Subgroups — C₁₃₉×#36162 #48030758

Order 35584.

2860 conjugacy classes of subgroups.

The subgroup lattice has 778 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	C₂²×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2855×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2849×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2482×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2467×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2460×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2454×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2435×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2427×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2411×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2408×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	#2367×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2363×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2344×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#123×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2280×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
20	#552×C₁₃₉	—	2	8	no	—
21	C₂×#126×C₁₃₉	C₂²	1	2	yes	complemented
22	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×#125×C₁₃₉	C₂²	1	2	yes	complemented
24	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×D₄×C₁₃₉	—	2	8	no	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
37	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
38	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
39	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
42	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
43	#399×C₁₃₉	C₂²	1	4	yes	complemented
44	#397×C₁₃₉	C₂²	1	4	yes	complemented
45	#396×C₁₃₉	C₂²	1	4	yes	complemented
46	#394×C₁₃₉	C₂²	1	2	yes	—
47	#394×C₁₃₉	C₂²	1	4	yes	—
48	#394×C₁₃₉	C₂²	1	4	yes	complemented
49	#392×C₁₃₉	C₂²	1	2	yes	—
50	#391×C₁₃₉	C₂²	1	2	yes	complemented
51	#390×C₁₃₉	C₂²	1	2	yes	—
52	#390×C₁₃₉	C₂²	1	2	yes	—
53	#390×C₁₃₉	C₂²	1	4	yes	complemented
54	#389×C₁₃₉	C₂²	1	2	yes	complemented
55	#389×C₁₃₉	C₂²	1	2	yes	complemented
56	#388×C₁₃₉	C₂²	1	2	yes	complemented
57	#388×C₁₃₉	C₂²	1	4	yes	complemented
58	#388×C₁₃₉	C₂²	1	4	yes	complemented
59	#388×C₁₃₉	C₂²	1	4	yes	complemented
60	#387×C₁₃₉	C₂²	1	2	yes	complemented
61	#387×C₁₃₉	C₂²	1	4	yes	complemented
62	#387×C₁₃₉	C₂²	1	4	yes	complemented
63	#386×C₁₃₉	C₂²	1	1	yes	characteristic
64	#386×C₁₃₉	C₂²	1	4	yes	complemented
65	#386×C₁₃₉	C₂²	1	4	yes	complemented
66	#385×C₁₃₉	C₂²	1	1	yes	characteristic
67	#385×C₁₃₉	C₂²	1	2	yes	—
68	#385×C₁₃₉	C₂²	1	4	yes	complemented
69	#385×C₁₃₉	C₂²	1	4	yes	complemented
70	#381×C₁₃₉	C₂²	1	1	yes	characteristic
71	#381×C₁₃₉	C₂²	1	2	yes	—
72	#381×C₁₃₉	C₂²	1	2	yes	—
73	#380×C₁₃₉	C₂²	1	1	yes	characteristic
74	#380×C₁₃₉	C₂²	1	4	yes	complemented
75	#380×C₁₃₉	C₂²	1	4	yes	complemented
76	#379×C₁₃₉	C₂²	1	2	yes	—
77	#379×C₁₃₉	C₂²	1	2	yes	—
78	#379×C₁₃₉	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
85	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
86	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₁₃₉	—	2	8	no	—
88	C₂²×D₄×C₁₃₉	—	2	4	no	—
89	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂³×C₄×C₁₃₉	—	2	8	no	—
94	C₂³×C₄×C₁₃₉	—	2	8	no	—
95	C₂³×C₄×C₁₃₉	—	4	4	no	—
96	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
99	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	#126×C₁₃₉	—	2	8	no	—
104	#125×C₁₃₉	—	2	8	no	—
105	#125×C₁₃₉	—	2	4	no	—
106	#124×C₁₃₉	—	2	8	no	—
107	#123×C₁₃₉	—	2	8	no	—
108	#123×C₁₃₉	—	2	4	no	—
109	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
110	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
111	#121×C₁₃₉	—	2	8	no	—
112	#120×C₁₃₉	—	4	4	no	—
113	C₄×Q₈×C₁₃₉	—	2	4	no	—
114	C₄×D₄×C₁₃₉	—	2	4	no	—
115	C₄×D₄×C₁₃₉	—	2	8	no	—
116	C₄×D₄×C₁₃₉	—	2	8	no	—
117	C₄×D₄×C₁₃₉	—	2	16	no	—
118	#117×C₁₃₉	—	2	8	no	—
119	#117×C₁₃₉	—	2	4	no	—
120	#117×C₁₃₉	—	4	4	no	—
121	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
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	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	4	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
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	4	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	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	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	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×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃₉	—	2	4	no	—
158	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
165	#95×C₁₃₉	C₂³	1	2	yes	—
166	#95×C₁₃₉	C₂³	1	2	yes	—
167	#95×C₁₃₉	C₂³	1	4	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	2	yes	—
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	4	yes	—
173	#95×C₁₃₉	C₂³	1	4	yes	—
174	#95×C₁₃₉	C₂³	1	4	yes	—
175	#95×C₁₃₉	C₂³	1	2	yes	—
176	C₂⁴×C₁₃₉	—	2	4	no	—
177	C₂⁴×C₁₃₉	—	2	8	no	—
178	C₂⁴×C₁₃₉	—	2	4	no	—
179	C₂⁴×C₁₃₉	—	2	4	no	—
180	C₂⁴×C₁₃₉	—	4	4	no	—
181	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
182	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
183	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
184	C₂×Q₈×C₁₃₉	—	2	2	no	—
185	C₂×Q₈×C₁₃₉	—	2	4	no	—
186	C₂×D₄×C₁₃₉	—	2	32	no	—
187	C₂×D₄×C₁₃₉	—	2	8	no	—
188	C₂×D₄×C₁₃₉	—	2	2	no	—
189	C₂×D₄×C₁₃₉	—	2	2	no	—
190	C₂×D₄×C₁₃₉	—	2	2	no	—
191	C₂×D₄×C₁₃₉	—	2	8	no	—
192	C₂×D₄×C₁₃₉	—	2	4	no	—
193	C₂×D₄×C₁₃₉	—	2	4	no	—
194	C₂×D₄×C₁₃₉	—	2	4	no	—
195	C₂×D₄×C₁₃₉	—	4	4	no	—
196	C₂×D₄×C₁₃₉	—	4	4	no	—
197	C₂×D₄×C₁₃₉	#41	1	8	yes	—
198	C₂²×C₄×C₁₃₉	—	2	2	no	—
199	C₂²×C₄×C₁₃₉	—	2	4	no	—
200	C₂²×C₄×C₁₃₉	—	2	4	no	—
201	C₂²×C₄×C₁₃₉	—	2	2	no	—
202	C₂²×C₄×C₁₃₉	—	2	4	no	—
203	C₂²×C₄×C₁₃₉	—	2	2	no	—
204	C₂²×C₄×C₁₃₉	—	2	2	no	—
205	C₂²×C₄×C₁₃₉	—	2	8	no	—
206	C₂²×C₄×C₁₃₉	—	2	8	no	—
207	C₂²×C₄×C₁₃₉	—	2	4	no	—
208	C₂²×C₄×C₁₃₉	—	2	8	no	—
209	C₂²×C₄×C₁₃₉	—	2	8	no	—
210	C₂²×C₄×C₁₃₉	—	4	4	no	—
211	C₂²×C₄×C₁₃₉	—	4	4	no	—
212	C₂²×C₄×C₁₃₉	—	4	2	no	—
213	C₂²×C₄×C₁₃₉	—	4	32	no	—
214	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
215	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
216	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
217	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
231	C₄⋊C₄×C₁₃₉	—	2	4	no	—
232	C₄⋊C₄×C₁₃₉	—	2	2	no	—
233	C₄⋊C₄×C₁₃₉	—	2	4	no	—
234	C₄⋊C₄×C₁₃₉	—	2	2	no	—
235	C₄⋊C₄×C₁₃₉	—	2	4	no	—
236	C₄⋊C₄×C₁₃₉	—	2	4	no	—
237	C₄⋊C₄×C₁₃₉	—	2	4	no	—
238	C₄⋊C₄×C₁₃₉	—	2	4	no	—
239	C₄⋊C₄×C₁₃₉	—	2	4	no	—
240	C₄⋊C₄×C₁₃₉	—	4	2	no	—
241	C₄⋊C₄×C₁₃₉	—	4	4	no	—
242	C₄⋊C₄×C₁₃₉	—	4	4	no	—
243	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
244	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
245	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
246	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
247	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
248	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
249	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
250	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
251	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
252	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
253	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
254	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
255	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
256	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
257	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
260	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
261	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
262	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
265	C₄²×C₁₃₉	—	2	4	no	—
266	C₄²×C₁₃₉	—	2	4	no	—
267	C₄²×C₁₃₉	—	2	4	no	—
268	C₄²×C₁₃₉	—	2	4	no	—
269	C₄²×C₁₃₉	—	2	2	no	—
270	C₄²×C₁₃₉	—	2	4	no	—
271	C₄²×C₁₃₉	—	4	4	no	—
272	C₂³×C₁₃₉	—	2	2	no	—
273	C₂³×C₁₃₉	—	2	2	no	—
274	C₂³×C₁₃₉	—	2	16	no	—
275	C₂³×C₁₃₉	—	2	4	no	—
276	C₂³×C₁₃₉	—	2	4	no	—
277	C₂³×C₁₃₉	—	2	4	no	—
278	C₂³×C₁₃₉	—	2	4	no	—
279	C₂³×C₁₃₉	—	2	4	no	—
280	C₂³×C₁₃₉	—	2	4	no	—
281	C₂³×C₁₃₉	—	2	1	no	—
282	C₂³×C₁₃₉	—	2	1	no	—
283	C₂³×C₁₃₉	—	2	2	no	—
284	C₂³×C₁₃₉	—	2	1	no	—
285	C₂³×C₁₃₉	—	2	2	no	—
286	C₂³×C₁₃₉	—	4	16	no	—
287	C₂³×C₁₃₉	—	4	16	no	—
288	C₂³×C₁₃₉	—	4	8	no	—
289	C₂³×C₁₃₉	—	4	8	no	—
290	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
291	C₂³×C₁₃₉	C₂×#41	1	8	yes	—
292	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
293	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
294	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
295	Q₈×C₁₃₉	—	4	4	no	—
296	D₄×C₁₃₉	—	2	16	no	—
297	D₄×C₁₃₉	—	2	16	no	—
298	D₄×C₁₃₉	—	4	4	no	—
299	D₄×C₁₃₉	—	8	8	no	—
300	C₂×C₄×C₁₃₉	—	2	8	no	—
301	C₂×C₄×C₁₃₉	—	2	16	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	2	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	2	2	no	—
309	C₂×C₄×C₁₃₉	—	2	8	no	—
310	C₂×C₄×C₁₃₉	—	2	1	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	1	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	1	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	2	no	—
320	C₂×C₄×C₁₃₉	—	2	4	no	—
321	C₂×C₄×C₁₃₉	—	2	4	no	—
322	C₂×C₄×C₁₃₉	—	2	1	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	4	no	—
325	C₂×C₄×C₁₃₉	—	2	1	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	4	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	4	no	—
332	C₂×C₄×C₁₃₉	—	2	2	no	—
333	C₂×C₄×C₁₃₉	—	4	16	no	—
334	C₂×C₄×C₁₃₉	—	4	16	no	—
335	C₂×C₄×C₁₃₉	—	4	4	no	—
336	C₂×C₄×C₁₃₉	—	4	4	no	—
337	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
338	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
340	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
342	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
343	C₂²×C₁₃₉	—	2	2	no	—
344	C₂²×C₁₃₉	—	2	4	no	—
345	C₂²×C₁₃₉	—	2	2	no	—
346	C₂²×C₁₃₉	—	2	4	no	—
347	C₂²×C₁₃₉	—	2	8	no	—
348	C₂²×C₁₃₉	—	2	8	no	—
349	C₂²×C₁₃₉	—	2	8	no	—
350	C₂²×C₁₃₉	—	4	32	no	—
351	C₂²×C₁₃₉	—	4	4	no	—
352	C₂²×C₁₃₉	—	4	4	no	—
353	C₂²×C₁₃₉	—	4	4	no	—
354	C₂²×C₁₃₉	—	4	4	no	—
355	C₂²×C₁₃₉	—	4	1	no	—
356	C₂²×C₁₃₉	—	4	1	no	—
357	C₂²×C₁₃₉	—	4	2	no	—
358	C₂²×C₁₃₉	—	4	1	no	—
359	C₂²×C₁₃₉	—	4	2	no	—
360	C₂²×C₁₃₉	#546	1	4	yes	—
361	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
362	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
363	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
364	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
365	C₂²×C₁₃₉	#585	1	2	yes	—
366	C₄×C₁₃₉	—	2	2	no	—
367	C₄×C₁₃₉	—	2	4	no	—
368	C₄×C₁₃₉	—	2	4	no	—
369	C₄×C₁₃₉	—	2	4	no	—
370	C₄×C₁₃₉	—	4	1	no	—
371	C₄×C₁₃₉	—	4	2	no	—
372	C₄×C₁₃₉	—	4	1	no	—
373	C₄×C₁₃₉	—	4	2	no	—
374	C₄×C₁₃₉	—	4	1	no	—
375	C₄×C₁₃₉	—	4	2	no	—
376	C₄×C₁₃₉	—	4	2	no	—
377	C₄×C₁₃₉	—	4	2	no	—
378	C₄×C₁₃₉	—	4	4	no	—
379	C₄×C₁₃₉	#525	1	4	yes	—
380	C₂×C₁₃₉	—	2	4	no	—
381	C₂×C₁₃₉	—	4	8	no	—
382	C₂×C₁₃₉	—	8	1	no	—
383	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
384	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
385	C₂×C₁₃₉	#3475	1	2	yes	—
386	C₂×C₁₃₉	#3487	1	1	yes	characteristic
387	C₂×C₁₃₉	#3513	1	2	yes	—
388	#36162	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
389	C₁₃₉	#36162	1	1	yes	characteristic, direct product factor, Sylow
390	C₂×#552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
391	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
392	#2855	C₂×C₁₃₉	1	1	yes	characteristic, complemented
393	#2849	C₂×C₁₃₉	1	2	yes	complemented
394	#2482	C₂×C₁₃₉	1	2	yes	complemented
395	#2467	C₂×C₁₃₉	1	4	yes	complemented
396	#2460	C₂×C₁₃₉	1	4	yes	complemented
397	#2454	C₂×C₁₃₉	1	2	yes	complemented
398	#2435	C₂×C₁₃₉	1	1	yes	characteristic, complemented
399	#2427	C₂×C₁₃₉	1	2	yes	complemented
400	#2411	C₂×C₁₃₉	1	2	yes	complemented
401	#2408	C₂×C₁₃₉	1	1	yes	characteristic
402	#2367	C₂×C₁₃₉	1	2	yes	complemented
403	#2363	C₂×C₁₃₉	1	2	yes	complemented
404	#2344	C₂×C₁₃₉	1	1	yes	characteristic, complemented
405	C₄×#123	C₂×C₁₃₉	1	1	yes	characteristic, complemented
406	#2280	C₂×C₁₃₉	1	2	yes	complemented
407	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
408	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
409	#552	—	2	8	no	—
410	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
411	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
412	C₂×#125	C₂²×C₁₃₉	1	2	yes	complemented
413	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
414	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
415	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
416	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
418	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
419	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
420	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
421	C₂×C₄×D₄	—	2	8	no	—
422	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
423	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
424	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
425	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
426	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
427	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
428	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
429	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
430	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
431	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
432	#399	C₂²×C₁₃₉	1	4	yes	complemented
433	#397	C₂²×C₁₃₉	1	4	yes	complemented
434	#396	C₂²×C₁₃₉	1	4	yes	complemented
435	#394	C₂²×C₁₃₉	1	2	yes	—
436	#394	C₂²×C₁₃₉	1	4	yes	—
437	#394	C₂²×C₁₃₉	1	4	yes	complemented
438	#392	C₂²×C₁₃₉	1	2	yes	—
439	#391	C₂²×C₁₃₉	1	2	yes	complemented
440	#390	C₂²×C₁₃₉	1	2	yes	—
441	#390	C₂²×C₁₃₉	1	2	yes	—
442	#390	C₂²×C₁₃₉	1	4	yes	complemented
443	#389	C₂²×C₁₃₉	1	2	yes	complemented
444	#389	C₂²×C₁₃₉	1	2	yes	complemented
445	#388	C₂²×C₁₃₉	1	4	yes	complemented
446	#388	C₂²×C₁₃₉	1	4	yes	complemented
447	#388	C₂²×C₁₃₉	1	4	yes	complemented
448	#388	C₂²×C₁₃₉	1	2	yes	complemented
449	#387	C₂²×C₁₃₉	1	4	yes	complemented
450	#387	C₂²×C₁₃₉	1	4	yes	complemented
451	#387	C₂²×C₁₃₉	1	2	yes	complemented
452	#386	C₂²×C₁₃₉	1	1	yes	characteristic
453	#386	C₂²×C₁₃₉	1	4	yes	complemented
454	#386	C₂²×C₁₃₉	1	4	yes	complemented
455	#385	C₂²×C₁₃₉	1	2	yes	—
456	#385	C₂²×C₁₃₉	1	1	yes	characteristic
457	#385	C₂²×C₁₃₉	1	4	yes	complemented
458	#385	C₂²×C₁₃₉	1	4	yes	complemented
459	#381	C₂²×C₁₃₉	1	2	yes	—
460	#381	C₂²×C₁₃₉	1	2	yes	—
461	#381	C₂²×C₁₃₉	1	1	yes	characteristic
462	#380	C₂²×C₁₃₉	1	1	yes	characteristic
463	#380	C₂²×C₁₃₉	1	4	yes	complemented
464	#380	C₂²×C₁₃₉	1	4	yes	complemented
465	#379	C₂²×C₁₃₉	1	2	yes	—
466	#379	C₂²×C₁₃₉	1	2	yes	—
467	#379	C₂²×C₁₃₉	1	2	yes	—
468	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
469	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
470	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
471	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
472	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
473	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
474	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
475	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
476	C₂²×D₄	—	2	8	no	—
477	C₂²×D₄	—	2	4	no	—
478	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
479	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
480	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
481	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
482	C₂³×C₄	—	2	8	no	—
483	C₂³×C₄	—	2	8	no	—
484	C₂³×C₄	—	4	4	no	—
485	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
487	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
488	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
489	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
492	#126	—	2	8	no	—
493	#125	—	2	8	no	—
494	#125	—	2	4	no	—
495	#124	—	2	8	no	—
496	#123	—	2	8	no	—
497	#123	—	2	4	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	#121	—	2	8	no	—
501	#120	—	4	4	no	—
502	C₄×Q₈	—	2	4	no	—
503	C₄×D₄	—	2	4	no	—
504	C₄×D₄	—	2	8	no	—
505	C₄×D₄	—	2	8	no	—
506	C₄×D₄	—	2	16	no	—
507	#117	—	2	8	no	—
508	#117	—	2	4	no	—
509	#117	—	4	4	no	—
510	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
511	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
521	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
526	C₂×C₂²⋊C₄	—	2	8	no	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
531	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
546	C₂×C₄²	—	2	4	no	—
547	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
553	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
554	#95	C₂³×C₁₃₉	1	2	yes	—
555	#95	C₂³×C₁₃₉	1	2	yes	—
556	#95	C₂³×C₁₃₉	1	2	yes	—
557	#95	C₂³×C₁₃₉	1	4	yes	—
558	#95	C₂³×C₁₃₉	1	4	yes	—
559	#95	C₂³×C₁₃₉	1	2	yes	—
560	#95	C₂³×C₁₃₉	1	4	yes	—
561	#95	C₂³×C₁₃₉	1	2	yes	—
562	#95	C₂³×C₁₃₉	1	2	yes	—
563	#95	C₂³×C₁₃₉	1	4	yes	—
564	#95	C₂³×C₁₃₉	1	4	yes	—
565	C₂⁴	—	2	4	no	—
566	C₂⁴	—	2	8	no	—
567	C₂⁴	—	2	4	no	—
568	C₂⁴	—	2	4	no	—
569	C₂⁴	—	4	4	no	—
570	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
571	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
572	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	2	4	no	—
575	C₂×D₄	—	2	32	no	—
576	C₂×D₄	—	2	8	no	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	8	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	4	4	no	—
585	C₂×D₄	—	4	4	no	—
586	C₂×D₄	#41×C₁₃₉	1	8	yes	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	8	no	—
595	C₂²×C₄	—	2	8	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	2	8	no	—
598	C₂²×C₄	—	2	8	no	—
599	C₂²×C₄	—	4	4	no	—
600	C₂²×C₄	—	4	4	no	—
601	C₂²×C₄	—	4	2	no	—
602	C₂²×C₄	—	4	32	no	—
603	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
604	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
605	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
606	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
608	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	4	4	no	—
631	C₄⋊C₄	—	4	4	no	—
632	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
633	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
634	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	8	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	8	no	—
640	C₂²⋊C₄	—	2	8	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	8	no	—
644	C₂²⋊C₄	—	2	8	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	4	4	no	—
650	C₂²⋊C₄	—	4	2	no	—
651	C₂²⋊C₄	—	4	4	no	—
652	C₂²⋊C₄	—	4	4	no	—
653	C₂²⋊C₄	—	4	4	no	—
654	C₄²	—	2	4	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	4	4	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	16	no	—
664	C₂³	—	2	4	no	—
665	C₂³	—	2	4	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	4	16	no	—
676	C₂³	—	4	16	no	—
677	C₂³	—	4	8	no	—
678	C₂³	—	4	8	no	—
679	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
680	C₂³	C₂×#41×C₁₃₉	1	8	yes	—
681	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
682	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
683	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
684	Q₈	—	4	4	no	—
685	D₄	—	2	16	no	—
686	D₄	—	2	16	no	—
687	D₄	—	4	4	no	—
688	D₄	—	8	8	no	—
689	C₂×C₄	—	2	8	no	—
690	C₂×C₄	—	2	16	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	8	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	4	16	no	—
723	C₂×C₄	—	4	16	no	—
724	C₂×C₄	—	4	4	no	—
725	C₂×C₄	—	4	4	no	—
726	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
727	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
729	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
730	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
731	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
732	C₂²	—	2	2	no	—
733	C₂²	—	2	4	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	8	no	—
737	C₂²	—	2	8	no	—
738	C₂²	—	2	8	no	—
739	C₂²	—	4	32	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	4	no	—
742	C₂²	—	4	4	no	—
743	C₂²	—	4	4	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	2	no	—
749	C₂²	#546×C₁₃₉	1	4	yes	—
750	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
751	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
752	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
753	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
754	C₂²	#585×C₁₃₉	1	2	yes	—
755	C₄	—	2	2	no	—
756	C₄	—	2	4	no	—
757	C₄	—	2	4	no	—
758	C₄	—	2	4	no	—
759	C₄	—	4	1	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	1	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	1	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	4	no	—
767	C₄	—	4	2	no	—
768	C₄	#525×C₁₃₉	1	4	yes	—
769	C₂	—	2	4	no	—
770	C₂	—	4	8	no	—
771	C₂	—	8	1	no	—
772	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
773	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
774	C₂	#3475×C₁₃₉	1	2	yes	—
775	C₂	#3487×C₁₃₉	1	1	yes	characteristic
776	C₂	#3513×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2408×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. C₂²×C₄×D₄×C₁₃₉	C₂	semidirect
3. #2855×C₁₃₉	C₂	semidirect
4. #2849×C₁₃₉	C₂	semidirect
5. #2482×C₁₃₉	C₂	semidirect
6. #2467×C₁₃₉	C₂	semidirect
7. #2460×C₁₃₉	C₂	semidirect
8. #2454×C₁₃₉	C₂	semidirect
9. #2435×C₁₃₉	C₂	semidirect
10. #2427×C₁₃₉	C₂	semidirect
11. #2411×C₁₃₉	C₂	semidirect
13. #2367×C₁₃₉	C₂	semidirect
14. #2363×C₁₃₉	C₂	semidirect
15. #2344×C₁₃₉	C₂	semidirect
16. C₄×#123×C₁₃₉	C₂	semidirect
17. #2280×C₁₃₉	C₂	semidirect
21. C₂×#126×C₁₃₉	C₂²	semidirect
22. C₂×#125×C₁₃₉	C₂²	semidirect
23. C₂×#125×C₁₃₉	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
31. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
39. C₂×#117×C₁₃₉	C₂²	semidirect
43. #399×C₁₃₉	C₂²	semidirect
44. #397×C₁₃₉	C₂²	semidirect
45. #396×C₁₃₉	C₂²	semidirect
48. #394×C₁₃₉	C₂²	semidirect
50. #391×C₁₃₉	C₂²	semidirect
53. #390×C₁₃₉	C₂²	semidirect
54. #389×C₁₃₉	C₂²	semidirect
55. #389×C₁₃₉	C₂²	semidirect
56. #388×C₁₃₉	C₂²	semidirect
57. #388×C₁₃₉	C₂²	semidirect
58. #388×C₁₃₉	C₂²	semidirect
59. #388×C₁₃₉	C₂²	semidirect
60. #387×C₁₃₉	C₂²	semidirect
61. #387×C₁₃₉	C₂²	semidirect
62. #387×C₁₃₉	C₂²	semidirect
64. #386×C₁₃₉	C₂²	semidirect
65. #386×C₁₃₉	C₂²	semidirect
68. #385×C₁₃₉	C₂²	semidirect
69. #385×C₁₃₉	C₂²	semidirect
74. #380×C₁₃₉	C₂²	semidirect
75. #380×C₁₃₉	C₂²	semidirect
79. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
80. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
82. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
121. C₂×C₄⋊C₄×C₁₃₉	D₄	semidirect
388. #36162	C₁₃₉	direct (N × H)
389. C₁₃₉	#36162	direct (N × H)
390. C₂×#552	C₂×C₁₃₉	semidirect
391. C₂²×C₄×D₄	C₂×C₁₃₉	semidirect
392. #2855	C₂×C₁₃₉	semidirect
393. #2849	C₂×C₁₃₉	semidirect
394. #2482	C₂×C₁₃₉	semidirect
395. #2467	C₂×C₁₃₉	semidirect
396. #2460	C₂×C₁₃₉	semidirect
397. #2454	C₂×C₁₃₉	semidirect
398. #2435	C₂×C₁₃₉	semidirect
399. #2427	C₂×C₁₃₉	semidirect
400. #2411	C₂×C₁₃₉	semidirect
402. #2367	C₂×C₁₃₉	semidirect
403. #2363	C₂×C₁₃₉	semidirect
404. #2344	C₂×C₁₃₉	semidirect
405. C₄×#123	C₂×C₁₃₉	semidirect
406. #2280	C₂×C₁₃₉	semidirect
410. C₂×#126	C₂²×C₁₃₉	semidirect
411. C₂×#125	C₂²×C₁₃₉	semidirect
412. C₂×#125	C₂²×C₁₃₉	semidirect
417. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
420. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
428. C₂×#117	C₂²×C₁₃₉	semidirect
432. #399	C₂²×C₁₃₉	semidirect
433. #397	C₂²×C₁₃₉	semidirect
434. #396	C₂²×C₁₃₉	semidirect
437. #394	C₂²×C₁₃₉	semidirect
439. #391	C₂²×C₁₃₉	semidirect
442. #390	C₂²×C₁₃₉	semidirect
443. #389	C₂²×C₁₃₉	semidirect
444. #389	C₂²×C₁₃₉	semidirect
445. #388	C₂²×C₁₃₉	semidirect
446. #388	C₂²×C₁₃₉	semidirect
447. #388	C₂²×C₁₃₉	semidirect
448. #388	C₂²×C₁₃₉	semidirect
449. #387	C₂²×C₁₃₉	semidirect
450. #387	C₂²×C₁₃₉	semidirect
451. #387	C₂²×C₁₃₉	semidirect
453. #386	C₂²×C₁₃₉	semidirect
454. #386	C₂²×C₁₃₉	semidirect
457. #385	C₂²×C₁₃₉	semidirect
458. #385	C₂²×C₁₃₉	semidirect
463. #380	C₂²×C₁₃₉	semidirect
464. #380	C₂²×C₁₃₉	semidirect
468. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
469. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
471. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
472. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
473. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
510. C₂×C₄⋊C₄	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
C₂²×C₄×D₄×C₁₃₉	2
#2855×C₁₃₉	2
#2849×C₁₃₉	2
#2482×C₁₃₉	2
#2467×C₁₃₉	2
#2460×C₁₃₉	2
#2454×C₁₃₉	2
#2435×C₁₃₉	2
#2427×C₁₃₉	2
#2411×C₁₃₉	2
#2408×C₁₃₉	2
#2367×C₁₃₉	2
#2363×C₁₃₉	2
#2344×C₁₃₉	2
C₄×#123×C₁₃₉	2
#2280×C₁₃₉	2
#36162	139

Subgroups — C139×#36162 #48030758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36162 #48030758