Subgroups — C₁₃₉×#37328 #48031924

Order 35584.

1416 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2859×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2859×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2802×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2783×C₁₃₉	C₂	1	2	yes	maximal
5	#2776×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2772×C₁₃₉	C₂	1	2	yes	maximal
7	#2766×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2725×C₁₃₉	C₂	1	2	yes	maximal
9	#2725×C₁₃₉	C₂	1	2	yes	maximal
10	#2719×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2629×C₁₃₉	C₂	1	1	yes	maximal, characteristic
12	#2629×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	#2509×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2508×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2507×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2506×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2497×C₁₃₉	C₂	1	1	yes	maximal, characteristic
18	#2496×C₁₃₉	C₂	1	1	yes	maximal, characteristic
19	#2495×C₁₃₉	C₂	1	1	yes	maximal, characteristic
20	#2494×C₁₃₉	C₂	1	1	yes	maximal, characteristic
21	#2330×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#2330×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#2298×C₁₃₉	C₂	1	1	yes	maximal, characteristic
24	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
30	#401×C₁₃₉	C₂²	1	2	yes	—
31	#400×C₁₃₉	C₂²	1	2	yes	—
32	#400×C₁₃₉	C₂²	1	2	yes	—
33	#400×C₁₃₉	C₂²	1	2	yes	—
34	#400×C₁₃₉	C₂²	1	2	yes	—
35	#400×C₁₃₉	C₂²	1	2	yes	—
36	#400×C₁₃₉	C₂²	1	2	yes	—
37	#400×C₁₃₉	C₂²	1	2	yes	—
38	#398×C₁₃₉	C₂²	1	2	yes	—
39	#398×C₁₃₉	C₂²	1	2	yes	—
40	#398×C₁₃₉	C₂²	1	2	yes	—
41	#398×C₁₃₉	C₂²	1	2	yes	—
42	#398×C₁₃₉	C₂²	1	2	yes	—
43	#398×C₁₃₉	C₂²	1	2	yes	—
44	#398×C₁₃₉	C₂²	1	2	yes	—
45	#398×C₁₃₉	C₂²	1	2	yes	—
46	#397×C₁₃₉	C₂²	1	2	yes	—
47	#397×C₁₃₉	C₂²	1	2	yes	—
48	#397×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	#396×C₁₃₉	C₂²	1	2	yes	—
53	#396×C₁₃₉	C₂²	1	2	yes	—
54	#389×C₁₃₉	C₂²	1	2	yes	—
55	#389×C₁₃₉	C₂²	1	2	yes	—
56	#389×C₁₃₉	C₂²	1	2	yes	—
57	#389×C₁₃₉	C₂²	1	2	yes	—
58	#389×C₁₃₉	C₂²	1	2	yes	—
59	#389×C₁₃₉	C₂²	1	2	yes	—
60	#389×C₁₃₉	C₂²	1	2	yes	—
61	#389×C₁₃₉	C₂²	1	2	yes	—
62	#389×C₁₃₉	C₂²	1	2	yes	—
63	#389×C₁₃₉	C₂²	1	2	yes	—
64	#389×C₁₃₉	C₂²	1	2	yes	—
65	#389×C₁₃₉	C₂²	1	1	yes	characteristic
66	#389×C₁₃₉	C₂²	1	1	yes	characteristic
67	#389×C₁₃₉	C₂²	1	1	yes	characteristic
68	#389×C₁₃₉	C₂²	1	1	yes	characteristic
69	#389×C₁₃₉	C₂²	1	2	yes	—
70	#389×C₁₃₉	C₂²	1	1	yes	characteristic
71	#389×C₁₃₉	C₂²	1	1	yes	characteristic
72	#389×C₁₃₉	C₂²	1	1	yes	characteristic
73	#389×C₁₃₉	C₂²	1	1	yes	characteristic
74	#389×C₁₃₉	C₂²	1	1	yes	characteristic
75	#389×C₁₃₉	C₂²	1	1	yes	characteristic
76	#389×C₁₃₉	C₂²	1	1	yes	characteristic
77	#389×C₁₃₉	C₂²	1	1	yes	characteristic
78	#388×C₁₃₉	C₂²	1	1	yes	characteristic
79	#388×C₁₃₉	C₂²	1	2	yes	—
80	#388×C₁₃₉	C₂²	1	2	yes	—
81	#388×C₁₃₉	C₂²	1	1	yes	characteristic
82	#388×C₁₃₉	C₂²	1	2	yes	—
83	#388×C₁₃₉	C₂²	1	1	yes	characteristic
84	#388×C₁₃₉	C₂²	1	1	yes	characteristic
85	#387×C₁₃₉	C₂²	1	1	yes	characteristic
86	#387×C₁₃₉	C₂²	1	2	yes	—
87	#387×C₁₃₉	C₂²	1	2	yes	—
88	#387×C₁₃₉	C₂²	1	2	yes	—
89	#387×C₁₃₉	C₂²	1	2	yes	—
90	#387×C₁₃₉	C₂²	1	2	yes	—
91	#387×C₁₃₉	C₂²	1	2	yes	—
92	#387×C₁₃₉	C₂²	1	2	yes	—
93	#387×C₁₃₉	C₂²	1	1	yes	characteristic
94	#387×C₁₃₉	C₂²	1	2	yes	—
95	#387×C₁₃₉	C₂²	1	2	yes	—
96	#387×C₁₃₉	C₂²	1	2	yes	—
97	#387×C₁₃₉	C₂²	1	1	yes	characteristic
98	#387×C₁₃₉	C₂²	1	2	yes	—
99	#387×C₁₃₉	C₂²	1	1	yes	characteristic
100	#384×C₁₃₉	C₂²	1	1	yes	characteristic
101	#384×C₁₃₉	C₂²	1	1	yes	characteristic
102	#384×C₁₃₉	C₂²	1	1	yes	characteristic
103	#384×C₁₃₉	C₂²	1	1	yes	characteristic
104	#383×C₁₃₉	C₂²	1	2	yes	—
105	#382×C₁₃₉	C₂²	1	2	yes	—
106	#382×C₁₃₉	C₂²	1	2	yes	—
107	#382×C₁₃₉	C₂²	1	1	yes	characteristic
108	#382×C₁₃₉	C₂²	1	1	yes	characteristic
109	#380×C₁₃₉	C₂²	1	1	yes	characteristic
110	#380×C₁₃₉	C₂²	1	1	yes	characteristic
111	#380×C₁₃₉	C₂²	1	1	yes	characteristic
112	#380×C₁₃₉	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
121	#376×C₁₃₉	C₂²	1	1	yes	characteristic
122	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
123	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
124	#126×C₁₃₉	—	4	4	no	—
125	#125×C₁₃₉	—	2	4	no	—
126	#125×C₁₃₉	—	2	4	no	—
127	#125×C₁₃₉	—	4	4	no	—
128	#125×C₁₃₉	—	4	4	no	—
129	#117×C₁₃₉	—	2	4	no	—
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	1	yes	characteristic
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×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	1	yes	characteristic
177	C₂×C₂²⋊C₄×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	1	yes	characteristic
183	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
190	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
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	#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	1	yes	characteristic
211	#95×C₁₃₉	C₂³	1	2	yes	—
212	#95×C₁₃₉	C₂³	1	2	yes	—
213	#95×C₁₃₉	C₂³	1	1	yes	characteristic
214	#95×C₁₃₉	C₂³	1	1	yes	characteristic
215	#95×C₁₃₉	C₂³	1	1	yes	characteristic
216	#95×C₁₃₉	C₂³	1	1	yes	characteristic
217	#95×C₁₃₉	C₂³	1	1	yes	characteristic
218	#95×C₁₃₉	C₂³	1	1	yes	characteristic
219	#95×C₁₃₉	C₂³	1	2	yes	—
220	#95×C₁₃₉	C₂³	1	2	yes	—
221	#95×C₁₃₉	C₂³	1	2	yes	—
222	#95×C₁₃₉	C₂³	1	2	yes	—
223	#95×C₁₃₉	C₂³	1	1	yes	characteristic
224	#95×C₁₃₉	C₂³	1	1	yes	characteristic
225	#95×C₁₃₉	C₂³	1	1	yes	characteristic
226	#95×C₁₃₉	C₂³	1	1	yes	characteristic
227	#95×C₁₃₉	C₂³	1	1	yes	characteristic
228	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃₉	—	2	2	no	—
230	C₂²×C₄×C₁₃₉	—	2	2	no	—
231	C₂²×C₄×C₁₃₉	—	2	2	no	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
247	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
254	C₄⋊C₄×C₁₃₉	—	2	2	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	2	no	—
261	C₄⋊C₄×C₁₃₉	—	2	2	no	—
262	C₄⋊C₄×C₁₃₉	—	2	2	no	—
263	C₄⋊C₄×C₁₃₉	—	2	2	no	—
264	C₄⋊C₄×C₁₃₉	—	2	2	no	—
265	C₄⋊C₄×C₁₃₉	—	2	4	no	—
266	C₄⋊C₄×C₁₃₉	—	2	4	no	—
267	C₄⋊C₄×C₁₃₉	—	2	4	no	—
268	C₄⋊C₄×C₁₃₉	—	2	4	no	—
269	C₄⋊C₄×C₁₃₉	—	2	2	no	—
270	C₄⋊C₄×C₁₃₉	—	2	2	no	—
271	C₄⋊C₄×C₁₃₉	—	2	2	no	—
272	C₄⋊C₄×C₁₃₉	—	2	2	no	—
273	C₄⋊C₄×C₁₃₉	—	2	2	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	—	4	2	no	—
278	C₄⋊C₄×C₁₃₉	—	4	1	no	—
279	C₄⋊C₄×C₁₃₉	—	4	1	no	—
280	C₄⋊C₄×C₁₃₉	—	4	2	no	—
281	C₄⋊C₄×C₁₃₉	—	4	2	no	—
282	C₄⋊C₄×C₁₃₉	—	4	2	no	—
283	C₄⋊C₄×C₁₃₉	—	4	2	no	—
284	C₄⋊C₄×C₁₃₉	—	4	2	no	—
285	C₄⋊C₄×C₁₃₉	—	4	2	no	—
286	C₄⋊C₄×C₁₃₉	—	4	2	no	—
287	C₄⋊C₄×C₁₃₉	—	4	2	no	—
288	C₄⋊C₄×C₁₃₉	—	4	2	no	—
289	C₄⋊C₄×C₁₃₉	—	4	2	no	—
290	C₄⋊C₄×C₁₃₉	—	4	2	no	—
291	C₄⋊C₄×C₁₃₉	—	4	2	no	—
292	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
293	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
294	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
295	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
296	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
297	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
298	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
299	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
300	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
301	C₂²⋊C₄×C₁₃₉	—	4	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	—	2	2	no	—
307	C₄²×C₁₃₉	—	2	2	no	—
308	C₄²×C₁₃₉	—	2	2	no	—
309	C₄²×C₁₃₉	—	4	1	no	—
310	C₄²×C₁₃₉	—	4	1	no	—
311	C₄²×C₁₃₉	—	4	2	no	—
312	C₄²×C₁₃₉	—	4	2	no	—
313	C₄²×C₁₃₉	—	4	2	no	—
314	C₄²×C₁₃₉	—	4	2	no	—
315	C₄²×C₁₃₉	#41	1	4	yes	—
316	C₂³×C₁₃₉	—	2	1	no	—
317	C₂³×C₁₃₉	—	2	1	no	—
318	C₂³×C₁₃₉	—	2	1	no	—
319	C₂³×C₁₃₉	—	2	1	no	—
320	C₂³×C₁₃₉	—	2	1	no	—
321	C₂³×C₁₃₉	—	2	1	no	—
322	C₂³×C₁₃₉	—	2	1	no	—
323	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
324	C₂×C₄×C₁₃₉	—	2	1	no	—
325	C₂×C₄×C₁₃₉	—	2	1	no	—
326	C₂×C₄×C₁₃₉	—	2	1	no	—
327	C₂×C₄×C₁₃₉	—	2	1	no	—
328	C₂×C₄×C₁₃₉	—	2	1	no	—
329	C₂×C₄×C₁₃₉	—	2	1	no	—
330	C₂×C₄×C₁₃₉	—	2	1	no	—
331	C₂×C₄×C₁₃₉	—	2	1	no	—
332	C₂×C₄×C₁₃₉	—	2	1	no	—
333	C₂×C₄×C₁₃₉	—	2	1	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	2	2	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	1	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	2	no	—
345	C₂×C₄×C₁₃₉	—	2	2	no	—
346	C₂×C₄×C₁₃₉	—	2	2	no	—
347	C₂×C₄×C₁₃₉	—	2	1	no	—
348	C₂×C₄×C₁₃₉	—	2	2	no	—
349	C₂×C₄×C₁₃₉	—	2	1	no	—
350	C₂×C₄×C₁₃₉	—	2	1	no	—
351	C₂×C₄×C₁₃₉	—	2	1	no	—
352	C₂×C₄×C₁₃₉	—	2	1	no	—
353	C₂×C₄×C₁₃₉	—	2	1	no	—
354	C₂×C₄×C₁₃₉	—	2	1	no	—
355	C₂×C₄×C₁₃₉	—	2	1	no	—
356	C₂×C₄×C₁₃₉	—	2	1	no	—
357	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
365	C₂×C₄×C₁₃₉	—	2	1	no	—
366	C₂×C₄×C₁₃₉	—	2	1	no	—
367	C₂×C₄×C₁₃₉	—	2	1	no	—
368	C₂×C₄×C₁₃₉	—	2	1	no	—
369	C₂×C₄×C₁₃₉	—	2	1	no	—
370	C₂×C₄×C₁₃₉	—	2	1	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	—	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	2	no	—
383	C₂×C₄×C₁₃₉	—	4	4	no	—
384	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
385	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
386	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
387	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
388	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
389	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
390	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
391	C₂²×C₁₃₉	—	4	1	no	—
392	C₂²×C₁₃₉	—	4	1	no	—
393	C₂²×C₁₃₉	—	4	1	no	—
394	C₂²×C₁₃₉	—	4	1	no	—
395	C₂²×C₁₃₉	—	4	1	no	—
396	C₂²×C₁₃₉	—	4	1	no	—
397	C₂²×C₁₃₉	—	4	1	no	—
398	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
399	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
401	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
402	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
403	C₂²×C₁₃₉	#585	1	1	yes	characteristic
404	C₂²×C₁₃₉	#585	1	1	yes	characteristic
405	C₄×C₁₃₉	—	2	2	no	—
406	C₄×C₁₃₉	—	2	2	no	—
407	C₄×C₁₃₉	—	2	2	no	—
408	C₄×C₁₃₉	—	2	2	no	—
409	C₄×C₁₃₉	—	4	1	no	—
410	C₄×C₁₃₉	—	4	1	no	—
411	C₄×C₁₃₉	—	4	2	no	—
412	C₄×C₁₃₉	—	4	2	no	—
413	C₄×C₁₃₉	—	4	1	no	—
414	C₄×C₁₃₉	—	4	2	no	—
415	C₄×C₁₃₉	—	4	2	no	—
416	C₄×C₁₃₉	—	4	1	no	—
417	C₄×C₁₃₉	—	4	1	no	—
418	C₄×C₁₃₉	—	4	2	no	—
419	C₄×C₁₃₉	—	4	2	no	—
420	C₄×C₁₃₉	—	4	1	no	—
421	C₄×C₁₃₉	—	4	1	no	—
422	C₄×C₁₃₉	—	4	1	no	—
423	C₄×C₁₃₉	—	4	2	no	—
424	C₄×C₁₃₉	—	4	2	no	—
425	C₄×C₁₃₉	—	4	1	no	—
426	C₄×C₁₃₉	#541	1	4	yes	—
427	C₂×C₁₃₉	—	8	1	no	—
428	C₂×C₁₃₉	C₂×#541	1	1	yes	characteristic
429	C₂×C₁₃₉	#3511	1	1	yes	characteristic
430	C₂×C₁₃₉	#3512	1	1	yes	characteristic
431	C₂×C₁₃₉	#3547	1	1	yes	characteristic
432	C₂×C₁₃₉	#3555	1	1	yes	characteristic
433	C₂×C₁₃₉	#3559	1	1	yes	characteristic
434	C₂×C₁₃₉	#3563	1	1	yes	characteristic
435	#37328	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
436	C₁₃₉	#37328	1	1	yes	characteristic, direct product factor, Sylow
437	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
438	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
439	#2802	C₂×C₁₃₉	1	2	yes	complemented
440	#2783	C₂×C₁₃₉	1	2	yes	—
441	#2776	C₂×C₁₃₉	1	2	yes	complemented
442	#2772	C₂×C₁₃₉	1	2	yes	—
443	#2766	C₂×C₁₃₉	1	2	yes	complemented
444	#2725	C₂×C₁₃₉	1	2	yes	—
445	#2725	C₂×C₁₃₉	1	2	yes	—
446	#2719	C₂×C₁₃₉	1	2	yes	complemented
447	#2629	C₂×C₁₃₉	1	1	yes	characteristic
448	#2629	C₂×C₁₃₉	1	1	yes	characteristic
449	#2509	C₂×C₁₃₉	1	1	yes	characteristic, complemented
450	#2508	C₂×C₁₃₉	1	1	yes	characteristic, complemented
451	#2507	C₂×C₁₃₉	1	1	yes	characteristic, complemented
452	#2506	C₂×C₁₃₉	1	1	yes	characteristic, complemented
453	#2497	C₂×C₁₃₉	1	1	yes	characteristic
454	#2496	C₂×C₁₃₉	1	1	yes	characteristic
455	#2495	C₂×C₁₃₉	1	1	yes	characteristic
456	#2494	C₂×C₁₃₉	1	1	yes	characteristic
457	#2330	C₂×C₁₃₉	1	1	yes	characteristic, complemented
458	#2330	C₂×C₁₃₉	1	1	yes	characteristic, complemented
459	#2298	C₂×C₁₃₉	1	1	yes	characteristic
460	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
461	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
462	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
463	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
464	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
465	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
466	#401	C₂²×C₁₃₉	1	2	yes	—
467	#400	C₂²×C₁₃₉	1	2	yes	—
468	#400	C₂²×C₁₃₉	1	2	yes	—
469	#400	C₂²×C₁₃₉	1	2	yes	—
470	#400	C₂²×C₁₃₉	1	2	yes	—
471	#400	C₂²×C₁₃₉	1	2	yes	—
472	#400	C₂²×C₁₃₉	1	2	yes	—
473	#400	C₂²×C₁₃₉	1	2	yes	—
474	#398	C₂²×C₁₃₉	1	2	yes	—
475	#398	C₂²×C₁₃₉	1	2	yes	—
476	#398	C₂²×C₁₃₉	1	2	yes	—
477	#398	C₂²×C₁₃₉	1	2	yes	—
478	#398	C₂²×C₁₃₉	1	2	yes	—
479	#398	C₂²×C₁₃₉	1	2	yes	—
480	#398	C₂²×C₁₃₉	1	2	yes	—
481	#398	C₂²×C₁₃₉	1	2	yes	—
482	#397	C₂²×C₁₃₉	1	2	yes	—
483	#397	C₂²×C₁₃₉	1	2	yes	—
484	#397	C₂²×C₁₃₉	1	2	yes	—
485	#396	C₂²×C₁₃₉	1	2	yes	—
486	#396	C₂²×C₁₃₉	1	2	yes	—
487	#396	C₂²×C₁₃₉	1	2	yes	—
488	#396	C₂²×C₁₃₉	1	2	yes	—
489	#396	C₂²×C₁₃₉	1	2	yes	—
490	#389	C₂²×C₁₃₉	1	2	yes	—
491	#389	C₂²×C₁₃₉	1	2	yes	—
492	#389	C₂²×C₁₃₉	1	2	yes	—
493	#389	C₂²×C₁₃₉	1	2	yes	—
494	#389	C₂²×C₁₃₉	1	1	yes	characteristic
495	#389	C₂²×C₁₃₉	1	1	yes	characteristic
496	#389	C₂²×C₁₃₉	1	1	yes	characteristic
497	#389	C₂²×C₁₃₉	1	1	yes	characteristic
498	#389	C₂²×C₁₃₉	1	2	yes	—
499	#389	C₂²×C₁₃₉	1	2	yes	—
500	#389	C₂²×C₁₃₉	1	2	yes	—
501	#389	C₂²×C₁₃₉	1	1	yes	characteristic
502	#389	C₂²×C₁₃₉	1	1	yes	characteristic
503	#389	C₂²×C₁₃₉	1	1	yes	characteristic
504	#389	C₂²×C₁₃₉	1	1	yes	characteristic
505	#389	C₂²×C₁₃₉	1	2	yes	—
506	#389	C₂²×C₁₃₉	1	2	yes	—
507	#389	C₂²×C₁₃₉	1	2	yes	—
508	#389	C₂²×C₁₃₉	1	1	yes	characteristic
509	#389	C₂²×C₁₃₉	1	1	yes	characteristic
510	#389	C₂²×C₁₃₉	1	1	yes	characteristic
511	#389	C₂²×C₁₃₉	1	1	yes	characteristic
512	#389	C₂²×C₁₃₉	1	2	yes	—
513	#389	C₂²×C₁₃₉	1	2	yes	—
514	#388	C₂²×C₁₃₉	1	1	yes	characteristic
515	#388	C₂²×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
520	#388	C₂²×C₁₃₉	1	1	yes	characteristic
521	#387	C₂²×C₁₃₉	1	2	yes	—
522	#387	C₂²×C₁₃₉	1	2	yes	—
523	#387	C₂²×C₁₃₉	1	2	yes	—
524	#387	C₂²×C₁₃₉	1	2	yes	—
525	#387	C₂²×C₁₃₉	1	1	yes	characteristic
526	#387	C₂²×C₁₃₉	1	2	yes	—
527	#387	C₂²×C₁₃₉	1	2	yes	—
528	#387	C₂²×C₁₃₉	1	2	yes	—
529	#387	C₂²×C₁₃₉	1	2	yes	—
530	#387	C₂²×C₁₃₉	1	2	yes	—
531	#387	C₂²×C₁₃₉	1	2	yes	—
532	#387	C₂²×C₁₃₉	1	2	yes	—
533	#387	C₂²×C₁₃₉	1	1	yes	characteristic
534	#387	C₂²×C₁₃₉	1	1	yes	characteristic
535	#387	C₂²×C₁₃₉	1	1	yes	characteristic
536	#384	C₂²×C₁₃₉	1	1	yes	characteristic
537	#384	C₂²×C₁₃₉	1	1	yes	characteristic
538	#384	C₂²×C₁₃₉	1	1	yes	characteristic
539	#384	C₂²×C₁₃₉	1	1	yes	characteristic
540	#383	C₂²×C₁₃₉	1	2	yes	—
541	#382	C₂²×C₁₃₉	1	1	yes	characteristic
542	#382	C₂²×C₁₃₉	1	1	yes	characteristic
543	#382	C₂²×C₁₃₉	1	2	yes	—
544	#382	C₂²×C₁₃₉	1	2	yes	—
545	#380	C₂²×C₁₃₉	1	1	yes	characteristic
546	#380	C₂²×C₁₃₉	1	1	yes	characteristic
547	#380	C₂²×C₁₃₉	1	1	yes	characteristic
548	#380	C₂²×C₁₃₉	1	1	yes	characteristic
549	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
550	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
551	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
552	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
553	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
554	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
555	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
556	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
557	#376	C₂²×C₁₃₉	1	1	yes	characteristic
558	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
559	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
560	#126	—	4	4	no	—
561	#125	—	2	4	no	—
562	#125	—	2	4	no	—
563	#125	—	4	4	no	—
564	#125	—	4	4	no	—
565	#117	—	2	4	no	—
566	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
607	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
614	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
622	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
623	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
626	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
627	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
628	#95	C₂³×C₁₃₉	1	1	yes	characteristic
629	#95	C₂³×C₁₃₉	1	1	yes	characteristic
630	#95	C₂³×C₁₃₉	1	1	yes	characteristic
631	#95	C₂³×C₁₃₉	1	1	yes	characteristic
632	#95	C₂³×C₁₃₉	1	1	yes	characteristic
633	#95	C₂³×C₁₃₉	1	1	yes	characteristic
634	#95	C₂³×C₁₃₉	1	1	yes	characteristic
635	#95	C₂³×C₁₃₉	1	1	yes	characteristic
636	#95	C₂³×C₁₃₉	1	1	yes	characteristic
637	#95	C₂³×C₁₃₉	1	1	yes	characteristic
638	#95	C₂³×C₁₃₉	1	1	yes	characteristic
639	#95	C₂³×C₁₃₉	1	1	yes	characteristic
640	#95	C₂³×C₁₃₉	1	2	yes	—
641	#95	C₂³×C₁₃₉	1	2	yes	—
642	#95	C₂³×C₁₃₉	1	2	yes	—
643	#95	C₂³×C₁₃₉	1	2	yes	—
644	#95	C₂³×C₁₃₉	1	2	yes	—
645	#95	C₂³×C₁₃₉	1	2	yes	—
646	#95	C₂³×C₁₃₉	1	2	yes	—
647	#95	C₂³×C₁₃₉	1	2	yes	—
648	#95	C₂³×C₁₃₉	1	2	yes	—
649	#95	C₂³×C₁₃₉	1	2	yes	—
650	#95	C₂³×C₁₃₉	1	2	yes	—
651	#95	C₂³×C₁₃₉	1	2	yes	—
652	#95	C₂³×C₁₃₉	1	2	yes	—
653	#95	C₂³×C₁₃₉	1	2	yes	—
654	#95	C₂³×C₁₃₉	1	2	yes	—
655	#95	C₂³×C₁₃₉	1	2	yes	—
656	#95	C₂³×C₁₃₉	1	2	yes	—
657	#95	C₂³×C₁₃₉	1	2	yes	—
658	#95	C₂³×C₁₃₉	1	2	yes	—
659	#95	C₂³×C₁₃₉	1	2	yes	—
660	#95	C₂³×C₁₃₉	1	2	yes	—
661	#95	C₂³×C₁₃₉	1	2	yes	—
662	#95	C₂³×C₁₃₉	1	2	yes	—
663	#95	C₂³×C₁₃₉	1	2	yes	—
664	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
681	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	—	4	2	no	—
713	C₄⋊C₄	—	4	2	no	—
714	C₄⋊C₄	—	4	1	no	—
715	C₄⋊C₄	—	4	1	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	2	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	4	1	no	—
733	C₂²⋊C₄	—	4	1	no	—
734	C₂²⋊C₄	—	4	2	no	—
735	C₂²⋊C₄	—	4	2	no	—
736	C₂²⋊C₄	—	4	2	no	—
737	C₂²⋊C₄	—	4	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	2	no	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	2	no	—
745	C₄²	—	4	1	no	—
746	C₄²	—	4	1	no	—
747	C₄²	—	4	2	no	—
748	C₄²	—	4	2	no	—
749	C₄²	—	4	2	no	—
750	C₄²	—	4	2	no	—
751	C₄²	#41×C₁₃₉	1	4	yes	—
752	C₂³	—	2	1	no	—
753	C₂³	—	2	1	no	—
754	C₂³	—	2	1	no	—
755	C₂³	—	2	1	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	2	1	no	—
758	C₂³	—	2	1	no	—
759	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	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	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
821	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
822	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
823	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
824	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
825	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
826	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
835	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
836	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
837	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
838	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
839	C₂²	#585×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	—	4	1	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	1	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	2	no	—
862	C₄	#541×C₁₃₉	1	4	yes	—
863	C₂	—	8	1	no	—
864	C₂	C₂×#541×C₁₃₉	1	1	yes	characteristic
865	C₂	#3511×C₁₃₉	1	1	yes	characteristic
866	C₂	#3512×C₁₃₉	1	1	yes	characteristic
867	C₂	#3547×C₁₃₉	1	1	yes	characteristic
868	C₂	#3555×C₁₃₉	1	1	yes	characteristic
869	C₂	#3559×C₁₃₉	1	1	yes	characteristic
870	C₂	#3563×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂⁴×C₁₃₉	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #2859×C₁₃₉	C₂	semidirect
2. #2859×C₁₃₉	C₂	semidirect
3. #2802×C₁₃₉	C₂	semidirect
5. #2776×C₁₃₉	C₂	semidirect
7. #2766×C₁₃₉	C₂	semidirect
10. #2719×C₁₃₉	C₂	semidirect
13. #2509×C₁₃₉	C₂	semidirect
14. #2508×C₁₃₉	C₂	semidirect
15. #2507×C₁₃₉	C₂	semidirect
16. #2506×C₁₃₉	C₂	semidirect
21. #2330×C₁₃₉	C₂	semidirect
22. #2330×C₁₃₉	C₂	semidirect
435. #37328	C₁₃₉	direct (N × H)
436. C₁₃₉	#37328	direct (N × H)
437. #2859	C₂×C₁₃₉	semidirect
438. #2859	C₂×C₁₃₉	semidirect
439. #2802	C₂×C₁₃₉	semidirect
441. #2776	C₂×C₁₃₉	semidirect
443. #2766	C₂×C₁₃₉	semidirect
446. #2719	C₂×C₁₃₉	semidirect
449. #2509	C₂×C₁₃₉	semidirect
450. #2508	C₂×C₁₃₉	semidirect
451. #2507	C₂×C₁₃₉	semidirect
452. #2506	C₂×C₁₃₉	semidirect
457. #2330	C₂×C₁₃₉	semidirect
458. #2330	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2859×C₁₃₉	2
#2802×C₁₃₉	2
#2783×C₁₃₉	2
#2776×C₁₃₉	2
#2772×C₁₃₉	2
#2766×C₁₃₉	2
#2725×C₁₃₉	2
#2719×C₁₃₉	2
#2629×C₁₃₉	2
#2509×C₁₃₉	2
#2508×C₁₃₉	2
#2507×C₁₃₉	2
#2506×C₁₃₉	2
#2497×C₁₃₉	2
#2496×C₁₃₉	2
#2495×C₁₃₉	2
#2494×C₁₃₉	2
#2330×C₁₃₉	2
#2298×C₁₃₉	2
#37328	139

Subgroups — C139×#37328 #48031924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37328 #48031924