Subgroups — C₁₃₉×#37273 #48031869

Order 35584.

2802 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#532×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2854×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2733×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2731×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2684×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2678×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2673×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2669×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2615×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2485×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2416×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2414×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2408×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2311×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
18	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	#535×C₁₃₉	—	2	8	no	—
20	#532×C₁₃₉	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
28	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
34	C₂×#121×C₁₃₉	C₂²	1	4	yes	complemented
35	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
36	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
37	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
40	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
44	#397×C₁₃₉	C₂²	1	4	yes	—
45	#396×C₁₃₉	C₂²	1	4	yes	complemented
46	#394×C₁₃₉	C₂²	1	4	yes	—
47	#394×C₁₃₉	C₂²	1	4	yes	—
48	#394×C₁₃₉	C₂²	1	4	yes	complemented
49	#394×C₁₃₉	C₂²	1	4	yes	complemented
50	#393×C₁₃₉	C₂²	1	4	yes	complemented
51	#392×C₁₃₉	C₂²	1	4	yes	—
52	#392×C₁₃₉	C₂²	1	4	yes	complemented
53	#392×C₁₃₉	C₂²	1	4	yes	complemented
54	#392×C₁₃₉	C₂²	1	4	yes	complemented
55	#392×C₁₃₉	C₂²	1	4	yes	complemented
56	#391×C₁₃₉	C₂²	1	2	yes	complemented
57	#390×C₁₃₉	C₂²	1	2	yes	—
58	#390×C₁₃₉	C₂²	1	2	yes	—
59	#390×C₁₃₉	C₂²	1	2	yes	—
60	#390×C₁₃₉	C₂²	1	4	yes	complemented
61	#389×C₁₃₉	C₂²	1	2	yes	complemented
62	#389×C₁₃₉	C₂²	1	2	yes	complemented
63	#388×C₁₃₉	C₂²	1	4	yes	complemented
64	#388×C₁₃₉	C₂²	1	4	yes	complemented
65	#388×C₁₃₉	C₂²	1	4	yes	complemented
66	#388×C₁₃₉	C₂²	1	4	yes	complemented
67	#387×C₁₃₉	C₂²	1	4	yes	complemented
68	#386×C₁₃₉	C₂²	1	2	yes	—
69	#386×C₁₃₉	C₂²	1	2	yes	complemented
70	#386×C₁₃₉	C₂²	1	4	yes	complemented
71	#386×C₁₃₉	C₂²	1	4	yes	complemented
72	#380×C₁₃₉	C₂²	1	2	yes	—
73	#380×C₁₃₉	C₂²	1	2	yes	complemented
74	#380×C₁₃₉	C₂²	1	2	yes	complemented
75	#380×C₁₃₉	C₂²	1	2	yes	complemented
76	#379×C₁₃₉	C₂²	1	4	yes	—
77	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
78	C₂×#41×C₁₃₉	—	2	4	no	—
79	C₂×#41×C₁₃₉	—	4	2	no	—
80	C₂×#41×C₁₃₉	—	4	2	no	—
81	C₂×#41×C₁₃₉	—	4	2	no	—
82	C₂×#41×C₁₃₉	—	4	2	no	—
83	C₂×#41×C₁₃₉	D₄	1	8	yes	complemented
84	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₃₉	—	2	4	no	—
87	C₂²×D₄×C₁₃₉	—	4	2	no	—
88	C₂²×D₄×C₁₃₉	—	4	2	no	—
89	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
94	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
99	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
109	#127×C₁₃₉	—	2	4	no	—
110	#127×C₁₃₉	—	2	8	no	—
111	#124×C₁₃₉	—	2	8	no	—
112	#124×C₁₃₉	—	2	4	no	—
113	#124×C₁₃₉	—	2	4	no	—
114	#123×C₁₃₉	—	4	8	no	—
115	#121×C₁₃₉	—	2	8	no	—
116	#121×C₁₃₉	—	2	8	no	—
117	#121×C₁₃₉	—	2	8	no	—
118	#121×C₁₃₉	—	2	8	no	—
119	#121×C₁₃₉	—	4	8	no	—
120	#121×C₁₃₉	—	4	4	no	—
121	#121×C₁₃₉	—	4	4	no	—
122	#120×C₁₃₉	—	2	8	no	—
123	#120×C₁₃₉	—	2	8	no	—
124	#120×C₁₃₉	—	4	8	no	—
125	C₄×D₄×C₁₃₉	—	2	8	no	—
126	C₄×D₄×C₁₃₉	—	2	8	no	—
127	#117×C₁₃₉	—	2	4	no	—
128	#117×C₁₃₉	—	4	2	no	—
129	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	4	yes	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₄²×C₁₃₉	—	2	4	no	—
157	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
162	#95×C₁₃₉	C₂³	1	4	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	4	yes	—
168	C₂⁴×C₁₃₉	—	2	4	no	—
169	C₂⁴×C₁₃₉	—	4	2	no	—
170	C₂⁴×C₁₃₉	—	4	2	no	—
171	C₂⁴×C₁₃₉	—	4	4	no	—
172	C₂⁴×C₁₃₉	—	4	4	no	—
173	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
174	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
175	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
176	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
177	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
178	#41×C₁₃₉	—	4	16	no	—
179	#41×C₁₃₉	—	4	16	no	—
180	C₂×Q₈×C₁₃₉	—	2	2	no	—
181	C₂×Q₈×C₁₃₉	—	4	1	no	—
182	C₂×Q₈×C₁₃₉	—	4	1	no	—
183	C₂×Q₈×C₁₃₉	—	4	1	no	—
184	C₂×Q₈×C₁₃₉	—	4	1	no	—
185	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
186	C₂×D₄×C₁₃₉	—	2	4	no	—
187	C₂×D₄×C₁₃₉	—	2	4	no	—
188	C₂×D₄×C₁₃₉	—	2	4	no	—
189	C₂×D₄×C₁₃₉	—	2	8	no	—
190	C₂×D₄×C₁₃₉	—	2	8	no	—
191	C₂×D₄×C₁₃₉	—	2	4	no	—
192	C₂×D₄×C₁₃₉	—	2	4	no	—
193	C₂×D₄×C₁₃₉	—	2	2	no	—
194	C₂×D₄×C₁₃₉	—	2	4	no	—
195	C₂×D₄×C₁₃₉	—	2	4	no	—
196	C₂×D₄×C₁₃₉	—	2	4	no	—
197	C₂×D₄×C₁₃₉	—	2	4	no	—
198	C₂×D₄×C₁₃₉	—	4	2	no	—
199	C₂×D₄×C₁₃₉	—	4	2	no	—
200	C₂×D₄×C₁₃₉	—	4	2	no	—
201	C₂×D₄×C₁₃₉	—	4	2	no	—
202	C₂×D₄×C₁₃₉	—	4	1	no	—
203	C₂×D₄×C₁₃₉	—	4	1	no	—
204	C₂×D₄×C₁₃₉	—	4	1	no	—
205	C₂×D₄×C₁₃₉	—	4	1	no	—
206	C₂×D₄×C₁₃₉	—	4	1	no	—
207	C₂×D₄×C₁₃₉	—	4	1	no	—
208	C₂×D₄×C₁₃₉	—	4	1	no	—
209	C₂×D₄×C₁₃₉	—	4	1	no	—
210	C₂×D₄×C₁₃₉	—	4	2	no	—
211	C₂×D₄×C₁₃₉	—	4	2	no	—
212	C₂×D₄×C₁₃₉	—	4	16	no	—
213	C₂×D₄×C₁₃₉	—	4	4	no	—
214	C₂×D₄×C₁₃₉	—	4	4	no	—
215	C₂×D₄×C₁₃₉	—	4	4	no	—
216	C₂×D₄×C₁₃₉	—	4	4	no	—
217	C₂×D₄×C₁₃₉	—	4	4	no	—
218	C₂×D₄×C₁₃₉	—	4	4	no	—
219	C₂×D₄×C₁₃₉	—	4	4	no	—
220	C₂×D₄×C₁₃₉	—	4	4	no	—
221	C₂×D₄×C₁₃₉	—	4	4	no	—
222	C₂×D₄×C₁₃₉	—	4	4	no	—
223	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
224	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
225	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
226	C₂²×C₄×C₁₃₉	—	2	2	no	—
227	C₂²×C₄×C₁₃₉	—	2	2	no	—
228	C₂²×C₄×C₁₃₉	—	2	2	no	—
229	C₂²×C₄×C₁₃₉	—	2	2	no	—
230	C₂²×C₄×C₁₃₉	—	2	2	no	—
231	C₂²×C₄×C₁₃₉	—	2	2	no	—
232	C₂²×C₄×C₁₃₉	—	2	4	no	—
233	C₂²×C₄×C₁₃₉	—	2	4	no	—
234	C₂²×C₄×C₁₃₉	—	2	4	no	—
235	C₂²×C₄×C₁₃₉	—	2	4	no	—
236	C₂²×C₄×C₁₃₉	—	2	4	no	—
237	C₂²×C₄×C₁₃₉	—	4	2	no	—
238	C₂²×C₄×C₁₃₉	—	4	2	no	—
239	C₂²×C₄×C₁₃₉	—	4	4	no	—
240	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
241	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
242	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
243	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
244	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
245	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
246	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
253	C₄⋊C₄×C₁₃₉	—	2	4	no	—
254	C₄⋊C₄×C₁₃₉	—	2	4	no	—
255	C₄⋊C₄×C₁₃₉	—	2	4	no	—
256	C₄⋊C₄×C₁₃₉	—	2	4	no	—
257	C₄⋊C₄×C₁₃₉	—	2	4	no	—
258	C₄⋊C₄×C₁₃₉	—	2	8	no	—
259	C₄⋊C₄×C₁₃₉	—	4	2	no	—
260	C₄⋊C₄×C₁₃₉	—	4	4	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
265	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
266	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
267	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
270	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
271	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
272	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
273	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
274	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
275	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
276	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
277	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
278	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
279	C₄²×C₁₃₉	—	2	4	no	—
280	C₄²×C₁₃₉	—	2	2	no	—
281	C₄²×C₁₃₉	—	2	2	no	—
282	C₄²×C₁₃₉	—	2	4	no	—
283	C₄²×C₁₃₉	—	4	2	no	—
284	C₂³×C₁₃₉	—	2	1	no	—
285	C₂³×C₁₃₉	—	2	2	no	—
286	C₂³×C₁₃₉	—	2	2	no	—
287	C₂³×C₁₃₉	—	2	1	no	—
288	C₂³×C₁₃₉	—	2	1	no	—
289	C₂³×C₁₃₉	—	2	1	no	—
290	C₂³×C₁₃₉	—	2	1	no	—
291	C₂³×C₁₃₉	—	2	1	no	—
292	C₂³×C₁₃₉	—	2	2	no	—
293	C₂³×C₁₃₉	—	2	2	no	—
294	C₂³×C₁₃₉	—	2	2	no	—
295	C₂³×C₁₃₉	—	2	2	no	—
296	C₂³×C₁₃₉	—	2	2	no	—
297	C₂³×C₁₃₉	—	2	4	no	—
298	C₂³×C₁₃₉	—	2	4	no	—
299	C₂³×C₁₃₉	—	2	4	no	—
300	C₂³×C₁₃₉	—	2	2	no	—
301	C₂³×C₁₃₉	—	2	4	no	—
302	C₂³×C₁₃₉	—	2	4	no	—
303	C₂³×C₁₃₉	—	2	2	no	—
304	C₂³×C₁₃₉	—	2	2	no	—
305	C₂³×C₁₃₉	—	2	2	no	—
306	C₂³×C₁₃₉	—	2	2	no	—
307	C₂³×C₁₃₉	—	2	4	no	—
308	C₂³×C₁₃₉	—	2	2	no	—
309	C₂³×C₁₃₉	—	2	4	no	—
310	C₂³×C₁₃₉	—	4	8	no	—
311	C₂³×C₁₃₉	—	8	8	no	—
312	C₂³×C₁₃₉	—	8	8	no	—
313	C₂³×C₁₃₉	—	8	4	no	—
314	C₂³×C₁₃₉	—	8	4	no	—
315	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
316	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
317	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
318	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
319	Q₈×C₁₃₉	—	4	4	no	—
320	Q₈×C₁₃₉	—	4	4	no	—
321	D₄×C₁₃₉	—	4	4	no	—
322	D₄×C₁₃₉	—	4	4	no	—
323	D₄×C₁₃₉	—	4	4	no	—
324	D₄×C₁₃₉	—	4	8	no	—
325	D₄×C₁₃₉	—	4	8	no	—
326	D₄×C₁₃₉	—	4	8	no	—
327	D₄×C₁₃₉	—	4	4	no	—
328	D₄×C₁₃₉	—	4	8	no	—
329	D₄×C₁₃₉	—	4	8	no	—
330	D₄×C₁₃₉	—	8	8	no	—
331	D₄×C₁₃₉	—	8	8	no	—
332	D₄×C₁₃₉	—	8	8	no	—
333	D₄×C₁₃₉	—	8	8	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	1	no	—
336	C₂×C₄×C₁₃₉	—	2	1	no	—
337	C₂×C₄×C₁₃₉	—	2	1	no	—
338	C₂×C₄×C₁₃₉	—	2	1	no	—
339	C₂×C₄×C₁₃₉	—	2	1	no	—
340	C₂×C₄×C₁₃₉	—	2	1	no	—
341	C₂×C₄×C₁₃₉	—	2	2	no	—
342	C₂×C₄×C₁₃₉	—	2	8	no	—
343	C₂×C₄×C₁₃₉	—	2	8	no	—
344	C₂×C₄×C₁₃₉	—	2	8	no	—
345	C₂×C₄×C₁₃₉	—	2	2	no	—
346	C₂×C₄×C₁₃₉	—	2	4	no	—
347	C₂×C₄×C₁₃₉	—	2	2	no	—
348	C₂×C₄×C₁₃₉	—	2	4	no	—
349	C₂×C₄×C₁₃₉	—	2	4	no	—
350	C₂×C₄×C₁₃₉	—	2	4	no	—
351	C₂×C₄×C₁₃₉	—	2	4	no	—
352	C₂×C₄×C₁₃₉	—	2	2	no	—
353	C₂×C₄×C₁₃₉	—	2	2	no	—
354	C₂×C₄×C₁₃₉	—	2	2	no	—
355	C₂×C₄×C₁₃₉	—	2	4	no	—
356	C₂×C₄×C₁₃₉	—	2	4	no	—
357	C₂×C₄×C₁₃₉	—	2	2	no	—
358	C₂×C₄×C₁₃₉	—	2	4	no	—
359	C₂×C₄×C₁₃₉	—	2	4	no	—
360	C₂×C₄×C₁₃₉	—	4	8	no	—
361	C₂×C₄×C₁₃₉	—	4	8	no	—
362	C₂×C₄×C₁₃₉	—	8	4	no	—
363	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
364	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
365	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
366	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
367	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
368	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
369	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
370	C₂²×C₁₃₉	—	2	2	no	—
371	C₂²×C₁₃₉	—	2	2	no	—
372	C₂²×C₁₃₉	—	2	2	no	—
373	C₂²×C₁₃₉	—	2	4	no	—
374	C₂²×C₁₃₉	—	2	4	no	—
375	C₂²×C₁₃₉	—	2	4	no	—
376	C₂²×C₁₃₉	—	4	2	no	—
377	C₂²×C₁₃₉	—	4	2	no	—
378	C₂²×C₁₃₉	—	4	2	no	—
379	C₂²×C₁₃₉	—	4	1	no	—
380	C₂²×C₁₃₉	—	4	1	no	—
381	C₂²×C₁₃₉	—	4	1	no	—
382	C₂²×C₁₃₉	—	4	1	no	—
383	C₂²×C₁₃₉	—	4	1	no	—
384	C₂²×C₁₃₉	—	4	1	no	—
385	C₂²×C₁₃₉	—	4	2	no	—
386	C₂²×C₁₃₉	—	4	4	no	—
387	C₂²×C₁₃₉	—	4	2	no	—
388	C₂²×C₁₃₉	—	4	2	no	—
389	C₂²×C₁₃₉	—	4	4	no	—
390	C₂²×C₁₃₉	—	4	4	no	—
391	C₂²×C₁₃₉	—	4	2	no	—
392	C₂²×C₁₃₉	—	4	4	no	—
393	C₂²×C₁₃₉	—	4	2	no	—
394	C₂²×C₁₃₉	—	4	4	no	—
395	C₂²×C₁₃₉	—	4	2	no	—
396	C₂²×C₁₃₉	—	4	4	no	—
397	C₂²×C₁₃₉	—	4	2	no	—
398	C₂²×C₁₃₉	—	4	4	no	—
399	C₂²×C₁₃₉	—	8	16	no	—
400	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
401	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
402	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
404	C₂²×C₁₃₉	#585	1	2	yes	—
405	C₄×C₁₃₉	—	2	2	no	—
406	C₄×C₁₃₉	—	2	2	no	—
407	C₄×C₁₃₉	—	2	2	no	—
408	C₄×C₁₃₉	—	2	4	no	—
409	C₄×C₁₃₉	—	4	2	no	—
410	C₄×C₁₃₉	—	4	2	no	—
411	C₄×C₁₃₉	—	4	4	no	—
412	C₄×C₁₃₉	—	4	4	no	—
413	C₄×C₁₃₉	—	4	4	no	—
414	C₄×C₁₃₉	#534	1	4	yes	—
415	C₂×C₁₃₉	—	4	2	no	—
416	C₂×C₁₃₉	—	4	2	no	—
417	C₂×C₁₃₉	—	4	2	no	—
418	C₂×C₁₃₉	—	8	2	no	—
419	C₂×C₁₃₉	—	8	4	no	—
420	C₂×C₁₃₉	C₂×#534	1	1	yes	characteristic
421	C₂×C₁₃₉	#3488	1	2	yes	—
422	C₂×C₁₃₉	#3546	1	2	yes	—
423	C₂×C₁₃₉	#3549	1	1	yes	characteristic
424	C₂×C₁₃₉	#3551	1	1	yes	characteristic
425	#37273	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
426	C₁₃₉	#37273	1	1	yes	characteristic, direct product factor, Sylow
427	C₂×#535	C₂×C₁₃₉	1	1	yes	characteristic, complemented
428	C₂×#532	C₂×C₁₃₉	1	1	yes	characteristic, complemented
429	#2854	C₂×C₁₃₉	1	2	yes	complemented
430	#2733	C₂×C₁₃₉	1	2	yes	complemented
431	#2731	C₂×C₁₃₉	1	2	yes	complemented
432	#2684	C₂×C₁₃₉	1	2	yes	complemented
433	#2678	C₂×C₁₃₉	1	4	yes	complemented
434	#2673	C₂×C₁₃₉	1	4	yes	complemented
435	#2669	C₂×C₁₃₉	1	2	yes	complemented
436	#2615	C₂×C₁₃₉	1	2	yes	complemented
437	#2485	C₂×C₁₃₉	1	2	yes	complemented
438	#2416	C₂×C₁₃₉	1	2	yes	complemented
439	#2414	C₂×C₁₃₉	1	2	yes	complemented
440	#2408	C₂×C₁₃₉	1	2	yes	complemented
441	#2311	C₂×C₁₃₉	1	1	yes	characteristic, complemented
442	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
443	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
444	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
445	#535	—	2	8	no	—
446	#532	—	2	8	no	—
447	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
448	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
449	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
450	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
451	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
452	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
453	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
454	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
455	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
456	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
457	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
458	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
459	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
460	C₂×#121	C₂²×C₁₃₉	1	4	yes	complemented
461	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
462	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
463	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
464	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
465	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
466	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
467	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
468	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
469	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
470	#397	C₂²×C₁₃₉	1	4	yes	—
471	#396	C₂²×C₁₃₉	1	4	yes	complemented
472	#394	C₂²×C₁₃₉	1	4	yes	—
473	#394	C₂²×C₁₃₉	1	4	yes	—
474	#394	C₂²×C₁₃₉	1	4	yes	complemented
475	#394	C₂²×C₁₃₉	1	4	yes	complemented
476	#393	C₂²×C₁₃₉	1	4	yes	complemented
477	#392	C₂²×C₁₃₉	1	4	yes	—
478	#392	C₂²×C₁₃₉	1	4	yes	complemented
479	#392	C₂²×C₁₃₉	1	4	yes	complemented
480	#392	C₂²×C₁₃₉	1	4	yes	complemented
481	#392	C₂²×C₁₃₉	1	4	yes	complemented
482	#391	C₂²×C₁₃₉	1	2	yes	complemented
483	#390	C₂²×C₁₃₉	1	2	yes	—
484	#390	C₂²×C₁₃₉	1	2	yes	—
485	#390	C₂²×C₁₃₉	1	2	yes	—
486	#390	C₂²×C₁₃₉	1	4	yes	complemented
487	#389	C₂²×C₁₃₉	1	2	yes	complemented
488	#389	C₂²×C₁₃₉	1	2	yes	complemented
489	#388	C₂²×C₁₃₉	1	4	yes	complemented
490	#388	C₂²×C₁₃₉	1	4	yes	complemented
491	#388	C₂²×C₁₃₉	1	4	yes	complemented
492	#388	C₂²×C₁₃₉	1	4	yes	complemented
493	#387	C₂²×C₁₃₉	1	4	yes	complemented
494	#386	C₂²×C₁₃₉	1	2	yes	—
495	#386	C₂²×C₁₃₉	1	2	yes	complemented
496	#386	C₂²×C₁₃₉	1	4	yes	complemented
497	#386	C₂²×C₁₃₉	1	4	yes	complemented
498	#380	C₂²×C₁₃₉	1	2	yes	—
499	#380	C₂²×C₁₃₉	1	2	yes	complemented
500	#380	C₂²×C₁₃₉	1	2	yes	complemented
501	#380	C₂²×C₁₃₉	1	2	yes	complemented
502	#379	C₂²×C₁₃₉	1	4	yes	—
503	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
504	C₂×#41	—	2	4	no	—
505	C₂×#41	—	4	2	no	—
506	C₂×#41	—	4	2	no	—
507	C₂×#41	—	4	2	no	—
508	C₂×#41	—	4	2	no	—
509	C₂×#41	D₄×C₁₃₉	1	8	yes	complemented
510	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
511	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
512	C₂²×D₄	—	2	4	no	—
513	C₂²×D₄	—	4	2	no	—
514	C₂²×D₄	—	4	2	no	—
515	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
516	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
519	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
520	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
521	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
522	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
523	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
524	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
525	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
526	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
527	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
528	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
532	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
533	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₄⋊Q₈	—	2	4	no	—
535	#127	—	2	4	no	—
536	#127	—	2	8	no	—
537	#124	—	2	8	no	—
538	#124	—	2	4	no	—
539	#124	—	2	4	no	—
540	#123	—	4	8	no	—
541	#121	—	2	8	no	—
542	#121	—	2	8	no	—
543	#121	—	2	8	no	—
544	#121	—	2	8	no	—
545	#121	—	4	8	no	—
546	#121	—	4	4	no	—
547	#121	—	4	4	no	—
548	#120	—	2	8	no	—
549	#120	—	2	8	no	—
550	#120	—	4	8	no	—
551	C₄×D₄	—	2	8	no	—
552	C₄×D₄	—	2	8	no	—
553	#117	—	2	4	no	—
554	#117	—	4	2	no	—
555	C₂×C₄⋊C₄	—	4	2	no	—
556	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
582	C₂×C₄²	—	2	4	no	—
583	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
584	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
585	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
586	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
587	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
588	#95	C₂³×C₁₃₉	1	4	yes	—
589	#95	C₂³×C₁₃₉	1	4	yes	—
590	#95	C₂³×C₁₃₉	1	4	yes	—
591	#95	C₂³×C₁₃₉	1	4	yes	—
592	#95	C₂³×C₁₃₉	1	4	yes	—
593	#95	C₂³×C₁₃₉	1	4	yes	—
594	C₂⁴	—	2	4	no	—
595	C₂⁴	—	4	2	no	—
596	C₂⁴	—	4	2	no	—
597	C₂⁴	—	4	4	no	—
598	C₂⁴	—	4	4	no	—
599	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
600	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
601	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
602	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
603	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
604	#41	—	4	16	no	—
605	#41	—	4	16	no	—
606	C₂×Q₈	—	2	2	no	—
607	C₂×Q₈	—	4	1	no	—
608	C₂×Q₈	—	4	1	no	—
609	C₂×Q₈	—	4	1	no	—
610	C₂×Q₈	—	4	1	no	—
611	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	8	no	—
616	C₂×D₄	—	2	8	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	4	2	no	—
625	C₂×D₄	—	4	2	no	—
626	C₂×D₄	—	4	2	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂×D₄	—	4	1	no	—
629	C₂×D₄	—	4	1	no	—
630	C₂×D₄	—	4	1	no	—
631	C₂×D₄	—	4	1	no	—
632	C₂×D₄	—	4	1	no	—
633	C₂×D₄	—	4	1	no	—
634	C₂×D₄	—	4	1	no	—
635	C₂×D₄	—	4	1	no	—
636	C₂×D₄	—	4	2	no	—
637	C₂×D₄	—	4	2	no	—
638	C₂×D₄	—	4	16	no	—
639	C₂×D₄	—	4	4	no	—
640	C₂×D₄	—	4	4	no	—
641	C₂×D₄	—	4	4	no	—
642	C₂×D₄	—	4	4	no	—
643	C₂×D₄	—	4	4	no	—
644	C₂×D₄	—	4	4	no	—
645	C₂×D₄	—	4	4	no	—
646	C₂×D₄	—	4	4	no	—
647	C₂×D₄	—	4	4	no	—
648	C₂×D₄	—	4	4	no	—
649	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
650	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
651	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	—	4	4	no	—
666	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
667	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
668	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
669	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
670	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
671	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
672	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	8	no	—
685	C₄⋊C₄	—	4	2	no	—
686	C₄⋊C₄	—	4	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	8	no	—
693	C₂²⋊C₄	—	2	8	no	—
694	C₂²⋊C₄	—	2	8	no	—
695	C₂²⋊C₄	—	2	8	no	—
696	C₂²⋊C₄	—	4	4	no	—
697	C₂²⋊C₄	—	4	4	no	—
698	C₂²⋊C₄	—	4	2	no	—
699	C₂²⋊C₄	—	4	4	no	—
700	C₂²⋊C₄	—	4	4	no	—
701	C₂²⋊C₄	—	4	4	no	—
702	C₂²⋊C₄	—	4	4	no	—
703	C₂²⋊C₄	—	4	4	no	—
704	C₂²⋊C₄	—	4	4	no	—
705	C₄²	—	2	4	no	—
706	C₄²	—	2	2	no	—
707	C₄²	—	2	2	no	—
708	C₄²	—	2	4	no	—
709	C₄²	—	4	2	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	4	no	—
724	C₂³	—	2	4	no	—
725	C₂³	—	2	4	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	4	no	—
728	C₂³	—	2	4	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	4	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	4	no	—
736	C₂³	—	4	8	no	—
737	C₂³	—	8	8	no	—
738	C₂³	—	8	8	no	—
739	C₂³	—	8	4	no	—
740	C₂³	—	8	4	no	—
741	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
742	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
743	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
744	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
745	Q₈	—	4	4	no	—
746	Q₈	—	4	4	no	—
747	D₄	—	4	4	no	—
748	D₄	—	4	4	no	—
749	D₄	—	4	4	no	—
750	D₄	—	4	8	no	—
751	D₄	—	4	8	no	—
752	D₄	—	4	8	no	—
753	D₄	—	4	4	no	—
754	D₄	—	4	8	no	—
755	D₄	—	4	8	no	—
756	D₄	—	8	8	no	—
757	D₄	—	8	8	no	—
758	D₄	—	8	8	no	—
759	D₄	—	8	8	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	8	no	—
769	C₂×C₄	—	2	8	no	—
770	C₂×C₄	—	2	8	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	4	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	2	4	no	—
786	C₂×C₄	—	4	8	no	—
787	C₂×C₄	—	4	8	no	—
788	C₂×C₄	—	8	4	no	—
789	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
790	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
791	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
792	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
793	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
794	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
795	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	4	no	—
800	C₂²	—	2	4	no	—
801	C₂²	—	2	4	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	4	no	—
813	C₂²	—	4	4	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	4	no	—
817	C₂²	—	4	4	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	4	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	4	no	—
824	C₂²	—	4	4	no	—
825	C₂²	—	8	16	no	—
826	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
827	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
828	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
829	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
830	C₂²	#585×C₁₃₉	1	2	yes	—
831	C₄	—	2	2	no	—
832	C₄	—	2	2	no	—
833	C₄	—	2	2	no	—
834	C₄	—	2	4	no	—
835	C₄	—	4	4	no	—
836	C₄	—	4	4	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	4	no	—
840	C₄	#534×C₁₃₉	1	4	yes	—
841	C₂	—	4	2	no	—
842	C₂	—	4	2	no	—
843	C₂	—	4	2	no	—
844	C₂	—	8	4	no	—
845	C₂	—	8	2	no	—
846	C₂	C₂×#534×C₁₃₉	1	1	yes	characteristic
847	C₂	#3488×C₁₃₉	1	2	yes	—
848	C₂	#3546×C₁₃₉	1	2	yes	—
849	C₂	#3549×C₁₃₉	1	1	yes	characteristic
850	C₂	#3551×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
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×#535×C₁₃₉	C₂	semidirect
2. C₂×#532×C₁₃₉	C₂	semidirect
3. #2854×C₁₃₉	C₂	semidirect
4. #2733×C₁₃₉	C₂	semidirect
5. #2731×C₁₃₉	C₂	semidirect
6. #2684×C₁₃₉	C₂	semidirect
7. #2678×C₁₃₉	C₂	semidirect
8. #2673×C₁₃₉	C₂	semidirect
9. #2669×C₁₃₉	C₂	semidirect
10. #2615×C₁₃₉	C₂	semidirect
11. #2485×C₁₃₉	C₂	semidirect
12. #2416×C₁₃₉	C₂	semidirect
13. #2414×C₁₃₉	C₂	semidirect
14. #2408×C₁₃₉	C₂	semidirect
15. #2311×C₁₃₉	C₂	semidirect
17. C₂²×#41×C₁₃₉	C₂²	semidirect
21. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
26. C₂×#124×C₁₃₉	C₂²	semidirect
27. C₂×#123×C₁₃₉	C₂²	semidirect
33. C₂×#121×C₁₃₉	C₂²	semidirect
34. C₂×#121×C₁₃₉	C₂²	semidirect
39. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
41. C₂×#117×C₁₃₉	C₂²	semidirect
42. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
43. C₂²×C₄²×C₁₃₉	C₂²	semidirect
45. #396×C₁₃₉	C₂²	semidirect
48. #394×C₁₃₉	C₂²	semidirect
49. #394×C₁₃₉	C₂²	semidirect
50. #393×C₁₃₉	C₂²	semidirect
52. #392×C₁₃₉	C₂²	semidirect
53. #392×C₁₃₉	C₂²	semidirect
54. #392×C₁₃₉	C₂²	semidirect
55. #392×C₁₃₉	C₂²	semidirect
56. #391×C₁₃₉	C₂²	semidirect
60. #390×C₁₃₉	C₂²	semidirect
61. #389×C₁₃₉	C₂²	semidirect
62. #389×C₁₃₉	C₂²	semidirect
63. #388×C₁₃₉	C₂²	semidirect
64. #388×C₁₃₉	C₂²	semidirect
65. #388×C₁₃₉	C₂²	semidirect
66. #388×C₁₃₉	C₂²	semidirect
67. #387×C₁₃₉	C₂²	semidirect
69. #386×C₁₃₉	C₂²	semidirect
70. #386×C₁₃₉	C₂²	semidirect
71. #386×C₁₃₉	C₂²	semidirect
73. #380×C₁₃₉	C₂²	semidirect
74. #380×C₁₃₉	C₂²	semidirect
75. #380×C₁₃₉	C₂²	semidirect
83. C₂×#41×C₁₃₉	D₄	semidirect
425. #37273	C₁₃₉	direct (N × H)
426. C₁₃₉	#37273	direct (N × H)
427. C₂×#535	C₂×C₁₃₉	semidirect
428. C₂×#532	C₂×C₁₃₉	semidirect
429. #2854	C₂×C₁₃₉	semidirect
430. #2733	C₂×C₁₃₉	semidirect
431. #2731	C₂×C₁₃₉	semidirect
432. #2684	C₂×C₁₃₉	semidirect
433. #2678	C₂×C₁₃₉	semidirect
434. #2673	C₂×C₁₃₉	semidirect
435. #2669	C₂×C₁₃₉	semidirect
436. #2615	C₂×C₁₃₉	semidirect
437. #2485	C₂×C₁₃₉	semidirect
438. #2416	C₂×C₁₃₉	semidirect
439. #2414	C₂×C₁₃₉	semidirect
440. #2408	C₂×C₁₃₉	semidirect
441. #2311	C₂×C₁₃₉	semidirect
443. C₂²×#41	C₂²×C₁₃₉	semidirect
447. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
452. C₂×#124	C₂²×C₁₃₉	semidirect
453. C₂×#123	C₂²×C₁₃₉	semidirect
459. C₂×#121	C₂²×C₁₃₉	semidirect
460. C₂×#121	C₂²×C₁₃₉	semidirect
465. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
467. C₂×#117	C₂²×C₁₃₉	semidirect
468. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
469. C₂²×C₄²	C₂²×C₁₃₉	semidirect
471. #396	C₂²×C₁₃₉	semidirect
474. #394	C₂²×C₁₃₉	semidirect
475. #394	C₂²×C₁₃₉	semidirect
476. #393	C₂²×C₁₃₉	semidirect
478. #392	C₂²×C₁₃₉	semidirect
479. #392	C₂²×C₁₃₉	semidirect
480. #392	C₂²×C₁₃₉	semidirect
481. #392	C₂²×C₁₃₉	semidirect
482. #391	C₂²×C₁₃₉	semidirect
486. #390	C₂²×C₁₃₉	semidirect
487. #389	C₂²×C₁₃₉	semidirect
488. #389	C₂²×C₁₃₉	semidirect
489. #388	C₂²×C₁₃₉	semidirect
490. #388	C₂²×C₁₃₉	semidirect
491. #388	C₂²×C₁₃₉	semidirect
492. #388	C₂²×C₁₃₉	semidirect
493. #387	C₂²×C₁₃₉	semidirect
495. #386	C₂²×C₁₃₉	semidirect
496. #386	C₂²×C₁₃₉	semidirect
497. #386	C₂²×C₁₃₉	semidirect
499. #380	C₂²×C₁₃₉	semidirect
500. #380	C₂²×C₁₃₉	semidirect
501. #380	C₂²×C₁₃₉	semidirect
509. C₂×#41	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×#535×C₁₃₉	2
C₂×#532×C₁₃₉	2
#2854×C₁₃₉	2
#2733×C₁₃₉	2
#2731×C₁₃₉	2
#2684×C₁₃₉	2
#2678×C₁₃₉	2
#2673×C₁₃₉	2
#2669×C₁₃₉	2
#2615×C₁₃₉	2
#2485×C₁₃₉	2
#2416×C₁₃₉	2
#2414×C₁₃₉	2
#2408×C₁₃₉	2
#2311×C₁₃₉	2
#37273	139

Subgroups — C139×#37273 #48031869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37273 #48031869