Subgroups — C₁₃₉×#37026 #48031622

Order 35584.

1428 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2865×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2808×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2796×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2783×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2762×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2761×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2756×C₁₃₉	C₂	1	2	yes	maximal
8	#2754×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2745×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2649×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2610×C₁₃₉	C₂	1	1	yes	maximal, characteristic
12	#2606×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2599×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2592×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2576×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2530×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2337×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2320×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2298×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
23	#401×C₁₃₉	C₂²	1	2	yes	—
24	#400×C₁₃₉	C₂²	1	2	yes	—
25	#400×C₁₃₉	C₂²	1	2	yes	—
26	#400×C₁₃₉	C₂²	1	2	yes	—
27	#400×C₁₃₉	C₂²	1	2	yes	—
28	#399×C₁₃₉	C₂²	1	2	yes	—
29	#398×C₁₃₉	C₂²	1	1	yes	characteristic
30	#398×C₁₃₉	C₂²	1	2	yes	—
31	#398×C₁₃₉	C₂²	1	2	yes	—
32	#397×C₁₃₉	C₂²	1	2	yes	—
33	#397×C₁₃₉	C₂²	1	2	yes	—
34	#397×C₁₃₉	C₂²	1	2	yes	—
35	#397×C₁₃₉	C₂²	1	1	yes	characteristic
36	#397×C₁₃₉	C₂²	1	2	yes	—
37	#397×C₁₃₉	C₂²	1	2	yes	—
38	#397×C₁₃₉	C₂²	1	2	yes	—
39	#396×C₁₃₉	C₂²	1	2	yes	—
40	#396×C₁₃₉	C₂²	1	2	yes	—
41	#395×C₁₃₉	C₂²	1	1	yes	characteristic
42	#395×C₁₃₉	C₂²	1	1	yes	characteristic
43	#394×C₁₃₉	C₂²	1	2	yes	—
44	#394×C₁₃₉	C₂²	1	2	yes	—
45	#394×C₁₃₉	C₂²	1	2	yes	—
46	#394×C₁₃₉	C₂²	1	1	yes	characteristic
47	#393×C₁₃₉	C₂²	1	1	yes	characteristic
48	#393×C₁₃₉	C₂²	1	2	yes	—
49	#393×C₁₃₉	C₂²	1	1	yes	characteristic
50	#392×C₁₃₉	C₂²	1	1	yes	characteristic
51	#391×C₁₃₉	C₂²	1	2	yes	—
52	#391×C₁₃₉	C₂²	1	2	yes	—
53	#391×C₁₃₉	C₂²	1	2	yes	—
54	#390×C₁₃₉	C₂²	1	2	yes	—
55	#390×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	#388×C₁₃₉	C₂²	1	2	yes	—
60	#388×C₁₃₉	C₂²	1	2	yes	—
61	#388×C₁₃₉	C₂²	1	2	yes	—
62	#388×C₁₃₉	C₂²	1	2	yes	—
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	#387×C₁₃₉	C₂²	1	2	yes	—
74	#387×C₁₃₉	C₂²	1	2	yes	—
75	#387×C₁₃₉	C₂²	1	2	yes	—
76	#387×C₁₃₉	C₂²	1	2	yes	—
77	#387×C₁₃₉	C₂²	1	2	yes	—
78	#387×C₁₃₉	C₂²	1	2	yes	—
79	#387×C₁₃₉	C₂²	1	2	yes	—
80	#387×C₁₃₉	C₂²	1	2	yes	—
81	#387×C₁₃₉	C₂²	1	2	yes	—
82	#387×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	#387×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	#385×C₁₃₉	C₂²	1	2	yes	—
91	#385×C₁₃₉	C₂²	1	2	yes	—
92	#385×C₁₃₉	C₂²	1	2	yes	—
93	#383×C₁₃₉	C₂²	1	2	yes	—
94	#383×C₁₃₉	C₂²	1	1	yes	characteristic
95	#382×C₁₃₉	C₂²	1	2	yes	—
96	#382×C₁₃₉	C₂²	1	2	yes	—
97	#381×C₁₃₉	C₂²	1	2	yes	—
98	#380×C₁₃₉	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
100	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
104	#376×C₁₃₉	C₂²	1	1	yes	characteristic
105	#376×C₁₃₉	C₂²	1	1	yes	characteristic
106	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
113	#124×C₁₃₉	—	2	4	no	—
114	C₄×Q₈×C₁₃₉	—	2	4	no	—
115	#117×C₁₃₉	—	2	4	no	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
164	#95×C₁₃₉	C₂³	1	2	yes	—
165	#95×C₁₃₉	C₂³	1	1	yes	characteristic
166	#95×C₁₃₉	C₂³	1	1	yes	characteristic
167	#95×C₁₃₉	C₂³	1	2	yes	—
168	#95×C₁₃₉	C₂³	1	2	yes	—
169	#95×C₁₃₉	C₂³	1	2	yes	—
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	2	yes	—
173	#95×C₁₃₉	C₂³	1	2	yes	—
174	#95×C₁₃₉	C₂³	1	2	yes	—
175	#95×C₁₃₉	C₂³	1	2	yes	—
176	#95×C₁₃₉	C₂³	1	2	yes	—
177	#95×C₁₃₉	C₂³	1	2	yes	—
178	#95×C₁₃₉	C₂³	1	2	yes	—
179	#95×C₁₃₉	C₂³	1	2	yes	—
180	#95×C₁₃₉	C₂³	1	2	yes	—
181	#95×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
186	#95×C₁₃₉	C₂³	1	2	yes	—
187	#95×C₁₃₉	C₂³	1	2	yes	—
188	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
198	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
199	C₂×Q₈×C₁₃₉	—	2	2	no	—
200	C₂×Q₈×C₁₃₉	—	2	2	no	—
201	C₂×Q₈×C₁₃₉	—	4	2	no	—
202	C₂×Q₈×C₁₃₉	—	4	2	no	—
203	C₂×D₄×C₁₃₉	—	2	2	no	—
204	C₂×D₄×C₁₃₉	—	4	2	no	—
205	C₂×D₄×C₁₃₉	—	4	2	no	—
206	C₂×D₄×C₁₃₉	—	4	2	no	—
207	C₂×D₄×C₁₃₉	—	4	2	no	—
208	C₂²×C₄×C₁₃₉	—	2	2	no	—
209	C₂²×C₄×C₁₃₉	—	4	1	no	—
210	C₂²×C₄×C₁₃₉	—	4	1	no	—
211	C₂²×C₄×C₁₃₉	—	4	2	no	—
212	C₂²×C₄×C₁₃₉	—	4	2	no	—
213	C₂²×C₄×C₁₃₉	—	4	2	no	—
214	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
231	C₄⋊C₄×C₁₃₉	—	2	2	no	—
232	C₄⋊C₄×C₁₃₉	—	2	2	no	—
233	C₄⋊C₄×C₁₃₉	—	2	2	no	—
234	C₄⋊C₄×C₁₃₉	—	2	4	no	—
235	C₄⋊C₄×C₁₃₉	—	4	2	no	—
236	C₄⋊C₄×C₁₃₉	—	4	2	no	—
237	C₄⋊C₄×C₁₃₉	—	4	2	no	—
238	C₄⋊C₄×C₁₃₉	—	4	2	no	—
239	C₄⋊C₄×C₁₃₉	—	4	2	no	—
240	C₄⋊C₄×C₁₃₉	—	4	2	no	—
241	C₄⋊C₄×C₁₃₉	—	4	2	no	—
242	C₄⋊C₄×C₁₃₉	—	4	2	no	—
243	C₄⋊C₄×C₁₃₉	—	4	2	no	—
244	C₄⋊C₄×C₁₃₉	—	4	2	no	—
245	C₄⋊C₄×C₁₃₉	—	4	2	no	—
246	C₄⋊C₄×C₁₃₉	—	4	2	no	—
247	C₄⋊C₄×C₁₃₉	—	4	2	no	—
248	C₄⋊C₄×C₁₃₉	—	4	2	no	—
249	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
250	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
251	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
252	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
253	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
254	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
255	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
256	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
257	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
258	C₂²⋊C₄×C₁₃₉	—	4	2	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	—	4	2	no	—
266	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
267	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
268	C₄²×C₁₃₉	—	2	2	no	—
269	C₄²×C₁₃₉	—	2	4	no	—
270	C₄²×C₁₃₉	—	4	1	no	—
271	C₄²×C₁₃₉	—	4	1	no	—
272	C₄²×C₁₃₉	—	4	1	no	—
273	C₄²×C₁₃₉	—	4	1	no	—
274	C₄²×C₁₃₉	—	4	2	no	—
275	C₄²×C₁₃₉	—	4	2	no	—
276	C₄²×C₁₃₉	—	4	2	no	—
277	C₄²×C₁₃₉	—	4	2	no	—
278	C₄²×C₁₃₉	#41	1	4	yes	—
279	C₂³×C₁₃₉	—	2	1	no	—
280	C₂³×C₁₃₉	—	2	2	no	—
281	C₂³×C₁₃₉	—	2	2	no	—
282	C₂³×C₁₃₉	—	2	1	no	—
283	C₂³×C₁₃₉	—	2	2	no	—
284	C₂³×C₁₃₉	—	2	2	no	—
285	C₂³×C₁₃₉	—	2	2	no	—
286	C₂³×C₁₃₉	—	2	2	no	—
287	C₂³×C₁₃₉	—	2	2	no	—
288	C₂³×C₁₃₉	—	2	2	no	—
289	C₂³×C₁₃₉	—	2	2	no	—
290	C₂³×C₁₃₉	—	2	1	no	—
291	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
292	Q₈×C₁₃₉	—	4	4	no	—
293	Q₈×C₁₃₉	—	8	2	no	—
294	D₄×C₁₃₉	—	8	2	no	—
295	D₄×C₁₃₉	—	8	4	no	—
296	C₂×C₄×C₁₃₉	—	2	1	no	—
297	C₂×C₄×C₁₃₉	—	2	1	no	—
298	C₂×C₄×C₁₃₉	—	2	2	no	—
299	C₂×C₄×C₁₃₉	—	2	2	no	—
300	C₂×C₄×C₁₃₉	—	2	1	no	—
301	C₂×C₄×C₁₃₉	—	2	1	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	1	no	—
306	C₂×C₄×C₁₃₉	—	2	2	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	2	2	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	2	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	2	no	—
322	C₂×C₄×C₁₃₉	—	2	2	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	2	no	—
325	C₂×C₄×C₁₃₉	—	2	1	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	2	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	2	no	—
332	C₂×C₄×C₁₃₉	—	2	2	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	1	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	2	2	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	4	4	no	—
341	C₂×C₄×C₁₃₉	—	8	4	no	—
342	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
343	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
344	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
345	C₂²×C₁₃₉	—	4	1	no	—
346	C₂²×C₁₃₉	—	4	2	no	—
347	C₂²×C₁₃₉	—	4	1	no	—
348	C₂²×C₁₃₉	—	4	2	no	—
349	C₂²×C₁₃₉	—	4	2	no	—
350	C₂²×C₁₃₉	—	4	1	no	—
351	C₂²×C₁₃₉	—	4	2	no	—
352	C₂²×C₁₃₉	—	4	2	no	—
353	C₂²×C₁₃₉	—	4	2	no	—
354	C₂²×C₁₃₉	—	4	2	no	—
355	C₂²×C₁₃₉	—	4	2	no	—
356	C₂²×C₁₃₉	—	4	2	no	—
357	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
358	C₂²×C₁₃₉	#585	1	2	yes	—
359	C₂²×C₁₃₉	#585	1	1	yes	characteristic
360	C₂²×C₁₃₉	#585	1	1	yes	characteristic
361	C₂²×C₁₃₉	#585	1	2	yes	—
362	C₄×C₁₃₉	—	2	2	no	—
363	C₄×C₁₃₉	—	2	2	no	—
364	C₄×C₁₃₉	—	2	2	no	—
365	C₄×C₁₃₉	—	4	1	no	—
366	C₄×C₁₃₉	—	4	2	no	—
367	C₄×C₁₃₉	—	4	2	no	—
368	C₄×C₁₃₉	—	4	1	no	—
369	C₄×C₁₃₉	—	4	1	no	—
370	C₄×C₁₃₉	—	4	2	no	—
371	C₄×C₁₃₉	—	4	2	no	—
372	C₄×C₁₃₉	—	4	2	no	—
373	C₄×C₁₃₉	—	4	2	no	—
374	C₄×C₁₃₉	—	4	2	no	—
375	C₄×C₁₃₉	—	4	2	no	—
376	C₄×C₁₃₉	—	4	2	no	—
377	C₄×C₁₃₉	—	4	2	no	—
378	C₄×C₁₃₉	—	4	2	no	—
379	C₂×C₁₃₉	—	8	1	no	—
380	C₂×C₁₃₉	—	8	2	no	—
381	C₂×C₁₃₉	#3455	1	1	yes	characteristic
382	C₂×C₁₃₉	#3493	1	1	yes	characteristic
383	C₂×C₁₃₉	#3510	1	1	yes	characteristic
384	C₂×C₁₃₉	#3566	1	2	yes	—
385	C₂×C₁₃₉	#3566	1	2	yes	—
386	#37026	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
387	C₁₃₉	#37026	1	1	yes	characteristic, direct product factor, Sylow
388	#2865	C₂×C₁₃₉	1	2	yes	complemented
389	#2808	C₂×C₁₃₉	1	2	yes	complemented
390	#2796	C₂×C₁₃₉	1	2	yes	complemented
391	#2783	C₂×C₁₃₉	1	2	yes	complemented
392	#2762	C₂×C₁₃₉	1	2	yes	complemented
393	#2761	C₂×C₁₃₉	1	2	yes	complemented
394	#2756	C₂×C₁₃₉	1	2	yes	—
395	#2754	C₂×C₁₃₉	1	2	yes	complemented
396	#2745	C₂×C₁₃₉	1	2	yes	complemented
397	#2649	C₂×C₁₃₉	1	2	yes	complemented
398	#2610	C₂×C₁₃₉	1	1	yes	characteristic
399	#2606	C₂×C₁₃₉	1	1	yes	characteristic, complemented
400	#2599	C₂×C₁₃₉	1	1	yes	characteristic, complemented
401	#2592	C₂×C₁₃₉	1	1	yes	characteristic, complemented
402	#2576	C₂×C₁₃₉	1	2	yes	complemented
403	#2530	C₂×C₁₃₉	1	2	yes	complemented
404	#2337	C₂×C₁₃₉	1	1	yes	characteristic, complemented
405	#2320	C₂×C₁₃₉	1	1	yes	characteristic, complemented
406	#2298	C₂×C₁₃₉	1	1	yes	characteristic, complemented
407	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
408	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
409	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
410	#401	C₂²×C₁₃₉	1	2	yes	—
411	#400	C₂²×C₁₃₉	1	2	yes	—
412	#400	C₂²×C₁₃₉	1	2	yes	—
413	#400	C₂²×C₁₃₉	1	2	yes	—
414	#400	C₂²×C₁₃₉	1	2	yes	—
415	#399	C₂²×C₁₃₉	1	2	yes	—
416	#398	C₂²×C₁₃₉	1	1	yes	characteristic
417	#398	C₂²×C₁₃₉	1	2	yes	—
418	#398	C₂²×C₁₃₉	1	2	yes	—
419	#397	C₂²×C₁₃₉	1	2	yes	—
420	#397	C₂²×C₁₃₉	1	2	yes	—
421	#397	C₂²×C₁₃₉	1	1	yes	characteristic
422	#397	C₂²×C₁₃₉	1	2	yes	—
423	#397	C₂²×C₁₃₉	1	2	yes	—
424	#397	C₂²×C₁₃₉	1	2	yes	—
425	#397	C₂²×C₁₃₉	1	2	yes	—
426	#396	C₂²×C₁₃₉	1	2	yes	—
427	#396	C₂²×C₁₃₉	1	2	yes	—
428	#395	C₂²×C₁₃₉	1	1	yes	characteristic
429	#395	C₂²×C₁₃₉	1	1	yes	characteristic
430	#394	C₂²×C₁₃₉	1	2	yes	—
431	#394	C₂²×C₁₃₉	1	1	yes	characteristic
432	#394	C₂²×C₁₃₉	1	2	yes	—
433	#394	C₂²×C₁₃₉	1	2	yes	—
434	#393	C₂²×C₁₃₉	1	2	yes	—
435	#393	C₂²×C₁₃₉	1	1	yes	characteristic
436	#393	C₂²×C₁₃₉	1	1	yes	characteristic
437	#392	C₂²×C₁₃₉	1	1	yes	characteristic
438	#391	C₂²×C₁₃₉	1	2	yes	—
439	#391	C₂²×C₁₃₉	1	2	yes	—
440	#391	C₂²×C₁₃₉	1	2	yes	—
441	#390	C₂²×C₁₃₉	1	2	yes	—
442	#390	C₂²×C₁₃₉	1	2	yes	—
443	#389	C₂²×C₁₃₉	1	2	yes	—
444	#389	C₂²×C₁₃₉	1	2	yes	—
445	#389	C₂²×C₁₃₉	1	2	yes	—
446	#388	C₂²×C₁₃₉	1	2	yes	—
447	#388	C₂²×C₁₃₉	1	2	yes	—
448	#388	C₂²×C₁₃₉	1	2	yes	—
449	#388	C₂²×C₁₃₉	1	2	yes	—
450	#388	C₂²×C₁₃₉	1	2	yes	—
451	#388	C₂²×C₁₃₉	1	2	yes	—
452	#388	C₂²×C₁₃₉	1	2	yes	—
453	#388	C₂²×C₁₃₉	1	2	yes	—
454	#388	C₂²×C₁₃₉	1	2	yes	—
455	#388	C₂²×C₁₃₉	1	2	yes	—
456	#388	C₂²×C₁₃₉	1	2	yes	—
457	#388	C₂²×C₁₃₉	1	2	yes	—
458	#388	C₂²×C₁₃₉	1	2	yes	—
459	#388	C₂²×C₁₃₉	1	2	yes	—
460	#387	C₂²×C₁₃₉	1	2	yes	—
461	#387	C₂²×C₁₃₉	1	2	yes	—
462	#387	C₂²×C₁₃₉	1	2	yes	—
463	#387	C₂²×C₁₃₉	1	2	yes	—
464	#387	C₂²×C₁₃₉	1	2	yes	—
465	#387	C₂²×C₁₃₉	1	2	yes	—
466	#387	C₂²×C₁₃₉	1	2	yes	—
467	#387	C₂²×C₁₃₉	1	2	yes	—
468	#387	C₂²×C₁₃₉	1	2	yes	—
469	#387	C₂²×C₁₃₉	1	2	yes	—
470	#387	C₂²×C₁₃₉	1	2	yes	—
471	#387	C₂²×C₁₃₉	1	2	yes	—
472	#387	C₂²×C₁₃₉	1	2	yes	—
473	#387	C₂²×C₁₃₉	1	2	yes	—
474	#386	C₂²×C₁₃₉	1	2	yes	—
475	#386	C₂²×C₁₃₉	1	2	yes	—
476	#386	C₂²×C₁₃₉	1	2	yes	—
477	#385	C₂²×C₁₃₉	1	2	yes	—
478	#385	C₂²×C₁₃₉	1	2	yes	—
479	#385	C₂²×C₁₃₉	1	2	yes	—
480	#383	C₂²×C₁₃₉	1	2	yes	—
481	#383	C₂²×C₁₃₉	1	1	yes	characteristic
482	#382	C₂²×C₁₃₉	1	2	yes	—
483	#382	C₂²×C₁₃₉	1	2	yes	—
484	#381	C₂²×C₁₃₉	1	2	yes	—
485	#380	C₂²×C₁₃₉	1	2	yes	—
486	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
487	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
488	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
489	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
490	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
491	#376	C₂²×C₁₃₉	1	1	yes	characteristic
492	#376	C₂²×C₁₃₉	1	1	yes	characteristic
493	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
494	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
495	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
496	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
497	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
498	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
500	#124	—	2	4	no	—
501	C₄×Q₈	—	2	4	no	—
502	#117	—	2	4	no	—
503	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
522	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
540	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
545	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
551	#95	C₂³×C₁₃₉	1	2	yes	—
552	#95	C₂³×C₁₃₉	1	1	yes	characteristic
553	#95	C₂³×C₁₃₉	1	1	yes	characteristic
554	#95	C₂³×C₁₃₉	1	2	yes	—
555	#95	C₂³×C₁₃₉	1	2	yes	—
556	#95	C₂³×C₁₃₉	1	2	yes	—
557	#95	C₂³×C₁₃₉	1	2	yes	—
558	#95	C₂³×C₁₃₉	1	2	yes	—
559	#95	C₂³×C₁₃₉	1	2	yes	—
560	#95	C₂³×C₁₃₉	1	2	yes	—
561	#95	C₂³×C₁₃₉	1	2	yes	—
562	#95	C₂³×C₁₃₉	1	2	yes	—
563	#95	C₂³×C₁₃₉	1	2	yes	—
564	#95	C₂³×C₁₃₉	1	2	yes	—
565	#95	C₂³×C₁₃₉	1	2	yes	—
566	#95	C₂³×C₁₃₉	1	2	yes	—
567	#95	C₂³×C₁₃₉	1	2	yes	—
568	#95	C₂³×C₁₃₉	1	2	yes	—
569	#95	C₂³×C₁₃₉	1	2	yes	—
570	#95	C₂³×C₁₃₉	1	1	yes	characteristic
571	#95	C₂³×C₁₃₉	1	2	yes	—
572	#95	C₂³×C₁₃₉	1	2	yes	—
573	#95	C₂³×C₁₃₉	1	2	yes	—
574	#95	C₂³×C₁₃₉	1	1	yes	characteristic
575	#95	C₂³×C₁₃₉	1	2	yes	—
576	#95	C₂³×C₁₃₉	1	2	yes	—
577	#95	C₂³×C₁₃₉	1	2	yes	—
578	#95	C₂³×C₁₃₉	1	2	yes	—
579	#95	C₂³×C₁₃₉	1	2	yes	—
580	#95	C₂³×C₁₃₉	1	2	yes	—
581	#95	C₂³×C₁₃₉	1	2	yes	—
582	#95	C₂³×C₁₃₉	1	2	yes	—
583	#95	C₂³×C₁₃₉	1	2	yes	—
584	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
585	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	—	2	2	no	—
588	C₂×Q₈	—	4	2	no	—
589	C₂×Q₈	—	4	2	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	4	2	no	—
592	C₂×D₄	—	4	2	no	—
593	C₂×D₄	—	4	2	no	—
594	C₂×D₄	—	4	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	4	1	no	—
597	C₂²×C₄	—	4	1	no	—
598	C₂²×C₄	—	4	2	no	—
599	C₂²×C₄	—	4	2	no	—
600	C₂²×C₄	—	4	2	no	—
601	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	2	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	—	4	2	no	—
627	C₄⋊C₄	—	4	2	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	4	2	no	—
631	C₄⋊C₄	—	4	2	no	—
632	C₄⋊C₄	—	4	2	no	—
633	C₄⋊C₄	—	4	2	no	—
634	C₄⋊C₄	—	4	2	no	—
635	C₄⋊C₄	—	4	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	4	2	no	—
643	C₂²⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	4	2	no	—
651	C₂²⋊C₄	—	4	2	no	—
652	C₂²⋊C₄	—	4	2	no	—
653	C₂²⋊C₄	—	4	2	no	—
654	C₂²⋊C₄	—	4	2	no	—
655	C₄²	—	2	2	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	4	1	no	—
658	C₄²	—	4	1	no	—
659	C₄²	—	4	1	no	—
660	C₄²	—	4	1	no	—
661	C₄²	—	4	2	no	—
662	C₄²	—	4	2	no	—
663	C₄²	—	4	2	no	—
664	C₄²	—	4	2	no	—
665	C₄²	#41×C₁₃₉	1	4	yes	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	1	no	—
678	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
679	Q₈	—	4	4	no	—
680	Q₈	—	8	2	no	—
681	D₄	—	8	2	no	—
682	D₄	—	8	4	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	4	4	no	—
728	C₂×C₄	—	8	4	no	—
729	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
730	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
731	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	1	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	1	no	—
744	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
745	C₂²	#585×C₁₃₉	1	2	yes	—
746	C₂²	#585×C₁₃₉	1	1	yes	characteristic
747	C₂²	#585×C₁₃₉	1	1	yes	characteristic
748	C₂²	#585×C₁₃₉	1	2	yes	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	1	no	—
762	C₄	—	4	1	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	1	no	—
766	C₂	—	8	2	no	—
767	C₂	—	8	1	no	—
768	C₂	#3455×C₁₃₉	1	1	yes	characteristic
769	C₂	#3493×C₁₃₉	1	1	yes	characteristic
770	C₂	#3510×C₁₃₉	1	1	yes	characteristic
771	C₂	#3566×C₁₃₉	1	2	yes	—
772	C₂	#3566×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#392×C₁₃₉	C₂²
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. #2865×C₁₃₉	C₂	semidirect
2. #2808×C₁₃₉	C₂	semidirect
3. #2796×C₁₃₉	C₂	semidirect
4. #2783×C₁₃₉	C₂	semidirect
5. #2762×C₁₃₉	C₂	semidirect
6. #2761×C₁₃₉	C₂	semidirect
8. #2754×C₁₃₉	C₂	semidirect
9. #2745×C₁₃₉	C₂	semidirect
10. #2649×C₁₃₉	C₂	semidirect
12. #2606×C₁₃₉	C₂	semidirect
13. #2599×C₁₃₉	C₂	semidirect
14. #2592×C₁₃₉	C₂	semidirect
15. #2576×C₁₃₉	C₂	semidirect
16. #2530×C₁₃₉	C₂	semidirect
17. #2337×C₁₃₉	C₂	semidirect
18. #2320×C₁₃₉	C₂	semidirect
19. #2298×C₁₃₉	C₂	semidirect
386. #37026	C₁₃₉	direct (N × H)
387. C₁₃₉	#37026	direct (N × H)
388. #2865	C₂×C₁₃₉	semidirect
389. #2808	C₂×C₁₃₉	semidirect
390. #2796	C₂×C₁₃₉	semidirect
391. #2783	C₂×C₁₃₉	semidirect
392. #2762	C₂×C₁₃₉	semidirect
393. #2761	C₂×C₁₃₉	semidirect
395. #2754	C₂×C₁₃₉	semidirect
396. #2745	C₂×C₁₃₉	semidirect
397. #2649	C₂×C₁₃₉	semidirect
399. #2606	C₂×C₁₃₉	semidirect
400. #2599	C₂×C₁₃₉	semidirect
401. #2592	C₂×C₁₃₉	semidirect
402. #2576	C₂×C₁₃₉	semidirect
403. #2530	C₂×C₁₃₉	semidirect
404. #2337	C₂×C₁₃₉	semidirect
405. #2320	C₂×C₁₃₉	semidirect
406. #2298	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2865×C₁₃₉	2
#2808×C₁₃₉	2
#2796×C₁₃₉	2
#2783×C₁₃₉	2
#2762×C₁₃₉	2
#2761×C₁₃₉	2
#2756×C₁₃₉	2
#2754×C₁₃₉	2
#2745×C₁₃₉	2
#2649×C₁₃₉	2
#2610×C₁₃₉	2
#2606×C₁₃₉	2
#2599×C₁₃₉	2
#2592×C₁₃₉	2
#2576×C₁₃₉	2
#2530×C₁₃₉	2
#2337×C₁₃₉	2
#2320×C₁₃₉	2
#2298×C₁₃₉	2
#37026	139

Subgroups — C139×#37026 #48031622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37026 #48031622