₂²×C₄×C₁₃₉	—	2	2	no	—
258	C₂²×C₄×C₁₃₉	—	2	2	no	—
259	C₂²×C₄×C₁₃₉	—	2	4	no	—
260	C₂²×C₄×C₁₃₉	—	2	4	no	—
261	C₂²×C₄×C₁₃₉	—	4	1	no	—
262	C₂²×C₄×C₁₃₉	—	4	1	no	—
263	C₂²×C₄×C₁₃₉	—	4	1	no	—
264	C₂²×C₄×C₁₃₉	—	4	1	no	—
265	C₂²×C₄×C₁₃₉	—	4	2	no	—
266	C₂²×C₄×C₁₃₉	—	4	2	no	—
267	C₂²×C₄×C₁₃₉	—	4	2	no	—
268	C₂²×C₄×C₁₃₉	—	4	2	no	—
269	C₂²×C₄×C₁₃₉	—	4	2	no	—
270	C₂²×C₄×C₁₃₉	—	4	2	no	—
271	C₂²×C₄×C₁₃₉	—	4	2	no	—
272	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	—	4	1	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	2	no	—
296	C₄⋊C₄×C₁₃₉	—	4	1	no	—
297	C₄⋊C₄×C₁₃₉	—	4	2	no	—
298	C₄⋊C₄×C₁₃₉	—	4	1	no	—
299	C₄⋊C₄×C₁₃₉	—	4	2	no	—
300	C₄⋊C₄×C₁₃₉	—	4	2	no	—
301	C₄⋊C₄×C₁₃₉	—	4	2	no	—
302	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
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	—	4	2	no	—
315	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
316	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
317	C₂²⋊C₄×C₁₃₉	—	4	2	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	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
330	C₄²×C₁₃₉	—	2	2	no	—
331	C₄²×C₁₃₉	—	2	2	no	—
332	C₄²×C₁₃₉	—	4	1	no	—
333	C₄²×C₁₃₉	—	4	1	no	—
334	C₄²×C₁₃₉	—	4	2	no	—
335	C₄²×C₁₃₉	—	4	2	no	—
336	C₄²×C₁₃₉	—	4	2	no	—
337	C₂³×C₁₃₉	—	2	1	no	—
338	C₂³×C₁₃₉	—	2	1	no	—
339	C₂³×C₁₃₉	—	2	1	no	—
340	C₂³×C₁₃₉	—	2	1	no	—
341	C₂³×C₁₃₉	—	2	1	no	—
342	C₂³×C₁₃₉	—	2	1	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	—	2	2	no	—
361	C₂³×C₁₃₉	—	2	2	no	—
362	C₂³×C₁₃₉	—	2	2	no	—
363	C₂³×C₁₃₉	—	2	2	no	—
364	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
365	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
366	Q₈×C₁₃₉	—	8	2	no	—
367	D₄×C₁₃₉	—	4	8	no	—
368	D₄×C₁₃₉	—	4	4	no	—
369	D₄×C₁₃₉	—	8	4	no	—
370	D₄×C₁₃₉	—	8	2	no	—
371	D₄×C₁₃₉	—	8	2	no	—
372	D₄×C₁₃₉	—	8	4	no	—
373	D₄×C₁₃₉	—	8	4	no	—
374	D₄×C₁₃₉	—	8	4	no	—
375	D₄×C₁₃₉	—	8	4	no	—
376	D₄×C₁₃₉	—	8	4	no	—
377	D₄×C₁₃₉	—	8	4	no	—
378	D₄×C₁₃₉	—	8	4	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	2	no	—
384	C₂×C₄×C₁₃₉	—	2	2	no	—
385	C₂×C₄×C₁₃₉	—	2	1	no	—
386	C₂×C₄×C₁₃₉	—	2	1	no	—
387	C₂×C₄×C₁₃₉	—	2	1	no	—
388	C₂×C₄×C₁₃₉	—	2	1	no	—
389	C₂×C₄×C₁₃₉	—	2	2	no	—
390	C₂×C₄×C₁₃₉	—	2	1	no	—
391	C₂×C₄×C₁₃₉	—	2	2	no	—
392	C₂×C₄×C₁₃₉	—	2	1	no	—
393	C₂×C₄×C₁₃₉	—	2	1	no	—
394	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
404	C₂×C₄×C₁₃₉	—	2	2	no	—
405	C₂×C₄×C₁₃₉	—	2	2	no	—
406	C₂×C₄×C₁₃₉	—	2	2	no	—
407	C₂×C₄×C₁₃₉	—	2	1	no	—
408	C₂×C₄×C₁₃₉	—	2	1	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	—	2	1	no	—
414	C₂×C₄×C₁₃₉	—	2	2	no	—
415	C₂×C₄×C₁₃₉	—	2	2	no	—
416	C₂×C₄×C₁₃₉	—	2	2	no	—
417	C₂×C₄×C₁₃₉	—	2	2	no	—
418	C₂×C₄×C₁₃₉	—	2	2	no	—
419	C₂×C₄×C₁₃₉	—	4	4	no	—
420	C₂×C₄×C₁₃₉	—	4	4	no	—
421	C₂×C₄×C₁₃₉	—	4	4	no	—
422	C₂×C₄×C₁₃₉	—	8	4	no	—
423	C₂×C₄×C₁₃₉	—	8	4	no	—
424	C₂×C₄×C₁₃₉	—	8	4	no	—
425	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
426	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
427	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
428	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
429	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
430	C₂²×C₁₃₉	—	2	2	no	—
431	C₂²×C₁₃₉	—	2	2	no	—
432	C₂²×C₁₃₉	—	2	2	no	—
433	C₂²×C₁₃₉	—	4	1	no	—
434	C₂²×C₁₃₉	—	4	1	no	—
435	C₂²×C₁₃₉	—	4	1	no	—
436	C₂²×C₁₃₉	—	4	1	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	—	4	2	no	—
446	C₂²×C₁₃₉	—	4	2	no	—
447	C₂²×C₁₃₉	—	4	2	no	—
448	C₂²×C₁₃₉	—	4	2	no	—
449	C₂²×C₁₃₉	—	4	2	no	—
450	C₂²×C₁₃₉	—	4	2	no	—
451	C₂²×C₁₃₉	—	4	2	no	—
452	C₂²×C₁₃₉	—	4	2	no	—
453	C₂²×C₁₃₉	—	4	2	no	—
454	C₂²×C₁₃₉	—	4	2	no	—
455	C₂²×C₁₃₉	—	4	2	no	—
456	C₂²×C₁₃₉	—	4	2	no	—
457	C₂²×C₁₃₉	—	4	2	no	—
458	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
459	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
460	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
461	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
462	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
463	C₂²×C₁₃₉	#585	1	1	yes	characteristic
464	C₂²×C₁₃₉	#585	1	1	yes	characteristic
465	C₄×C₁₃₉	—	2	2	no	—
466	C₄×C₁₃₉	—	2	4	no	—
467	C₄×C₁₃₉	—	2	2	no	—
468	C₄×C₁₃₉	—	2	2	no	—
469	C₄×C₁₃₉	—	2	2	no	—
470	C₄×C₁₃₉	—	4	1	no	—
471	C₄×C₁₃₉	—	4	2	no	—
472	C₄×C₁₃₉	—	4	2	no	—
473	C₄×C₁₃₉	—	4	2	no	—
474	C₄×C₁₃₉	—	4	1	no	—
475	C₄×C₁₃₉	—	4	2	no	—
476	C₄×C₁₃₉	—	4	2	no	—
477	C₄×C₁₃₉	—	4	2	no	—
478	C₄×C₁₃₉	—	4	2	no	—
479	C₄×C₁₃₉	—	4	2	no	—
480	C₂×C₁₃₉	—	4	2	no	—
481	C₂×C₁₃₉	—	8	2	no	—
482	C₂×C₁₃₉	—	8	2	no	—
483	C₂×C₁₃₉	—	8	2	no	—
484	C₂×C₁₃₉	#3460	1	1	yes	characteristic
485	C₂×C₁₃₉	#3517	1	1	yes	characteristic
486	C₂×C₁₃₉	#3519	1	1	yes	characteristic
487	C₂×C₁₃₉	#3534	1	1	yes	characteristic
488	C₂×C₁₃₉	#3537	1	1	yes	characteristic
489	C₂×C₁₃₉	#3545	1	1	yes	characteristic
490	C₂×C₁₃₉	#3546	1	1	yes	characteristic
491	#37217	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
492	C₁₃₉	#37217	1	1	yes	characteristic, direct product factor, Sylow
493	#2854	C₂×C₁₃₉	1	1	yes	characteristic, complemented
494	#2850	C₂×C₁₃₉	1	1	yes	characteristic, complemented
495	#2805	C₂×C₁₃₉	1	1	yes	characteristic, complemented
496	#2801	C₂×C₁₃₉	1	2	yes	complemented
497	#2778	C₂×C₁₃₉	1	2	yes	complemented
498	#2733	C₂×C₁₃₉	1	1	yes	characteristic, complemented
499	#2703	C₂×C₁₃₉	1	2	yes	complemented
500	#2682	C₂×C₁₃₉	1	1	yes	characteristic, complemented
501	#2682	C₂×C₁₃₉	1	1	yes	characteristic, complemented
502	#2673	C₂×C₁₃₉	1	2	yes	complemented
503	#2673	C₂×C₁₃₉	1	2	yes	complemented
504	#2672	C₂×C₁₃₉	1	2	yes	complemented
505	#2635	C₂×C₁₃₉	1	2	yes	complemented
506	#2576	C₂×C₁₃₉	1	2	yes	complemented
507	#2555	C₂×C₁₃₉	1	2	yes	complemented
508	#2457	C₂×C₁₃₉	1	2	yes	complemented
509	#2428	C₂×C₁₃₉	1	2	yes	complemented
510	#2335	C₂×C₁₃₉	1	2	yes	complemented
511	C₄×#121	C₂×C₁₃₉	1	1	yes	characteristic, complemented
512	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
513	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
514	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
515	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
516	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
517	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
518	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
519	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
520	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
521	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
522	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
523	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
524	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
525	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
526	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
527	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
528	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
529	#401	C₂²×C₁₃₉	1	2	yes	—
530	#400	C₂²×C₁₃₉	1	2	yes	—
531	#400	C₂²×C₁₃₉	1	2	yes	—
532	#399	C₂²×C₁₃₉	1	2	yes	—
533	#397	C₂²×C₁₃₉	1	2	yes	—
534	#396	C₂²×C₁₃₉	1	2	yes	—
535	#396	C₂²×C₁₃₉	1	2	yes	—
536	#395	C₂²×C₁₃₉	1	2	yes	—
537	#394	C₂²×C₁₃₉	1	2	yes	—
538	#394	C₂²×C₁₃₉	1	2	yes	—
539	#394	C₂²×C₁₃₉	1	2	yes	—
540	#394	C₂²×C₁₃₉	1	2	yes	—
541	#394	C₂²×C₁₃₉	1	2	yes	—
542	#394	C₂²×C₁₃₉	1	2	yes	—
543	#394	C₂²×C₁₃₉	1	2	yes	—
544	#394	C₂²×C₁₃₉	1	2	yes	—
545	#392	C₂²×C₁₃₉	1	2	yes	—
546	#392	C₂²×C₁₃₉	1	2	yes	—
547	#392	C₂²×C₁₃₉	1	2	yes	—
548	#392	C₂²×C₁₃₉	1	2	yes	—
549	#392	C₂²×C₁₃₉	1	2	yes	—
550	#392	C₂²×C₁₃₉	1	2	yes	—
551	#392	C₂²×C₁₃₉	1	2	yes	—
552	#392	C₂²×C₁₃₉	1	2	yes	—
553	#391	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	1	yes	characteristic
559	#389	C₂²×C₁₃₉	1	2	yes	—
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	2	yes	—
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	#388	C₂²×C₁₃₉	1	2	yes	—
573	#388	C₂²×C₁₃₉	1	2	yes	—
574	#388	C₂²×C₁₃₉	1	2	yes	—
575	#387	C₂²×C₁₃₉	1	2	yes	—
576	#387	C₂²×C₁₃₉	1	2	yes	—
577	#387	C₂²×C₁₃₉	1	2	yes	—
578	#386	C₂²×C₁₃₉	1	2	yes	—
579	#386	C₂²×C₁₃₉	1	2	yes	—
580	#386	C₂²×C₁₃₉	1	2	yes	—
581	#386	C₂²×C₁₃₉	1	2	yes	—
582	#386	C₂²×C₁₃₉	1	2	yes	—
583	#386	C₂²×C₁₃₉	1	2	yes	—
584	#386	C₂²×C₁₃₉	1	2	yes	—
585	#386	C₂²×C₁₃₉	1	2	yes	—
586	#386	C₂²×C₁₃₉	1	2	yes	—
587	#386	C₂²×C₁₃₉	1	2	yes	—
588	#385	C₂²×C₁₃₉	1	2	yes	—
589	#385	C₂²×C₁₃₉	1	2	yes	—
590	#382	C₂²×C₁₃₉	1	1	yes	characteristic
591	#381	C₂²×C₁₃₉	1	2	yes	—
592	#380	C₂²×C₁₃₉	1	2	yes	—
593	#380	C₂²×C₁₃₉	1	1	yes	characteristic
594	#380	C₂²×C₁₃₉	1	1	yes	characteristic
595	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
596	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
597	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
598	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
599	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
600	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
601	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
602	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
603	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
604	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
605	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
606	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
607	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
608	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
609	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
610	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
611	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
612	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
614	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
615	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
616	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
617	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
618	#127	—	4	4	no	—
619	#124	—	4	2	no	—
620	#124	—	4	4	no	—
621	#123	—	2	8	no	—
622	#123	—	4	4	no	—
623	#123	—	4	4	no	—
624	C₂²⋊Q₈	—	4	2	no	—
625	#121	—	2	4	no	—
626	#121	—	4	2	no	—
627	#121	—	4	4	no	—
628	#121	—	4	4	no	—
629	#121	—	4	4	no	—
630	#121	—	4	4	no	—
631	#121	—	4	2	no	—
632	C₄×D₄	—	4	2	no	—
633	C₄×D₄	—	4	4	no	—
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	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
677	C₂×C₄²	—	4	2	no	—
678	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
681	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
682	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
683	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
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	#95	C₂³×C₁₃₉	1	2	yes	—
697	#95	C₂³×C₁₃₉	1	2	yes	—
698	#95	C₂³×C₁₃₉	1	2	yes	—
699	#95	C₂³×C₁₃₉	1	2	yes	—
700	#95	C₂³×C₁₃₉	1	2	yes	—
701	#95	C₂³×C₁₃₉	1	2	yes	—
702	#95	C₂³×C₁₃₉	1	2	yes	—
703	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
704	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
705	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
706	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
707	C₂×Q₈	—	2	2	no	—
708	C₂×Q₈	—	4	1	no	—
709	C₂×Q₈	—	4	1	no	—
710	C₂×D₄	—	2	4	no	—
711	C₂×D₄	—	2	4	no	—
712	C₂×D₄	—	2	4	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	4	1	no	—
719	C₂×D₄	—	4	2	no	—
720	C₂×D₄	—	4	1	no	—
721	C₂×D₄	—	4	1	no	—
722	C₂×D₄	—	4	2	no	—
723	C₂×D₄	—	4	1	no	—
724	C₂×D₄	—	4	2	no	—
725	C₂×D₄	—	4	2	no	—
726	C₂×D₄	—	4	2	no	—
727	C₂×D₄	—	4	2	no	—
728	C₂×D₄	—	4	2	no	—
729	C₂×D₄	—	4	2	no	—
730	C₂×D₄	—	4	2	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	2	no	—
734	C₂×D₄	—	4	1	no	—
735	C₂×D₄	—	4	2	no	—
736	C₂×D₄	—	4	2	no	—
737	C₂×D₄	—	4	2	no	—
738	C₂×D₄	—	4	2	no	—
739	C₂×D₄	—	4	1	no	—
740	C₂×D₄	—	4	2	no	—
741	C₂×D₄	—	4	2	no	—
742	C₂×D₄	—	4	2	no	—
743	C₂×D₄	—	4	2	no	—
744	C₂×D₄	—	4	2	no	—
745	C₂×D₄	—	4	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	—	4	1	no	—
754	C₂²×C₄	—	4	1	no	—
755	C₂²×C₄	—	4	1	no	—
756	C₂²×C₄	—	4	1	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	C₂⁴×C₁₃₉	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	2	4	no	—
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	4	1	no	—
784	C₄⋊C₄	—	4	1	no	—
785	C₄⋊C₄	—	4	1	no	—
786	C₄⋊C₄	—	4	1	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	—	4	1	no	—
789	C₄⋊C₄	—	4	2	no	—
790	C₄⋊C₄	—	4	1	no	—
791	C₄⋊C₄	—	4	2	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	—	4	2	no	—
808	C₂²⋊C₄	—	4	2	no	—
809	C₂²⋊C₄	—	4	2	no	—
810	C₂²⋊C₄	—	4	2	no	—
811	C₂²⋊C₄	—	4	2	no	—
812	C₂²⋊C₄	—	4	2	no	—
813	C₂²⋊C₄	—	4	2	no	—
814	C₂²⋊C₄	—	4	2	no	—
815	C₂²⋊C₄	—	4	2	no	—
816	C₂²⋊C₄	—	4	2	no	—
817	C₂²⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	—	4	2	no	—
820	C₂²⋊C₄	—	4	2	no	—
821	C₂²⋊C₄	—	4	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	4	1	no	—
825	C₄²	—	4	1	no	—
826	C₄²	—	4	2	no	—
827	C₄²	—	4	2	no	—
828	C₄²	—	4	2	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
857	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
858	Q₈	—	8	2	no	—
859	D₄	—	4	8	no	—
860	D₄	—	4	4	no	—
861	D₄	—	8	2	no	—
862	D₄	—	8	2	no	—
863	D₄	—	8	4	no	—
864	D₄	—	8	4	no	—
865	D₄	—	8	4	no	—
866	D₄	—	8	4	no	—
867	D₄	—	8	4	no	—
868	D₄	—	8	4	no	—
869	D₄	—	8	4	no	—
870	D₄	—	8	4	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	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	1	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	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	4	4	no	—
912	C₂×C₄	—	4	4	no	—
913	C₂×C₄	—	4	4	no	—
914	C₂×C₄	—	8	4	no	—
915	C₂×C₄	—	8	4	no	—
916	C₂×C₄	—	8	4	no	—
917	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
918	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
919	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
920	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
921	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	4	1	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	1	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	2	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
951	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
952	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
953	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
954	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
955	C₂²	#585×C₁₃₉	1	1	yes	characteristic
956	C₂²	#585×C₁₃₉	1	1	yes	characteristic
957	C₄	—	2	2	no	—
958	C₄	—	2	2	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	4	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	1	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	1	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₂	—	4	2	no	—
973	C₂	—	8	2	no	—
974	C₂	—	8	2	no	—
975	C₂	—	8	2	no	—
976	C₂	#3460×C₁₃₉	1	1	yes	characteristic
977	C₂	#3517×C₁₃₉	1	1	yes	characteristic
978	C₂	#3519×C₁₃₉	1	1	yes	characteristic
979	C₂	#3534×C₁₃₉	1	1	yes	characteristic
980	C₂	#3537×C₁₃₉	1	1	yes	characteristic
981	C₂	#3545×C₁₃₉	1	1	yes	characteristic
982	C₂	#3546×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. #2854×C₁₃₉	C₂	semidirect
2. #2850×C₁₃₉	C₂	semidirect
3. #2805×C₁₃₉	C₂	semidirect
4. #2801×C₁₃₉	C₂	semidirect
5. #2778×C₁₃₉	C₂	semidirect
6. #2733×C₁₃₉	C₂	semidirect
7. #2703×C₁₃₉	C₂	semidirect
8. #2682×C₁₃₉	C₂	semidirect
9. #2682×C₁₃₉	C₂	semidirect
10. #2673×C₁₃₉	C₂	semidirect
11. #2673×C₁₃₉	C₂	semidirect
12. #2672×C₁₃₉	C₂	semidirect
13. #2635×C₁₃₉	C₂	semidirect
14. #2576×C₁₃₉	C₂	semidirect
15. #2555×C₁₃₉	C₂	semidirect
16. #2457×C₁₃₉	C₂	semidirect
17. #2428×C₁₃₉	C₂	semidirect
18. #2335×C₁₃₉	C₂	semidirect
19. C₄×#121×C₁₃₉	C₂	semidirect
491. #37217	C₁₃₉	direct (N × H)
492. C₁₃₉	#37217	direct (N × H)
493. #2854	C₂×C₁₃₉	semidirect
494. #2850	C₂×C₁₃₉	semidirect
495. #2805	C₂×C₁₃₉	semidirect
496. #2801	C₂×C₁₃₉	semidirect
497. #2778	C₂×C₁₃₉	semidirect
498. #2733	C₂×C₁₃₉	semidirect
499. #2703	C₂×C₁₃₉	semidirect
500. #2682	C₂×C₁₃₉	semidirect
501. #2682	C₂×C₁₃₉	semidirect
502. #2673	C₂×C₁₃₉	semidirect
503. #2673	C₂×C₁₃₉	semidirect
504. #2672	C₂×C₁₃₉	semidirect
505. #2635	C₂×C₁₃₉	semidirect
506. #2576	C₂×C₁₃₉	semidirect
507. #2555	C₂×C₁₃₉	semidirect
508. #2457	C₂×C₁₃₉	semidirect
509. #2428	C₂×C₁₃₉	semidirect
510. #2335	C₂×C₁₃₉	semidirect
511. C₄×#121	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2854×C₁₃₉	2
#2850×C₁₃₉	2
#2805×C₁₃₉	2
#2801×C₁₃₉	2
#2778×C₁₃₉	2
#2733×C₁₃₉	2
#2703×C₁₃₉	2
#2682×C₁₃₉	2
#2673×C₁₃₉	2
#2672×C₁₃₉	2
#2635×C₁₃₉	2
#2576×C₁₃₉	2
#2555×C₁₃₉	2
#2457×C₁₃₉	2
#2428×C₁₃₉	2
#2335×C₁₃₉	2
C₄×#121×C₁₃₉	2
#37217	139

Subgroups — C139×#37217 #48031813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37217 #48031813