Subgroups — C₁₃₉×#36274 #48030870

Order 35584.

2644 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2855×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2582×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2568×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2451×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2450×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2439×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2438×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2417×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2409×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	#2339×C₁₃₉	C₂	1	2	yes	maximal
16	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#391×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂³×Q₈×C₁₃₉	C₂²	1	2	yes	—
20	D₄×Q₈×C₁₃₉	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
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	4	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₄×#41×C₁₃₉	—	2	8	no	—
28	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×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×#117×C₁₃₉	C₂²	1	2	yes	—
38	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
40	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
41	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
42	#400×C₁₃₉	C₂²	1	4	yes	—
43	#398×C₁₃₉	C₂²	1	4	yes	—
44	#398×C₁₃₉	C₂²	1	4	yes	—
45	#396×C₁₃₉	C₂²	1	4	yes	—
46	#395×C₁₃₉	C₂²	1	4	yes	—
47	#393×C₁₃₉	C₂²	1	4	yes	—
48	#391×C₁₃₉	C₂²	1	1	yes	characteristic
49	#391×C₁₃₉	C₂²	1	2	yes	—
50	#391×C₁₃₉	C₂²	1	2	yes	—
51	#391×C₁₃₉	C₂²	1	2	yes	—
52	#391×C₁₃₉	C₂²	1	4	yes	—
53	#391×C₁₃₉	C₂²	1	4	yes	—
54	#391×C₁₃₉	C₂²	1	2	yes	—
55	#391×C₁₃₉	C₂²	1	2	yes	—
56	#391×C₁₃₉	C₂²	1	2	yes	—
57	#389×C₁₃₉	C₂²	1	1	yes	characteristic
58	#389×C₁₃₉	C₂²	1	2	yes	—
59	#389×C₁₃₉	C₂²	1	2	yes	—
60	#389×C₁₃₉	C₂²	1	2	yes	—
61	#389×C₁₃₉	C₂²	1	2	yes	—
62	#389×C₁₃₉	C₂²	1	2	yes	—
63	#387×C₁₃₉	C₂²	1	2	yes	—
64	#387×C₁₃₉	C₂²	1	4	yes	—
65	#387×C₁₃₉	C₂²	1	4	yes	—
66	#386×C₁₃₉	C₂²	1	4	yes	—
67	#386×C₁₃₉	C₂²	1	4	yes	—
68	#385×C₁₃₉	C₂²	1	2	yes	—
69	#385×C₁₃₉	C₂²	1	4	yes	—
70	#385×C₁₃₉	C₂²	1	4	yes	—
71	#385×C₁₃₉	C₂²	1	4	yes	—
72	#384×C₁₃₉	C₂²	1	1	yes	characteristic
73	#382×C₁₃₉	C₂²	1	2	yes	—
74	#381×C₁₃₉	C₂²	1	4	yes	—
75	#380×C₁₃₉	C₂²	1	1	yes	characteristic
76	#380×C₁₃₉	C₂²	1	2	yes	—
77	#380×C₁₃₉	C₂²	1	2	yes	—
78	#380×C₁₃₉	C₂²	1	2	yes	—
79	#380×C₁₃₉	C₂²	1	4	yes	—
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
83	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
84	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
85	C₂×#41×C₁₃₉	—	2	4	no	—
86	C₂×#41×C₁₃₉	—	2	4	no	—
87	C₂×#41×C₁₃₉	Q₈	1	8	yes	complemented
88	C₂²×Q₈×C₁₃₉	—	2	8	no	—
89	C₂²×Q₈×C₁₃₉	—	2	8	no	—
90	C₂²×Q₈×C₁₃₉	—	4	4	no	—
91	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
93	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
105	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
106	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
107	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
108	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
109	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
110	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
111	C₄×Q₈×C₁₃₉	—	2	4	no	—
112	C₄×Q₈×C₁₃₉	—	2	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	8	no	—
118	C₄×D₄×C₁₃₉	—	2	8	no	—
119	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
120	#117×C₁₃₉	—	2	4	no	—
121	#117×C₁₃₉	—	2	8	no	—
122	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
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	4	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	4	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄²×C₁₃₉	—	2	8	no	—
151	C₂×C₄²×C₁₃₉	—	2	4	no	—
152	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
161	#95×C₁₃₉	C₂³	1	4	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	2	yes	—
166	#95×C₁₃₉	C₂³	1	4	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	4	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	2	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	C₂⁴	1	1	yes	characteristic
177	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
178	#41×C₁₃₉	—	2	32	no	—
179	C₂×Q₈×C₁₃₉	—	2	2	no	—
180	C₂×Q₈×C₁₃₉	—	2	2	no	—
181	C₂×Q₈×C₁₃₉	—	2	8	no	—
182	C₂×Q₈×C₁₃₉	—	2	4	no	—
183	C₂×Q₈×C₁₃₉	—	2	2	no	—
184	C₂×Q₈×C₁₃₉	—	2	8	no	—
185	C₂×Q₈×C₁₃₉	—	2	4	no	—
186	C₂×Q₈×C₁₃₉	—	2	2	no	—
187	C₂×Q₈×C₁₃₉	—	2	4	no	—
188	C₂×Q₈×C₁₃₉	—	4	4	no	—
189	C₂×Q₈×C₁₃₉	—	4	32	no	—
190	C₂×Q₈×C₁₃₉	C₂×Q₈	1	4	yes	complemented
191	C₂×Q₈×C₁₃₉	#41	1	4	yes	complemented
192	C₂×D₄×C₁₃₉	—	2	4	no	—
193	C₂×D₄×C₁₃₉	—	2	4	no	—
194	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
195	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
196	C₂×D₄×C₁₃₉	C₂×Q₈	1	8	yes	complemented
197	C₂×D₄×C₁₃₉	#41	1	4	yes	—
198	C₂²×C₄×C₁₃₉	—	2	4	no	—
199	C₂²×C₄×C₁₃₉	—	2	4	no	—
200	C₂²×C₄×C₁₃₉	—	2	2	no	—
201	C₂²×C₄×C₁₃₉	—	2	4	no	—
202	C₂²×C₄×C₁₃₉	—	2	2	no	—
203	C₂²×C₄×C₁₃₉	—	2	4	no	—
204	C₂²×C₄×C₁₃₉	—	2	4	no	—
205	C₂²×C₄×C₁₃₉	—	2	8	no	—
206	C₂²×C₄×C₁₃₉	—	2	8	no	—
207	C₂²×C₄×C₁₃₉	—	2	2	no	—
208	C₂²×C₄×C₁₃₉	—	2	2	no	—
209	C₂²×C₄×C₁₃₉	—	2	2	no	—
210	C₂²×C₄×C₁₃₉	—	2	8	no	—
211	C₂²×C₄×C₁₃₉	—	2	2	no	—
212	C₂²×C₄×C₁₃₉	—	2	2	no	—
213	C₂²×C₄×C₁₃₉	—	2	4	no	—
214	C₂²×C₄×C₁₃₉	—	4	1	no	—
215	C₂²×C₄×C₁₃₉	—	4	2	no	—
216	C₂²×C₄×C₁₃₉	—	4	4	no	—
217	C₂²×C₄×C₁₃₉	—	4	4	no	—
218	C₂²×C₄×C₁₃₉	—	4	4	no	—
219	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
220	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	complemented
221	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	complemented
222	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
226	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
237	C₄⋊C₄×C₁₃₉	—	2	4	no	—
238	C₄⋊C₄×C₁₃₉	—	2	4	no	—
239	C₄⋊C₄×C₁₃₉	—	2	2	no	—
240	C₄⋊C₄×C₁₃₉	—	2	4	no	—
241	C₄⋊C₄×C₁₃₉	—	2	4	no	—
242	C₄⋊C₄×C₁₃₉	—	2	2	no	—
243	C₄⋊C₄×C₁₃₉	—	2	8	no	—
244	C₄⋊C₄×C₁₃₉	—	2	4	no	—
245	C₄⋊C₄×C₁₃₉	—	2	4	no	—
246	C₄⋊C₄×C₁₃₉	—	2	2	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	no	—
248	C₄⋊C₄×C₁₃₉	—	2	2	no	—
249	C₄⋊C₄×C₁₃₉	—	2	4	no	—
250	C₄⋊C₄×C₁₃₉	—	2	4	no	—
251	C₄⋊C₄×C₁₃₉	—	4	4	no	—
252	C₄⋊C₄×C₁₃₉	—	4	2	no	—
253	C₄⋊C₄×C₁₃₉	—	4	4	no	—
254	C₄⋊C₄×C₁₃₉	—	4	4	no	—
255	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
256	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
257	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
261	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
262	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
263	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
264	C₄²×C₁₃₉	—	2	2	no	—
265	C₄²×C₁₃₉	—	2	4	no	—
266	C₄²×C₁₃₉	—	2	2	no	—
267	C₄²×C₁₃₉	—	2	4	no	—
268	C₄²×C₁₃₉	—	2	2	no	—
269	C₄²×C₁₃₉	—	2	4	no	—
270	C₄²×C₁₃₉	—	2	4	no	—
271	C₄²×C₁₃₉	—	2	4	no	—
272	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
273	C₂³×C₁₃₉	—	2	2	no	—
274	C₂³×C₁₃₉	—	2	2	no	—
275	C₂³×C₁₃₉	—	2	2	no	—
276	C₂³×C₁₃₉	—	2	2	no	—
277	C₂³×C₁₃₉	—	2	1	no	—
278	C₂³×C₁₃₉	—	2	1	no	—
279	C₂³×C₁₃₉	—	2	1	no	—
280	C₂³×C₁₃₉	—	2	1	no	—
281	C₂³×C₁₃₉	—	2	1	no	—
282	C₂³×C₁₃₉	—	2	1	no	—
283	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
284	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
285	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
286	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
287	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
288	Q₈×C₁₃₉	—	2	8	no	—
289	Q₈×C₁₃₉	—	2	8	no	—
290	Q₈×C₁₃₉	—	4	16	no	—
291	Q₈×C₁₃₉	—	4	8	no	—
292	D₄×C₁₃₉	—	2	16	no	—
293	D₄×C₁₃₉	C₂²⋊Q₈	1	16	yes	complemented
294	C₂×C₄×C₁₃₉	—	2	16	no	—
295	C₂×C₄×C₁₃₉	—	2	1	no	—
296	C₂×C₄×C₁₃₉	—	2	1	no	—
297	C₂×C₄×C₁₃₉	—	2	2	no	—
298	C₂×C₄×C₁₃₉	—	2	2	no	—
299	C₂×C₄×C₁₃₉	—	2	1	no	—
300	C₂×C₄×C₁₃₉	—	2	2	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	1	no	—
305	C₂×C₄×C₁₃₉	—	2	1	no	—
306	C₂×C₄×C₁₃₉	—	2	1	no	—
307	C₂×C₄×C₁₃₉	—	2	8	no	—
308	C₂×C₄×C₁₃₉	—	2	16	no	—
309	C₂×C₄×C₁₃₉	—	2	1	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	4	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	4	no	—
317	C₂×C₄×C₁₃₉	—	2	1	no	—
318	C₂×C₄×C₁₃₉	—	2	4	no	—
319	C₂×C₄×C₁₃₉	—	2	4	no	—
320	C₂×C₄×C₁₃₉	—	2	4	no	—
321	C₂×C₄×C₁₃₉	—	2	2	no	—
322	C₂×C₄×C₁₃₉	—	2	1	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	2	no	—
325	C₂×C₄×C₁₃₉	—	2	2	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	—	4	4	no	—
331	C₂×C₄×C₁₃₉	—	4	8	no	—
332	C₂×C₄×C₁₃₉	—	4	16	no	—
333	C₂×C₄×C₁₃₉	—	4	4	no	—
334	C₂×C₄×C₁₃₉	—	8	8	no	—
335	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
336	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
340	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
341	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
342	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
343	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
344	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
345	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
346	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
347	C₂²×C₁₃₉	—	2	4	no	—
348	C₂²×C₁₃₉	—	2	4	no	—
349	C₂²×C₁₃₉	—	2	4	no	—
350	C₂²×C₁₃₉	—	2	4	no	—
351	C₂²×C₁₃₉	—	2	4	no	—
352	C₂²×C₁₃₉	—	2	4	no	—
353	C₂²×C₁₃₉	—	2	2	no	—
354	C₂²×C₁₃₉	—	2	2	no	—
355	C₂²×C₁₃₉	—	2	2	no	—
356	C₂²×C₁₃₉	—	4	1	no	—
357	C₂²×C₁₃₉	—	4	1	no	—
358	C₂²×C₁₃₉	—	4	1	no	—
359	C₂²×C₁₃₉	—	4	1	no	—
360	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	8	yes	—
361	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
362	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
363	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
364	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
365	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
366	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
367	C₂²×C₁₃₉	#585	1	1	yes	characteristic
368	C₄×C₁₃₉	—	2	2	no	—
369	C₄×C₁₃₉	—	2	4	no	—
370	C₄×C₁₃₉	—	2	4	no	—
371	C₄×C₁₃₉	—	2	4	no	—
372	C₄×C₁₃₉	—	2	2	no	—
373	C₄×C₁₃₉	—	2	2	no	—
374	C₄×C₁₃₉	—	4	1	no	—
375	C₄×C₁₃₉	—	4	4	no	—
376	C₄×C₁₃₉	—	4	2	no	—
377	C₄×C₁₃₉	—	4	2	no	—
378	C₄×C₁₃₉	—	4	2	no	—
379	C₄×C₁₃₉	—	4	4	no	—
380	C₄×C₁₃₉	—	4	2	no	—
381	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	4	yes	—
382	C₄×C₁₃₉	#546	1	4	yes	—
383	C₂×C₁₃₉	—	2	8	no	—
384	C₂×C₁₃₉	—	4	2	no	—
385	C₂×C₁₃₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
386	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
387	C₂×C₁₃₉	Q₈×#41	1	1	yes	characteristic
388	C₂×C₁₃₉	#3482	1	1	yes	characteristic
389	C₂×C₁₃₉	#3489	1	1	yes	characteristic
390	C₂×C₁₃₉	#3503	1	1	yes	characteristic
391	C₂×C₁₃₉	#3514	1	1	yes	characteristic
392	#36274	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
393	C₁₃₉	#36274	1	1	yes	characteristic, direct product factor, Sylow
394	C₂×D₄×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
395	C₂×C₄×#41	C₂×C₁₃₉	1	1	yes	characteristic
396	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
397	#2855	C₂×C₁₃₉	1	2	yes	complemented
398	#2582	C₂×C₁₃₉	1	1	yes	characteristic, complemented
399	#2568	C₂×C₁₃₉	1	1	yes	characteristic, complemented
400	#2451	C₂×C₁₃₉	1	2	yes	complemented
401	#2450	C₂×C₁₃₉	1	4	yes	complemented
402	#2439	C₂×C₁₃₉	1	2	yes	complemented
403	#2438	C₂×C₁₃₉	1	4	yes	complemented
404	#2417	C₂×C₁₃₉	1	2	yes	complemented
405	#2409	C₂×C₁₃₉	1	2	yes	complemented
406	#2349	C₂×C₁₃₉	1	2	yes	complemented
407	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
408	#2339	C₂×C₁₃₉	1	2	yes	—
409	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
410	C₂×#391	C₂×C₁₃₉	1	2	yes	complemented
411	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
412	C₂³×Q₈	C₂²×C₁₃₉	1	2	yes	—
413	D₄×Q₈	—	2	8	no	—
414	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
415	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
416	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
417	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
418	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
419	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
420	C₄×#41	—	2	8	no	—
421	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
422	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
423	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
424	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
425	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
426	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
427	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
428	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
429	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
430	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
431	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
432	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
433	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
434	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
435	#400	C₂²×C₁₃₉	1	4	yes	—
436	#398	C₂²×C₁₃₉	1	4	yes	—
437	#398	C₂²×C₁₃₉	1	4	yes	—
438	#396	C₂²×C₁₃₉	1	4	yes	—
439	#395	C₂²×C₁₃₉	1	4	yes	—
440	#393	C₂²×C₁₃₉	1	4	yes	—
441	#391	C₂²×C₁₃₉	1	2	yes	—
442	#391	C₂²×C₁₃₉	1	2	yes	—
443	#391	C₂²×C₁₃₉	1	2	yes	—
444	#391	C₂²×C₁₃₉	1	2	yes	—
445	#391	C₂²×C₁₃₉	1	2	yes	—
446	#391	C₂²×C₁₃₉	1	2	yes	—
447	#391	C₂²×C₁₃₉	1	4	yes	—
448	#391	C₂²×C₁₃₉	1	4	yes	—
449	#391	C₂²×C₁₃₉	1	1	yes	characteristic
450	#389	C₂²×C₁₃₉	1	2	yes	—
451	#389	C₂²×C₁₃₉	1	2	yes	—
452	#389	C₂²×C₁₃₉	1	1	yes	characteristic
453	#389	C₂²×C₁₃₉	1	2	yes	—
454	#389	C₂²×C₁₃₉	1	2	yes	—
455	#389	C₂²×C₁₃₉	1	2	yes	—
456	#387	C₂²×C₁₃₉	1	4	yes	—
457	#387	C₂²×C₁₃₉	1	4	yes	—
458	#387	C₂²×C₁₃₉	1	2	yes	—
459	#386	C₂²×C₁₃₉	1	4	yes	—
460	#386	C₂²×C₁₃₉	1	4	yes	—
461	#385	C₂²×C₁₃₉	1	4	yes	—
462	#385	C₂²×C₁₃₉	1	4	yes	—
463	#385	C₂²×C₁₃₉	1	4	yes	—
464	#385	C₂²×C₁₃₉	1	2	yes	—
465	#384	C₂²×C₁₃₉	1	1	yes	characteristic
466	#382	C₂²×C₁₃₉	1	2	yes	—
467	#381	C₂²×C₁₃₉	1	4	yes	—
468	#380	C₂²×C₁₃₉	1	2	yes	—
469	#380	C₂²×C₁₃₉	1	2	yes	—
470	#380	C₂²×C₁₃₉	1	2	yes	—
471	#380	C₂²×C₁₃₉	1	4	yes	—
472	#380	C₂²×C₁₃₉	1	1	yes	characteristic
473	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
474	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
475	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
476	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
477	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
478	C₂×#41	—	2	4	no	—
479	C₂×#41	—	2	4	no	—
480	C₂×#41	Q₈×C₁₃₉	1	8	yes	complemented
481	C₂²×Q₈	—	2	8	no	—
482	C₂²×Q₈	—	2	8	no	—
483	C₂²×Q₈	—	4	4	no	—
484	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
485	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
486	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
487	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
488	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
489	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
492	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
493	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
494	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
496	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
498	C₄⋊Q₈	—	2	8	no	—
499	C₄⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	—	2	4	no	—
501	C₂²⋊Q₈	—	2	8	no	—
502	C₂²⋊Q₈	—	2	16	no	—
503	C₂²⋊Q₈	—	4	4	no	—
504	C₄×Q₈	—	2	4	no	—
505	C₄×Q₈	—	2	4	no	—
506	C₄×Q₈	—	2	4	no	—
507	C₄×D₄	—	2	4	no	—
508	C₄×D₄	—	2	8	no	—
509	C₄×D₄	—	2	8	no	—
510	C₄×D₄	—	2	8	no	—
511	C₄×D₄	—	2	8	no	—
512	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
513	#117	—	2	4	no	—
514	#117	—	2	8	no	—
515	C₂×C₄⋊C₄	—	4	4	no	—
516	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₄²	—	2	8	no	—
544	C₂×C₄²	—	2	4	no	—
545	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
552	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
554	#95	C₂³×C₁₃₉	1	2	yes	—
555	#95	C₂³×C₁₃₉	1	2	yes	—
556	#95	C₂³×C₁₃₉	1	4	yes	—
557	#95	C₂³×C₁₃₉	1	4	yes	—
558	#95	C₂³×C₁₃₉	1	4	yes	—
559	#95	C₂³×C₁₃₉	1	4	yes	—
560	#95	C₂³×C₁₃₉	1	4	yes	—
561	#95	C₂³×C₁₃₉	1	4	yes	—
562	#95	C₂³×C₁₃₉	1	2	yes	—
563	#95	C₂³×C₁₃₉	1	2	yes	—
564	#95	C₂³×C₁₃₉	1	2	yes	—
565	#95	C₂³×C₁₃₉	1	4	yes	—
566	#95	C₂³×C₁₃₉	1	4	yes	—
567	#95	C₂³×C₁₃₉	1	4	yes	—
568	#95	C₂³×C₁₃₉	1	4	yes	—
569	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
570	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
571	#41	—	2	32	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	2	8	no	—
575	C₂×Q₈	—	2	4	no	—
576	C₂×Q₈	—	2	2	no	—
577	C₂×Q₈	—	2	8	no	—
578	C₂×Q₈	—	2	4	no	—
579	C₂×Q₈	—	2	2	no	—
580	C₂×Q₈	—	2	4	no	—
581	C₂×Q₈	—	4	4	no	—
582	C₂×Q₈	—	4	32	no	—
583	C₂×Q₈	C₂×Q₈×C₁₃₉	1	4	yes	complemented
584	C₂×Q₈	#41×C₁₃₉	1	4	yes	complemented
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
588	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
589	C₂×D₄	C₂×Q₈×C₁₃₉	1	8	yes	complemented
590	C₂×D₄	#41×C₁₃₉	1	4	yes	—
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	—	2	8	no	—
599	C₂²×C₄	—	2	8	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	8	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	4	1	no	—
608	C₂²×C₄	—	4	2	no	—
609	C₂²×C₄	—	4	4	no	—
610	C₂²×C₄	—	4	4	no	—
611	C₂²×C₄	—	4	4	no	—
612	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
613	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	complemented
614	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	complemented
615	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
619	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
620	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
623	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
628	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
629	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	8	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	4	4	no	—
645	C₄⋊C₄	—	4	2	no	—
646	C₄⋊C₄	—	4	4	no	—
647	C₄⋊C₄	—	4	4	no	—
648	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	8	no	—
651	C₂²⋊C₄	—	2	8	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	4	2	no	—
655	C₂²⋊C₄	—	4	4	no	—
656	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	2	no	—
660	C₄²	—	2	4	no	—
661	C₄²	—	2	2	no	—
662	C₄²	—	2	4	no	—
663	C₄²	—	2	4	no	—
664	C₄²	—	2	4	no	—
665	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
677	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
678	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
679	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
680	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
681	Q₈	—	2	8	no	—
682	Q₈	—	2	8	no	—
683	Q₈	—	4	16	no	—
684	Q₈	—	4	8	no	—
685	D₄	—	2	16	no	—
686	D₄	C₂²⋊Q₈×C₁₃₉	1	16	yes	complemented
687	C₂×C₄	—	2	16	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	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	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	8	no	—
701	C₂×C₄	—	2	16	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	4	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	1	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	4	4	no	—
724	C₂×C₄	—	4	16	no	—
725	C₂×C₄	—	4	8	no	—
726	C₂×C₄	—	4	4	no	—
727	C₂×C₄	—	8	8	no	—
728	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
729	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
730	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
731	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
732	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
733	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
734	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
735	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
736	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
737	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
738	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
739	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
740	C₂²	—	2	4	no	—
741	C₂²	—	2	4	no	—
742	C₂²	—	2	4	no	—
743	C₂²	—	2	4	no	—
744	C₂²	—	2	4	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	4	1	no	—
753	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	8	yes	—
754	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
755	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
756	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
757	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
758	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
759	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
760	C₂²	#585×C₁₃₉	1	1	yes	characteristic
761	C₄	—	2	2	no	—
762	C₄	—	2	4	no	—
763	C₄	—	2	4	no	—
764	C₄	—	2	4	no	—
765	C₄	—	2	2	no	—
766	C₄	—	2	2	no	—
767	C₄	—	4	4	no	—
768	C₄	—	4	1	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	4	no	—
774	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	4	yes	—
775	C₄	#546×C₁₃₉	1	4	yes	—
776	C₂	—	2	8	no	—
777	C₂	—	4	2	no	—
778	C₂	C₂²×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
779	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
780	C₂	Q₈×#41×C₁₃₉	1	1	yes	characteristic
781	C₂	#3482×C₁₃₉	1	1	yes	characteristic
782	C₂	#3489×C₁₃₉	1	1	yes	characteristic
783	C₂	#3503×C₁₃₉	1	1	yes	characteristic
784	C₂	#3514×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×#41×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×D₄×Q₈×C₁₃₉	C₂	semidirect
3. #2857×C₁₃₉	C₂	semidirect
4. #2855×C₁₃₉	C₂	semidirect
5. #2582×C₁₃₉	C₂	semidirect
6. #2568×C₁₃₉	C₂	semidirect
7. #2451×C₁₃₉	C₂	semidirect
8. #2450×C₁₃₉	C₂	semidirect
9. #2439×C₁₃₉	C₂	semidirect
10. #2438×C₁₃₉	C₂	semidirect
11. #2417×C₁₃₉	C₂	semidirect
12. #2409×C₁₃₉	C₂	semidirect
13. #2349×C₁₃₉	C₂	semidirect
14. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
16. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
17. C₂×#391×C₁₃₉	C₂	semidirect
87. C₂×#41×C₁₃₉	Q₈	semidirect
190. C₂×Q₈×C₁₃₉	C₂×Q₈	semidirect
191. C₂×Q₈×C₁₃₉	#41	semidirect
196. C₂×D₄×C₁₃₉	C₂×Q₈	semidirect
220. C₂²×C₄×C₁₃₉	C₂×Q₈	semidirect
221. C₂²×C₄×C₁₃₉	C₂×Q₈	semidirect
293. D₄×C₁₃₉	C₂²⋊Q₈	semidirect
392. #36274	C₁₃₉	direct (N × H)
393. C₁₃₉	#36274	direct (N × H)
394. C₂×D₄×Q₈	C₂×C₁₃₉	semidirect
396. #2857	C₂×C₁₃₉	semidirect
397. #2855	C₂×C₁₃₉	semidirect
398. #2582	C₂×C₁₃₉	semidirect
399. #2568	C₂×C₁₃₉	semidirect
400. #2451	C₂×C₁₃₉	semidirect
401. #2450	C₂×C₁₃₉	semidirect
402. #2439	C₂×C₁₃₉	semidirect
403. #2438	C₂×C₁₃₉	semidirect
404. #2417	C₂×C₁₃₉	semidirect
405. #2409	C₂×C₁₃₉	semidirect
406. #2349	C₂×C₁₃₉	semidirect
407. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
409. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
410. C₂×#391	C₂×C₁₃₉	semidirect
480. C₂×#41	Q₈×C₁₃₉	semidirect
583. C₂×Q₈	C₂×Q₈×C₁₃₉	semidirect
584. C₂×Q₈	#41×C₁₃₉	semidirect
589. C₂×D₄	C₂×Q₈×C₁₃₉	semidirect
613. C₂²×C₄	C₂×Q₈×C₁₃₉	semidirect
614. C₂²×C₄	C₂×Q₈×C₁₃₉	semidirect
686. D₄	C₂²⋊Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₁₃₉	2
C₂×C₄×#41×C₁₃₉	2
#2857×C₁₃₉	2
#2855×C₁₃₉	2
#2582×C₁₃₉	2
#2568×C₁₃₉	2
#2451×C₁₃₉	2
#2450×C₁₃₉	2
#2439×C₁₃₉	2
#2438×C₁₃₉	2
#2417×C₁₃₉	2
#2409×C₁₃₉	2
#2349×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
#2339×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
C₂×#391×C₁₃₉	2
#36274	139

Subgroups — C139×#36274 #48030870

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36274 #48030870