Subgroups — C₁₃₉×#36460 #48031056

Order 35584.

1980 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2860×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2571×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2559×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2548×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2526×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2512×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2500×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2426×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2420×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2366×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2363×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2357×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	Q₈×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#124×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#117×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
20	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
32	#400×C₁₃₉	C₂²	1	4	yes	—
33	#397×C₁₃₉	C₂²	1	4	yes	—
34	#396×C₁₃₉	C₂²	1	4	yes	—
35	#394×C₁₃₉	C₂²	1	4	yes	—
36	#394×C₁₃₉	C₂²	1	4	yes	—
37	#394×C₁₃₉	C₂²	1	4	yes	—
38	#391×C₁₃₉	C₂²	1	1	yes	characteristic
39	#390×C₁₃₉	C₂²	1	2	yes	—
40	#390×C₁₃₉	C₂²	1	2	yes	—
41	#390×C₁₃₉	C₂²	1	2	yes	—
42	#390×C₁₃₉	C₂²	1	2	yes	—
43	#390×C₁₃₉	C₂²	1	2	yes	—
44	#390×C₁₃₉	C₂²	1	2	yes	—
45	#390×C₁₃₉	C₂²	1	2	yes	—
46	#390×C₁₃₉	C₂²	1	4	yes	—
47	#390×C₁₃₉	C₂²	1	2	yes	—
48	#389×C₁₃₉	C₂²	1	2	yes	—
49	#389×C₁₃₉	C₂²	1	4	yes	—
50	#389×C₁₃₉	C₂²	1	1	yes	characteristic
51	#389×C₁₃₉	C₂²	1	2	yes	—
52	#389×C₁₃₉	C₂²	1	2	yes	—
53	#388×C₁₃₉	C₂²	1	4	yes	—
54	#388×C₁₃₉	C₂²	1	4	yes	—
55	#388×C₁₃₉	C₂²	1	4	yes	—
56	#388×C₁₃₉	C₂²	1	4	yes	—
57	#388×C₁₃₉	C₂²	1	4	yes	—
58	#388×C₁₃₉	C₂²	1	4	yes	—
59	#387×C₁₃₉	C₂²	1	2	yes	—
60	#386×C₁₃₉	C₂²	1	4	yes	—
61	#386×C₁₃₉	C₂²	1	4	yes	—
62	#385×C₁₃₉	C₂²	1	2	yes	—
63	#384×C₁₃₉	C₂²	1	2	yes	—
64	#384×C₁₃₉	C₂²	1	1	yes	characteristic
65	#382×C₁₃₉	C₂²	1	2	yes	—
66	#382×C₁₃₉	C₂²	1	2	yes	—
67	#381×C₁₃₉	C₂²	1	4	yes	—
68	#380×C₁₃₉	C₂²	1	1	yes	characteristic
69	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
70	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
73	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
74	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
75	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
77	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
78	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
79	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
81	#376×C₁₃₉	C₂²	1	2	yes	—
82	C₄³×C₁₃₉	C₂²	1	2	yes	—
83	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
87	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
92	#127×C₁₃₉	—	2	4	no	—
93	#126×C₁₃₉	—	4	8	no	—
94	#124×C₁₃₉	—	2	8	no	—
95	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
96	#121×C₁₃₉	—	2	8	no	—
97	#121×C₁₃₉	—	4	4	no	—
98	#121×C₁₃₉	—	4	4	no	—
99	C₄×Q₈×C₁₃₉	—	2	4	no	—
100	C₄×Q₈×C₁₃₉	—	4	4	no	—
101	C₄×D₄×C₁₃₉	—	2	8	no	—
102	C₄×D₄×C₁₃₉	—	4	4	no	—
103	#117×C₁₃₉	—	2	4	no	—
104	#117×C₁₃₉	—	2	4	no	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
135	C₂×C₄²×C₁₃₉	—	2	4	no	—
136	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
149	#95×C₁₃₉	C₂³	1	2	yes	—
150	#95×C₁₃₉	C₂³	1	2	yes	—
151	#95×C₁₃₉	C₂³	1	4	yes	—
152	#95×C₁₃₉	C₂³	1	2	yes	—
153	#95×C₁₃₉	C₂³	1	2	yes	—
154	#95×C₁₃₉	C₂³	1	4	yes	—
155	#95×C₁₃₉	C₂³	1	4	yes	—
156	#95×C₁₃₉	C₂³	1	2	yes	—
157	#95×C₁₃₉	C₂³	1	2	yes	—
158	#95×C₁₃₉	C₂³	1	2	yes	—
159	#95×C₁₃₉	C₂³	1	2	yes	—
160	#95×C₁₃₉	C₂³	1	2	yes	—
161	#95×C₁₃₉	C₂³	1	4	yes	—
162	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
163	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
164	C₂×Q₈×C₁₃₉	—	2	2	no	—
165	C₂×Q₈×C₁₃₉	—	2	2	no	—
166	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
167	C₂×D₄×C₁₃₉	—	2	8	no	—
168	C₂×D₄×C₁₃₉	—	2	4	no	—
169	C₂×D₄×C₁₃₉	—	2	4	no	—
170	C₂×D₄×C₁₃₉	—	2	4	no	—
171	C₂×D₄×C₁₃₉	—	2	4	no	—
172	C₂×D₄×C₁₃₉	—	2	4	no	—
173	C₂×D₄×C₁₃₉	—	2	4	no	—
174	C₂×D₄×C₁₃₉	—	2	4	no	—
175	C₂×D₄×C₁₃₉	—	4	2	no	—
176	C₂×D₄×C₁₃₉	—	4	4	no	—
177	C₂×D₄×C₁₃₉	—	4	4	no	—
178	C₂×D₄×C₁₃₉	—	4	2	no	—
179	C₂²×C₄×C₁₃₉	—	2	2	no	—
180	C₂²×C₄×C₁₃₉	—	2	2	no	—
181	C₂²×C₄×C₁₃₉	—	2	2	no	—
182	C₂²×C₄×C₁₃₉	—	2	2	no	—
183	C₂²×C₄×C₁₃₉	—	2	2	no	—
184	C₂²×C₄×C₁₃₉	—	2	2	no	—
185	C₂²×C₄×C₁₃₉	—	2	2	no	—
186	C₂²×C₄×C₁₃₉	—	2	8	no	—
187	C₂²×C₄×C₁₃₉	—	4	1	no	—
188	C₂²×C₄×C₁₃₉	—	4	4	no	—
189	C₂²×C₄×C₁₃₉	—	4	4	no	—
190	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
191	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
206	C₄⋊C₄×C₁₃₉	—	2	2	no	—
207	C₄⋊C₄×C₁₃₉	—	2	2	no	—
208	C₄⋊C₄×C₁₃₉	—	2	2	no	—
209	C₄⋊C₄×C₁₃₉	—	2	4	no	—
210	C₄⋊C₄×C₁₃₉	—	2	2	no	—
211	C₄⋊C₄×C₁₃₉	—	2	4	no	—
212	C₄⋊C₄×C₁₃₉	—	2	2	no	—
213	C₄⋊C₄×C₁₃₉	—	2	4	no	—
214	C₄⋊C₄×C₁₃₉	—	2	2	no	—
215	C₄⋊C₄×C₁₃₉	—	2	4	no	—
216	C₄⋊C₄×C₁₃₉	—	2	4	no	—
217	C₄⋊C₄×C₁₃₉	—	4	4	no	—
218	C₄⋊C₄×C₁₃₉	—	4	2	no	—
219	C₄⋊C₄×C₁₃₉	—	4	4	no	—
220	C₄⋊C₄×C₁₃₉	—	4	4	no	—
221	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
222	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
223	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
224	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
225	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
226	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
227	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
228	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
229	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
230	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
231	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
232	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
233	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
234	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
235	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
236	C₄²×C₁₃₉	—	2	2	no	—
237	C₄²×C₁₃₉	—	2	2	no	—
238	C₄²×C₁₃₉	—	2	2	no	—
239	C₄²×C₁₃₉	—	2	4	no	—
240	C₄²×C₁₃₉	—	2	4	no	—
241	C₄²×C₁₃₉	—	2	4	no	—
242	C₄²×C₁₃₉	—	2	4	no	—
243	C₄²×C₁₃₉	—	2	4	no	—
244	C₄²×C₁₃₉	—	2	4	no	—
245	C₄²×C₁₃₉	—	2	4	no	—
246	C₄²×C₁₃₉	—	4	2	no	—
247	C₄²×C₁₃₉	—	4	4	no	—
248	C₄²×C₁₃₉	#41	1	4	yes	—
249	C₂³×C₁₃₉	—	2	1	no	—
250	C₂³×C₁₃₉	—	2	1	no	—
251	C₂³×C₁₃₉	—	2	1	no	—
252	C₂³×C₁₃₉	—	2	1	no	—
253	C₂³×C₁₃₉	—	2	1	no	—
254	C₂³×C₁₃₉	—	2	1	no	—
255	C₂³×C₁₃₉	—	2	4	no	—
256	C₂³×C₁₃₉	—	2	4	no	—
257	C₂³×C₁₃₉	—	2	4	no	—
258	C₂³×C₁₃₉	—	2	4	no	—
259	C₂³×C₁₃₉	—	2	4	no	—
260	C₂³×C₁₃₉	—	2	4	no	—
261	C₂³×C₁₃₉	—	2	4	no	—
262	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
263	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
264	Q₈×C₁₃₉	—	2	8	no	—
265	D₄×C₁₃₉	—	4	8	no	—
266	D₄×C₁₃₉	—	4	8	no	—
267	D₄×C₁₃₉	—	8	4	no	—
268	D₄×C₁₃₉	—	8	8	no	—
269	C₂×C₄×C₁₃₉	—	2	1	no	—
270	C₂×C₄×C₁₃₉	—	2	1	no	—
271	C₂×C₄×C₁₃₉	—	2	1	no	—
272	C₂×C₄×C₁₃₉	—	2	2	no	—
273	C₂×C₄×C₁₃₉	—	2	2	no	—
274	C₂×C₄×C₁₃₉	—	2	2	no	—
275	C₂×C₄×C₁₃₉	—	2	1	no	—
276	C₂×C₄×C₁₃₉	—	2	1	no	—
277	C₂×C₄×C₁₃₉	—	2	2	no	—
278	C₂×C₄×C₁₃₉	—	2	1	no	—
279	C₂×C₄×C₁₃₉	—	2	8	no	—
280	C₂×C₄×C₁₃₉	—	2	1	no	—
281	C₂×C₄×C₁₃₉	—	2	2	no	—
282	C₂×C₄×C₁₃₉	—	2	2	no	—
283	C₂×C₄×C₁₃₉	—	2	2	no	—
284	C₂×C₄×C₁₃₉	—	2	2	no	—
285	C₂×C₄×C₁₃₉	—	2	2	no	—
286	C₂×C₄×C₁₃₉	—	2	2	no	—
287	C₂×C₄×C₁₃₉	—	2	2	no	—
288	C₂×C₄×C₁₃₉	—	2	2	no	—
289	C₂×C₄×C₁₃₉	—	2	2	no	—
290	C₂×C₄×C₁₃₉	—	2	4	no	—
291	C₂×C₄×C₁₃₉	—	2	1	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	2	no	—
295	C₂×C₄×C₁₃₉	—	2	4	no	—
296	C₂×C₄×C₁₃₉	—	2	4	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	2	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	4	4	no	—
305	C₂×C₄×C₁₃₉	—	4	4	no	—
306	C₂×C₄×C₁₃₉	—	8	8	no	—
307	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
308	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
309	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
310	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
311	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
312	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
313	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
314	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
315	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
316	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
317	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
318	C₂²×C₁₃₉	—	2	2	no	—
319	C₂²×C₁₃₉	—	2	2	no	—
320	C₂²×C₁₃₉	—	2	2	no	—
321	C₂²×C₁₃₉	—	4	1	no	—
322	C₂²×C₁₃₉	—	4	1	no	—
323	C₂²×C₁₃₉	—	4	1	no	—
324	C₂²×C₁₃₉	—	4	1	no	—
325	C₂²×C₁₃₉	—	4	4	no	—
326	C₂²×C₁₃₉	—	4	4	no	—
327	C₂²×C₁₃₉	—	4	4	no	—
328	C₂²×C₁₃₉	—	4	4	no	—
329	C₂²×C₁₃₉	—	4	4	no	—
330	C₂²×C₁₃₉	—	4	4	no	—
331	C₂²×C₁₃₉	—	4	4	no	—
332	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
333	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
334	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
335	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
336	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
337	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂²×C₁₃₉	#585	1	1	yes	characteristic
339	C₄×C₁₃₉	—	2	2	no	—
340	C₄×C₁₃₉	—	2	4	no	—
341	C₄×C₁₃₉	—	2	2	no	—
342	C₄×C₁₃₉	—	2	2	no	—
343	C₄×C₁₃₉	—	2	4	no	—
344	C₄×C₁₃₉	—	4	1	no	—
345	C₄×C₁₃₉	—	4	2	no	—
346	C₄×C₁₃₉	—	4	2	no	—
347	C₄×C₁₃₉	—	4	2	no	—
348	C₄×C₁₃₉	—	4	2	no	—
349	C₄×C₁₃₉	—	4	2	no	—
350	C₄×C₁₃₉	—	4	4	no	—
351	C₄×C₁₃₉	—	4	2	no	—
352	C₄×C₁₃₉	#529	1	4	yes	—
353	C₄×C₁₃₉	#553	1	4	yes	—
354	C₂×C₁₃₉	—	4	2	no	—
355	C₂×C₁₃₉	—	8	4	no	—
356	C₂×C₁₃₉	C₂×#529	1	1	yes	characteristic
357	C₂×C₁₃₉	C₂×#553	1	1	yes	characteristic
358	C₂×C₁₃₉	#3480	1	1	yes	characteristic
359	C₂×C₁₃₉	#3483	1	1	yes	characteristic
360	C₂×C₁₃₉	#3494	1	1	yes	characteristic
361	C₂×C₁₃₉	#3508	1	1	yes	characteristic
362	C₂×C₁₃₉	#3514	1	1	yes	characteristic
363	#36460	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
364	C₁₃₉	#36460	1	1	yes	characteristic, direct product factor, Sylow
365	#2860	C₂×C₁₃₉	1	2	yes	complemented
366	#2856	C₂×C₁₃₉	1	1	yes	characteristic
367	#2571	C₂×C₁₃₉	1	1	yes	characteristic, complemented
368	#2559	C₂×C₁₃₉	1	4	yes	complemented
369	#2548	C₂×C₁₃₉	1	1	yes	characteristic, complemented
370	#2526	C₂×C₁₃₉	1	4	yes	complemented
371	#2512	C₂×C₁₃₉	1	2	yes	complemented
372	#2500	C₂×C₁₃₉	1	2	yes	complemented
373	#2426	C₂×C₁₃₉	1	2	yes	complemented
374	#2420	C₂×C₁₃₉	1	2	yes	complemented
375	#2366	C₂×C₁₃₉	1	1	yes	characteristic, complemented
376	#2363	C₂×C₁₃₉	1	2	yes	complemented
377	#2357	C₂×C₁₃₉	1	2	yes	complemented
378	Q₈×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
379	C₄×#124	C₂×C₁₃₉	1	2	yes	complemented
380	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
381	C₄×#117	C₂×C₁₃₉	1	1	yes	characteristic, complemented
382	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
383	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
384	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
385	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
386	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
387	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
388	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
389	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
390	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
391	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
392	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
393	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
394	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
395	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
396	#400	C₂²×C₁₃₉	1	4	yes	—
397	#397	C₂²×C₁₃₉	1	4	yes	—
398	#396	C₂²×C₁₃₉	1	4	yes	—
399	#394	C₂²×C₁₃₉	1	4	yes	—
400	#394	C₂²×C₁₃₉	1	4	yes	—
401	#394	C₂²×C₁₃₉	1	4	yes	—
402	#391	C₂²×C₁₃₉	1	1	yes	characteristic
403	#390	C₂²×C₁₃₉	1	2	yes	—
404	#390	C₂²×C₁₃₉	1	2	yes	—
405	#390	C₂²×C₁₃₉	1	2	yes	—
406	#390	C₂²×C₁₃₉	1	2	yes	—
407	#390	C₂²×C₁₃₉	1	2	yes	—
408	#390	C₂²×C₁₃₉	1	2	yes	—
409	#390	C₂²×C₁₃₉	1	4	yes	—
410	#390	C₂²×C₁₃₉	1	2	yes	—
411	#390	C₂²×C₁₃₉	1	2	yes	—
412	#389	C₂²×C₁₃₉	1	2	yes	—
413	#389	C₂²×C₁₃₉	1	2	yes	—
414	#389	C₂²×C₁₃₉	1	1	yes	characteristic
415	#389	C₂²×C₁₃₉	1	2	yes	—
416	#389	C₂²×C₁₃₉	1	4	yes	—
417	#388	C₂²×C₁₃₉	1	4	yes	—
418	#388	C₂²×C₁₃₉	1	4	yes	—
419	#388	C₂²×C₁₃₉	1	4	yes	—
420	#388	C₂²×C₁₃₉	1	4	yes	—
421	#388	C₂²×C₁₃₉	1	4	yes	—
422	#388	C₂²×C₁₃₉	1	4	yes	—
423	#387	C₂²×C₁₃₉	1	2	yes	—
424	#386	C₂²×C₁₃₉	1	4	yes	—
425	#386	C₂²×C₁₃₉	1	4	yes	—
426	#385	C₂²×C₁₃₉	1	2	yes	—
427	#384	C₂²×C₁₃₉	1	1	yes	characteristic
428	#384	C₂²×C₁₃₉	1	2	yes	—
429	#382	C₂²×C₁₃₉	1	2	yes	—
430	#382	C₂²×C₁₃₉	1	2	yes	—
431	#381	C₂²×C₁₃₉	1	4	yes	—
432	#380	C₂²×C₁₃₉	1	1	yes	characteristic
433	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
434	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
435	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
436	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
437	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
439	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
440	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
441	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
442	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
443	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
444	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
445	#376	C₂²×C₁₃₉	1	2	yes	—
446	C₄³	C₂²×C₁₃₉	1	2	yes	—
447	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
448	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
449	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
450	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
451	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
452	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
456	#127	—	2	4	no	—
457	#126	—	4	8	no	—
458	#124	—	2	8	no	—
459	C₂²⋊Q₈	—	2	4	no	—
460	#121	—	2	8	no	—
461	#121	—	4	4	no	—
462	#121	—	4	4	no	—
463	C₄×Q₈	—	2	4	no	—
464	C₄×Q₈	—	4	4	no	—
465	C₄×D₄	—	2	8	no	—
466	C₄×D₄	—	4	4	no	—
467	#117	—	2	4	no	—
468	#117	—	2	4	no	—
469	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
481	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
483	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
484	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
499	C₂×C₄²	—	2	4	no	—
500	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
501	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
502	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
503	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
504	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
505	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
506	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
507	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
510	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
511	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
512	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
513	#95	C₂³×C₁₃₉	1	2	yes	—
514	#95	C₂³×C₁₃₉	1	2	yes	—
515	#95	C₂³×C₁₃₉	1	2	yes	—
516	#95	C₂³×C₁₃₉	1	2	yes	—
517	#95	C₂³×C₁₃₉	1	2	yes	—
518	#95	C₂³×C₁₃₉	1	2	yes	—
519	#95	C₂³×C₁₃₉	1	4	yes	—
520	#95	C₂³×C₁₃₉	1	4	yes	—
521	#95	C₂³×C₁₃₉	1	2	yes	—
522	#95	C₂³×C₁₃₉	1	2	yes	—
523	#95	C₂³×C₁₃₉	1	4	yes	—
524	#95	C₂³×C₁₃₉	1	2	yes	—
525	#95	C₂³×C₁₃₉	1	4	yes	—
526	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
527	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	2	2	no	—
530	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
531	C₂×D₄	—	2	8	no	—
532	C₂×D₄	—	2	4	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	4	2	no	—
540	C₂×D₄	—	4	4	no	—
541	C₂×D₄	—	4	4	no	—
542	C₂×D₄	—	4	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	8	no	—
551	C₂²×C₄	—	4	1	no	—
552	C₂²×C₄	—	4	4	no	—
553	C₂²×C₄	—	4	4	no	—
554	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
555	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
560	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
562	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
564	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
568	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
569	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	4	4	no	—
582	C₄⋊C₄	—	4	2	no	—
583	C₄⋊C₄	—	4	4	no	—
584	C₄⋊C₄	—	4	4	no	—
585	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	8	no	—
589	C₂²⋊C₄	—	2	8	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	8	no	—
592	C₂²⋊C₄	—	2	8	no	—
593	C₂²⋊C₄	—	2	8	no	—
594	C₂²⋊C₄	—	4	4	no	—
595	C₂²⋊C₄	—	4	2	no	—
596	C₂²⋊C₄	—	4	4	no	—
597	C₂²⋊C₄	—	4	4	no	—
598	C₂²⋊C₄	—	4	4	no	—
599	C₂²⋊C₄	—	4	4	no	—
600	C₄²	—	2	2	no	—
601	C₄²	—	2	2	no	—
602	C₄²	—	2	2	no	—
603	C₄²	—	2	4	no	—
604	C₄²	—	2	4	no	—
605	C₄²	—	2	4	no	—
606	C₄²	—	2	4	no	—
607	C₄²	—	2	4	no	—
608	C₄²	—	2	4	no	—
609	C₄²	—	2	4	no	—
610	C₄²	—	4	2	no	—
611	C₄²	—	4	4	no	—
612	C₄²	#41×C₁₃₉	1	4	yes	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	4	no	—
620	C₂³	—	2	4	no	—
621	C₂³	—	2	4	no	—
622	C₂³	—	2	4	no	—
623	C₂³	—	2	4	no	—
624	C₂³	—	2	4	no	—
625	C₂³	—	2	4	no	—
626	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
627	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
628	Q₈	—	2	8	no	—
629	D₄	—	4	8	no	—
630	D₄	—	4	8	no	—
631	D₄	—	8	4	no	—
632	D₄	—	8	8	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	8	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	4	4	no	—
669	C₂×C₄	—	4	4	no	—
670	C₂×C₄	—	8	8	no	—
671	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
672	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
673	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
674	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
675	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
676	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
677	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
678	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
679	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
680	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
681	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	4	no	—
690	C₂²	—	4	4	no	—
691	C₂²	—	4	4	no	—
692	C₂²	—	4	4	no	—
693	C₂²	—	4	4	no	—
694	C₂²	—	4	4	no	—
695	C₂²	—	4	4	no	—
696	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
697	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
698	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
699	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
700	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
701	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
702	C₂²	#585×C₁₃₉	1	1	yes	characteristic
703	C₄	—	2	2	no	—
704	C₄	—	2	4	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	2	no	—
707	C₄	—	2	4	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	4	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	#529×C₁₃₉	1	4	yes	—
717	C₄	#553×C₁₃₉	1	4	yes	—
718	C₂	—	4	2	no	—
719	C₂	—	8	4	no	—
720	C₂	C₂×#529×C₁₃₉	1	1	yes	characteristic
721	C₂	C₂×#553×C₁₃₉	1	1	yes	characteristic
722	C₂	#3480×C₁₃₉	1	1	yes	characteristic
723	C₂	#3483×C₁₃₉	1	1	yes	characteristic
724	C₂	#3494×C₁₃₉	1	1	yes	characteristic
725	C₂	#3508×C₁₃₉	1	1	yes	characteristic
726	C₂	#3514×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2856×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. #2860×C₁₃₉	C₂	semidirect
3. #2571×C₁₃₉	C₂	semidirect
4. #2559×C₁₃₉	C₂	semidirect
5. #2548×C₁₃₉	C₂	semidirect
6. #2526×C₁₃₉	C₂	semidirect
7. #2512×C₁₃₉	C₂	semidirect
8. #2500×C₁₃₉	C₂	semidirect
9. #2426×C₁₃₉	C₂	semidirect
10. #2420×C₁₃₉	C₂	semidirect
11. #2366×C₁₃₉	C₂	semidirect
12. #2363×C₁₃₉	C₂	semidirect
13. #2357×C₁₃₉	C₂	semidirect
14. Q₈×C₄⋊C₄×C₁₃₉	C₂	semidirect
15. C₄×#124×C₁₃₉	C₂	semidirect
16. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
17. C₄×#117×C₁₃₉	C₂	semidirect
363. #36460	C₁₃₉	direct (N × H)
364. C₁₃₉	#36460	direct (N × H)
365. #2860	C₂×C₁₃₉	semidirect
367. #2571	C₂×C₁₃₉	semidirect
368. #2559	C₂×C₁₃₉	semidirect
369. #2548	C₂×C₁₃₉	semidirect
370. #2526	C₂×C₁₃₉	semidirect
371. #2512	C₂×C₁₃₉	semidirect
372. #2500	C₂×C₁₃₉	semidirect
373. #2426	C₂×C₁₃₉	semidirect
374. #2420	C₂×C₁₃₉	semidirect
375. #2366	C₂×C₁₃₉	semidirect
376. #2363	C₂×C₁₃₉	semidirect
377. #2357	C₂×C₁₃₉	semidirect
378. Q₈×C₄⋊C₄	C₂×C₁₃₉	semidirect
379. C₄×#124	C₂×C₁₃₉	semidirect
380. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
381. C₄×#117	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2860×C₁₃₉	2
#2856×C₁₃₉	2
#2571×C₁₃₉	2
#2559×C₁₃₉	2
#2548×C₁₃₉	2
#2526×C₁₃₉	2
#2512×C₁₃₉	2
#2500×C₁₃₉	2
#2426×C₁₃₉	2
#2420×C₁₃₉	2
#2366×C₁₃₉	2
#2363×C₁₃₉	2
#2357×C₁₃₉	2
Q₈×C₄⋊C₄×C₁₃₉	2
C₄×#124×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
C₄×#117×C₁₃₉	2
#36460	139

Subgroups — C139×#36460 #48031056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36460 #48031056