Subgroups — C₁₃₉×#37212 #48031808

Order 35584.

1466 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2855×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2851×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2810×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2809×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2806×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2805×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2789×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2787×C₁₃₉	C₂	1	2	yes	maximal
9	#2745×C₁₃₉	C₂	1	2	yes	maximal
10	#2744×C₁₃₉	C₂	1	2	yes	maximal
11	#2734×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2729×C₁₃₉	C₂	1	2	yes	maximal
13	#2655×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2530×C₁₃₉	C₂	1	2	yes	maximal
15	#2528×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2465×C₁₃₉	C₂	1	2	yes	maximal
17	#2462×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2327×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
27	#401×C₁₃₉	C₂²	1	2	yes	—
28	#401×C₁₃₉	C₂²	1	2	yes	—
29	#400×C₁₃₉	C₂²	1	2	yes	—
30	#400×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	#398×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	#397×C₁₃₉	C₂²	1	2	yes	—
44	#397×C₁₃₉	C₂²	1	2	yes	—
45	#396×C₁₃₉	C₂²	1	2	yes	—
46	#395×C₁₃₉	C₂²	1	2	yes	—
47	#395×C₁₃₉	C₂²	1	2	yes	—
48	#395×C₁₃₉	C₂²	1	2	yes	—
49	#395×C₁₃₉	C₂²	1	2	yes	—
50	#393×C₁₃₉	C₂²	1	2	yes	—
51	#391×C₁₃₉	C₂²	1	1	yes	characteristic
52	#391×C₁₃₉	C₂²	1	2	yes	—
53	#391×C₁₃₉	C₂²	1	2	yes	—
54	#391×C₁₃₉	C₂²	1	1	yes	characteristic
55	#391×C₁₃₉	C₂²	1	1	yes	characteristic
56	#391×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	1	yes	characteristic
61	#389×C₁₃₉	C₂²	1	1	yes	characteristic
62	#389×C₁₃₉	C₂²	1	1	yes	characteristic
63	#389×C₁₃₉	C₂²	1	1	yes	characteristic
64	#389×C₁₃₉	C₂²	1	1	yes	characteristic
65	#389×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	#387×C₁₃₉	C₂²	1	2	yes	—
71	#387×C₁₃₉	C₂²	1	2	yes	—
72	#387×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	#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	#385×C₁₃₉	C₂²	1	2	yes	—
93	#385×C₁₃₉	C₂²	1	2	yes	—
94	#385×C₁₃₉	C₂²	1	2	yes	—
95	#385×C₁₃₉	C₂²	1	2	yes	—
96	#382×C₁₃₉	C₂²	1	1	yes	characteristic
97	#382×C₁₃₉	C₂²	1	2	yes	—
98	#381×C₁₃₉	C₂²	1	2	yes	—
99	#380×C₁₃₉	C₂²	1	1	yes	characteristic
100	#380×C₁₃₉	C₂²	1	1	yes	characteristic
101	#380×C₁₃₉	C₂²	1	1	yes	characteristic
102	#380×C₁₃₉	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
105	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
106	#376×C₁₃₉	C₂²	1	2	yes	—
107	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
108	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
114	#125×C₁₃₉	—	4	2	no	—
115	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
116	C₂²⋊Q₈×C₁₃₉	—	4	2	no	—
117	C₄×Q₈×C₁₃₉	—	4	2	no	—
118	C₄×Q₈×C₁₃₉	—	4	4	no	—
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	1	yes	characteristic
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	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×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₁₃₉	—	4	2	no	—
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	2	yes	—
164	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
165	#95×C₁₃₉	C₂³	1	2	yes	—
166	#95×C₁₃₉	C₂³	1	2	yes	—
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	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	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
202	C₂×Q₈×C₁₃₉	—	2	4	no	—
203	C₂×Q₈×C₁₃₉	—	2	2	no	—
204	C₂×Q₈×C₁₃₉	—	4	1	no	—
205	C₂×Q₈×C₁₃₉	—	4	2	no	—
206	C₂×Q₈×C₁₃₉	—	4	1	no	—
207	C₂×Q₈×C₁₃₉	—	4	2	no	—
208	C₂×Q₈×C₁₃₉	—	4	1	no	—
209	C₂×Q₈×C₁₃₉	—	4	1	no	—
210	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
211	C₂²×C₄×C₁₃₉	—	2	2	no	—
212	C₂²×C₄×C₁₃₉	—	2	2	no	—
213	C₂²×C₄×C₁₃₉	—	2	2	no	—
214	C₂²×C₄×C₁₃₉	—	2	2	no	—
215	C₂²×C₄×C₁₃₉	—	2	2	no	—
216	C₂²×C₄×C₁₃₉	—	4	1	no	—
217	C₂²×C₄×C₁₃₉	—	4	1	no	—
218	C₂²×C₄×C₁₃₉	—	4	1	no	—
219	C₂²×C₄×C₁₃₉	—	4	1	no	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	2	yes	—
229	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₁₃₉	—	2	2	no	—
239	C₄⋊C₄×C₁₃₉	—	2	4	no	—
240	C₄⋊C₄×C₁₃₉	—	2	4	no	—
241	C₄⋊C₄×C₁₃₉	—	2	4	no	—
242	C₄⋊C₄×C₁₃₉	—	2	4	no	—
243	C₄⋊C₄×C₁₃₉	—	2	4	no	—
244	C₄⋊C₄×C₁₃₉	—	2	4	no	—
245	C₄⋊C₄×C₁₃₉	—	2	4	no	—
246	C₄⋊C₄×C₁₃₉	—	2	2	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	no	—
248	C₄⋊C₄×C₁₃₉	—	2	2	no	—
249	C₄⋊C₄×C₁₃₉	—	2	4	no	—
250	C₄⋊C₄×C₁₃₉	—	2	2	no	—
251	C₄⋊C₄×C₁₃₉	—	4	1	no	—
252	C₄⋊C₄×C₁₃₉	—	4	1	no	—
253	C₄⋊C₄×C₁₃₉	—	4	2	no	—
254	C₄⋊C₄×C₁₃₉	—	4	2	no	—
255	C₄⋊C₄×C₁₃₉	—	4	2	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	1	no	—
261	C₄⋊C₄×C₁₃₉	—	4	2	no	—
262	C₄⋊C₄×C₁₃₉	—	4	2	no	—
263	C₄⋊C₄×C₁₃₉	—	4	1	no	—
264	C₄⋊C₄×C₁₃₉	—	4	1	no	—
265	C₄⋊C₄×C₁₃₉	—	4	1	no	—
266	C₄⋊C₄×C₁₃₉	—	4	2	no	—
267	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
270	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
271	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
272	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
273	C₄²×C₁₃₉	—	2	4	no	—
274	C₄²×C₁₃₉	—	2	2	no	—
275	C₄²×C₁₃₉	—	2	2	no	—
276	C₄²×C₁₃₉	—	2	4	no	—
277	C₄²×C₁₃₉	—	4	1	no	—
278	C₄²×C₁₃₉	—	4	1	no	—
279	C₄²×C₁₃₉	—	4	2	no	—
280	C₄²×C₁₃₉	—	4	2	no	—
281	C₄²×C₁₃₉	—	4	2	no	—
282	C₄²×C₁₃₉	—	4	2	no	—
283	C₂³×C₁₃₉	—	2	1	no	—
284	C₂³×C₁₃₉	—	2	1	no	—
285	C₂³×C₁₃₉	—	2	1	no	—
286	C₂³×C₁₃₉	—	2	1	no	—
287	C₂³×C₁₃₉	—	2	1	no	—
288	C₂³×C₁₃₉	—	2	1	no	—
289	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
290	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
291	Q₈×C₁₃₉	—	4	4	no	—
292	Q₈×C₁₃₉	—	4	8	no	—
293	Q₈×C₁₃₉	—	8	2	no	—
294	C₂×C₄×C₁₃₉	—	2	1	no	—
295	C₂×C₄×C₁₃₉	—	2	1	no	—
296	C₂×C₄×C₁₃₉	—	2	2	no	—
297	C₂×C₄×C₁₃₉	—	2	1	no	—
298	C₂×C₄×C₁₃₉	—	2	1	no	—
299	C₂×C₄×C₁₃₉	—	2	1	no	—
300	C₂×C₄×C₁₃₉	—	2	1	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	2	1	no	—
303	C₂×C₄×C₁₃₉	—	2	1	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	2	no	—
307	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
312	C₂×C₄×C₁₃₉	—	2	1	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	2	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	1	no	—
329	C₂×C₄×C₁₃₉	—	2	1	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	2	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	—	2	1	no	—
341	C₂×C₄×C₁₃₉	—	2	2	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	4	4	no	—
344	C₂×C₄×C₁₃₉	—	4	4	no	—
345	C₂×C₄×C₁₃₉	—	4	4	no	—
346	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
347	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
348	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
349	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
350	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
351	C₂²×C₁₃₉	—	2	2	no	—
352	C₂²×C₁₃₉	—	2	2	no	—
353	C₂²×C₁₃₉	—	2	2	no	—
354	C₂²×C₁₃₉	—	4	1	no	—
355	C₂²×C₁₃₉	—	4	1	no	—
356	C₂²×C₁₃₉	—	4	1	no	—
357	C₂²×C₁₃₉	—	4	1	no	—
358	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
359	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
360	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
361	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
362	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
363	C₂²×C₁₃₉	#585	1	1	yes	characteristic
364	C₂²×C₁₃₉	#585	1	1	yes	characteristic
365	C₄×C₁₃₉	—	2	2	no	—
366	C₄×C₁₃₉	—	2	4	no	—
367	C₄×C₁₃₉	—	2	2	no	—
368	C₄×C₁₃₉	—	2	2	no	—
369	C₄×C₁₃₉	—	2	2	no	—
370	C₄×C₁₃₉	—	4	1	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	C₄×C₁₃₉	—	4	1	no	—
380	C₄×C₁₃₉	—	4	2	no	—
381	C₄×C₁₃₉	—	4	2	no	—
382	C₄×C₁₃₉	—	4	2	no	—
383	C₂×C₁₃₉	—	4	2	no	—
384	C₂×C₁₃₉	#3459	1	1	yes	characteristic
385	C₂×C₁₃₉	#3518	1	1	yes	characteristic
386	C₂×C₁₃₉	#3523	1	1	yes	characteristic
387	C₂×C₁₃₉	#3535	1	1	yes	characteristic
388	C₂×C₁₃₉	#3538	1	1	yes	characteristic
389	C₂×C₁₃₉	#3553	1	1	yes	characteristic
390	C₂×C₁₃₉	#3555	1	1	yes	characteristic
391	#37212	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
392	C₁₃₉	#37212	1	1	yes	characteristic, direct product factor, Sylow
393	#2855	C₂×C₁₃₉	1	1	yes	characteristic
394	#2851	C₂×C₁₃₉	1	1	yes	characteristic
395	#2810	C₂×C₁₃₉	1	1	yes	characteristic, complemented
396	#2809	C₂×C₁₃₉	1	1	yes	characteristic, complemented
397	#2806	C₂×C₁₃₉	1	1	yes	characteristic, complemented
398	#2805	C₂×C₁₃₉	1	2	yes	complemented
399	#2789	C₂×C₁₃₉	1	2	yes	complemented
400	#2787	C₂×C₁₃₉	1	2	yes	—
401	#2745	C₂×C₁₃₉	1	2	yes	—
402	#2744	C₂×C₁₃₉	1	2	yes	—
403	#2734	C₂×C₁₃₉	1	1	yes	characteristic, complemented
404	#2729	C₂×C₁₃₉	1	2	yes	—
405	#2655	C₂×C₁₃₉	1	2	yes	complemented
406	#2530	C₂×C₁₃₉	1	2	yes	—
407	#2528	C₂×C₁₃₉	1	2	yes	complemented
408	#2465	C₂×C₁₃₉	1	2	yes	—
409	#2462	C₂×C₁₃₉	1	2	yes	complemented
410	#2327	C₂×C₁₃₉	1	2	yes	complemented
411	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic
412	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
413	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
414	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
415	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
416	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
418	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
419	#401	C₂²×C₁₃₉	1	2	yes	—
420	#401	C₂²×C₁₃₉	1	2	yes	—
421	#400	C₂²×C₁₃₉	1	2	yes	—
422	#400	C₂²×C₁₃₉	1	2	yes	—
423	#400	C₂²×C₁₃₉	1	2	yes	—
424	#400	C₂²×C₁₃₉	1	2	yes	—
425	#400	C₂²×C₁₃₉	1	2	yes	—
426	#400	C₂²×C₁₃₉	1	2	yes	—
427	#400	C₂²×C₁₃₉	1	2	yes	—
428	#400	C₂²×C₁₃₉	1	2	yes	—
429	#398	C₂²×C₁₃₉	1	2	yes	—
430	#398	C₂²×C₁₃₉	1	2	yes	—
431	#398	C₂²×C₁₃₉	1	2	yes	—
432	#398	C₂²×C₁₃₉	1	2	yes	—
433	#398	C₂²×C₁₃₉	1	2	yes	—
434	#398	C₂²×C₁₃₉	1	2	yes	—
435	#397	C₂²×C₁₃₉	1	2	yes	—
436	#397	C₂²×C₁₃₉	1	2	yes	—
437	#396	C₂²×C₁₃₉	1	2	yes	—
438	#395	C₂²×C₁₃₉	1	2	yes	—
439	#395	C₂²×C₁₃₉	1	2	yes	—
440	#395	C₂²×C₁₃₉	1	2	yes	—
441	#395	C₂²×C₁₃₉	1	2	yes	—
442	#393	C₂²×C₁₃₉	1	2	yes	—
443	#391	C₂²×C₁₃₉	1	2	yes	—
444	#391	C₂²×C₁₃₉	1	2	yes	—
445	#391	C₂²×C₁₃₉	1	1	yes	characteristic
446	#391	C₂²×C₁₃₉	1	1	yes	characteristic
447	#391	C₂²×C₁₃₉	1	2	yes	—
448	#391	C₂²×C₁₃₉	1	1	yes	characteristic
449	#389	C₂²×C₁₃₉	1	1	yes	characteristic
450	#389	C₂²×C₁₃₉	1	1	yes	characteristic
451	#389	C₂²×C₁₃₉	1	1	yes	characteristic
452	#389	C₂²×C₁₃₉	1	1	yes	characteristic
453	#389	C₂²×C₁₃₉	1	2	yes	—
454	#389	C₂²×C₁₃₉	1	2	yes	—
455	#389	C₂²×C₁₃₉	1	2	yes	—
456	#389	C₂²×C₁₃₉	1	2	yes	—
457	#389	C₂²×C₁₃₉	1	1	yes	characteristic
458	#388	C₂²×C₁₃₉	1	2	yes	—
459	#388	C₂²×C₁₃₉	1	2	yes	—
460	#388	C₂²×C₁₃₉	1	2	yes	—
461	#388	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	#387	C₂²×C₁₃₉	1	2	yes	—
475	#387	C₂²×C₁₃₉	1	2	yes	—
476	#387	C₂²×C₁₃₉	1	2	yes	—
477	#387	C₂²×C₁₃₉	1	2	yes	—
478	#387	C₂²×C₁₃₉	1	2	yes	—
479	#387	C₂²×C₁₃₉	1	2	yes	—
480	#387	C₂²×C₁₃₉	1	2	yes	—
481	#387	C₂²×C₁₃₉	1	2	yes	—
482	#387	C₂²×C₁₃₉	1	2	yes	—
483	#387	C₂²×C₁₃₉	1	2	yes	—
484	#385	C₂²×C₁₃₉	1	2	yes	—
485	#385	C₂²×C₁₃₉	1	2	yes	—
486	#385	C₂²×C₁₃₉	1	2	yes	—
487	#385	C₂²×C₁₃₉	1	2	yes	—
488	#382	C₂²×C₁₃₉	1	2	yes	—
489	#382	C₂²×C₁₃₉	1	1	yes	characteristic
490	#381	C₂²×C₁₃₉	1	2	yes	—
491	#380	C₂²×C₁₃₉	1	1	yes	characteristic
492	#380	C₂²×C₁₃₉	1	1	yes	characteristic
493	#380	C₂²×C₁₃₉	1	1	yes	characteristic
494	#380	C₂²×C₁₃₉	1	1	yes	characteristic
495	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
496	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
497	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
498	#376	C₂²×C₁₃₉	1	2	yes	—
499	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
500	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
501	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
505	C₄⋊Q₈	—	2	8	no	—
506	#125	—	4	2	no	—
507	C₂²⋊Q₈	—	2	4	no	—
508	C₂²⋊Q₈	—	4	2	no	—
509	C₄×Q₈	—	4	2	no	—
510	C₄×Q₈	—	4	4	no	—
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	1	yes	characteristic
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	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₄²	—	4	2	no	—
547	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
550	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
552	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
553	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
554	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
555	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
556	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
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	#95	C₂³×C₁₃₉	1	2	yes	—
585	#95	C₂³×C₁₃₉	1	2	yes	—
586	#95	C₂³×C₁₃₉	1	2	yes	—
587	#95	C₂³×C₁₃₉	1	2	yes	—
588	#95	C₂³×C₁₃₉	1	2	yes	—
589	#95	C₂³×C₁₃₉	1	2	yes	—
590	#95	C₂³×C₁₃₉	1	2	yes	—
591	#95	C₂³×C₁₃₉	1	2	yes	—
592	#95	C₂³×C₁₃₉	1	2	yes	—
593	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
594	C₂×Q₈	—	2	4	no	—
595	C₂×Q₈	—	2	2	no	—
596	C₂×Q₈	—	4	1	no	—
597	C₂×Q₈	—	4	2	no	—
598	C₂×Q₈	—	4	1	no	—
599	C₂×Q₈	—	4	2	no	—
600	C₂×Q₈	—	4	1	no	—
601	C₂×Q₈	—	4	1	no	—
602	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	4	1	no	—
609	C₂²×C₄	—	4	1	no	—
610	C₂²×C₄	—	4	1	no	—
611	C₂²×C₄	—	4	1	no	—
612	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
628	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
629	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	4	1	no	—
644	C₄⋊C₄	—	4	1	no	—
645	C₄⋊C₄	—	4	2	no	—
646	C₄⋊C₄	—	4	2	no	—
647	C₄⋊C₄	—	4	2	no	—
648	C₄⋊C₄	—	4	2	no	—
649	C₄⋊C₄	—	4	2	no	—
650	C₄⋊C₄	—	4	2	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	1	no	—
653	C₄⋊C₄	—	4	2	no	—
654	C₄⋊C₄	—	4	2	no	—
655	C₄⋊C₄	—	4	1	no	—
656	C₄⋊C₄	—	4	1	no	—
657	C₄⋊C₄	—	4	1	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₄²	—	2	4	no	—
666	C₄²	—	2	2	no	—
667	C₄²	—	2	2	no	—
668	C₄²	—	2	4	no	—
669	C₄²	—	4	1	no	—
670	C₄²	—	4	1	no	—
671	C₄²	—	4	2	no	—
672	C₄²	—	4	2	no	—
673	C₄²	—	4	2	no	—
674	C₄²	—	4	2	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
682	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
683	Q₈	—	4	4	no	—
684	Q₈	—	4	8	no	—
685	Q₈	—	8	2	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	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	2	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	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	4	4	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	4	4	no	—
738	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
739	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
740	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
741	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
742	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	1	no	—
750	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
751	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
752	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
753	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
754	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
755	C₂²	#585×C₁₃₉	1	1	yes	characteristic
756	C₂²	#585×C₁₃₉	1	1	yes	characteristic
757	C₄	—	2	2	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	2	2	no	—
761	C₄	—	2	4	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	1	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	1	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₂	—	4	2	no	—
776	C₂	#3459×C₁₃₉	1	1	yes	characteristic
777	C₂	#3518×C₁₃₉	1	1	yes	characteristic
778	C₂	#3523×C₁₃₉	1	1	yes	characteristic
779	C₂	#3535×C₁₃₉	1	1	yes	characteristic
780	C₂	#3538×C₁₃₉	1	1	yes	characteristic
781	C₂	#3553×C₁₃₉	1	1	yes	characteristic
782	C₂	#3555×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
3. #2810×C₁₃₉	C₂	semidirect
4. #2809×C₁₃₉	C₂	semidirect
5. #2806×C₁₃₉	C₂	semidirect
6. #2805×C₁₃₉	C₂	semidirect
7. #2789×C₁₃₉	C₂	semidirect
11. #2734×C₁₃₉	C₂	semidirect
13. #2655×C₁₃₉	C₂	semidirect
15. #2528×C₁₃₉	C₂	semidirect
17. #2462×C₁₃₉	C₂	semidirect
18. #2327×C₁₃₉	C₂	semidirect
391. #37212	C₁₃₉	direct (N × H)
392. C₁₃₉	#37212	direct (N × H)
395. #2810	C₂×C₁₃₉	semidirect
396. #2809	C₂×C₁₃₉	semidirect
397. #2806	C₂×C₁₃₉	semidirect
398. #2805	C₂×C₁₃₉	semidirect
399. #2789	C₂×C₁₃₉	semidirect
403. #2734	C₂×C₁₃₉	semidirect
405. #2655	C₂×C₁₃₉	semidirect
407. #2528	C₂×C₁₃₉	semidirect
409. #2462	C₂×C₁₃₉	semidirect
410. #2327	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2855×C₁₃₉	2
#2851×C₁₃₉	2
#2810×C₁₃₉	2
#2809×C₁₃₉	2
#2806×C₁₃₉	2
#2805×C₁₃₉	2
#2789×C₁₃₉	2
#2787×C₁₃₉	2
#2745×C₁₃₉	2
#2744×C₁₃₉	2
#2734×C₁₃₉	2
#2729×C₁₃₉	2
#2655×C₁₃₉	2
#2530×C₁₃₉	2
#2528×C₁₃₉	2
#2465×C₁₃₉	2
#2462×C₁₃₉	2
#2327×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
#37212	139

Subgroups — C139×#37212 #48031808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37212 #48031808