Subgroups — C₁₃₉×#36210 #48030806

Order 35584.

1802 conjugacy classes of subgroups.

The subgroup lattice has 768 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	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2562×C₁₃₉	C₂	1	2	yes	maximal
5	#2514×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2509×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2495×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2494×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2494×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2485×C₁₃₉	C₂	1	2	yes	maximal
11	#2421×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2415×C₁₃₉	C₂	1	2	yes	maximal
13	#2370×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2362×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2347×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2285×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2285×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
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	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
30	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
32	#401×C₁₃₉	C₂²	1	4	yes	—
33	#400×C₁₃₉	C₂²	1	4	yes	—
34	#400×C₁₃₉	C₂²	1	4	yes	—
35	#397×C₁₃₉	C₂²	1	4	yes	—
36	#397×C₁₃₉	C₂²	1	4	yes	—
37	#394×C₁₃₉	C₂²	1	4	yes	—
38	#391×C₁₃₉	C₂²	1	2	yes	—
39	#391×C₁₃₉	C₂²	1	2	yes	—
40	#391×C₁₃₉	C₂²	1	2	yes	—
41	#389×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	#389×C₁₃₉	C₂²	1	2	yes	—
48	#389×C₁₃₉	C₂²	1	2	yes	—
49	#389×C₁₃₉	C₂²	1	2	yes	—
50	#389×C₁₃₉	C₂²	1	2	yes	—
51	#389×C₁₃₉	C₂²	1	4	yes	—
52	#388×C₁₃₉	C₂²	1	4	yes	—
53	#388×C₁₃₉	C₂²	1	4	yes	—
54	#388×C₁₃₉	C₂²	1	4	yes	—
55	#388×C₁₃₉	C₂²	1	4	yes	—
56	#387×C₁₃₉	C₂²	1	4	yes	—
57	#387×C₁₃₉	C₂²	1	4	yes	—
58	#387×C₁₃₉	C₂²	1	4	yes	—
59	#384×C₁₃₉	C₂²	1	1	yes	characteristic
60	#384×C₁₃₉	C₂²	1	1	yes	characteristic
61	#384×C₁₃₉	C₂²	1	1	yes	characteristic
62	#383×C₁₃₉	C₂²	1	4	yes	—
63	#382×C₁₃₉	C₂²	1	2	yes	—
64	#382×C₁₃₉	C₂²	1	2	yes	—
65	#382×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	#380×C₁₃₉	C₂²	1	2	yes	—
70	#380×C₁₃₉	C₂²	1	2	yes	—
71	#380×C₁₃₉	C₂²	1	2	yes	—
72	#380×C₁₃₉	C₂²	1	2	yes	—
73	#380×C₁₃₉	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
75	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
77	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
78	C₄×C₄⋊C₄×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	2	yes	—
82	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
83	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
90	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
91	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
100	#125×C₁₃₉	—	2	8	no	—
101	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
102	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
103	C₄×Q₈×C₁₃₉	—	4	4	no	—
104	C₄×D₄×C₁₃₉	—	2	4	no	—
105	C₄×D₄×C₁₃₉	—	2	4	no	—
106	C₄×D₄×C₁₃₉	—	2	4	no	—
107	#117×C₁₃₉	—	2	8	no	—
108	#117×C₁₃₉	—	4	4	no	—
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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	2	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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	4	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
133	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
138	C₂×C₄²×C₁₃₉	—	2	4	no	—
139	C₂×C₄²×C₁₃₉	—	2	4	no	—
140	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
153	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
156	#95×C₁₃₉	C₂³	1	4	yes	—
157	#95×C₁₃₉	C₂³	1	4	yes	—
158	#95×C₁₃₉	C₂³	1	4	yes	—
159	#95×C₁₃₉	C₂³	1	4	yes	—
160	#95×C₁₃₉	C₂³	1	4	yes	—
161	#95×C₁₃₉	C₂³	1	4	yes	—
162	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	#95×C₁₃₉	C₂³	1	1	yes	characteristic
169	#95×C₁₃₉	C₂³	1	1	yes	characteristic
170	#95×C₁₃₉	C₂³	1	1	yes	characteristic
171	#95×C₁₃₉	C₂³	1	1	yes	characteristic
172	#95×C₁₃₉	C₂³	1	1	yes	characteristic
173	#95×C₁₃₉	C₂³	1	4	yes	—
174	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
175	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
176	C₂×Q₈×C₁₃₉	—	2	4	no	—
177	C₂×Q₈×C₁₃₉	—	2	4	no	—
178	C₂×Q₈×C₁₃₉	—	2	4	no	—
179	C₂×D₄×C₁₃₉	—	2	2	no	—
180	C₂×D₄×C₁₃₉	—	2	2	no	—
181	C₂×D₄×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	2	no	—
187	C₂²×C₄×C₁₃₉	—	2	2	no	—
188	C₂²×C₄×C₁₃₉	—	2	2	no	—
189	C₂²×C₄×C₁₃₉	—	2	2	no	—
190	C₂²×C₄×C₁₃₉	—	2	2	no	—
191	C₂²×C₄×C₁₃₉	—	2	2	no	—
192	C₂²×C₄×C₁₃₉	—	2	2	no	—
193	C₂²×C₄×C₁₃₉	—	2	2	no	—
194	C₂²×C₄×C₁₃₉	—	2	2	no	—
195	C₂²×C₄×C₁₃₉	—	2	2	no	—
196	C₂²×C₄×C₁₃₉	—	2	2	no	—
197	C₂²×C₄×C₁₃₉	—	2	2	no	—
198	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
199	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
200	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
216	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
217	C₄⋊C₄×C₁₃₉	—	2	4	no	—
218	C₄⋊C₄×C₁₃₉	—	2	4	no	—
219	C₄⋊C₄×C₁₃₉	—	2	2	no	—
220	C₄⋊C₄×C₁₃₉	—	2	2	no	—
221	C₄⋊C₄×C₁₃₉	—	2	2	no	—
222	C₄⋊C₄×C₁₃₉	—	2	4	no	—
223	C₄⋊C₄×C₁₃₉	—	2	8	no	—
224	C₄⋊C₄×C₁₃₉	—	2	8	no	—
225	C₄⋊C₄×C₁₃₉	—	2	8	no	—
226	C₄⋊C₄×C₁₃₉	—	2	4	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	4	no	—
233	C₄⋊C₄×C₁₃₉	—	2	4	no	—
234	C₄⋊C₄×C₁₃₉	—	4	4	no	—
235	C₄⋊C₄×C₁₃₉	—	4	4	no	—
236	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
237	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
238	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
239	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
240	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
241	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
242	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
243	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
244	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
245	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
246	C₄²×C₁₃₉	—	2	2	no	—
247	C₄²×C₁₃₉	—	2	2	no	—
248	C₄²×C₁₃₉	—	2	2	no	—
249	C₄²×C₁₃₉	—	2	2	no	—
250	C₄²×C₁₃₉	—	2	2	no	—
251	C₄²×C₁₃₉	—	2	2	no	—
252	C₄²×C₁₃₉	—	2	8	no	—
253	C₄²×C₁₃₉	—	2	2	no	—
254	C₄²×C₁₃₉	—	2	2	no	—
255	C₄²×C₁₃₉	—	2	2	no	—
256	C₄²×C₁₃₉	—	2	2	no	—
257	C₄²×C₁₃₉	—	2	2	no	—
258	C₄²×C₁₃₉	—	4	4	no	—
259	C₄²×C₁₃₉	—	4	4	no	—
260	C₄²×C₁₃₉	#41	1	4	yes	—
261	C₄²×C₁₃₉	#41	1	4	yes	—
262	C₂³×C₁₃₉	—	2	1	no	—
263	C₂³×C₁₃₉	—	2	1	no	—
264	C₂³×C₁₃₉	—	2	1	no	—
265	C₂³×C₁₃₉	—	2	1	no	—
266	C₂³×C₁₃₉	—	2	1	no	—
267	C₂³×C₁₃₉	—	2	1	no	—
268	C₂³×C₁₃₉	—	2	1	no	—
269	C₂³×C₁₃₉	—	2	1	no	—
270	C₂³×C₁₃₉	—	2	1	no	—
271	C₂³×C₁₃₉	—	2	1	no	—
272	C₂³×C₁₃₉	—	2	1	no	—
273	C₂³×C₁₃₉	—	2	1	no	—
274	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
275	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
276	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
277	Q₈×C₁₃₉	—	4	8	no	—
278	D₄×C₁₃₉	—	2	8	no	—
279	C₂×C₄×C₁₃₉	—	2	1	no	—
280	C₂×C₄×C₁₃₉	—	2	1	no	—
281	C₂×C₄×C₁₃₉	—	2	1	no	—
282	C₂×C₄×C₁₃₉	—	2	1	no	—
283	C₂×C₄×C₁₃₉	—	2	1	no	—
284	C₂×C₄×C₁₃₉	—	2	1	no	—
285	C₂×C₄×C₁₃₉	—	2	1	no	—
286	C₂×C₄×C₁₃₉	—	2	1	no	—
287	C₂×C₄×C₁₃₉	—	2	8	no	—
288	C₂×C₄×C₁₃₉	—	2	8	no	—
289	C₂×C₄×C₁₃₉	—	2	1	no	—
290	C₂×C₄×C₁₃₉	—	2	1	no	—
291	C₂×C₄×C₁₃₉	—	2	1	no	—
292	C₂×C₄×C₁₃₉	—	2	1	no	—
293	C₂×C₄×C₁₃₉	—	2	1	no	—
294	C₂×C₄×C₁₃₉	—	2	1	no	—
295	C₂×C₄×C₁₃₉	—	2	4	no	—
296	C₂×C₄×C₁₃₉	—	2	4	no	—
297	C₂×C₄×C₁₃₉	—	2	4	no	—
298	C₂×C₄×C₁₃₉	—	2	1	no	—
299	C₂×C₄×C₁₃₉	—	2	1	no	—
300	C₂×C₄×C₁₃₉	—	2	1	no	—
301	C₂×C₄×C₁₃₉	—	2	1	no	—
302	C₂×C₄×C₁₃₉	—	2	4	no	—
303	C₂×C₄×C₁₃₉	—	2	4	no	—
304	C₂×C₄×C₁₃₉	—	2	4	no	—
305	C₂×C₄×C₁₃₉	—	2	4	no	—
306	C₂×C₄×C₁₃₉	—	2	1	no	—
307	C₂×C₄×C₁₃₉	—	2	4	no	—
308	C₂×C₄×C₁₃₉	—	2	4	no	—
309	C₂×C₄×C₁₃₉	—	2	4	no	—
310	C₂×C₄×C₁₃₉	—	2	1	no	—
311	C₂×C₄×C₁₃₉	—	2	1	no	—
312	C₂×C₄×C₁₃₉	—	2	1	no	—
313	C₂×C₄×C₁₃₉	—	2	1	no	—
314	C₂×C₄×C₁₃₉	—	2	4	no	—
315	C₂×C₄×C₁₃₉	—	2	4	no	—
316	C₂×C₄×C₁₃₉	—	2	1	no	—
317	C₂×C₄×C₁₃₉	—	2	1	no	—
318	C₂×C₄×C₁₃₉	—	2	1	no	—
319	C₂×C₄×C₁₃₉	—	4	4	no	—
320	C₂×C₄×C₁₃₉	—	4	4	no	—
321	C₂×C₄×C₁₃₉	—	4	4	no	—
322	C₂×C₄×C₁₃₉	—	4	4	no	—
323	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
324	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
325	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
326	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
327	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
328	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
329	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
330	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
331	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
332	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
333	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
334	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
335	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
336	C₂²×C₁₃₉	—	2	2	no	—
337	C₂²×C₁₃₉	—	2	2	no	—
338	C₂²×C₁₃₉	—	2	2	no	—
339	C₂²×C₁₃₉	—	2	2	no	—
340	C₂²×C₁₃₉	—	2	2	no	—
341	C₂²×C₁₃₉	—	2	2	no	—
342	C₂²×C₁₃₉	—	4	1	no	—
343	C₂²×C₁₃₉	—	4	1	no	—
344	C₂²×C₁₃₉	—	4	1	no	—
345	C₂²×C₁₃₉	—	4	1	no	—
346	C₂²×C₁₃₉	—	4	1	no	—
347	C₂²×C₁₃₉	—	4	1	no	—
348	C₂²×C₁₃₉	—	4	1	no	—
349	C₂²×C₁₃₉	—	4	1	no	—
350	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
351	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
352	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
353	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
354	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
355	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
356	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
357	C₄×C₁₃₉	—	2	2	no	—
358	C₄×C₁₃₉	—	2	2	no	—
359	C₄×C₁₃₉	—	2	2	no	—
360	C₄×C₁₃₉	—	2	2	no	—
361	C₄×C₁₃₉	—	4	4	no	—
362	C₄×C₁₃₉	—	4	1	no	—
363	C₄×C₁₃₉	—	4	1	no	—
364	C₄×C₁₃₉	—	4	4	no	—
365	C₄×C₁₃₉	—	4	1	no	—
366	C₄×C₁₃₉	—	4	1	no	—
367	C₄×C₁₃₉	—	4	1	no	—
368	C₄×C₁₃₉	—	4	4	no	—
369	C₄×C₁₃₉	—	4	1	no	—
370	C₄×C₁₃₉	—	4	4	no	—
371	C₄×C₁₃₉	#552	1	4	yes	—
372	C₄×C₁₃₉	#553	1	4	yes	—
373	C₄×C₁₃₉	#556	1	4	yes	—
374	C₂×C₁₃₉	—	4	2	no	—
375	C₂×C₁₃₉	—	4	2	no	—
376	C₂×C₁₃₉	#3444	1	1	yes	characteristic
377	C₂×C₁₃₉	C₂×#552	1	1	yes	characteristic
378	C₂×C₁₃₉	C₂×#553	1	1	yes	characteristic
379	C₂×C₁₃₉	C₂×#556	1	1	yes	characteristic
380	C₂×C₁₃₉	#3509	1	1	yes	characteristic
381	C₂×C₁₃₉	#3511	1	1	yes	characteristic
382	C₂×C₁₃₉	#3511	1	1	yes	characteristic
383	#36210	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
384	C₁₃₉	#36210	1	1	yes	characteristic, direct product factor, Sylow
385	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
386	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
387	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
388	#2562	C₂×C₁₃₉	1	2	yes	—
389	#2514	C₂×C₁₃₉	1	2	yes	complemented
390	#2509	C₂×C₁₃₉	1	2	yes	complemented
391	#2495	C₂×C₁₃₉	1	2	yes	complemented
392	#2494	C₂×C₁₃₉	1	2	yes	complemented
393	#2494	C₂×C₁₃₉	1	2	yes	complemented
394	#2485	C₂×C₁₃₉	1	2	yes	—
395	#2421	C₂×C₁₃₉	1	2	yes	complemented
396	#2415	C₂×C₁₃₉	1	2	yes	—
397	#2370	C₂×C₁₃₉	1	2	yes	complemented
398	#2362	C₂×C₁₃₉	1	2	yes	complemented
399	#2347	C₂×C₁₃₉	1	2	yes	complemented
400	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
401	#2285	C₂×C₁₃₉	1	1	yes	characteristic, complemented
402	#2285	C₂×C₁₃₉	1	1	yes	characteristic, complemented
403	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic
404	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
405	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
406	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
407	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
408	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
409	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
410	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
411	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
412	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
413	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
414	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
415	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
416	#401	C₂²×C₁₃₉	1	4	yes	—
417	#400	C₂²×C₁₃₉	1	4	yes	—
418	#400	C₂²×C₁₃₉	1	4	yes	—
419	#397	C₂²×C₁₃₉	1	4	yes	—
420	#397	C₂²×C₁₃₉	1	4	yes	—
421	#394	C₂²×C₁₃₉	1	4	yes	—
422	#391	C₂²×C₁₃₉	1	2	yes	—
423	#391	C₂²×C₁₃₉	1	2	yes	—
424	#391	C₂²×C₁₃₉	1	2	yes	—
425	#389	C₂²×C₁₃₉	1	2	yes	—
426	#389	C₂²×C₁₃₉	1	2	yes	—
427	#389	C₂²×C₁₃₉	1	2	yes	—
428	#389	C₂²×C₁₃₉	1	2	yes	—
429	#389	C₂²×C₁₃₉	1	2	yes	—
430	#389	C₂²×C₁₃₉	1	2	yes	—
431	#389	C₂²×C₁₃₉	1	2	yes	—
432	#389	C₂²×C₁₃₉	1	2	yes	—
433	#389	C₂²×C₁₃₉	1	2	yes	—
434	#389	C₂²×C₁₃₉	1	2	yes	—
435	#389	C₂²×C₁₃₉	1	4	yes	—
436	#388	C₂²×C₁₃₉	1	4	yes	—
437	#388	C₂²×C₁₃₉	1	4	yes	—
438	#388	C₂²×C₁₃₉	1	4	yes	—
439	#388	C₂²×C₁₃₉	1	4	yes	—
440	#387	C₂²×C₁₃₉	1	4	yes	—
441	#387	C₂²×C₁₃₉	1	4	yes	—
442	#387	C₂²×C₁₃₉	1	4	yes	—
443	#384	C₂²×C₁₃₉	1	1	yes	characteristic
444	#384	C₂²×C₁₃₉	1	1	yes	characteristic
445	#384	C₂²×C₁₃₉	1	1	yes	characteristic
446	#383	C₂²×C₁₃₉	1	4	yes	—
447	#382	C₂²×C₁₃₉	1	2	yes	—
448	#382	C₂²×C₁₃₉	1	2	yes	—
449	#382	C₂²×C₁₃₉	1	2	yes	—
450	#380	C₂²×C₁₃₉	1	2	yes	—
451	#380	C₂²×C₁₃₉	1	2	yes	—
452	#380	C₂²×C₁₃₉	1	2	yes	—
453	#380	C₂²×C₁₃₉	1	2	yes	—
454	#380	C₂²×C₁₃₉	1	2	yes	—
455	#380	C₂²×C₁₃₉	1	2	yes	—
456	#380	C₂²×C₁₃₉	1	2	yes	—
457	#380	C₂²×C₁₃₉	1	2	yes	—
458	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
459	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
460	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
461	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
462	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
463	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
464	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
465	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
466	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
467	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
468	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
469	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
470	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
471	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
472	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
473	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
474	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
475	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
476	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
483	C₄⋊Q₈	—	2	4	no	—
484	#125	—	2	8	no	—
485	C₂²⋊Q₈	—	2	8	no	—
486	C₂²⋊Q₈	—	4	4	no	—
487	C₄×Q₈	—	4	4	no	—
488	C₄×D₄	—	2	4	no	—
489	C₄×D₄	—	2	4	no	—
490	C₄×D₄	—	2	4	no	—
491	#117	—	2	8	no	—
492	#117	—	4	4	no	—
493	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
505	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
506	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
514	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
517	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
522	C₂×C₄²	—	2	4	no	—
523	C₂×C₄²	—	2	4	no	—
524	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
525	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
535	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
536	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
537	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
538	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
540	#95	C₂³×C₁₃₉	1	1	yes	characteristic
541	#95	C₂³×C₁₃₉	1	1	yes	characteristic
542	#95	C₂³×C₁₃₉	1	1	yes	characteristic
543	#95	C₂³×C₁₃₉	1	1	yes	characteristic
544	#95	C₂³×C₁₃₉	1	1	yes	characteristic
545	#95	C₂³×C₁₃₉	1	1	yes	characteristic
546	#95	C₂³×C₁₃₉	1	4	yes	—
547	#95	C₂³×C₁₃₉	1	4	yes	—
548	#95	C₂³×C₁₃₉	1	4	yes	—
549	#95	C₂³×C₁₃₉	1	4	yes	—
550	#95	C₂³×C₁₃₉	1	4	yes	—
551	#95	C₂³×C₁₃₉	1	4	yes	—
552	#95	C₂³×C₁₃₉	1	4	yes	—
553	#95	C₂³×C₁₃₉	1	4	yes	—
554	#95	C₂³×C₁₃₉	1	4	yes	—
555	#95	C₂³×C₁₃₉	1	4	yes	—
556	#95	C₂³×C₁₃₉	1	4	yes	—
557	#95	C₂³×C₁₃₉	1	4	yes	—
558	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
559	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
560	C₂×Q₈	—	2	4	no	—
561	C₂×Q₈	—	2	4	no	—
562	C₂×Q₈	—	2	4	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
583	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
584	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
585	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
590	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
592	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
593	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
594	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	8	no	—
608	C₄⋊C₄	—	2	8	no	—
609	C₄⋊C₄	—	2	8	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	4	4	no	—
619	C₄⋊C₄	—	4	4	no	—
620	C₂²⋊C₄	—	2	8	no	—
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	—	2	2	no	—
623	C₂²⋊C₄	—	2	8	no	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	4	4	no	—
629	C₂²⋊C₄	—	4	4	no	—
630	C₄²	—	2	2	no	—
631	C₄²	—	2	2	no	—
632	C₄²	—	2	2	no	—
633	C₄²	—	2	2	no	—
634	C₄²	—	2	2	no	—
635	C₄²	—	2	2	no	—
636	C₄²	—	2	8	no	—
637	C₄²	—	2	2	no	—
638	C₄²	—	2	2	no	—
639	C₄²	—	2	2	no	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	2	no	—
642	C₄²	—	4	4	no	—
643	C₄²	—	4	4	no	—
644	C₄²	#41×C₁₃₉	1	4	yes	—
645	C₄²	#41×C₁₃₉	1	4	yes	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	1	no	—
658	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
659	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
660	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
661	Q₈	—	4	8	no	—
662	D₄	—	2	8	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	8	no	—
672	C₂×C₄	—	2	8	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	4	4	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	4	no	—
706	C₂×C₄	—	4	4	no	—
707	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
708	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
709	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
710	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
711	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
712	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
713	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
714	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
715	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
716	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
717	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
718	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
719	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
735	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
736	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
737	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
738	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
739	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
740	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
741	C₄	—	2	2	no	—
742	C₄	—	2	2	no	—
743	C₄	—	2	2	no	—
744	C₄	—	2	2	no	—
745	C₄	—	4	4	no	—
746	C₄	—	4	1	no	—
747	C₄	—	4	1	no	—
748	C₄	—	4	4	no	—
749	C₄	—	4	1	no	—
750	C₄	—	4	1	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	4	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	4	no	—
755	C₄	#552×C₁₃₉	1	4	yes	—
756	C₄	#553×C₁₃₉	1	4	yes	—
757	C₄	#556×C₁₃₉	1	4	yes	—
758	C₂	—	4	2	no	—
759	C₂	—	4	2	no	—
760	C₂	#3444×C₁₃₉	1	1	yes	characteristic
761	C₂	C₂×#552×C₁₃₉	1	1	yes	characteristic
762	C₂	C₂×#553×C₁₃₉	1	1	yes	characteristic
763	C₂	C₂×#556×C₁₃₉	1	1	yes	characteristic
764	C₂	#3509×C₁₃₉	1	1	yes	characteristic
765	C₂	#3511×C₁₃₉	1	1	yes	characteristic
766	C₂	#3511×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	C₂³
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. #2857×C₁₃₉	C₂	semidirect
3. #2857×C₁₃₉	C₂	semidirect
5. #2514×C₁₃₉	C₂	semidirect
6. #2509×C₁₃₉	C₂	semidirect
7. #2495×C₁₃₉	C₂	semidirect
8. #2494×C₁₃₉	C₂	semidirect
9. #2494×C₁₃₉	C₂	semidirect
11. #2421×C₁₃₉	C₂	semidirect
13. #2370×C₁₃₉	C₂	semidirect
14. #2362×C₁₃₉	C₂	semidirect
15. #2347×C₁₃₉	C₂	semidirect
16. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
17. #2285×C₁₃₉	C₂	semidirect
18. #2285×C₁₃₉	C₂	semidirect
383. #36210	C₁₃₉	direct (N × H)
384. C₁₃₉	#36210	direct (N × H)
385. #2859	C₂×C₁₃₉	semidirect
386. #2857	C₂×C₁₃₉	semidirect
387. #2857	C₂×C₁₃₉	semidirect
389. #2514	C₂×C₁₃₉	semidirect
390. #2509	C₂×C₁₃₉	semidirect
391. #2495	C₂×C₁₃₉	semidirect
392. #2494	C₂×C₁₃₉	semidirect
393. #2494	C₂×C₁₃₉	semidirect
395. #2421	C₂×C₁₃₉	semidirect
397. #2370	C₂×C₁₃₉	semidirect
398. #2362	C₂×C₁₃₉	semidirect
399. #2347	C₂×C₁₃₉	semidirect
400. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
401. #2285	C₂×C₁₃₉	semidirect
402. #2285	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
#2857×C₁₃₉	2
#2562×C₁₃₉	2
#2514×C₁₃₉	2
#2509×C₁₃₉	2
#2495×C₁₃₉	2
#2494×C₁₃₉	2
#2485×C₁₃₉	2
#2421×C₁₃₉	2
#2415×C₁₃₉	2
#2370×C₁₃₉	2
#2362×C₁₃₉	2
#2347×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
#2285×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36210	139

Subgroups — C139×#36210 #48030806

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36210 #48030806