Subgroups — C₁₃₉×#36174 #48030770

Order 35584.

1874 conjugacy classes of subgroups.

The subgroup lattice has 714 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	#2850×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2538×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2537×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#2526×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2518×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2495×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2490×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2489×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2420×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2363×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2355×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2354×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2346×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2283×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
29	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
30	#400×C₁₃₉	C₂²	1	4	yes	—
31	#397×C₁₃₉	C₂²	1	4	yes	—
32	#397×C₁₃₉	C₂²	1	4	yes	—
33	#396×C₁₃₉	C₂²	1	4	yes	—
34	#394×C₁₃₉	C₂²	1	4	yes	—
35	#394×C₁₃₉	C₂²	1	4	yes	—
36	#391×C₁₃₉	C₂²	1	1	yes	characteristic
37	#391×C₁₃₉	C₂²	1	2	yes	—
38	#390×C₁₃₉	C₂²	1	4	yes	—
39	#390×C₁₃₉	C₂²	1	2	yes	—
40	#390×C₁₃₉	C₂²	1	1	yes	characteristic
41	#390×C₁₃₉	C₂²	1	2	yes	—
42	#389×C₁₃₉	C₂²	1	2	yes	—
43	#389×C₁₃₉	C₂²	1	2	yes	—
44	#389×C₁₃₉	C₂²	1	2	yes	—
45	#389×C₁₃₉	C₂²	1	2	yes	—
46	#389×C₁₃₉	C₂²	1	2	yes	—
47	#388×C₁₃₉	C₂²	1	2	yes	—
48	#388×C₁₃₉	C₂²	1	4	yes	—
49	#388×C₁₃₉	C₂²	1	4	yes	—
50	#388×C₁₃₉	C₂²	1	4	yes	—
51	#388×C₁₃₉	C₂²	1	2	yes	—
52	#388×C₁₃₉	C₂²	1	4	yes	—
53	#388×C₁₃₉	C₂²	1	4	yes	—
54	#387×C₁₃₉	C₂²	1	4	yes	—
55	#386×C₁₃₉	C₂²	1	4	yes	—
56	#386×C₁₃₉	C₂²	1	4	yes	—
57	#384×C₁₃₉	C₂²	1	1	yes	characteristic
58	#384×C₁₃₉	C₂²	1	1	yes	characteristic
59	#383×C₁₃₉	C₂²	1	4	yes	—
60	#382×C₁₃₉	C₂²	1	4	yes	—
61	#382×C₁₃₉	C₂²	1	1	yes	characteristic
62	#382×C₁₃₉	C₂²	1	2	yes	—
63	#382×C₁₃₉	C₂²	1	2	yes	—
64	#381×C₁₃₉	C₂²	1	4	yes	—
65	#380×C₁₃₉	C₂²	1	2	yes	—
66	#380×C₁₃₉	C₂²	1	2	yes	—
67	#380×C₁₃₉	C₂²	1	2	yes	—
68	#380×C₁₃₉	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
70	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
71	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
77	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
78	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
81	#376×C₁₃₉	C₂²	1	4	yes	—
82	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
83	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
87	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
90	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
91	#125×C₁₃₉	—	4	4	no	—
92	#124×C₁₃₉	—	2	4	no	—
93	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
94	#121×C₁₃₉	—	2	8	no	—
95	#121×C₁₃₉	—	4	4	no	—
96	C₄×Q₈×C₁₃₉	—	2	4	no	—
97	C₄×D₄×C₁₃₉	—	2	4	no	—
98	C₄×D₄×C₁₃₉	—	2	4	no	—
99	C₄×D₄×C₁₃₉	—	2	4	no	—
100	C₄×D₄×C₁₃₉	—	2	4	no	—
101	#117×C₁₃₉	—	2	8	no	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	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	2	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	2	yes	—
131	C₂×C₄²×C₁₃₉	—	2	8	no	—
132	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
136	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
143	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
145	#95×C₁₃₉	C₂³	1	4	yes	—
146	#95×C₁₃₉	C₂³	1	2	yes	—
147	#95×C₁₃₉	C₂³	1	2	yes	—
148	#95×C₁₃₉	C₂³	1	4	yes	—
149	#95×C₁₃₉	C₂³	1	4	yes	—
150	#95×C₁₃₉	C₂³	1	4	yes	—
151	#95×C₁₃₉	C₂³	1	2	yes	—
152	#95×C₁₃₉	C₂³	1	4	yes	—
153	#95×C₁₃₉	C₂³	1	2	yes	—
154	#95×C₁₃₉	C₂³	1	4	yes	—
155	#95×C₁₃₉	C₂³	1	2	yes	—
156	#95×C₁₃₉	C₂³	1	2	yes	—
157	#95×C₁₃₉	C₂³	1	2	yes	—
158	#95×C₁₃₉	C₂³	1	4	yes	—
159	#95×C₁₃₉	C₂³	1	4	yes	—
160	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
161	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
162	C₂×Q₈×C₁₃₉	—	2	2	no	—
163	C₂×Q₈×C₁₃₉	—	2	2	no	—
164	C₂×Q₈×C₁₃₉	—	2	2	no	—
165	C₂×D₄×C₁₃₉	—	2	8	no	—
166	C₂×D₄×C₁₃₉	—	2	2	no	—
167	C₂×D₄×C₁₃₉	—	2	2	no	—
168	C₂×D₄×C₁₃₉	—	2	2	no	—
169	C₂×D₄×C₁₃₉	—	2	2	no	—
170	C₂×D₄×C₁₃₉	—	2	2	no	—
171	C₂×D₄×C₁₃₉	—	4	4	no	—
172	C₂×D₄×C₁₃₉	—	4	4	no	—
173	C₂×D₄×C₁₃₉	#41	1	4	yes	—
174	C₂²×C₄×C₁₃₉	—	2	4	no	—
175	C₂²×C₄×C₁₃₉	—	2	4	no	—
176	C₂²×C₄×C₁₃₉	—	2	4	no	—
177	C₂²×C₄×C₁₃₉	—	2	4	no	—
178	C₂²×C₄×C₁₃₉	—	2	4	no	—
179	C₂²×C₄×C₁₃₉	—	2	4	no	—
180	C₂²×C₄×C₁₃₉	—	2	4	no	—
181	C₂²×C₄×C₁₃₉	—	2	4	no	—
182	C₂²×C₄×C₁₃₉	—	2	4	no	—
183	C₂²×C₄×C₁₃₉	—	2	4	no	—
184	C₂²×C₄×C₁₃₉	—	4	2	no	—
185	C₂²×C₄×C₁₃₉	—	4	2	no	—
186	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
201	C₄⋊C₄×C₁₃₉	—	2	4	no	—
202	C₄⋊C₄×C₁₃₉	—	2	2	no	—
203	C₄⋊C₄×C₁₃₉	—	2	2	no	—
204	C₄⋊C₄×C₁₃₉	—	2	2	no	—
205	C₄⋊C₄×C₁₃₉	—	2	2	no	—
206	C₄⋊C₄×C₁₃₉	—	2	4	no	—
207	C₄⋊C₄×C₁₃₉	—	2	4	no	—
208	C₄⋊C₄×C₁₃₉	—	2	4	no	—
209	C₄⋊C₄×C₁₃₉	—	2	4	no	—
210	C₄⋊C₄×C₁₃₉	—	4	2	no	—
211	C₄⋊C₄×C₁₃₉	—	4	2	no	—
212	C₄⋊C₄×C₁₃₉	—	4	4	no	—
213	C₄⋊C₄×C₁₃₉	—	4	4	no	—
214	C₄⋊C₄×C₁₃₉	—	4	4	no	—
215	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
216	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
217	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
218	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
219	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
220	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
221	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
222	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
223	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
224	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
225	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
226	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
227	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
228	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
229	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
230	C₄²×C₁₃₉	—	2	4	no	—
231	C₄²×C₁₃₉	—	2	4	no	—
232	C₄²×C₁₃₉	—	2	4	no	—
233	C₄²×C₁₃₉	—	2	8	no	—
234	C₄²×C₁₃₉	—	2	2	no	—
235	C₄²×C₁₃₉	—	2	2	no	—
236	C₄²×C₁₃₉	—	2	4	no	—
237	C₄²×C₁₃₉	—	2	2	no	—
238	C₄²×C₁₃₉	—	4	4	no	—
239	C₄²×C₁₃₉	—	4	1	no	—
240	C₄²×C₁₃₉	—	4	1	no	—
241	C₄²×C₁₃₉	#41	1	4	yes	—
242	C₄²×C₁₃₉	#41	1	4	yes	—
243	C₂³×C₁₃₉	—	2	2	no	—
244	C₂³×C₁₃₉	—	2	2	no	—
245	C₂³×C₁₃₉	—	2	2	no	—
246	C₂³×C₁₃₉	—	2	2	no	—
247	C₂³×C₁₃₉	—	2	2	no	—
248	C₂³×C₁₃₉	—	2	2	no	—
249	C₂³×C₁₃₉	—	2	2	no	—
250	C₂³×C₁₃₉	—	2	2	no	—
251	C₂³×C₁₃₉	—	2	2	no	—
252	C₂³×C₁₃₉	—	2	2	no	—
253	C₂³×C₁₃₉	—	2	2	no	—
254	C₂³×C₁₃₉	—	2	2	no	—
255	C₂³×C₁₃₉	—	2	2	no	—
256	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
257	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
258	Q₈×C₁₃₉	—	4	4	no	—
259	D₄×C₁₃₉	—	2	8	no	—
260	D₄×C₁₃₉	—	4	4	no	—
261	D₄×C₁₃₉	—	8	8	no	—
262	C₂×C₄×C₁₃₉	—	2	2	no	—
263	C₂×C₄×C₁₃₉	—	2	1	no	—
264	C₂×C₄×C₁₃₉	—	2	1	no	—
265	C₂×C₄×C₁₃₉	—	2	2	no	—
266	C₂×C₄×C₁₃₉	—	2	1	no	—
267	C₂×C₄×C₁₃₉	—	2	1	no	—
268	C₂×C₄×C₁₃₉	—	2	1	no	—
269	C₂×C₄×C₁₃₉	—	2	1	no	—
270	C₂×C₄×C₁₃₉	—	2	2	no	—
271	C₂×C₄×C₁₃₉	—	2	2	no	—
272	C₂×C₄×C₁₃₉	—	2	2	no	—
273	C₂×C₄×C₁₃₉	—	2	1	no	—
274	C₂×C₄×C₁₃₉	—	2	1	no	—
275	C₂×C₄×C₁₃₉	—	2	4	no	—
276	C₂×C₄×C₁₃₉	—	2	2	no	—
277	C₂×C₄×C₁₃₉	—	2	2	no	—
278	C₂×C₄×C₁₃₉	—	2	2	no	—
279	C₂×C₄×C₁₃₉	—	2	2	no	—
280	C₂×C₄×C₁₃₉	—	2	2	no	—
281	C₂×C₄×C₁₃₉	—	2	2	no	—
282	C₂×C₄×C₁₃₉	—	2	2	no	—
283	C₂×C₄×C₁₃₉	—	2	4	no	—
284	C₂×C₄×C₁₃₉	—	2	1	no	—
285	C₂×C₄×C₁₃₉	—	2	1	no	—
286	C₂×C₄×C₁₃₉	—	2	2	no	—
287	C₂×C₄×C₁₃₉	—	2	2	no	—
288	C₂×C₄×C₁₃₉	—	2	4	no	—
289	C₂×C₄×C₁₃₉	—	2	4	no	—
290	C₂×C₄×C₁₃₉	—	2	2	no	—
291	C₂×C₄×C₁₃₉	—	2	1	no	—
292	C₂×C₄×C₁₃₉	—	2	1	no	—
293	C₂×C₄×C₁₃₉	—	2	4	no	—
294	C₂×C₄×C₁₃₉	—	2	2	no	—
295	C₂×C₄×C₁₃₉	—	2	4	no	—
296	C₂×C₄×C₁₃₉	—	2	2	no	—
297	C₂×C₄×C₁₃₉	—	4	8	no	—
298	C₂×C₄×C₁₃₉	—	4	8	no	—
299	C₂×C₄×C₁₃₉	—	4	8	no	—
300	C₂×C₄×C₁₃₉	—	4	8	no	—
301	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
302	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
303	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
304	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
305	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
306	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
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	2	yes	—
310	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
311	C₂²×C₁₃₉	—	2	4	no	—
312	C₂²×C₁₃₉	—	2	4	no	—
313	C₂²×C₁₃₉	—	2	4	no	—
314	C₂²×C₁₃₉	—	4	2	no	—
315	C₂²×C₁₃₉	—	4	2	no	—
316	C₂²×C₁₃₉	—	4	2	no	—
317	C₂²×C₁₃₉	—	4	2	no	—
318	C₂²×C₁₃₉	—	4	2	no	—
319	C₂²×C₁₃₉	—	4	2	no	—
320	C₂²×C₁₃₉	—	4	2	no	—
321	C₂²×C₁₃₉	—	4	2	no	—
322	C₂²×C₁₃₉	—	4	2	no	—
323	C₂²×C₁₃₉	—	4	2	no	—
324	C₂²×C₁₃₉	—	4	2	no	—
325	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
326	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
327	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
328	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
329	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
330	C₂²×C₁₃₉	#585	1	1	yes	characteristic
331	C₂²×C₁₃₉	#585	1	1	yes	characteristic
332	C₄×C₁₃₉	—	2	2	no	—
333	C₄×C₁₃₉	—	2	2	no	—
334	C₄×C₁₃₉	—	2	4	no	—
335	C₄×C₁₃₉	—	2	2	no	—
336	C₄×C₁₃₉	—	4	2	no	—
337	C₄×C₁₃₉	—	4	2	no	—
338	C₄×C₁₃₉	—	4	2	no	—
339	C₄×C₁₃₉	—	4	2	no	—
340	C₄×C₁₃₉	—	4	2	no	—
341	C₄×C₁₃₉	—	4	1	no	—
342	C₄×C₁₃₉	—	4	4	no	—
343	C₄×C₁₃₉	—	4	1	no	—
344	C₄×C₁₃₉	—	4	4	no	—
345	C₄×C₁₃₉	#529	1	4	yes	—
346	C₄×C₁₃₉	#555	1	4	yes	—
347	C₂×C₁₃₉	—	4	4	no	—
348	C₂×C₁₃₉	—	8	2	no	—
349	C₂×C₁₃₉	C₂×#529	1	1	yes	characteristic
350	C₂×C₁₃₉	C₂×#555	1	1	yes	characteristic
351	C₂×C₁₃₉	#3475	1	1	yes	characteristic
352	C₂×C₁₃₉	#3475	1	1	yes	characteristic
353	C₂×C₁₃₉	#3512	1	1	yes	characteristic
354	C₂×C₁₃₉	#3514	1	1	yes	characteristic
355	C₂×C₁₃₉	#3517	1	1	yes	characteristic
356	#36174	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
357	C₁₃₉	#36174	1	1	yes	characteristic, direct product factor, Sylow
358	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
359	#2850	C₂×C₁₃₉	1	2	yes	complemented
360	#2538	C₂×C₁₃₉	1	1	yes	characteristic, complemented
361	#2537	C₂×C₁₃₉	1	1	yes	characteristic
362	#2526	C₂×C₁₃₉	1	4	yes	complemented
363	#2518	C₂×C₁₃₉	1	4	yes	complemented
364	#2495	C₂×C₁₃₉	1	2	yes	complemented
365	#2490	C₂×C₁₃₉	1	2	yes	complemented
366	#2489	C₂×C₁₃₉	1	2	yes	complemented
367	#2420	C₂×C₁₃₉	1	2	yes	complemented
368	#2363	C₂×C₁₃₉	1	2	yes	complemented
369	#2355	C₂×C₁₃₉	1	1	yes	characteristic, complemented
370	#2354	C₂×C₁₃₉	1	1	yes	characteristic, complemented
371	#2346	C₂×C₁₃₉	1	2	yes	complemented
372	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
373	#2283	C₂×C₁₃₉	1	2	yes	complemented
374	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
375	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
376	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
377	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
378	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
379	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
380	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
381	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
382	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
383	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
384	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
385	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
386	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
387	#400	C₂²×C₁₃₉	1	4	yes	—
388	#397	C₂²×C₁₃₉	1	4	yes	—
389	#397	C₂²×C₁₃₉	1	4	yes	—
390	#396	C₂²×C₁₃₉	1	4	yes	—
391	#394	C₂²×C₁₃₉	1	4	yes	—
392	#394	C₂²×C₁₃₉	1	4	yes	—
393	#391	C₂²×C₁₃₉	1	2	yes	—
394	#391	C₂²×C₁₃₉	1	1	yes	characteristic
395	#390	C₂²×C₁₃₉	1	2	yes	—
396	#390	C₂²×C₁₃₉	1	2	yes	—
397	#390	C₂²×C₁₃₉	1	4	yes	—
398	#390	C₂²×C₁₃₉	1	1	yes	characteristic
399	#389	C₂²×C₁₃₉	1	2	yes	—
400	#389	C₂²×C₁₃₉	1	2	yes	—
401	#389	C₂²×C₁₃₉	1	2	yes	—
402	#389	C₂²×C₁₃₉	1	2	yes	—
403	#389	C₂²×C₁₃₉	1	2	yes	—
404	#388	C₂²×C₁₃₉	1	4	yes	—
405	#388	C₂²×C₁₃₉	1	4	yes	—
406	#388	C₂²×C₁₃₉	1	4	yes	—
407	#388	C₂²×C₁₃₉	1	4	yes	—
408	#388	C₂²×C₁₃₉	1	4	yes	—
409	#388	C₂²×C₁₃₉	1	2	yes	—
410	#388	C₂²×C₁₃₉	1	2	yes	—
411	#387	C₂²×C₁₃₉	1	4	yes	—
412	#386	C₂²×C₁₃₉	1	4	yes	—
413	#386	C₂²×C₁₃₉	1	4	yes	—
414	#384	C₂²×C₁₃₉	1	1	yes	characteristic
415	#384	C₂²×C₁₃₉	1	1	yes	characteristic
416	#383	C₂²×C₁₃₉	1	4	yes	—
417	#382	C₂²×C₁₃₉	1	2	yes	—
418	#382	C₂²×C₁₃₉	1	4	yes	—
419	#382	C₂²×C₁₃₉	1	2	yes	—
420	#382	C₂²×C₁₃₉	1	1	yes	characteristic
421	#381	C₂²×C₁₃₉	1	4	yes	—
422	#380	C₂²×C₁₃₉	1	2	yes	—
423	#380	C₂²×C₁₃₉	1	2	yes	—
424	#380	C₂²×C₁₃₉	1	2	yes	—
425	#380	C₂²×C₁₃₉	1	2	yes	—
426	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
427	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
428	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
429	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
430	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
431	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
432	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
433	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
434	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
435	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
436	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
437	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
438	#376	C₂²×C₁₃₉	1	4	yes	—
439	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
440	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
441	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
442	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
443	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
444	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
445	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
446	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
447	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
448	#125	—	4	4	no	—
449	#124	—	2	4	no	—
450	C₂²⋊Q₈	—	4	4	no	—
451	#121	—	2	8	no	—
452	#121	—	4	4	no	—
453	C₄×Q₈	—	2	4	no	—
454	C₄×D₄	—	2	4	no	—
455	C₄×D₄	—	2	4	no	—
456	C₄×D₄	—	2	4	no	—
457	C₄×D₄	—	2	4	no	—
458	#117	—	2	8	no	—
459	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
470	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
471	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
474	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
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×C₄²	—	2	8	no	—
489	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
490	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
493	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
495	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
496	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
497	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
500	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
501	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
502	#95	C₂³×C₁₃₉	1	2	yes	—
503	#95	C₂³×C₁₃₉	1	4	yes	—
504	#95	C₂³×C₁₃₉	1	4	yes	—
505	#95	C₂³×C₁₃₉	1	4	yes	—
506	#95	C₂³×C₁₃₉	1	2	yes	—
507	#95	C₂³×C₁₃₉	1	2	yes	—
508	#95	C₂³×C₁₃₉	1	2	yes	—
509	#95	C₂³×C₁₃₉	1	2	yes	—
510	#95	C₂³×C₁₃₉	1	2	yes	—
511	#95	C₂³×C₁₃₉	1	4	yes	—
512	#95	C₂³×C₁₃₉	1	2	yes	—
513	#95	C₂³×C₁₃₉	1	4	yes	—
514	#95	C₂³×C₁₃₉	1	4	yes	—
515	#95	C₂³×C₁₃₉	1	4	yes	—
516	#95	C₂³×C₁₃₉	1	4	yes	—
517	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
518	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
519	C₂×Q₈	—	2	2	no	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	—	2	2	no	—
522	C₂×D₄	—	2	8	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	2	2	no	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	2	no	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	4	4	no	—
529	C₂×D₄	—	4	4	no	—
530	C₂×D₄	#41×C₁₃₉	1	4	yes	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
549	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
552	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
555	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
557	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	2	no	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	4	2	no	—
568	C₄⋊C₄	—	4	2	no	—
569	C₄⋊C₄	—	4	4	no	—
570	C₄⋊C₄	—	4	4	no	—
571	C₄⋊C₄	—	4	4	no	—
572	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	8	no	—
575	C₂²⋊C₄	—	2	8	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	4	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	4	2	no	—
583	C₂²⋊C₄	—	4	4	no	—
584	C₂²⋊C₄	—	4	4	no	—
585	C₂²⋊C₄	—	4	4	no	—
586	C₂²⋊C₄	—	4	4	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	2	4	no	—
589	C₄²	—	2	4	no	—
590	C₄²	—	2	8	no	—
591	C₄²	—	2	2	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	2	4	no	—
594	C₄²	—	2	2	no	—
595	C₄²	—	4	4	no	—
596	C₄²	—	4	1	no	—
597	C₄²	—	4	1	no	—
598	C₄²	#41×C₁₃₉	1	4	yes	—
599	C₄²	#41×C₁₃₉	1	4	yes	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	2	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	2	no	—
613	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
614	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
615	Q₈	—	4	4	no	—
616	D₄	—	2	8	no	—
617	D₄	—	4	4	no	—
618	D₄	—	8	8	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	4	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	4	8	no	—
655	C₂×C₄	—	4	8	no	—
656	C₂×C₄	—	4	8	no	—
657	C₂×C₄	—	4	8	no	—
658	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
659	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
660	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
661	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
662	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
663	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
664	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
665	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
666	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
667	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
668	C₂²	—	2	4	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	4	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	4	2	no	—
676	C₂²	—	4	2	no	—
677	C₂²	—	4	2	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	2	no	—
682	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
683	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
684	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
685	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
686	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
687	C₂²	#585×C₁₃₉	1	1	yes	characteristic
688	C₂²	#585×C₁₃₉	1	1	yes	characteristic
689	C₄	—	2	2	no	—
690	C₄	—	2	2	no	—
691	C₄	—	2	4	no	—
692	C₄	—	2	2	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	2	no	—
696	C₄	—	4	2	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	4	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	4	no	—
702	C₄	#529×C₁₃₉	1	4	yes	—
703	C₄	#555×C₁₃₉	1	4	yes	—
704	C₂	—	4	4	no	—
705	C₂	—	8	2	no	—
706	C₂	C₂×#529×C₁₃₉	1	1	yes	characteristic
707	C₂	C₂×#555×C₁₃₉	1	1	yes	characteristic
708	C₂	#3475×C₁₃₉	1	1	yes	characteristic
709	C₂	#3475×C₁₃₉	1	1	yes	characteristic
710	C₂	#3512×C₁₃₉	1	1	yes	characteristic
711	C₂	#3514×C₁₃₉	1	1	yes	characteristic
712	C₂	#3517×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2537×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. #2859×C₁₃₉	C₂	semidirect
2. #2850×C₁₃₉	C₂	semidirect
3. #2538×C₁₃₉	C₂	semidirect
5. #2526×C₁₃₉	C₂	semidirect
6. #2518×C₁₃₉	C₂	semidirect
7. #2495×C₁₃₉	C₂	semidirect
8. #2490×C₁₃₉	C₂	semidirect
9. #2489×C₁₃₉	C₂	semidirect
10. #2420×C₁₃₉	C₂	semidirect
11. #2363×C₁₃₉	C₂	semidirect
12. #2355×C₁₃₉	C₂	semidirect
13. #2354×C₁₃₉	C₂	semidirect
14. #2346×C₁₃₉	C₂	semidirect
15. C₄×#124×C₁₃₉	C₂	semidirect
16. #2283×C₁₃₉	C₂	semidirect
17. C₄²×D₄×C₁₃₉	C₂	semidirect
356. #36174	C₁₃₉	direct (N × H)
357. C₁₃₉	#36174	direct (N × H)
358. #2859	C₂×C₁₃₉	semidirect
359. #2850	C₂×C₁₃₉	semidirect
360. #2538	C₂×C₁₃₉	semidirect
362. #2526	C₂×C₁₃₉	semidirect
363. #2518	C₂×C₁₃₉	semidirect
364. #2495	C₂×C₁₃₉	semidirect
365. #2490	C₂×C₁₃₉	semidirect
366. #2489	C₂×C₁₃₉	semidirect
367. #2420	C₂×C₁₃₉	semidirect
368. #2363	C₂×C₁₃₉	semidirect
369. #2355	C₂×C₁₃₉	semidirect
370. #2354	C₂×C₁₃₉	semidirect
371. #2346	C₂×C₁₃₉	semidirect
372. C₄×#124	C₂×C₁₃₉	semidirect
373. #2283	C₂×C₁₃₉	semidirect
374. C₄²×D₄	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
#2850×C₁₃₉	2
#2538×C₁₃₉	2
#2537×C₁₃₉	2
#2526×C₁₃₉	2
#2518×C₁₃₉	2
#2495×C₁₃₉	2
#2490×C₁₃₉	2
#2489×C₁₃₉	2
#2420×C₁₃₉	2
#2363×C₁₃₉	2
#2355×C₁₃₉	2
#2354×C₁₃₉	2
#2346×C₁₃₉	2
C₄×#124×C₁₃₉	2
#2283×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36174	139

Subgroups — C139×#36174 #48030770

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36174 #48030770