Subgroups — C₁₃₉×#37010 #48031606

Order 35584.

1706 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	2	yes	maximal, complemented
2	#2754×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2752×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2730×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2721×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2694×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2687×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2685×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2684×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2651×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2607×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2560×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2539×C₁₃₉	C₂	1	1	yes	maximal, characteristic
14	#2526×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2500×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2482×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2333×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2312×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2298×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#125×C₁₃₉	C₂²	1	2	yes	complemented
22	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
25	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	#400×C₁₃₉	C₂²	1	2	yes	complemented
30	#399×C₁₃₉	C₂²	1	2	yes	—
31	#399×C₁₃₉	C₂²	1	2	yes	—
32	#399×C₁₃₉	C₂²	1	2	yes	—
33	#399×C₁₃₉	C₂²	1	2	yes	complemented
34	#398×C₁₃₉	C₂²	1	2	yes	complemented
35	#398×C₁₃₉	C₂²	1	2	yes	complemented
36	#398×C₁₃₉	C₂²	1	2	yes	complemented
37	#397×C₁₃₉	C₂²	1	2	yes	—
38	#397×C₁₃₉	C₂²	1	2	yes	—
39	#397×C₁₃₉	C₂²	1	2	yes	—
40	#397×C₁₃₉	C₂²	1	2	yes	complemented
41	#397×C₁₃₉	C₂²	1	2	yes	complemented
42	#396×C₁₃₉	C₂²	1	2	yes	—
43	#396×C₁₃₉	C₂²	1	2	yes	complemented
44	#394×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	#393×C₁₃₉	C₂²	1	2	yes	—
51	#393×C₁₃₉	C₂²	1	2	yes	—
52	#392×C₁₃₉	C₂²	1	2	yes	—
53	#391×C₁₃₉	C₂²	1	2	yes	complemented
54	#391×C₁₃₉	C₂²	1	2	yes	complemented
55	#391×C₁₃₉	C₂²	1	2	yes	complemented
56	#390×C₁₃₉	C₂²	1	2	yes	—
57	#390×C₁₃₉	C₂²	1	2	yes	—
58	#390×C₁₃₉	C₂²	1	2	yes	—
59	#390×C₁₃₉	C₂²	1	2	yes	—
60	#390×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
61	#390×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
62	#389×C₁₃₉	C₂²	1	2	yes	complemented
63	#388×C₁₃₉	C₂²	1	2	yes	—
64	#388×C₁₃₉	C₂²	1	2	yes	—
65	#388×C₁₃₉	C₂²	1	2	yes	—
66	#388×C₁₃₉	C₂²	1	2	yes	—
67	#388×C₁₃₉	C₂²	1	2	yes	—
68	#388×C₁₃₉	C₂²	1	2	yes	—
69	#388×C₁₃₉	C₂²	1	2	yes	—
70	#388×C₁₃₉	C₂²	1	2	yes	—
71	#388×C₁₃₉	C₂²	1	2	yes	—
72	#388×C₁₃₉	C₂²	1	2	yes	—
73	#388×C₁₃₉	C₂²	1	2	yes	—
74	#388×C₁₃₉	C₂²	1	2	yes	complemented
75	#388×C₁₃₉	C₂²	1	2	yes	complemented
76	#388×C₁₃₉	C₂²	1	2	yes	complemented
77	#388×C₁₃₉	C₂²	1	2	yes	complemented
78	#388×C₁₃₉	C₂²	1	2	yes	complemented
79	#387×C₁₃₉	C₂²	1	2	yes	complemented
80	#387×C₁₃₉	C₂²	1	2	yes	complemented
81	#387×C₁₃₉	C₂²	1	2	yes	complemented
82	#387×C₁₃₉	C₂²	1	2	yes	complemented
83	#387×C₁₃₉	C₂²	1	2	yes	complemented
84	#387×C₁₃₉	C₂²	1	2	yes	complemented
85	#386×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	complemented
89	#385×C₁₃₉	C₂²	1	1	yes	characteristic
90	#385×C₁₃₉	C₂²	1	1	yes	characteristic
91	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
92	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
93	#381×C₁₃₉	C₂²	1	1	yes	characteristic
94	#381×C₁₃₉	C₂²	1	2	yes	complemented
95	#380×C₁₃₉	C₂²	1	2	yes	—
96	#379×C₁₃₉	C₂²	1	2	yes	—
97	#379×C₁₃₉	C₂²	1	1	yes	characteristic
98	#379×C₁₃₉	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
105	#376×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
106	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	#126×C₁₃₉	—	4	4	no	—
117	#125×C₁₃₉	—	4	4	no	—
118	#124×C₁₃₉	—	4	4	no	—
119	#123×C₁₃₉	—	4	4	no	—
120	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
121	#121×C₁₃₉	—	2	4	no	—
122	#120×C₁₃₉	—	4	4	no	—
123	#117×C₁₃₉	—	2	4	no	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
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	#95×C₁₃₉	C₂³	1	2	yes	—
183	#95×C₁₃₉	C₂³	1	2	yes	—
184	#95×C₁₃₉	C₂³	1	2	yes	—
185	#95×C₁₃₉	C₂³	1	2	yes	—
186	#95×C₁₃₉	C₂³	1	2	yes	—
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	C₂⁴×C₁₃₉	—	2	2	no	—
204	C₂⁴×C₁₃₉	—	4	2	no	—
205	C₂⁴×C₁₃₉	—	4	2	no	—
206	C₂⁴×C₁₃₉	—	4	1	no	—
207	C₂⁴×C₁₃₉	—	4	1	no	—
208	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
209	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
210	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
211	C₂×Q₈×C₁₃₉	—	2	4	no	—
212	C₂×Q₈×C₁₃₉	—	4	2	no	—
213	C₂×Q₈×C₁₃₉	—	4	2	no	—
214	C₂×D₄×C₁₃₉	—	2	4	no	—
215	C₂×D₄×C₁₃₉	—	2	2	no	—
216	C₂×D₄×C₁₃₉	—	2	4	no	—
217	C₂×D₄×C₁₃₉	—	4	2	no	—
218	C₂×D₄×C₁₃₉	—	4	2	no	—
219	C₂×D₄×C₁₃₉	—	4	2	no	—
220	C₂×D₄×C₁₃₉	—	4	1	no	—
221	C₂×D₄×C₁₃₉	—	4	1	no	—
222	C₂×D₄×C₁₃₉	—	4	2	no	—
223	C₂×D₄×C₁₃₉	—	4	2	no	—
224	C₂×D₄×C₁₃₉	—	4	2	no	—
225	C₂×D₄×C₁₃₉	—	4	2	no	—
226	C₂²×C₄×C₁₃₉	—	2	2	no	—
227	C₂²×C₄×C₁₃₉	—	4	1	no	—
228	C₂²×C₄×C₁₃₉	—	4	1	no	—
229	C₂²×C₄×C₁₃₉	—	4	2	no	—
230	C₂²×C₄×C₁₃₉	—	4	2	no	—
231	C₂²×C₄×C₁₃₉	—	4	2	no	—
232	C₂²×C₄×C₁₃₉	—	4	2	no	—
233	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
234	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
246	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
250	C₄⋊C₄×C₁₃₉	—	2	2	no	—
251	C₄⋊C₄×C₁₃₉	—	2	2	no	—
252	C₄⋊C₄×C₁₃₉	—	2	2	no	—
253	C₄⋊C₄×C₁₃₉	—	2	4	no	—
254	C₄⋊C₄×C₁₃₉	—	2	4	no	—
255	C₄⋊C₄×C₁₃₉	—	2	4	no	—
256	C₄⋊C₄×C₁₃₉	—	4	2	no	—
257	C₄⋊C₄×C₁₃₉	—	4	2	no	—
258	C₄⋊C₄×C₁₃₉	—	4	2	no	—
259	C₄⋊C₄×C₁₃₉	—	4	2	no	—
260	C₄⋊C₄×C₁₃₉	—	4	2	no	—
261	C₄⋊C₄×C₁₃₉	—	4	2	no	—
262	C₄⋊C₄×C₁₃₉	—	4	2	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	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
270	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
271	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
272	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
273	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
274	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
275	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
276	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
277	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
278	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
279	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
280	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
281	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
282	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
283	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
284	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
285	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
286	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
287	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
288	C₂²⋊C₄×C₁₃₉	—	4	2	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	C₄²×C₁₃₉	—	2	2	no	—
297	C₄²×C₁₃₉	—	2	2	no	—
298	C₄²×C₁₃₉	—	2	4	no	—
299	C₄²×C₁₃₉	—	4	1	no	—
300	C₄²×C₁₃₉	—	4	1	no	—
301	C₄²×C₁₃₉	—	4	1	no	—
302	C₄²×C₁₃₉	—	4	1	no	—
303	C₄²×C₁₃₉	—	4	1	no	—
304	C₄²×C₁₃₉	—	4	1	no	—
305	C₄²×C₁₃₉	—	4	2	no	—
306	C₄²×C₁₃₉	—	4	2	no	—
307	C₂³×C₁₃₉	—	2	2	no	—
308	C₂³×C₁₃₉	—	2	2	no	—
309	C₂³×C₁₃₉	—	2	1	no	—
310	C₂³×C₁₃₉	—	2	1	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	—	4	4	no	—
326	C₂³×C₁₃₉	—	8	2	no	—
327	C₂³×C₁₃₉	—	8	2	no	—
328	C₂³×C₁₃₉	—	8	4	no	—
329	C₂³×C₁₃₉	—	8	4	no	—
330	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
331	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
332	Q₈×C₁₃₉	—	8	4	no	—
333	D₄×C₁₃₉	—	8	2	no	—
334	D₄×C₁₃₉	—	8	4	no	—
335	D₄×C₁₃₉	—	8	4	no	—
336	D₄×C₁₃₉	—	8	4	no	—
337	C₂×C₄×C₁₃₉	—	2	1	no	—
338	C₂×C₄×C₁₃₉	—	2	1	no	—
339	C₂×C₄×C₁₃₉	—	2	1	no	—
340	C₂×C₄×C₁₃₉	—	2	1	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	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	2	no	—
351	C₂×C₄×C₁₃₉	—	2	2	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	2	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	—	2	2	no	—
378	C₂×C₄×C₁₃₉	—	4	4	no	—
379	C₂×C₄×C₁₃₉	—	8	2	no	—
380	C₂×C₄×C₁₃₉	—	8	4	no	—
381	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
382	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
383	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
384	C₂²×C₁₃₉	—	2	2	no	—
385	C₂²×C₁₃₉	—	2	2	no	—
386	C₂²×C₁₃₉	—	2	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	—	4	2	no	—
401	C₂²×C₁₃₉	—	4	2	no	—
402	C₂²×C₁₃₉	—	4	2	no	—
403	C₂²×C₁₃₉	—	8	8	no	—
404	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
405	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
406	C₂²×C₁₃₉	#585	1	2	yes	—
407	C₂²×C₁₃₉	#585	1	1	yes	characteristic
408	C₂²×C₁₃₉	#585	1	1	yes	characteristic
409	C₄×C₁₃₉	—	2	2	no	—
410	C₄×C₁₃₉	—	2	2	no	—
411	C₄×C₁₃₉	—	2	4	no	—
412	C₄×C₁₃₉	—	4	1	no	—
413	C₄×C₁₃₉	—	4	1	no	—
414	C₄×C₁₃₉	—	4	1	no	—
415	C₄×C₁₃₉	—	4	1	no	—
416	C₄×C₁₃₉	—	4	2	no	—
417	C₄×C₁₃₉	—	4	2	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	C₄×C₁₃₉	—	4	2	no	—
425	C₂×C₁₃₉	—	4	2	no	—
426	C₂×C₁₃₉	—	8	2	no	—
427	C₂×C₁₃₉	—	8	2	no	—
428	C₂×C₁₃₉	#3455	1	1	yes	characteristic
429	C₂×C₁₃₉	#3491	1	1	yes	characteristic
430	C₂×C₁₃₉	#3508	1	1	yes	characteristic
431	C₂×C₁₃₉	#3545	1	2	yes	—
432	C₂×C₁₃₉	#3562	1	2	yes	—
433	#37010	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
434	C₁₃₉	#37010	1	1	yes	characteristic, direct product factor, Sylow
435	#2861	C₂×C₁₃₉	1	2	yes	complemented
436	#2754	C₂×C₁₃₉	1	2	yes	complemented
437	#2752	C₂×C₁₃₉	1	2	yes	complemented
438	#2730	C₂×C₁₃₉	1	2	yes	complemented
439	#2721	C₂×C₁₃₉	1	2	yes	complemented
440	#2694	C₂×C₁₃₉	1	2	yes	complemented
441	#2687	C₂×C₁₃₉	1	2	yes	complemented
442	#2685	C₂×C₁₃₉	1	2	yes	complemented
443	#2684	C₂×C₁₃₉	1	2	yes	complemented
444	#2651	C₂×C₁₃₉	1	2	yes	complemented
445	#2607	C₂×C₁₃₉	1	1	yes	characteristic, complemented
446	#2560	C₂×C₁₃₉	1	2	yes	complemented
447	#2539	C₂×C₁₃₉	1	1	yes	characteristic
448	#2526	C₂×C₁₃₉	1	2	yes	complemented
449	#2500	C₂×C₁₃₉	1	1	yes	characteristic, complemented
450	#2482	C₂×C₁₃₉	1	1	yes	characteristic, complemented
451	#2333	C₂×C₁₃₉	1	1	yes	characteristic, complemented
452	#2312	C₂×C₁₃₉	1	1	yes	characteristic, complemented
453	#2298	C₂×C₁₃₉	1	1	yes	characteristic, complemented
454	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
455	C₂×#125	C₂²×C₁₃₉	1	2	yes	complemented
456	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
457	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
458	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
459	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
460	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
461	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
462	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
463	#400	C₂²×C₁₃₉	1	2	yes	complemented
464	#399	C₂²×C₁₃₉	1	2	yes	—
465	#399	C₂²×C₁₃₉	1	2	yes	—
466	#399	C₂²×C₁₃₉	1	2	yes	—
467	#399	C₂²×C₁₃₉	1	2	yes	complemented
468	#398	C₂²×C₁₃₉	1	2	yes	complemented
469	#398	C₂²×C₁₃₉	1	2	yes	complemented
470	#398	C₂²×C₁₃₉	1	2	yes	complemented
471	#397	C₂²×C₁₃₉	1	2	yes	—
472	#397	C₂²×C₁₃₉	1	2	yes	—
473	#397	C₂²×C₁₃₉	1	2	yes	—
474	#397	C₂²×C₁₃₉	1	2	yes	complemented
475	#397	C₂²×C₁₃₉	1	2	yes	complemented
476	#396	C₂²×C₁₃₉	1	2	yes	—
477	#396	C₂²×C₁₃₉	1	2	yes	complemented
478	#394	C₂²×C₁₃₉	1	2	yes	—
479	#394	C₂²×C₁₃₉	1	2	yes	—
480	#394	C₂²×C₁₃₉	1	2	yes	—
481	#394	C₂²×C₁₃₉	1	2	yes	—
482	#394	C₂²×C₁₃₉	1	2	yes	—
483	#394	C₂²×C₁₃₉	1	2	yes	—
484	#393	C₂²×C₁₃₉	1	2	yes	—
485	#393	C₂²×C₁₃₉	1	2	yes	—
486	#392	C₂²×C₁₃₉	1	2	yes	—
487	#391	C₂²×C₁₃₉	1	2	yes	complemented
488	#391	C₂²×C₁₃₉	1	2	yes	complemented
489	#391	C₂²×C₁₃₉	1	2	yes	complemented
490	#390	C₂²×C₁₃₉	1	2	yes	—
491	#390	C₂²×C₁₃₉	1	2	yes	—
492	#390	C₂²×C₁₃₉	1	2	yes	—
493	#390	C₂²×C₁₃₉	1	2	yes	—
494	#390	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
495	#390	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
496	#389	C₂²×C₁₃₉	1	2	yes	complemented
497	#388	C₂²×C₁₃₉	1	2	yes	—
498	#388	C₂²×C₁₃₉	1	2	yes	—
499	#388	C₂²×C₁₃₉	1	2	yes	—
500	#388	C₂²×C₁₃₉	1	2	yes	—
501	#388	C₂²×C₁₃₉	1	2	yes	—
502	#388	C₂²×C₁₃₉	1	2	yes	—
503	#388	C₂²×C₁₃₉	1	2	yes	—
504	#388	C₂²×C₁₃₉	1	2	yes	—
505	#388	C₂²×C₁₃₉	1	2	yes	—
506	#388	C₂²×C₁₃₉	1	2	yes	—
507	#388	C₂²×C₁₃₉	1	2	yes	—
508	#388	C₂²×C₁₃₉	1	2	yes	complemented
509	#388	C₂²×C₁₃₉	1	2	yes	complemented
510	#388	C₂²×C₁₃₉	1	2	yes	complemented
511	#388	C₂²×C₁₃₉	1	2	yes	complemented
512	#388	C₂²×C₁₃₉	1	2	yes	complemented
513	#387	C₂²×C₁₃₉	1	2	yes	complemented
514	#387	C₂²×C₁₃₉	1	2	yes	complemented
515	#387	C₂²×C₁₃₉	1	2	yes	complemented
516	#387	C₂²×C₁₃₉	1	2	yes	complemented
517	#387	C₂²×C₁₃₉	1	2	yes	complemented
518	#387	C₂²×C₁₃₉	1	2	yes	complemented
519	#386	C₂²×C₁₃₉	1	2	yes	—
520	#386	C₂²×C₁₃₉	1	2	yes	—
521	#386	C₂²×C₁₃₉	1	2	yes	—
522	#386	C₂²×C₁₃₉	1	2	yes	complemented
523	#385	C₂²×C₁₃₉	1	1	yes	characteristic
524	#385	C₂²×C₁₃₉	1	1	yes	characteristic
525	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
526	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
527	#381	C₂²×C₁₃₉	1	1	yes	characteristic
528	#381	C₂²×C₁₃₉	1	2	yes	complemented
529	#380	C₂²×C₁₃₉	1	2	yes	—
530	#379	C₂²×C₁₃₉	1	2	yes	—
531	#379	C₂²×C₁₃₉	1	1	yes	characteristic
532	#379	C₂²×C₁₃₉	1	1	yes	characteristic
533	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
534	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
535	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
536	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
537	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
538	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
539	#376	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
540	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
541	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
542	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
543	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
546	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
547	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
550	#126	—	4	4	no	—
551	#125	—	4	4	no	—
552	#124	—	4	4	no	—
553	#123	—	4	4	no	—
554	C₂²⋊Q₈	—	4	4	no	—
555	#121	—	2	4	no	—
556	#120	—	4	4	no	—
557	#117	—	2	4	no	—
558	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
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×C₂²⋊C₄	—	2	4	no	—
576	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
580	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
608	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
609	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
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	#95	C₂³×C₁₃₉	1	2	yes	—
617	#95	C₂³×C₁₃₉	1	2	yes	—
618	#95	C₂³×C₁₃₉	1	2	yes	—
619	#95	C₂³×C₁₃₉	1	2	yes	—
620	#95	C₂³×C₁₃₉	1	2	yes	—
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	C₂⁴	—	2	2	no	—
638	C₂⁴	—	4	2	no	—
639	C₂⁴	—	4	2	no	—
640	C₂⁴	—	4	1	no	—
641	C₂⁴	—	4	1	no	—
642	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
643	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
644	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
645	C₂×Q₈	—	2	4	no	—
646	C₂×Q₈	—	4	2	no	—
647	C₂×Q₈	—	4	2	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	4	2	no	—
652	C₂×D₄	—	4	2	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	4	1	no	—
655	C₂×D₄	—	4	1	no	—
656	C₂×D₄	—	4	2	no	—
657	C₂×D₄	—	4	2	no	—
658	C₂×D₄	—	4	2	no	—
659	C₂×D₄	—	4	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	4	1	no	—
662	C₂²×C₄	—	4	1	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
668	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	4	2	no	—
692	C₄⋊C₄	—	4	2	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₄⋊C₄	—	4	2	no	—
695	C₄⋊C₄	—	4	2	no	—
696	C₄⋊C₄	—	4	2	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	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	4	2	no	—
710	C₂²⋊C₄	—	4	2	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	4	2	no	—
714	C₂²⋊C₄	—	4	2	no	—
715	C₂²⋊C₄	—	4	2	no	—
716	C₂²⋊C₄	—	4	2	no	—
717	C₂²⋊C₄	—	4	1	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	1	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	4	2	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	C₄²	—	2	2	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	4	no	—
733	C₄²	—	4	1	no	—
734	C₄²	—	4	1	no	—
735	C₄²	—	4	1	no	—
736	C₄²	—	4	1	no	—
737	C₄²	—	4	1	no	—
738	C₄²	—	4	1	no	—
739	C₄²	—	4	2	no	—
740	C₄²	—	4	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	1	no	—
744	C₂³	—	2	1	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	—	4	4	no	—
760	C₂³	—	8	2	no	—
761	C₂³	—	8	2	no	—
762	C₂³	—	8	4	no	—
763	C₂³	—	8	4	no	—
764	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
765	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
766	Q₈	—	8	4	no	—
767	D₄	—	8	4	no	—
768	D₄	—	8	2	no	—
769	D₄	—	8	4	no	—
770	D₄	—	8	4	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	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	2	no	—
785	C₂×C₄	—	2	2	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	2	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	—	2	2	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	8	2	no	—
814	C₂×C₄	—	8	4	no	—
815	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
816	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
817	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	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	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	8	8	no	—
838	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
839	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
840	C₂²	#585×C₁₃₉	1	1	yes	characteristic
841	C₂²	#585×C₁₃₉	1	2	yes	—
842	C₂²	#585×C₁₃₉	1	1	yes	characteristic
843	C₄	—	2	4	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	2	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	1	no	—
858	C₄	—	4	1	no	—
859	C₂	—	4	2	no	—
860	C₂	—	8	2	no	—
861	C₂	—	8	2	no	—
862	C₂	#3455×C₁₃₉	1	1	yes	characteristic
863	C₂	#3491×C₁₃₉	1	1	yes	characteristic
864	C₂	#3508×C₁₃₉	1	1	yes	characteristic
865	C₂	#3545×C₁₃₉	1	2	yes	—
866	C₂	#3562×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2539×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. #2754×C₁₃₉	C₂	semidirect
3. #2752×C₁₃₉	C₂	semidirect
4. #2730×C₁₃₉	C₂	semidirect
5. #2721×C₁₃₉	C₂	semidirect
6. #2694×C₁₃₉	C₂	semidirect
7. #2687×C₁₃₉	C₂	semidirect
8. #2685×C₁₃₉	C₂	semidirect
9. #2684×C₁₃₉	C₂	semidirect
10. #2651×C₁₃₉	C₂	semidirect
11. #2607×C₁₃₉	C₂	semidirect
12. #2560×C₁₃₉	C₂	semidirect
14. #2526×C₁₃₉	C₂	semidirect
15. #2500×C₁₃₉	C₂	semidirect
16. #2482×C₁₃₉	C₂	semidirect
17. #2333×C₁₃₉	C₂	semidirect
18. #2312×C₁₃₉	C₂	semidirect
19. #2298×C₁₃₉	C₂	semidirect
21. C₂×#125×C₁₃₉	C₂²	semidirect
24. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
29. #400×C₁₃₉	C₂²	semidirect
33. #399×C₁₃₉	C₂²	semidirect
34. #398×C₁₃₉	C₂²	semidirect
35. #398×C₁₃₉	C₂²	semidirect
36. #398×C₁₃₉	C₂²	semidirect
40. #397×C₁₃₉	C₂²	semidirect
41. #397×C₁₃₉	C₂²	semidirect
43. #396×C₁₃₉	C₂²	semidirect
53. #391×C₁₃₉	C₂²	semidirect
54. #391×C₁₃₉	C₂²	semidirect
55. #391×C₁₃₉	C₂²	semidirect
60. #390×C₁₃₉	C₂²	semidirect
61. #390×C₁₃₉	C₂²	semidirect
62. #389×C₁₃₉	C₂²	semidirect
74. #388×C₁₃₉	C₂²	semidirect
75. #388×C₁₃₉	C₂²	semidirect
76. #388×C₁₃₉	C₂²	semidirect
77. #388×C₁₃₉	C₂²	semidirect
78. #388×C₁₃₉	C₂²	semidirect
79. #387×C₁₃₉	C₂²	semidirect
80. #387×C₁₃₉	C₂²	semidirect
81. #387×C₁₃₉	C₂²	semidirect
82. #387×C₁₃₉	C₂²	semidirect
83. #387×C₁₃₉	C₂²	semidirect
84. #387×C₁₃₉	C₂²	semidirect
88. #386×C₁₃₉	C₂²	semidirect
91. #384×C₁₃₉	C₂²	semidirect
92. #382×C₁₃₉	C₂²	semidirect
94. #381×C₁₃₉	C₂²	semidirect
99. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
100. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
105. #376×C₁₃₉	C₂²	semidirect
106. C₄³×C₁₃₉	C₂²	semidirect
433. #37010	C₁₃₉	direct (N × H)
434. C₁₃₉	#37010	direct (N × H)
435. #2861	C₂×C₁₃₉	semidirect
436. #2754	C₂×C₁₃₉	semidirect
437. #2752	C₂×C₁₃₉	semidirect
438. #2730	C₂×C₁₃₉	semidirect
439. #2721	C₂×C₁₃₉	semidirect
440. #2694	C₂×C₁₃₉	semidirect
441. #2687	C₂×C₁₃₉	semidirect
442. #2685	C₂×C₁₃₉	semidirect
443. #2684	C₂×C₁₃₉	semidirect
444. #2651	C₂×C₁₃₉	semidirect
445. #2607	C₂×C₁₃₉	semidirect
446. #2560	C₂×C₁₃₉	semidirect
448. #2526	C₂×C₁₃₉	semidirect
449. #2500	C₂×C₁₃₉	semidirect
450. #2482	C₂×C₁₃₉	semidirect
451. #2333	C₂×C₁₃₉	semidirect
452. #2312	C₂×C₁₃₉	semidirect
453. #2298	C₂×C₁₃₉	semidirect
455. C₂×#125	C₂²×C₁₃₉	semidirect
458. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
463. #400	C₂²×C₁₃₉	semidirect
467. #399	C₂²×C₁₃₉	semidirect
468. #398	C₂²×C₁₃₉	semidirect
469. #398	C₂²×C₁₃₉	semidirect
470. #398	C₂²×C₁₃₉	semidirect
474. #397	C₂²×C₁₃₉	semidirect
475. #397	C₂²×C₁₃₉	semidirect
477. #396	C₂²×C₁₃₉	semidirect
487. #391	C₂²×C₁₃₉	semidirect
488. #391	C₂²×C₁₃₉	semidirect
489. #391	C₂²×C₁₃₉	semidirect
494. #390	C₂²×C₁₃₉	semidirect
495. #390	C₂²×C₁₃₉	semidirect
496. #389	C₂²×C₁₃₉	semidirect
508. #388	C₂²×C₁₃₉	semidirect
509. #388	C₂²×C₁₃₉	semidirect
510. #388	C₂²×C₁₃₉	semidirect
511. #388	C₂²×C₁₃₉	semidirect
512. #388	C₂²×C₁₃₉	semidirect
513. #387	C₂²×C₁₃₉	semidirect
514. #387	C₂²×C₁₃₉	semidirect
515. #387	C₂²×C₁₃₉	semidirect
516. #387	C₂²×C₁₃₉	semidirect
517. #387	C₂²×C₁₃₉	semidirect
518. #387	C₂²×C₁₃₉	semidirect
522. #386	C₂²×C₁₃₉	semidirect
525. #384	C₂²×C₁₃₉	semidirect
526. #382	C₂²×C₁₃₉	semidirect
528. #381	C₂²×C₁₃₉	semidirect
533. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
534. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
538. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
539. #376	C₂²×C₁₃₉	semidirect
540. C₄³	C₂²×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
#2754×C₁₃₉	2
#2752×C₁₃₉	2
#2730×C₁₃₉	2
#2721×C₁₃₉	2
#2694×C₁₃₉	2
#2687×C₁₃₉	2
#2685×C₁₃₉	2
#2684×C₁₃₉	2
#2651×C₁₃₉	2
#2607×C₁₃₉	2
#2560×C₁₃₉	2
#2539×C₁₃₉	2
#2526×C₁₃₉	2
#2500×C₁₃₉	2
#2482×C₁₃₉	2
#2333×C₁₃₉	2
#2312×C₁₃₉	2
#2298×C₁₃₉	2
#37010	139

Subgroups — C139×#37010 #48031606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37010 #48031606