Subgroups — C₁₃₉×#36080 #48030676

Order 35584.

2320 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#520×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2634×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2616×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2598×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2562×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2503×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2487×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2468×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2457×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2442×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2417×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2396×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2388×C₁₃₉	C₂	1	1	yes	maximal, characteristic
15	#2362×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2352×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2347×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
19	#552×C₁₃₉	—	2	8	no	—
20	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
27	#520×C₁₃₉	—	2	8	no	—
28	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
34	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
35	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
36	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	#400×C₁₃₉	C₂²	1	2	yes	—
41	#400×C₁₃₉	C₂²	1	2	yes	—
42	#400×C₁₃₉	C₂²	1	2	yes	—
43	#400×C₁₃₉	C₂²	1	4	yes	—
44	#399×C₁₃₉	C₂²	1	2	yes	—
45	#398×C₁₃₉	C₂²	1	4	yes	—
46	#398×C₁₃₉	C₂²	1	4	yes	—
47	#396×C₁₃₉	C₂²	1	4	yes	—
48	#395×C₁₃₉	C₂²	1	2	yes	—
49	#395×C₁₃₉	C₂²	1	1	yes	characteristic
50	#394×C₁₃₉	C₂²	1	1	yes	characteristic
51	#394×C₁₃₉	C₂²	1	2	yes	—
52	#394×C₁₃₉	C₂²	1	4	yes	—
53	#394×C₁₃₉	C₂²	1	2	yes	—
54	#393×C₁₃₉	C₂²	1	1	yes	characteristic
55	#392×C₁₃₉	C₂²	1	1	yes	characteristic
56	#392×C₁₃₉	C₂²	1	2	yes	—
57	#391×C₁₃₉	C₂²	1	2	yes	—
58	#389×C₁₃₉	C₂²	1	2	yes	—
59	#389×C₁₃₉	C₂²	1	2	yes	—
60	#388×C₁₃₉	C₂²	1	4	yes	—
61	#388×C₁₃₉	C₂²	1	4	yes	—
62	#388×C₁₃₉	C₂²	1	4	yes	—
63	#388×C₁₃₉	C₂²	1	4	yes	—
64	#387×C₁₃₉	C₂²	1	4	yes	—
65	#387×C₁₃₉	C₂²	1	4	yes	—
66	#386×C₁₃₉	C₂²	1	4	yes	—
67	#386×C₁₃₉	C₂²	1	4	yes	—
68	#386×C₁₃₉	C₂²	1	2	yes	—
69	#385×C₁₃₉	C₂²	1	4	yes	—
70	#385×C₁₃₉	C₂²	1	2	yes	—
71	#383×C₁₃₉	C₂²	1	2	yes	—
72	#382×C₁₃₉	C₂²	1	2	yes	—
73	#381×C₁₃₉	C₂²	1	4	yes	—
74	#380×C₁₃₉	C₂²	1	4	yes	—
75	#380×C₁₃₉	C₂²	1	4	yes	—
76	#380×C₁₃₉	C₂²	1	1	yes	characteristic
77	#380×C₁₃₉	C₂²	1	2	yes	—
78	#380×C₁₃₉	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
85	C₂×#41×C₁₃₉	—	2	4	no	—
86	C₂×#41×C₁₃₉	—	2	8	no	—
87	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
99	#126×C₁₃₉	—	2	8	no	—
100	#125×C₁₃₉	—	2	4	no	—
101	#125×C₁₃₉	—	2	8	no	—
102	#123×C₁₃₉	—	2	8	no	—
103	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
104	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
105	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
106	C₄×Q₈×C₁₃₉	—	2	4	no	—
107	C₄×Q₈×C₁₃₉	—	2	8	no	—
108	C₄×D₄×C₁₃₉	—	2	4	no	—
109	C₄×D₄×C₁₃₉	—	2	8	no	—
110	C₄×D₄×C₁₃₉	—	2	16	no	—
111	C₄×D₄×C₁₃₉	—	2	8	no	—
112	#117×C₁₃₉	—	2	8	no	—
113	#117×C₁₃₉	—	2	8	no	—
114	#117×C₁₃₉	D₄	1	8	yes	complemented
115	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
116	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
117	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
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	2	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	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	1	yes	characteristic
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	4	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	4	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
152	C₂×C₄²×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	4	yes	—
156	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
157	#95×C₁₃₉	C₂³	1	4	yes	—
158	#95×C₁₃₉	C₂³	1	2	yes	—
159	#95×C₁₃₉	C₂³	1	1	yes	characteristic
160	#95×C₁₃₉	C₂³	1	2	yes	—
161	#95×C₁₃₉	C₂³	1	4	yes	—
162	#95×C₁₃₉	C₂³	1	2	yes	—
163	#95×C₁₃₉	C₂³	1	4	yes	—
164	#95×C₁₃₉	C₂³	1	4	yes	—
165	#95×C₁₃₉	C₂³	1	4	yes	—
166	#95×C₁₃₉	C₂³	1	4	yes	—
167	#95×C₁₃₉	C₂³	1	1	yes	characteristic
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	4	yes	—
170	#95×C₁₃₉	C₂³	1	4	yes	—
171	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
172	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
173	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
174	#41×C₁₃₉	—	2	32	no	—
175	C₂×Q₈×C₁₃₉	—	2	2	no	—
176	C₂×Q₈×C₁₃₉	—	2	2	no	—
177	C₂×Q₈×C₁₃₉	—	2	4	no	—
178	C₂×Q₈×C₁₃₉	—	2	4	no	—
179	C₂×D₄×C₁₃₉	—	2	4	no	—
180	C₂×D₄×C₁₃₉	—	2	4	no	—
181	C₂×D₄×C₁₃₉	—	2	4	no	—
182	C₂×D₄×C₁₃₉	—	2	2	no	—
183	C₂×D₄×C₁₃₉	—	2	4	no	—
184	C₂×D₄×C₁₃₉	—	2	2	no	—
185	C₂×D₄×C₁₃₉	—	2	4	no	—
186	C₂×D₄×C₁₃₉	—	2	2	no	—
187	C₂×D₄×C₁₃₉	—	2	4	no	—
188	C₂×D₄×C₁₃₉	—	4	1	no	—
189	C₂×D₄×C₁₃₉	—	4	2	no	—
190	C₂²×C₄×C₁₃₉	—	2	4	no	—
191	C₂²×C₄×C₁₃₉	—	2	4	no	—
192	C₂²×C₄×C₁₃₉	—	2	4	no	—
193	C₂²×C₄×C₁₃₉	—	2	4	no	—
194	C₂²×C₄×C₁₃₉	—	2	4	no	—
195	C₂²×C₄×C₁₃₉	—	2	4	no	—
196	C₂²×C₄×C₁₃₉	—	2	2	no	—
197	C₂²×C₄×C₁₃₉	—	2	4	no	—
198	C₂²×C₄×C₁₃₉	—	2	8	no	—
199	C₂²×C₄×C₁₃₉	—	4	2	no	—
200	C₂²×C₄×C₁₃₉	—	4	4	no	—
201	C₂²×C₄×C₁₃₉	—	4	4	no	—
202	C₂²×C₄×C₁₃₉	—	4	4	no	—
203	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
205	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₁₃₉	—	2	4	no	—
220	C₄⋊C₄×C₁₃₉	—	2	8	no	—
221	C₄⋊C₄×C₁₃₉	—	2	4	no	—
222	C₄⋊C₄×C₁₃₉	—	2	2	no	—
223	C₄⋊C₄×C₁₃₉	—	2	4	no	—
224	C₄⋊C₄×C₁₃₉	—	2	4	no	—
225	C₄⋊C₄×C₁₃₉	—	2	4	no	—
226	C₄⋊C₄×C₁₃₉	—	2	2	no	—
227	C₄⋊C₄×C₁₃₉	—	2	4	no	—
228	C₄⋊C₄×C₁₃₉	—	2	4	no	—
229	C₄⋊C₄×C₁₃₉	—	2	4	no	—
230	C₄⋊C₄×C₁₃₉	—	2	4	no	—
231	C₄⋊C₄×C₁₃₉	—	2	4	no	—
232	C₄⋊C₄×C₁₃₉	—	2	8	no	—
233	C₄⋊C₄×C₁₃₉	—	4	4	no	—
234	C₄⋊C₄×C₁₃₉	—	4	4	no	—
235	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
236	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
237	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
238	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
239	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
240	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
241	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
242	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
243	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
244	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
245	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
246	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
247	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
248	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
249	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
250	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
251	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
252	C₄²×C₁₃₉	—	2	8	no	—
253	C₄²×C₁₃₉	—	2	4	no	—
254	C₄²×C₁₃₉	—	2	2	no	—
255	C₄²×C₁₃₉	—	2	4	no	—
256	C₄²×C₁₃₉	—	4	4	no	—
257	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
258	C₂³×C₁₃₉	—	2	1	no	—
259	C₂³×C₁₃₉	—	2	2	no	—
260	C₂³×C₁₃₉	—	2	2	no	—
261	C₂³×C₁₃₉	—	2	2	no	—
262	C₂³×C₁₃₉	—	2	2	no	—
263	C₂³×C₁₃₉	—	2	1	no	—
264	C₂³×C₁₃₉	—	2	2	no	—
265	C₂³×C₁₃₉	—	2	2	no	—
266	C₂³×C₁₃₉	—	2	1	no	—
267	C₂³×C₁₃₉	—	2	2	no	—
268	C₂³×C₁₃₉	—	2	2	no	—
269	C₂³×C₁₃₉	—	2	2	no	—
270	C₂³×C₁₃₉	—	2	1	no	—
271	C₂³×C₁₃₉	—	2	2	no	—
272	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
273	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
274	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
275	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
276	Q₈×C₁₃₉	—	2	8	no	—
277	Q₈×C₁₃₉	—	4	4	no	—
278	D₄×C₁₃₉	—	2	8	no	—
279	D₄×C₁₃₉	—	2	16	no	—
280	D₄×C₁₃₉	—	4	4	no	—
281	D₄×C₁₃₉	—	4	8	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	4	no	—
288	C₂×C₄×C₁₃₉	—	2	8	no	—
289	C₂×C₄×C₁₃₉	—	2	16	no	—
290	C₂×C₄×C₁₃₉	—	2	1	no	—
291	C₂×C₄×C₁₃₉	—	2	2	no	—
292	C₂×C₄×C₁₃₉	—	2	4	no	—
293	C₂×C₄×C₁₃₉	—	2	1	no	—
294	C₂×C₄×C₁₃₉	—	2	1	no	—
295	C₂×C₄×C₁₃₉	—	2	2	no	—
296	C₂×C₄×C₁₃₉	—	2	2	no	—
297	C₂×C₄×C₁₃₉	—	2	2	no	—
298	C₂×C₄×C₁₃₉	—	2	4	no	—
299	C₂×C₄×C₁₃₉	—	2	2	no	—
300	C₂×C₄×C₁₃₉	—	2	4	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	2	1	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	4	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	4	no	—
312	C₂×C₄×C₁₃₉	—	2	4	no	—
313	C₂×C₄×C₁₃₉	—	2	4	no	—
314	C₂×C₄×C₁₃₉	—	4	8	no	—
315	C₂×C₄×C₁₃₉	—	4	4	no	—
316	C₂×C₄×C₁₃₉	—	8	8	no	—
317	C₂×C₄×C₁₃₉	—	8	4	no	—
318	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
319	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
321	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
323	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
324	C₂²×C₁₃₉	—	2	2	no	—
325	C₂²×C₁₃₉	—	2	4	no	—
326	C₂²×C₁₃₉	—	2	2	no	—
327	C₂²×C₁₃₉	—	2	2	no	—
328	C₂²×C₁₃₉	—	2	4	no	—
329	C₂²×C₁₃₉	—	2	4	no	—
330	C₂²×C₁₃₉	—	2	2	no	—
331	C₂²×C₁₃₉	—	2	4	no	—
332	C₂²×C₁₃₉	—	4	1	no	—
333	C₂²×C₁₃₉	—	4	2	no	—
334	C₂²×C₁₃₉	—	4	2	no	—
335	C₂²×C₁₃₉	—	4	2	no	—
336	C₂²×C₁₃₉	—	4	2	no	—
337	C₂²×C₁₃₉	—	4	1	no	—
338	C₂²×C₁₃₉	—	4	2	no	—
339	C₂²×C₁₃₉	—	4	2	no	—
340	C₂²×C₁₃₉	—	4	2	no	—
341	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
342	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
343	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
344	C₂²×C₁₃₉	#585	1	1	yes	characteristic
345	C₂²×C₁₃₉	#585	1	2	yes	—
346	C₄×C₁₃₉	—	2	2	no	—
347	C₄×C₁₃₉	—	2	4	no	—
348	C₄×C₁₃₉	—	2	4	no	—
349	C₄×C₁₃₉	—	2	4	no	—
350	C₄×C₁₃₉	—	4	1	no	—
351	C₄×C₁₃₉	—	4	2	no	—
352	C₄×C₁₃₉	—	4	2	no	—
353	C₄×C₁₃₉	—	4	1	no	—
354	C₄×C₁₃₉	—	4	2	no	—
355	C₄×C₁₃₉	—	4	1	no	—
356	C₄×C₁₃₉	—	4	4	no	—
357	C₄×C₁₃₉	—	4	2	no	—
358	C₄×C₁₃₉	—	4	4	no	—
359	C₄×C₁₃₉	#525	1	4	yes	—
360	C₂×C₁₃₉	—	4	2	no	—
361	C₂×C₁₃₉	—	4	4	no	—
362	C₂×C₁₃₉	—	4	2	no	—
363	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
364	C₂×C₁₃₉	#3489	1	1	yes	characteristic
365	C₂×C₁₃₉	#3495	1	2	yes	—
366	C₂×C₁₃₉	#3500	1	1	yes	characteristic
367	C₂×C₁₃₉	#3512	1	2	yes	—
368	#36080	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
369	C₁₃₉	#36080	1	1	yes	characteristic, direct product factor, Sylow
370	C₂×#552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
371	C₂×#520	C₂×C₁₃₉	1	1	yes	characteristic, complemented
372	#2634	C₂×C₁₃₉	1	2	yes	complemented
373	#2616	C₂×C₁₃₉	1	1	yes	characteristic, complemented
374	#2598	C₂×C₁₃₉	1	2	yes	complemented
375	#2562	C₂×C₁₃₉	1	2	yes	complemented
376	#2503	C₂×C₁₃₉	1	1	yes	characteristic, complemented
377	#2487	C₂×C₁₃₉	1	1	yes	characteristic, complemented
378	#2468	C₂×C₁₃₉	1	4	yes	complemented
379	#2457	C₂×C₁₃₉	1	4	yes	complemented
380	#2442	C₂×C₁₃₉	1	2	yes	complemented
381	#2417	C₂×C₁₃₉	1	2	yes	complemented
382	#2396	C₂×C₁₃₉	1	2	yes	complemented
383	#2388	C₂×C₁₃₉	1	1	yes	characteristic
384	#2362	C₂×C₁₃₉	1	2	yes	complemented
385	#2352	C₂×C₁₃₉	1	2	yes	complemented
386	#2347	C₂×C₁₃₉	1	1	yes	characteristic, complemented
387	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
388	#552	—	2	8	no	—
389	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
390	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
391	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
392	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
393	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
394	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
395	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
396	#520	—	2	8	no	—
397	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
398	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
399	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
400	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
401	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
402	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
403	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
404	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
405	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
406	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
407	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
408	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
409	#400	C₂²×C₁₃₉	1	2	yes	—
410	#400	C₂²×C₁₃₉	1	2	yes	—
411	#400	C₂²×C₁₃₉	1	2	yes	—
412	#400	C₂²×C₁₃₉	1	4	yes	—
413	#399	C₂²×C₁₃₉	1	2	yes	—
414	#398	C₂²×C₁₃₉	1	4	yes	—
415	#398	C₂²×C₁₃₉	1	4	yes	—
416	#396	C₂²×C₁₃₉	1	4	yes	—
417	#395	C₂²×C₁₃₉	1	2	yes	—
418	#395	C₂²×C₁₃₉	1	1	yes	characteristic
419	#394	C₂²×C₁₃₉	1	1	yes	characteristic
420	#394	C₂²×C₁₃₉	1	2	yes	—
421	#394	C₂²×C₁₃₉	1	4	yes	—
422	#394	C₂²×C₁₃₉	1	2	yes	—
423	#393	C₂²×C₁₃₉	1	1	yes	characteristic
424	#392	C₂²×C₁₃₉	1	1	yes	characteristic
425	#392	C₂²×C₁₃₉	1	2	yes	—
426	#391	C₂²×C₁₃₉	1	2	yes	—
427	#389	C₂²×C₁₃₉	1	2	yes	—
428	#389	C₂²×C₁₃₉	1	2	yes	—
429	#388	C₂²×C₁₃₉	1	4	yes	—
430	#388	C₂²×C₁₃₉	1	4	yes	—
431	#388	C₂²×C₁₃₉	1	4	yes	—
432	#388	C₂²×C₁₃₉	1	4	yes	—
433	#387	C₂²×C₁₃₉	1	4	yes	—
434	#387	C₂²×C₁₃₉	1	4	yes	—
435	#386	C₂²×C₁₃₉	1	4	yes	—
436	#386	C₂²×C₁₃₉	1	4	yes	—
437	#386	C₂²×C₁₃₉	1	2	yes	—
438	#385	C₂²×C₁₃₉	1	4	yes	—
439	#385	C₂²×C₁₃₉	1	2	yes	—
440	#383	C₂²×C₁₃₉	1	2	yes	—
441	#382	C₂²×C₁₃₉	1	2	yes	—
442	#381	C₂²×C₁₃₉	1	4	yes	—
443	#380	C₂²×C₁₃₉	1	4	yes	—
444	#380	C₂²×C₁₃₉	1	4	yes	—
445	#380	C₂²×C₁₃₉	1	1	yes	characteristic
446	#380	C₂²×C₁₃₉	1	2	yes	—
447	#380	C₂²×C₁₃₉	1	2	yes	—
448	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
449	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
450	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
451	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
452	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
453	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
454	C₂×#41	—	2	4	no	—
455	C₂×#41	—	2	8	no	—
456	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
457	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
458	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
459	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
460	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
461	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
462	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
464	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
466	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
467	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
468	#126	—	2	8	no	—
469	#125	—	2	4	no	—
470	#125	—	2	8	no	—
471	#123	—	2	8	no	—
472	C₂²⋊Q₈	—	2	4	no	—
473	C₂²⋊Q₈	—	2	8	no	—
474	C₂²⋊Q₈	—	2	4	no	—
475	C₄×Q₈	—	2	4	no	—
476	C₄×Q₈	—	2	8	no	—
477	C₄×D₄	—	2	4	no	—
478	C₄×D₄	—	2	8	no	—
479	C₄×D₄	—	2	16	no	—
480	C₄×D₄	—	2	8	no	—
481	#117	—	2	8	no	—
482	#117	—	2	8	no	—
483	#117	D₄×C₁₃₉	1	8	yes	complemented
484	C₂×C₄⋊C₄	—	2	4	no	—
485	C₂×C₄⋊C₄	—	2	8	no	—
486	C₂×C₄⋊C₄	—	2	4	no	—
487	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
502	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
505	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
506	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
520	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
521	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
522	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
523	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
524	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
525	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
526	#95	C₂³×C₁₃₉	1	2	yes	—
527	#95	C₂³×C₁₃₉	1	1	yes	characteristic
528	#95	C₂³×C₁₃₉	1	4	yes	—
529	#95	C₂³×C₁₃₉	1	4	yes	—
530	#95	C₂³×C₁₃₉	1	1	yes	characteristic
531	#95	C₂³×C₁₃₉	1	2	yes	—
532	#95	C₂³×C₁₃₉	1	4	yes	—
533	#95	C₂³×C₁₃₉	1	2	yes	—
534	#95	C₂³×C₁₃₉	1	4	yes	—
535	#95	C₂³×C₁₃₉	1	4	yes	—
536	#95	C₂³×C₁₃₉	1	4	yes	—
537	#95	C₂³×C₁₃₉	1	4	yes	—
538	#95	C₂³×C₁₃₉	1	4	yes	—
539	#95	C₂³×C₁₃₉	1	4	yes	—
540	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
541	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
542	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
543	#41	—	2	32	no	—
544	C₂×Q₈	—	2	2	no	—
545	C₂×Q₈	—	2	2	no	—
546	C₂×Q₈	—	2	4	no	—
547	C₂×Q₈	—	2	4	no	—
548	C₂×D₄	—	2	4	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	4	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	4	no	—
557	C₂×D₄	—	4	1	no	—
558	C₂×D₄	—	4	2	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	8	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	4	4	no	—
570	C₂²×C₄	—	4	4	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
573	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
574	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
577	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
579	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	8	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	8	no	—
602	C₄⋊C₄	—	4	4	no	—
603	C₄⋊C₄	—	4	4	no	—
604	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
605	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	8	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	8	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	4	2	no	—
615	C₂²⋊C₄	—	4	2	no	—
616	C₂²⋊C₄	—	4	4	no	—
617	C₂²⋊C₄	—	4	2	no	—
618	C₂²⋊C₄	—	4	2	no	—
619	C₂²⋊C₄	—	4	4	no	—
620	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
621	C₄²	—	2	8	no	—
622	C₄²	—	2	4	no	—
623	C₄²	—	2	2	no	—
624	C₄²	—	2	4	no	—
625	C₄²	—	4	4	no	—
626	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	2	no	—
641	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
642	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
643	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
644	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
645	Q₈	—	2	8	no	—
646	Q₈	—	4	4	no	—
647	D₄	—	2	8	no	—
648	D₄	—	2	16	no	—
649	D₄	—	4	4	no	—
650	D₄	—	4	8	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	8	no	—
658	C₂×C₄	—	2	16	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	4	8	no	—
684	C₂×C₄	—	4	4	no	—
685	C₂×C₄	—	8	8	no	—
686	C₂×C₄	—	8	4	no	—
687	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
688	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
689	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
690	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
691	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
692	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	4	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	4	no	—
698	C₂²	—	2	4	no	—
699	C₂²	—	2	2	no	—
700	C₂²	—	2	4	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
711	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
712	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
713	C₂²	#585×C₁₃₉	1	1	yes	characteristic
714	C₂²	#585×C₁₃₉	1	2	yes	—
715	C₄	—	2	2	no	—
716	C₄	—	2	4	no	—
717	C₄	—	2	4	no	—
718	C₄	—	2	4	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	4	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	4	no	—
728	C₄	#525×C₁₃₉	1	4	yes	—
729	C₂	—	4	2	no	—
730	C₂	—	4	4	no	—
731	C₂	—	4	2	no	—
732	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
733	C₂	#3489×C₁₃₉	1	1	yes	characteristic
734	C₂	#3495×C₁₃₉	1	2	yes	—
735	C₂	#3500×C₁₃₉	1	1	yes	characteristic
736	C₂	#3512×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2388×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. C₂×#552×C₁₃₉	C₂	semidirect
2. C₂×#520×C₁₃₉	C₂	semidirect
3. #2634×C₁₃₉	C₂	semidirect
4. #2616×C₁₃₉	C₂	semidirect
5. #2598×C₁₃₉	C₂	semidirect
6. #2562×C₁₃₉	C₂	semidirect
7. #2503×C₁₃₉	C₂	semidirect
8. #2487×C₁₃₉	C₂	semidirect
9. #2468×C₁₃₉	C₂	semidirect
10. #2457×C₁₃₉	C₂	semidirect
11. #2442×C₁₃₉	C₂	semidirect
12. #2417×C₁₃₉	C₂	semidirect
13. #2396×C₁₃₉	C₂	semidirect
15. #2362×C₁₃₉	C₂	semidirect
16. #2352×C₁₃₉	C₂	semidirect
17. #2347×C₁₃₉	C₂	semidirect
114. #117×C₁₃₉	D₄	semidirect
368. #36080	C₁₃₉	direct (N × H)
369. C₁₃₉	#36080	direct (N × H)
370. C₂×#552	C₂×C₁₃₉	semidirect
371. C₂×#520	C₂×C₁₃₉	semidirect
372. #2634	C₂×C₁₃₉	semidirect
373. #2616	C₂×C₁₃₉	semidirect
374. #2598	C₂×C₁₃₉	semidirect
375. #2562	C₂×C₁₃₉	semidirect
376. #2503	C₂×C₁₃₉	semidirect
377. #2487	C₂×C₁₃₉	semidirect
378. #2468	C₂×C₁₃₉	semidirect
379. #2457	C₂×C₁₃₉	semidirect
380. #2442	C₂×C₁₃₉	semidirect
381. #2417	C₂×C₁₃₉	semidirect
382. #2396	C₂×C₁₃₉	semidirect
384. #2362	C₂×C₁₃₉	semidirect
385. #2352	C₂×C₁₃₉	semidirect
386. #2347	C₂×C₁₃₉	semidirect
483. #117	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#552×C₁₃₉	2
C₂×#520×C₁₃₉	2
#2634×C₁₃₉	2
#2616×C₁₃₉	2
#2598×C₁₃₉	2
#2562×C₁₃₉	2
#2503×C₁₃₉	2
#2487×C₁₃₉	2
#2468×C₁₃₉	2
#2457×C₁₃₉	2
#2442×C₁₃₉	2
#2417×C₁₃₉	2
#2396×C₁₃₉	2
#2388×C₁₃₉	2
#2362×C₁₃₉	2
#2352×C₁₃₉	2
#2347×C₁₃₉	2
#36080	139

Subgroups — C139×#36080 #48030676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36080 #48030676