Subgroups — C₁₃₉×#36154 #48030750

Order 35584.

2968 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2848×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2563×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2538×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2487×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2454×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2450×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2442×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2437×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2417×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2349×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	2	yes	maximal
16	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#380×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	#554×C₁₃₉	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×#125×C₁₃₉	C₂²	1	2	yes	complemented
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
28	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₁₃₉	—	2	8	no	—
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
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	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
40	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
41	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
42	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
43	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
44	#400×C₁₃₉	C₂²	1	4	yes	complemented
45	#399×C₁₃₉	C₂²	1	4	yes	complemented
46	#398×C₁₃₉	C₂²	1	4	yes	complemented
47	#396×C₁₃₉	C₂²	1	4	yes	complemented
48	#396×C₁₃₉	C₂²	1	4	yes	complemented
49	#393×C₁₃₉	C₂²	1	4	yes	complemented
50	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
51	#391×C₁₃₉	C₂²	1	2	yes	complemented
52	#390×C₁₃₉	C₂²	1	2	yes	—
53	#390×C₁₃₉	C₂²	1	2	yes	—
54	#389×C₁₃₉	C₂²	1	2	yes	complemented
55	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
56	#389×C₁₃₉	C₂²	1	2	yes	complemented
57	#389×C₁₃₉	C₂²	1	2	yes	complemented
58	#389×C₁₃₉	C₂²	1	2	yes	complemented
59	#387×C₁₃₉	C₂²	1	2	yes	complemented
60	#386×C₁₃₉	C₂²	1	4	yes	—
61	#386×C₁₃₉	C₂²	1	4	yes	—
62	#385×C₁₃₉	C₂²	1	2	yes	—
63	#385×C₁₃₉	C₂²	1	4	yes	—
64	#385×C₁₃₉	C₂²	1	4	yes	complemented
65	#385×C₁₃₉	C₂²	1	4	yes	complemented
66	#385×C₁₃₉	C₂²	1	4	yes	complemented
67	#385×C₁₃₉	C₂²	1	4	yes	complemented
68	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
69	#382×C₁₃₉	C₂²	1	2	yes	complemented
70	#380×C₁₃₉	C₂²	1	1	yes	characteristic
71	#380×C₁₃₉	C₂²	1	2	yes	—
72	#380×C₁₃₉	C₂²	1	4	yes	—
73	#380×C₁₃₉	C₂²	1	2	yes	—
74	#380×C₁₃₉	C₂²	1	2	yes	complemented
75	#380×C₁₃₉	C₂²	1	2	yes	complemented
76	#380×C₁₃₉	C₂²	1	4	yes	complemented
77	#380×C₁₃₉	C₂²	1	2	yes	complemented
78	#380×C₁₃₉	C₂²	1	2	yes	complemented
79	#380×C₁₃₉	C₂²	1	4	yes	complemented
80	#379×C₁₃₉	C₂²	1	4	yes	—
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
82	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
84	C₂×#95×C₁₃₉	C₂²	1	4	yes	complemented
85	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
86	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃₉	—	2	4	no	—
89	C₂²×D₄×C₁₃₉	—	2	4	no	—
90	C₂²×D₄×C₁₃₉	Q₈	1	8	yes	complemented
91	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃₉	—	2	8	no	—
95	C₂³×C₄×C₁₃₉	—	2	8	no	—
96	C₂³×C₄×C₁₃₉	—	4	4	no	—
97	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
106	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
107	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
108	#125×C₁₃₉	—	2	8	no	—
109	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
110	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
111	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
112	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
113	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
114	C₄×Q₈×C₁₃₉	—	2	4	no	—
115	C₄×D₄×C₁₃₉	—	2	4	no	—
116	C₄×D₄×C₁₃₉	—	2	8	no	—
117	C₄×D₄×C₁₃₉	—	2	8	no	—
118	C₄×D₄×C₁₃₉	—	2	8	no	—
119	C₄×D₄×C₁₃₉	—	2	4	no	—
120	C₄×D₄×C₁₃₉	—	2	8	no	—
121	C₄×D₄×C₁₃₉	—	2	4	no	—
122	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
124	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
125	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
146	C₂×C₂²⋊C₄×C₁₃₉	—	4	8	no	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃₉	—	2	4	no	—
161	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
167	#95×C₁₃₉	C₂³	1	2	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	2	yes	—
170	#95×C₁₃₉	C₂³	1	4	yes	—
171	#95×C₁₃₉	C₂³	1	4	yes	—
172	#95×C₁₃₉	C₂³	1	4	yes	—
173	#95×C₁₃₉	C₂³	1	2	yes	—
174	#95×C₁₃₉	C₂³	1	4	yes	—
175	#95×C₁₃₉	C₂³	1	2	yes	—
176	#95×C₁₃₉	C₂³	1	4	yes	—
177	#95×C₁₃₉	C₂³	1	2	yes	—
178	C₂⁴×C₁₃₉	—	2	4	no	—
179	C₂⁴×C₁₃₉	—	2	4	no	—
180	C₂⁴×C₁₃₉	—	2	4	no	—
181	C₂⁴×C₁₃₉	—	2	4	no	—
182	C₂⁴×C₁₃₉	—	4	2	no	—
183	C₂⁴×C₁₃₉	—	4	2	no	—
184	C₂⁴×C₁₃₉	C₂×Q₈	1	8	yes	—
185	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
186	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
187	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
188	C₂×Q₈×C₁₃₉	—	2	2	no	—
189	C₂×Q₈×C₁₃₉	—	2	4	no	—
190	C₂×Q₈×C₁₃₉	—	2	2	no	—
191	C₂×Q₈×C₁₃₉	—	2	2	no	—
192	C₂×Q₈×C₁₃₉	—	4	2	no	—
193	C₂×Q₈×C₁₃₉	—	4	2	no	—
194	C₂×D₄×C₁₃₉	—	2	4	no	—
195	C₂×D₄×C₁₃₉	—	2	4	no	—
196	C₂×D₄×C₁₃₉	—	2	32	no	—
197	C₂×D₄×C₁₃₉	—	2	2	no	—
198	C₂×D₄×C₁₃₉	—	2	2	no	—
199	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
200	C₂×D₄×C₁₃₉	C₂×Q₈	1	8	yes	—
201	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
202	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
203	C₂×D₄×C₁₃₉	#41	1	4	yes	—
204	C₂²×C₄×C₁₃₉	—	2	2	no	—
205	C₂²×C₄×C₁₃₉	—	2	2	no	—
206	C₂²×C₄×C₁₃₉	—	2	4	no	—
207	C₂²×C₄×C₁₃₉	—	2	2	no	—
208	C₂²×C₄×C₁₃₉	—	2	4	no	—
209	C₂²×C₄×C₁₃₉	—	2	2	no	—
210	C₂²×C₄×C₁₃₉	—	2	4	no	—
211	C₂²×C₄×C₁₃₉	—	2	4	no	—
212	C₂²×C₄×C₁₃₉	—	2	2	no	—
213	C₂²×C₄×C₁₃₉	—	2	8	no	—
214	C₂²×C₄×C₁₃₉	—	2	8	no	—
215	C₂²×C₄×C₁₃₉	—	2	2	no	—
216	C₂²×C₄×C₁₃₉	—	2	4	no	—
217	C₂²×C₄×C₁₃₉	—	2	4	no	—
218	C₂²×C₄×C₁₃₉	—	2	4	no	—
219	C₂²×C₄×C₁₃₉	—	2	4	no	—
220	C₂²×C₄×C₁₃₉	—	2	4	no	—
221	C₂²×C₄×C₁₃₉	—	2	4	no	—
222	C₂²×C₄×C₁₃₉	—	2	4	no	—
223	C₂²×C₄×C₁₃₉	—	4	2	no	—
224	C₂²×C₄×C₁₃₉	—	4	2	no	—
225	C₂²×C₄×C₁₃₉	—	4	2	no	—
226	C₂²×C₄×C₁₃₉	—	4	1	no	—
227	C₂²×C₄×C₁₃₉	—	4	32	no	—
228	C₂²×C₄×C₁₃₉	—	4	4	no	—
229	C₂²×C₄×C₁₃₉	—	4	4	no	—
230	C₂²×C₄×C₁₃₉	—	4	4	no	—
231	C₂²×C₄×C₁₃₉	—	4	4	no	—
232	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
233	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
234	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
235	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
240	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
241	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
249	C₄⋊C₄×C₁₃₉	—	2	2	no	—
250	C₄⋊C₄×C₁₃₉	—	2	4	no	—
251	C₄⋊C₄×C₁₃₉	—	2	2	no	—
252	C₄⋊C₄×C₁₃₉	—	2	8	no	—
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	8	no	—
257	C₄⋊C₄×C₁₃₉	—	2	4	no	—
258	C₄⋊C₄×C₁₃₉	—	2	2	no	—
259	C₄⋊C₄×C₁₃₉	—	2	4	no	—
260	C₄⋊C₄×C₁₃₉	—	2	2	no	—
261	C₄⋊C₄×C₁₃₉	—	2	4	no	—
262	C₄⋊C₄×C₁₃₉	—	4	4	no	—
263	C₄⋊C₄×C₁₃₉	—	4	2	no	—
264	C₄⋊C₄×C₁₃₉	—	4	2	no	—
265	C₄⋊C₄×C₁₃₉	—	4	4	no	—
266	C₄⋊C₄×C₁₃₉	—	4	4	no	—
267	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
268	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
270	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
271	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
272	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
273	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
274	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
275	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
276	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
277	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
278	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
279	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
280	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
281	C₄²×C₁₃₉	—	2	2	no	—
282	C₄²×C₁₃₉	—	2	2	no	—
283	C₄²×C₁₃₉	—	2	2	no	—
284	C₄²×C₁₃₉	—	2	4	no	—
285	C₄²×C₁₃₉	—	2	4	no	—
286	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
287	C₂³×C₁₃₉	—	2	1	no	—
288	C₂³×C₁₃₉	—	2	2	no	—
289	C₂³×C₁₃₉	—	2	1	no	—
290	C₂³×C₁₃₉	—	2	2	no	—
291	C₂³×C₁₃₉	—	2	1	no	—
292	C₂³×C₁₃₉	—	2	2	no	—
293	C₂³×C₁₃₉	—	2	2	no	—
294	C₂³×C₁₃₉	—	2	1	no	—
295	C₂³×C₁₃₉	—	2	16	no	—
296	C₂³×C₁₃₉	—	2	16	no	—
297	C₂³×C₁₃₉	—	2	2	no	—
298	C₂³×C₁₃₉	—	2	2	no	—
299	C₂³×C₁₃₉	—	2	2	no	—
300	C₂³×C₁₃₉	—	2	2	no	—
301	C₂³×C₁₃₉	—	2	2	no	—
302	C₂³×C₁₃₉	—	2	2	no	—
303	C₂³×C₁₃₉	—	4	8	no	—
304	C₂³×C₁₃₉	—	4	8	no	—
305	C₂³×C₁₃₉	—	4	8	no	—
306	C₂³×C₁₃₉	—	4	8	no	—
307	C₂³×C₁₃₉	—	4	8	no	—
308	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
309	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
310	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
311	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
312	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
313	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
314	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
315	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
316	Q₈×C₁₃₉	—	4	4	no	—
317	Q₈×C₁₃₉	—	8	4	no	—
318	D₄×C₁₃₉	—	2	16	no	—
319	D₄×C₁₃₉	—	2	8	no	—
320	D₄×C₁₃₉	C₂²⋊Q₈	1	16	yes	complemented
321	C₂×C₄×C₁₃₉	—	2	1	no	—
322	C₂×C₄×C₁₃₉	—	2	1	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	1	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	1	no	—
327	C₂×C₄×C₁₃₉	—	2	1	no	—
328	C₂×C₄×C₁₃₉	—	2	1	no	—
329	C₂×C₄×C₁₃₉	—	2	8	no	—
330	C₂×C₄×C₁₃₉	—	2	8	no	—
331	C₂×C₄×C₁₃₉	—	2	16	no	—
332	C₂×C₄×C₁₃₉	—	2	1	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	4	no	—
337	C₂×C₄×C₁₃₉	—	2	2	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	4	no	—
341	C₂×C₄×C₁₃₉	—	2	2	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	2	no	—
345	C₂×C₄×C₁₃₉	—	2	4	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	2	no	—
350	C₂×C₄×C₁₃₉	—	2	1	no	—
351	C₂×C₄×C₁₃₉	—	2	2	no	—
352	C₂×C₄×C₁₃₉	—	2	2	no	—
353	C₂×C₄×C₁₃₉	—	2	4	no	—
354	C₂×C₄×C₁₃₉	—	2	1	no	—
355	C₂×C₄×C₁₃₉	—	2	2	no	—
356	C₂×C₄×C₁₃₉	—	4	8	no	—
357	C₂×C₄×C₁₃₉	—	4	4	no	—
358	C₂×C₄×C₁₃₉	—	4	8	no	—
359	C₂×C₄×C₁₃₉	—	4	8	no	—
360	C₂×C₄×C₁₃₉	—	4	8	no	—
361	C₂×C₄×C₁₃₉	—	8	8	no	—
362	C₂×C₄×C₁₃₉	—	8	8	no	—
363	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
364	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
365	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
366	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
367	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
368	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
369	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
370	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
371	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
372	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
373	C₂²×C₁₃₉	—	2	2	no	—
374	C₂²×C₁₃₉	—	2	2	no	—
375	C₂²×C₁₃₉	—	2	4	no	—
376	C₂²×C₁₃₉	—	2	4	no	—
377	C₂²×C₁₃₉	—	2	2	no	—
378	C₂²×C₁₃₉	—	2	4	no	—
379	C₂²×C₁₃₉	—	2	2	no	—
380	C₂²×C₁₃₉	—	2	4	no	—
381	C₂²×C₁₃₉	—	2	2	no	—
382	C₂²×C₁₃₉	—	2	4	no	—
383	C₂²×C₁₃₉	—	2	4	no	—
384	C₂²×C₁₃₉	—	2	2	no	—
385	C₂²×C₁₃₉	—	2	4	no	—
386	C₂²×C₁₃₉	—	2	4	no	—
387	C₂²×C₁₃₉	—	2	4	no	—
388	C₂²×C₁₃₉	—	4	32	no	—
389	C₂²×C₁₃₉	—	4	2	no	—
390	C₂²×C₁₃₉	—	4	2	no	—
391	C₂²×C₁₃₉	—	4	2	no	—
392	C₂²×C₁₃₉	—	4	2	no	—
393	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	8	yes	—
394	C₂²×C₁₃₉	#554	1	4	yes	complemented
395	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
396	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
397	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
398	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
399	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
401	C₂²×C₁₃₉	#585	1	1	yes	characteristic
402	C₄×C₁₃₉	—	2	2	no	—
403	C₄×C₁₃₉	—	2	2	no	—
404	C₄×C₁₃₉	—	2	4	no	—
405	C₄×C₁₃₉	—	2	2	no	—
406	C₄×C₁₃₉	—	4	2	no	—
407	C₄×C₁₃₉	—	4	2	no	—
408	C₄×C₁₃₉	—	4	2	no	—
409	C₄×C₁₃₉	—	4	1	no	—
410	C₄×C₁₃₉	—	4	2	no	—
411	C₄×C₁₃₉	—	4	4	no	—
412	C₄×C₁₃₉	—	4	4	no	—
413	C₄×C₁₃₉	—	4	2	no	—
414	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	4	yes	—
415	C₄×C₁₃₉	#546	1	4	yes	—
416	C₂×C₁₃₉	—	2	4	no	—
417	C₂×C₁₃₉	—	2	8	no	—
418	C₂×C₁₃₉	—	4	4	no	—
419	C₂×C₁₃₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
420	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
421	C₂×C₁₃₉	C₂×#554	1	1	yes	characteristic
422	C₂×C₁₃₉	#3475	1	1	yes	characteristic
423	C₂×C₁₃₉	#3488	1	1	yes	characteristic
424	C₂×C₁₃₉	#3501	1	1	yes	characteristic
425	C₂×C₁₃₉	#3519	1	1	yes	characteristic
426	#36154	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
427	C₁₃₉	#36154	1	1	yes	characteristic, direct product factor, Sylow
428	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic, complemented
429	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic
430	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
431	#2848	C₂×C₁₃₉	1	2	yes	complemented
432	#2563	C₂×C₁₃₉	1	1	yes	characteristic, complemented
433	#2538	C₂×C₁₃₉	1	1	yes	characteristic, complemented
434	#2487	C₂×C₁₃₉	1	2	yes	complemented
435	#2454	C₂×C₁₃₉	1	2	yes	complemented
436	#2450	C₂×C₁₃₉	1	4	yes	complemented
437	#2442	C₂×C₁₃₉	1	2	yes	complemented
438	#2437	C₂×C₁₃₉	1	4	yes	complemented
439	#2417	C₂×C₁₃₉	1	2	yes	complemented
440	#2349	C₂×C₁₃₉	1	2	yes	complemented
441	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
442	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	2	yes	—
443	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
444	C₂×#380	C₂×C₁₃₉	1	2	yes	complemented
445	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
446	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
447	#554	—	2	8	no	—
448	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
449	C₂×#125	C₂²×C₁₃₉	1	2	yes	complemented
450	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
451	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
452	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
453	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
454	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
455	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
456	C₂×C₄×D₄	—	2	8	no	—
457	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
458	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
459	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
460	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
461	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
462	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
463	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
464	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
465	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
466	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
467	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
468	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
469	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
470	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
471	#400	C₂²×C₁₃₉	1	4	yes	complemented
472	#399	C₂²×C₁₃₉	1	4	yes	complemented
473	#398	C₂²×C₁₃₉	1	4	yes	complemented
474	#396	C₂²×C₁₃₉	1	4	yes	complemented
475	#396	C₂²×C₁₃₉	1	4	yes	complemented
476	#393	C₂²×C₁₃₉	1	4	yes	complemented
477	#391	C₂²×C₁₃₉	1	2	yes	complemented
478	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
479	#390	C₂²×C₁₃₉	1	2	yes	—
480	#390	C₂²×C₁₃₉	1	2	yes	—
481	#389	C₂²×C₁₃₉	1	2	yes	complemented
482	#389	C₂²×C₁₃₉	1	2	yes	complemented
483	#389	C₂²×C₁₃₉	1	2	yes	complemented
484	#389	C₂²×C₁₃₉	1	2	yes	complemented
485	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
486	#387	C₂²×C₁₃₉	1	2	yes	complemented
487	#386	C₂²×C₁₃₉	1	4	yes	—
488	#386	C₂²×C₁₃₉	1	4	yes	—
489	#385	C₂²×C₁₃₉	1	4	yes	—
490	#385	C₂²×C₁₃₉	1	2	yes	—
491	#385	C₂²×C₁₃₉	1	4	yes	complemented
492	#385	C₂²×C₁₃₉	1	4	yes	complemented
493	#385	C₂²×C₁₃₉	1	4	yes	complemented
494	#385	C₂²×C₁₃₉	1	4	yes	complemented
495	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
496	#382	C₂²×C₁₃₉	1	2	yes	complemented
497	#380	C₂²×C₁₃₉	1	2	yes	—
498	#380	C₂²×C₁₃₉	1	2	yes	—
499	#380	C₂²×C₁₃₉	1	4	yes	—
500	#380	C₂²×C₁₃₉	1	1	yes	characteristic
501	#380	C₂²×C₁₃₉	1	2	yes	complemented
502	#380	C₂²×C₁₃₉	1	2	yes	complemented
503	#380	C₂²×C₁₃₉	1	2	yes	complemented
504	#380	C₂²×C₁₃₉	1	4	yes	complemented
505	#380	C₂²×C₁₃₉	1	4	yes	complemented
506	#380	C₂²×C₁₃₉	1	2	yes	complemented
507	#379	C₂²×C₁₃₉	1	4	yes	—
508	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
509	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
510	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
511	C₂×#95	C₂²×C₁₃₉	1	4	yes	complemented
512	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
513	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
514	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
515	C₂²×D₄	—	2	4	no	—
516	C₂²×D₄	—	2	4	no	—
517	C₂²×D₄	Q₈×C₁₃₉	1	8	yes	complemented
518	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
519	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
520	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
521	C₂³×C₄	—	2	8	no	—
522	C₂³×C₄	—	2	8	no	—
523	C₂³×C₄	—	4	4	no	—
524	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
525	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
526	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
527	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
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	4	yes	—
533	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
534	C₄⋊Q₈	—	2	4	no	—
535	#125	—	2	8	no	—
536	C₂²⋊Q₈	—	2	8	no	—
537	C₂²⋊Q₈	—	2	4	no	—
538	C₂²⋊Q₈	—	2	16	no	—
539	C₂²⋊Q₈	—	4	4	no	—
540	C₂²⋊Q₈	—	4	4	no	—
541	C₄×Q₈	—	2	4	no	—
542	C₄×D₄	—	2	4	no	—
543	C₄×D₄	—	2	8	no	—
544	C₄×D₄	—	2	8	no	—
545	C₄×D₄	—	2	8	no	—
546	C₄×D₄	—	2	4	no	—
547	C₄×D₄	—	2	8	no	—
548	C₄×D₄	—	2	4	no	—
549	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
550	C₂×C₄⋊C₄	—	2	8	no	—
551	C₂×C₄⋊C₄	—	2	4	no	—
552	C₂×C₄⋊C₄	—	4	4	no	—
553	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	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	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
566	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
567	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
572	C₂×C₂²⋊C₄	—	2	8	no	—
573	C₂×C₂²⋊C₄	—	4	8	no	—
574	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	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	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₄²	—	2	4	no	—
588	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
589	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
591	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
592	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
593	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
594	#95	C₂³×C₁₃₉	1	2	yes	—
595	#95	C₂³×C₁₃₉	1	4	yes	—
596	#95	C₂³×C₁₃₉	1	4	yes	—
597	#95	C₂³×C₁₃₉	1	4	yes	—
598	#95	C₂³×C₁₃₉	1	2	yes	—
599	#95	C₂³×C₁₃₉	1	2	yes	—
600	#95	C₂³×C₁₃₉	1	2	yes	—
601	#95	C₂³×C₁₃₉	1	2	yes	—
602	#95	C₂³×C₁₃₉	1	4	yes	—
603	#95	C₂³×C₁₃₉	1	4	yes	—
604	#95	C₂³×C₁₃₉	1	4	yes	—
605	C₂⁴	—	2	4	no	—
606	C₂⁴	—	2	4	no	—
607	C₂⁴	—	2	4	no	—
608	C₂⁴	—	2	4	no	—
609	C₂⁴	—	4	2	no	—
610	C₂⁴	—	4	2	no	—
611	C₂⁴	C₂×Q₈×C₁₃₉	1	8	yes	—
612	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
613	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
614	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
615	C₂×Q₈	—	2	2	no	—
616	C₂×Q₈	—	2	4	no	—
617	C₂×Q₈	—	2	2	no	—
618	C₂×Q₈	—	2	2	no	—
619	C₂×Q₈	—	4	2	no	—
620	C₂×Q₈	—	4	2	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	32	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
627	C₂×D₄	C₂×Q₈×C₁₃₉	1	8	yes	—
628	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
629	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
630	C₂×D₄	#41×C₁₃₉	1	4	yes	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	8	no	—
641	C₂²×C₄	—	2	8	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	4	2	no	—
651	C₂²×C₄	—	4	2	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	1	no	—
654	C₂²×C₄	—	4	32	no	—
655	C₂²×C₄	—	4	4	no	—
656	C₂²×C₄	—	4	4	no	—
657	C₂²×C₄	—	4	4	no	—
658	C₂²×C₄	—	4	4	no	—
659	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
660	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
661	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
662	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
667	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
668	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	8	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	8	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	4	4	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	4	2	no	—
692	C₄⋊C₄	—	4	4	no	—
693	C₄⋊C₄	—	4	4	no	—
694	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	8	no	—
697	C₂²⋊C₄	—	2	8	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	8	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	4	4	no	—
704	C₂²⋊C₄	—	4	4	no	—
705	C₂²⋊C₄	—	4	4	no	—
706	C₂²⋊C₄	—	4	4	no	—
707	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
708	C₄²	—	2	2	no	—
709	C₄²	—	2	2	no	—
710	C₄²	—	2	2	no	—
711	C₄²	—	2	4	no	—
712	C₄²	—	2	4	no	—
713	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	16	no	—
723	C₂³	—	2	16	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	4	8	no	—
731	C₂³	—	4	8	no	—
732	C₂³	—	4	8	no	—
733	C₂³	—	4	8	no	—
734	C₂³	—	4	8	no	—
735	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
736	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
737	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
738	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
739	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
740	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
741	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
742	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
743	Q₈	—	4	4	no	—
744	Q₈	—	8	4	no	—
745	D₄	—	2	16	no	—
746	D₄	—	2	8	no	—
747	D₄	C₂²⋊Q₈×C₁₃₉	1	16	yes	complemented
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	8	no	—
757	C₂×C₄	—	2	8	no	—
758	C₂×C₄	—	2	16	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	4	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	4	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	4	8	no	—
784	C₂×C₄	—	4	8	no	—
785	C₂×C₄	—	4	8	no	—
786	C₂×C₄	—	4	4	no	—
787	C₂×C₄	—	4	8	no	—
788	C₂×C₄	—	8	8	no	—
789	C₂×C₄	—	8	8	no	—
790	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
791	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
792	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
793	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
794	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
795	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
796	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
797	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
798	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
799	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	4	no	—
803	C₂²	—	2	4	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	4	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	4	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	4	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	4	no	—
813	C₂²	—	2	4	no	—
814	C₂²	—	2	4	no	—
815	C₂²	—	4	32	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	8	yes	—
821	C₂²	#554×C₁₃₉	1	4	yes	complemented
822	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
823	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
824	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
825	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
826	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
827	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
828	C₂²	#585×C₁₃₉	1	1	yes	characteristic
829	C₄	—	2	2	no	—
830	C₄	—	2	2	no	—
831	C₄	—	2	4	no	—
832	C₄	—	2	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	4	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	4	no	—
841	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	4	yes	—
842	C₄	#546×C₁₃₉	1	4	yes	—
843	C₂	—	2	4	no	—
844	C₂	—	2	8	no	—
845	C₂	—	4	4	no	—
846	C₂	C₂²×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
847	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
848	C₂	C₂×#554×C₁₃₉	1	1	yes	characteristic
849	C₂	#3475×C₁₃₉	1	1	yes	characteristic
850	C₂	#3488×C₁₃₉	1	1	yes	characteristic
851	C₂	#3501×C₁₃₉	1	1	yes	characteristic
852	C₂	#3519×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂³×D₄×C₁₃₉	C₂²
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×#554×C₁₃₉	C₂	semidirect
3. #2857×C₁₃₉	C₂	semidirect
4. #2848×C₁₃₉	C₂	semidirect
5. #2563×C₁₃₉	C₂	semidirect
6. #2538×C₁₃₉	C₂	semidirect
7. #2487×C₁₃₉	C₂	semidirect
8. #2454×C₁₃₉	C₂	semidirect
9. #2450×C₁₃₉	C₂	semidirect
10. #2442×C₁₃₉	C₂	semidirect
11. #2437×C₁₃₉	C₂	semidirect
12. #2417×C₁₃₉	C₂	semidirect
13. #2349×C₁₃₉	C₂	semidirect
14. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
16. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
17. C₂×#380×C₁₃₉	C₂	semidirect
21. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
22. C₂×#125×C₁₃₉	C₂²	semidirect
25. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
28. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
39. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
40. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
44. #400×C₁₃₉	C₂²	semidirect
45. #399×C₁₃₉	C₂²	semidirect
46. #398×C₁₃₉	C₂²	semidirect
47. #396×C₁₃₉	C₂²	semidirect
48. #396×C₁₃₉	C₂²	semidirect
49. #393×C₁₃₉	C₂²	semidirect
50. #391×C₁₃₉	C₂²	semidirect
51. #391×C₁₃₉	C₂²	semidirect
54. #389×C₁₃₉	C₂²	semidirect
55. #389×C₁₃₉	C₂²	semidirect
56. #389×C₁₃₉	C₂²	semidirect
57. #389×C₁₃₉	C₂²	semidirect
58. #389×C₁₃₉	C₂²	semidirect
59. #387×C₁₃₉	C₂²	semidirect
64. #385×C₁₃₉	C₂²	semidirect
65. #385×C₁₃₉	C₂²	semidirect
66. #385×C₁₃₉	C₂²	semidirect
67. #385×C₁₃₉	C₂²	semidirect
68. #384×C₁₃₉	C₂²	semidirect
69. #382×C₁₃₉	C₂²	semidirect
74. #380×C₁₃₉	C₂²	semidirect
75. #380×C₁₃₉	C₂²	semidirect
76. #380×C₁₃₉	C₂²	semidirect
77. #380×C₁₃₉	C₂²	semidirect
78. #380×C₁₃₉	C₂²	semidirect
79. #380×C₁₃₉	C₂²	semidirect
81. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
82. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
84. C₂×#95×C₁₃₉	C₂²	semidirect
90. C₂²×D₄×C₁₃₉	Q₈	semidirect
320. D₄×C₁₃₉	C₂²⋊Q₈	semidirect
394. C₂²×C₁₃₉	#554	semidirect
426. #36154	C₁₃₉	direct (N × H)
427. C₁₃₉	#36154	direct (N × H)
428. C₂×#554	C₂×C₁₃₉	semidirect
430. #2857	C₂×C₁₃₉	semidirect
431. #2848	C₂×C₁₃₉	semidirect
432. #2563	C₂×C₁₃₉	semidirect
433. #2538	C₂×C₁₃₉	semidirect
434. #2487	C₂×C₁₃₉	semidirect
435. #2454	C₂×C₁₃₉	semidirect
436. #2450	C₂×C₁₃₉	semidirect
437. #2442	C₂×C₁₃₉	semidirect
438. #2437	C₂×C₁₃₉	semidirect
439. #2417	C₂×C₁₃₉	semidirect
440. #2349	C₂×C₁₃₉	semidirect
441. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
443. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
444. C₂×#380	C₂×C₁₃₉	semidirect
448. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
449. C₂×#125	C₂²×C₁₃₉	semidirect
452. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
453. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
454. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
455. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
466. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
467. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
471. #400	C₂²×C₁₃₉	semidirect
472. #399	C₂²×C₁₃₉	semidirect
473. #398	C₂²×C₁₃₉	semidirect
474. #396	C₂²×C₁₃₉	semidirect
475. #396	C₂²×C₁₃₉	semidirect
476. #393	C₂²×C₁₃₉	semidirect
477. #391	C₂²×C₁₃₉	semidirect
478. #391	C₂²×C₁₃₉	semidirect
481. #389	C₂²×C₁₃₉	semidirect
482. #389	C₂²×C₁₃₉	semidirect
483. #389	C₂²×C₁₃₉	semidirect
484. #389	C₂²×C₁₃₉	semidirect
485. #389	C₂²×C₁₃₉	semidirect
486. #387	C₂²×C₁₃₉	semidirect
491. #385	C₂²×C₁₃₉	semidirect
492. #385	C₂²×C₁₃₉	semidirect
493. #385	C₂²×C₁₃₉	semidirect
494. #385	C₂²×C₁₃₉	semidirect
495. #384	C₂²×C₁₃₉	semidirect
496. #382	C₂²×C₁₃₉	semidirect
501. #380	C₂²×C₁₃₉	semidirect
502. #380	C₂²×C₁₃₉	semidirect
503. #380	C₂²×C₁₃₉	semidirect
504. #380	C₂²×C₁₃₉	semidirect
505. #380	C₂²×C₁₃₉	semidirect
506. #380	C₂²×C₁₃₉	semidirect
508. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
509. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
511. C₂×#95	C₂²×C₁₃₉	semidirect
517. C₂²×D₄	Q₈×C₁₃₉	semidirect
747. D₄	C₂²⋊Q₈×C₁₃₉	semidirect
821. C₂²	#554×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₁₃₉	2
C₂²×C₄×D₄×C₁₃₉	2
#2857×C₁₃₉	2
#2848×C₁₃₉	2
#2563×C₁₃₉	2
#2538×C₁₃₉	2
#2487×C₁₃₉	2
#2454×C₁₃₉	2
#2450×C₁₃₉	2
#2442×C₁₃₉	2
#2437×C₁₃₉	2
#2417×C₁₃₉	2
#2349×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
C₂×#380×C₁₃₉	2
#36154	139

Subgroups — C139×#36154 #48030750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36154 #48030750