Subgroups — C₁₃₉×#36551 #48031147

Order 35584.

1984 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2851×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2589×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	#2563×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2552×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2509×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2497×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2487×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2454×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2450×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2369×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₄⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2345×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	C₄×#121×C₁₃₉	C₂	1	1	yes	maximal, characteristic
16	C₄×#121×C₁₃₉	C₂	1	2	yes	maximal
17	C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
26	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
29	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
31	#400×C₁₃₉	C₂²	1	4	yes	—
32	#400×C₁₃₉	C₂²	1	4	yes	—
33	#399×C₁₃₉	C₂²	1	4	yes	—
34	#398×C₁₃₉	C₂²	1	4	yes	—
35	#396×C₁₃₉	C₂²	1	4	yes	—
36	#393×C₁₃₉	C₂²	1	4	yes	—
37	#391×C₁₃₉	C₂²	1	2	yes	—
38	#391×C₁₃₉	C₂²	1	4	yes	—
39	#390×C₁₃₉	C₂²	1	2	yes	—
40	#390×C₁₃₉	C₂²	1	1	yes	characteristic
41	#389×C₁₃₉	C₂²	1	2	yes	—
42	#389×C₁₃₉	C₂²	1	2	yes	—
43	#389×C₁₃₉	C₂²	1	1	yes	characteristic
44	#389×C₁₃₉	C₂²	1	4	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	#388×C₁₃₉	C₂²	1	2	yes	—
51	#388×C₁₃₉	C₂²	1	4	yes	—
52	#387×C₁₃₉	C₂²	1	4	yes	—
53	#387×C₁₃₉	C₂²	1	4	yes	—
54	#387×C₁₃₉	C₂²	1	4	yes	—
55	#386×C₁₃₉	C₂²	1	2	yes	—
56	#386×C₁₃₉	C₂²	1	4	yes	—
57	#385×C₁₃₉	C₂²	1	4	yes	—
58	#385×C₁₃₉	C₂²	1	4	yes	—
59	#385×C₁₃₉	C₂²	1	4	yes	—
60	#385×C₁₃₉	C₂²	1	4	yes	—
61	#384×C₁₃₉	C₂²	1	1	yes	characteristic
62	#384×C₁₃₉	C₂²	1	2	yes	—
63	#382×C₁₃₉	C₂²	1	2	yes	—
64	#380×C₁₃₉	C₂²	1	1	yes	characteristic
65	#380×C₁₃₉	C₂²	1	2	yes	—
66	#380×C₁₃₉	C₂²	1	2	yes	—
67	#380×C₁₃₉	C₂²	1	2	yes	—
68	#380×C₁₃₉	C₂²	1	4	yes	—
69	#380×C₁₃₉	C₂²	1	2	yes	—
70	#380×C₁₃₉	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
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×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
81	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
83	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
84	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
94	#125×C₁₃₉	—	4	4	no	—
95	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
96	#121×C₁₃₉	Q₈	1	8	yes	complemented
97	C₄×D₄×C₁₃₉	—	2	8	no	—
98	C₄×D₄×C₁₃₉	—	2	4	no	—
99	C₄×D₄×C₁₃₉	—	4	4	no	—
100	C₄×D₄×C₁₃₉	—	4	8	no	—
101	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
102	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
103	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	4	yes	—
133	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃₉	—	2	4	no	—
135	C₂×C₄²×C₁₃₉	—	4	4	no	—
136	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
145	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
146	#95×C₁₃₉	C₂³	1	2	yes	—
147	#95×C₁₃₉	C₂³	1	2	yes	—
148	#95×C₁₃₉	C₂³	1	2	yes	—
149	#95×C₁₃₉	C₂³	1	4	yes	—
150	#95×C₁₃₉	C₂³	1	4	yes	—
151	#95×C₁₃₉	C₂³	1	2	yes	—
152	#95×C₁₃₉	C₂³	1	4	yes	—
153	#95×C₁₃₉	C₂³	1	4	yes	—
154	#95×C₁₃₉	C₂³	1	4	yes	—
155	#95×C₁₃₉	C₂³	1	4	yes	—
156	#95×C₁₃₉	C₂³	1	2	yes	—
157	#95×C₁₃₉	C₂³	1	2	yes	—
158	#95×C₁₃₉	C₂³	1	2	yes	—
159	#95×C₁₃₉	C₂³	1	4	yes	—
160	#95×C₁₃₉	C₂³	1	4	yes	—
161	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
162	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
163	C₂×Q₈×C₁₃₉	—	2	4	no	—
164	C₂×Q₈×C₁₃₉	—	4	2	no	—
165	C₂×Q₈×C₁₃₉	—	4	2	no	—
166	C₂×D₄×C₁₃₉	—	2	4	no	—
167	C₂×D₄×C₁₃₉	—	2	4	no	—
168	C₂×D₄×C₁₃₉	—	2	2	no	—
169	C₂×D₄×C₁₃₉	—	2	2	no	—
170	C₂×D₄×C₁₃₉	C₂×Q₈	1	8	yes	—
171	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
172	C₂²×C₄×C₁₃₉	—	2	2	no	—
173	C₂²×C₄×C₁₃₉	—	2	2	no	—
174	C₂²×C₄×C₁₃₉	—	2	2	no	—
175	C₂²×C₄×C₁₃₉	—	2	2	no	—
176	C₂²×C₄×C₁₃₉	—	2	4	no	—
177	C₂²×C₄×C₁₃₉	—	2	4	no	—
178	C₂²×C₄×C₁₃₉	—	2	2	no	—
179	C₂²×C₄×C₁₃₉	—	2	2	no	—
180	C₂²×C₄×C₁₃₉	—	2	4	no	—
181	C₂²×C₄×C₁₃₉	—	2	4	no	—
182	C₂²×C₄×C₁₃₉	—	2	4	no	—
183	C₂²×C₄×C₁₃₉	—	2	4	no	—
184	C₂²×C₄×C₁₃₉	—	2	8	no	—
185	C₂²×C₄×C₁₃₉	—	4	2	no	—
186	C₂²×C₄×C₁₃₉	—	4	2	no	—
187	C₂²×C₄×C₁₃₉	—	4	1	no	—
188	C₂²×C₄×C₁₃₉	—	4	2	no	—
189	C₂²×C₄×C₁₃₉	—	4	4	no	—
190	C₂²×C₄×C₁₃₉	—	4	4	no	—
191	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
192	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
193	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
208	C₄⋊C₄×C₁₃₉	—	2	4	no	—
209	C₄⋊C₄×C₁₃₉	—	2	4	no	—
210	C₄⋊C₄×C₁₃₉	—	2	8	no	—
211	C₄⋊C₄×C₁₃₉	—	2	2	no	—
212	C₄⋊C₄×C₁₃₉	—	2	2	no	—
213	C₄⋊C₄×C₁₃₉	—	2	2	no	—
214	C₄⋊C₄×C₁₃₉	—	2	4	no	—
215	C₄⋊C₄×C₁₃₉	—	2	4	no	—
216	C₄⋊C₄×C₁₃₉	—	2	2	no	—
217	C₄⋊C₄×C₁₃₉	—	2	4	no	—
218	C₄⋊C₄×C₁₃₉	—	2	4	no	—
219	C₄⋊C₄×C₁₃₉	—	2	4	no	—
220	C₄⋊C₄×C₁₃₉	—	2	2	no	—
221	C₄⋊C₄×C₁₃₉	—	4	4	no	—
222	C₄⋊C₄×C₁₃₉	—	4	4	no	—
223	C₄⋊C₄×C₁₃₉	—	4	2	no	—
224	C₄⋊C₄×C₁₃₉	—	4	4	no	—
225	C₄⋊C₄×C₁₃₉	—	4	4	no	—
226	C₄⋊C₄×C₁₃₉	—	4	4	no	—
227	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
228	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
229	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
230	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
231	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
232	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
233	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
234	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
235	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
236	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
237	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
238	C₄²×C₁₃₉	—	2	2	no	—
239	C₄²×C₁₃₉	—	2	2	no	—
240	C₄²×C₁₃₉	—	2	2	no	—
241	C₄²×C₁₃₉	—	2	4	no	—
242	C₄²×C₁₃₉	—	2	4	no	—
243	C₄²×C₁₃₉	—	2	4	no	—
244	C₄²×C₁₃₉	—	4	2	no	—
245	C₄²×C₁₃₉	—	4	2	no	—
246	C₄²×C₁₃₉	—	4	4	no	—
247	C₄²×C₁₃₉	#41	1	4	yes	—
248	C₂³×C₁₃₉	—	2	1	no	—
249	C₂³×C₁₃₉	—	2	1	no	—
250	C₂³×C₁₃₉	—	2	1	no	—
251	C₂³×C₁₃₉	—	2	1	no	—
252	C₂³×C₁₃₉	—	2	2	no	—
253	C₂³×C₁₃₉	—	2	2	no	—
254	C₂³×C₁₃₉	—	2	2	no	—
255	C₂³×C₁₃₉	—	2	2	no	—
256	C₂³×C₁₃₉	—	2	2	no	—
257	C₂³×C₁₃₉	—	2	2	no	—
258	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
259	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
260	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
261	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
262	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
263	Q₈×C₁₃₉	—	8	4	no	—
264	D₄×C₁₃₉	—	2	16	no	—
265	D₄×C₁₃₉	—	2	8	no	—
266	C₂×C₄×C₁₃₉	—	2	1	no	—
267	C₂×C₄×C₁₃₉	—	2	1	no	—
268	C₂×C₄×C₁₃₉	—	2	2	no	—
269	C₂×C₄×C₁₃₉	—	2	1	no	—
270	C₂×C₄×C₁₃₉	—	2	2	no	—
271	C₂×C₄×C₁₃₉	—	2	1	no	—
272	C₂×C₄×C₁₃₉	—	2	2	no	—
273	C₂×C₄×C₁₃₉	—	2	2	no	—
274	C₂×C₄×C₁₃₉	—	2	1	no	—
275	C₂×C₄×C₁₃₉	—	2	1	no	—
276	C₂×C₄×C₁₃₉	—	2	8	no	—
277	C₂×C₄×C₁₃₉	—	2	8	no	—
278	C₂×C₄×C₁₃₉	—	2	1	no	—
279	C₂×C₄×C₁₃₉	—	2	2	no	—
280	C₂×C₄×C₁₃₉	—	2	2	no	—
281	C₂×C₄×C₁₃₉	—	2	2	no	—
282	C₂×C₄×C₁₃₉	—	2	2	no	—
283	C₂×C₄×C₁₃₉	—	2	2	no	—
284	C₂×C₄×C₁₃₉	—	2	2	no	—
285	C₂×C₄×C₁₃₉	—	2	2	no	—
286	C₂×C₄×C₁₃₉	—	2	4	no	—
287	C₂×C₄×C₁₃₉	—	2	4	no	—
288	C₂×C₄×C₁₃₉	—	2	2	no	—
289	C₂×C₄×C₁₃₉	—	2	2	no	—
290	C₂×C₄×C₁₃₉	—	2	2	no	—
291	C₂×C₄×C₁₃₉	—	2	4	no	—
292	C₂×C₄×C₁₃₉	—	2	4	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	4	no	—
295	C₂×C₄×C₁₃₉	—	2	2	no	—
296	C₂×C₄×C₁₃₉	—	2	1	no	—
297	C₂×C₄×C₁₃₉	—	2	1	no	—
298	C₂×C₄×C₁₃₉	—	2	2	no	—
299	C₂×C₄×C₁₃₉	—	2	2	no	—
300	C₂×C₄×C₁₃₉	—	2	4	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	4	4	no	—
303	C₂×C₄×C₁₃₉	—	4	8	no	—
304	C₂×C₄×C₁₃₉	—	4	8	no	—
305	C₂×C₄×C₁₃₉	—	4	8	no	—
306	C₂×C₄×C₁₃₉	—	8	8	no	—
307	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
308	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
309	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
310	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
311	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
312	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
313	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
314	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
315	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
316	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
317	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
318	C₂²×C₁₃₉	—	2	2	no	—
319	C₂²×C₁₃₉	—	2	2	no	—
320	C₂²×C₁₃₉	—	2	2	no	—
321	C₂²×C₁₃₉	—	2	2	no	—
322	C₂²×C₁₃₉	—	2	2	no	—
323	C₂²×C₁₃₉	—	2	2	no	—
324	C₂²×C₁₃₉	—	2	4	no	—
325	C₂²×C₁₃₉	—	2	4	no	—
326	C₂²×C₁₃₉	—	2	4	no	—
327	C₂²×C₁₃₉	—	4	2	no	—
328	C₂²×C₁₃₉	—	4	2	no	—
329	C₂²×C₁₃₉	—	4	2	no	—
330	C₂²×C₁₃₉	—	4	2	no	—
331	C₂²×C₁₃₉	#554	1	4	yes	—
332	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
333	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
334	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
335	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
336	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
337	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂²×C₁₃₉	#585	1	1	yes	characteristic
339	C₄×C₁₃₉	—	2	2	no	—
340	C₄×C₁₃₉	—	2	2	no	—
341	C₄×C₁₃₉	—	2	4	no	—
342	C₄×C₁₃₉	—	2	2	no	—
343	C₄×C₁₃₉	—	2	4	no	—
344	C₄×C₁₃₉	—	4	2	no	—
345	C₄×C₁₃₉	—	4	1	no	—
346	C₄×C₁₃₉	—	4	4	no	—
347	C₄×C₁₃₉	—	4	2	no	—
348	C₄×C₁₃₉	—	4	2	no	—
349	C₄×C₁₃₉	—	4	2	no	—
350	C₄×C₁₃₉	—	4	2	no	—
351	C₄×C₁₃₉	—	4	4	no	—
352	C₄×C₁₃₉	#529	1	4	yes	—
353	C₄×C₁₃₉	#554	1	4	yes	—
354	C₂×C₁₃₉	—	2	4	no	—
355	C₂×C₁₃₉	—	4	4	no	—
356	C₂×C₁₃₉	C₂×#529	1	1	yes	characteristic
357	C₂×C₁₃₉	C₂×#554	1	1	yes	characteristic
358	C₂×C₁₃₉	C₂×#554	1	1	yes	characteristic
359	C₂×C₁₃₉	Q₈×#41	1	1	yes	characteristic
360	C₂×C₁₃₉	#3494	1	1	yes	characteristic
361	C₂×C₁₃₉	#3506	1	1	yes	characteristic
362	C₂×C₁₃₉	#3519	1	1	yes	characteristic
363	#36551	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
364	C₁₃₉	#36551	1	1	yes	characteristic, direct product factor, Sylow
365	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
366	#2851	C₂×C₁₃₉	1	2	yes	complemented
367	#2589	C₂×C₁₃₉	1	4	yes	complemented
368	#2563	C₂×C₁₃₉	1	1	yes	characteristic, complemented
369	#2552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
370	#2509	C₂×C₁₃₉	1	2	yes	complemented
371	#2497	C₂×C₁₃₉	1	2	yes	complemented
372	#2487	C₂×C₁₃₉	1	2	yes	complemented
373	#2454	C₂×C₁₃₉	1	2	yes	complemented
374	#2450	C₂×C₁₃₉	1	4	yes	complemented
375	#2369	C₂×C₁₃₉	1	1	yes	characteristic, complemented
376	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
377	D₄×C₄⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
378	#2345	C₂×C₁₃₉	1	2	yes	complemented
379	C₄×#121	C₂×C₁₃₉	1	1	yes	characteristic
380	C₄×#121	C₂×C₁₃₉	1	2	yes	—
381	C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
382	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
383	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
384	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
385	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
386	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
387	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
388	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
389	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
390	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
391	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
392	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
393	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
394	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
395	#400	C₂²×C₁₃₉	1	4	yes	—
396	#400	C₂²×C₁₃₉	1	4	yes	—
397	#399	C₂²×C₁₃₉	1	4	yes	—
398	#398	C₂²×C₁₃₉	1	4	yes	—
399	#396	C₂²×C₁₃₉	1	4	yes	—
400	#393	C₂²×C₁₃₉	1	4	yes	—
401	#391	C₂²×C₁₃₉	1	2	yes	—
402	#391	C₂²×C₁₃₉	1	4	yes	—
403	#390	C₂²×C₁₃₉	1	2	yes	—
404	#390	C₂²×C₁₃₉	1	1	yes	characteristic
405	#389	C₂²×C₁₃₉	1	4	yes	—
406	#389	C₂²×C₁₃₉	1	2	yes	—
407	#389	C₂²×C₁₃₉	1	2	yes	—
408	#389	C₂²×C₁₃₉	1	2	yes	—
409	#389	C₂²×C₁₃₉	1	2	yes	—
410	#389	C₂²×C₁₃₉	1	2	yes	—
411	#389	C₂²×C₁₃₉	1	2	yes	—
412	#389	C₂²×C₁₃₉	1	1	yes	characteristic
413	#389	C₂²×C₁₃₉	1	2	yes	—
414	#388	C₂²×C₁₃₉	1	2	yes	—
415	#388	C₂²×C₁₃₉	1	4	yes	—
416	#387	C₂²×C₁₃₉	1	4	yes	—
417	#387	C₂²×C₁₃₉	1	4	yes	—
418	#387	C₂²×C₁₃₉	1	4	yes	—
419	#386	C₂²×C₁₃₉	1	2	yes	—
420	#386	C₂²×C₁₃₉	1	4	yes	—
421	#385	C₂²×C₁₃₉	1	4	yes	—
422	#385	C₂²×C₁₃₉	1	4	yes	—
423	#385	C₂²×C₁₃₉	1	4	yes	—
424	#385	C₂²×C₁₃₉	1	4	yes	—
425	#384	C₂²×C₁₃₉	1	1	yes	characteristic
426	#384	C₂²×C₁₃₉	1	2	yes	—
427	#382	C₂²×C₁₃₉	1	2	yes	—
428	#380	C₂²×C₁₃₉	1	2	yes	—
429	#380	C₂²×C₁₃₉	1	2	yes	—
430	#380	C₂²×C₁₃₉	1	1	yes	characteristic
431	#380	C₂²×C₁₃₉	1	2	yes	—
432	#380	C₂²×C₁₃₉	1	4	yes	—
433	#380	C₂²×C₁₃₉	1	2	yes	—
434	#380	C₂²×C₁₃₉	1	2	yes	—
435	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
436	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
437	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
439	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
440	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
441	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
443	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
444	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
445	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
446	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
447	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
448	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
449	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
451	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
452	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
456	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
457	C₄⋊Q₈	—	2	4	no	—
458	#125	—	4	4	no	—
459	C₂²⋊Q₈	—	4	4	no	—
460	#121	Q₈×C₁₃₉	1	8	yes	complemented
461	C₄×D₄	—	2	8	no	—
462	C₄×D₄	—	2	4	no	—
463	C₄×D₄	—	4	4	no	—
464	C₄×D₄	—	4	8	no	—
465	C₂×C₄⋊C₄	—	2	4	no	—
466	C₂×C₄⋊C₄	—	2	4	no	—
467	C₂×C₄⋊C₄	—	2	8	no	—
468	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
475	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
482	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
483	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
485	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
486	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
487	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
489	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
498	C₂×C₄²	—	2	4	no	—
499	C₂×C₄²	—	4	4	no	—
500	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
501	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
502	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
503	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
507	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
508	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
509	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
510	#95	C₂³×C₁₃₉	1	2	yes	—
511	#95	C₂³×C₁₃₉	1	2	yes	—
512	#95	C₂³×C₁₃₉	1	2	yes	—
513	#95	C₂³×C₁₃₉	1	2	yes	—
514	#95	C₂³×C₁₃₉	1	2	yes	—
515	#95	C₂³×C₁₃₉	1	4	yes	—
516	#95	C₂³×C₁₃₉	1	2	yes	—
517	#95	C₂³×C₁₃₉	1	4	yes	—
518	#95	C₂³×C₁₃₉	1	4	yes	—
519	#95	C₂³×C₁₃₉	1	4	yes	—
520	#95	C₂³×C₁₃₉	1	2	yes	—
521	#95	C₂³×C₁₃₉	1	4	yes	—
522	#95	C₂³×C₁₃₉	1	4	yes	—
523	#95	C₂³×C₁₃₉	1	4	yes	—
524	#95	C₂³×C₁₃₉	1	4	yes	—
525	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
526	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
527	C₂×Q₈	—	2	4	no	—
528	C₂×Q₈	—	4	2	no	—
529	C₂×Q₈	—	4	2	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	C₂×Q₈×C₁₃₉	1	8	yes	—
535	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	8	no	—
549	C₂²×C₄	—	4	2	no	—
550	C₂²×C₄	—	4	2	no	—
551	C₂²×C₄	—	4	1	no	—
552	C₂²×C₄	—	4	2	no	—
553	C₂²×C₄	—	4	4	no	—
554	C₂²×C₄	—	4	4	no	—
555	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
556	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
560	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
562	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
565	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
566	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
568	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
570	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
571	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	8	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	4	4	no	—
586	C₄⋊C₄	—	4	4	no	—
587	C₄⋊C₄	—	4	2	no	—
588	C₄⋊C₄	—	4	4	no	—
589	C₄⋊C₄	—	4	4	no	—
590	C₄⋊C₄	—	4	4	no	—
591	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
592	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	2	8	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	—	4	2	no	—
598	C₂²⋊C₄	—	4	4	no	—
599	C₂²⋊C₄	—	4	4	no	—
600	C₂²⋊C₄	—	4	4	no	—
601	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
602	C₄²	—	2	2	no	—
603	C₄²	—	2	2	no	—
604	C₄²	—	2	2	no	—
605	C₄²	—	2	4	no	—
606	C₄²	—	2	4	no	—
607	C₄²	—	2	4	no	—
608	C₄²	—	4	2	no	—
609	C₄²	—	4	2	no	—
610	C₄²	—	4	4	no	—
611	C₄²	#41×C₁₃₉	1	4	yes	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	2	no	—
622	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
623	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
624	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
625	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
626	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
627	Q₈	—	8	4	no	—
628	D₄	—	2	16	no	—
629	D₄	—	2	8	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	8	no	—
641	C₂×C₄	—	2	8	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	4	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	8	no	—
668	C₂×C₄	—	4	8	no	—
669	C₂×C₄	—	4	8	no	—
670	C₂×C₄	—	8	8	no	—
671	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
672	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
673	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
674	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
675	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
676	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
677	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
678	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
679	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
680	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
681	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	4	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	#554×C₁₃₉	1	4	yes	—
696	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
697	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
698	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
699	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
700	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
701	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
702	C₂²	#585×C₁₃₉	1	1	yes	characteristic
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	4	no	—
706	C₄	—	2	2	no	—
707	C₄	—	2	4	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	1	no	—
710	C₄	—	4	4	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	4	no	—
716	C₄	#529×C₁₃₉	1	4	yes	—
717	C₄	#554×C₁₃₉	1	4	yes	—
718	C₂	—	2	4	no	—
719	C₂	—	4	4	no	—
720	C₂	C₂×#529×C₁₃₉	1	1	yes	characteristic
721	C₂	C₂×#554×C₁₃₉	1	1	yes	characteristic
722	C₂	C₂×#554×C₁₃₉	1	1	yes	characteristic
723	C₂	Q₈×#41×C₁₃₉	1	1	yes	characteristic
724	C₂	#3494×C₁₃₉	1	1	yes	characteristic
725	C₂	#3506×C₁₃₉	1	1	yes	characteristic
726	C₂	#3519×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#121×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. #2857×C₁₃₉	C₂	semidirect
2. #2851×C₁₃₉	C₂	semidirect
3. #2589×C₁₃₉	C₂	semidirect
4. #2563×C₁₃₉	C₂	semidirect
5. #2552×C₁₃₉	C₂	semidirect
6. #2509×C₁₃₉	C₂	semidirect
7. #2497×C₁₃₉	C₂	semidirect
8. #2487×C₁₃₉	C₂	semidirect
9. #2454×C₁₃₉	C₂	semidirect
10. #2450×C₁₃₉	C₂	semidirect
11. #2369×C₁₃₉	C₂	semidirect
12. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
13. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
14. #2345×C₁₃₉	C₂	semidirect
17. C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
96. #121×C₁₃₉	Q₈	semidirect
363. #36551	C₁₃₉	direct (N × H)
364. C₁₃₉	#36551	direct (N × H)
365. #2857	C₂×C₁₃₉	semidirect
366. #2851	C₂×C₁₃₉	semidirect
367. #2589	C₂×C₁₃₉	semidirect
368. #2563	C₂×C₁₃₉	semidirect
369. #2552	C₂×C₁₃₉	semidirect
370. #2509	C₂×C₁₃₉	semidirect
371. #2497	C₂×C₁₃₉	semidirect
372. #2487	C₂×C₁₃₉	semidirect
373. #2454	C₂×C₁₃₉	semidirect
374. #2450	C₂×C₁₃₉	semidirect
375. #2369	C₂×C₁₃₉	semidirect
376. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
377. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
378. #2345	C₂×C₁₃₉	semidirect
381. C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
460. #121	Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2857×C₁₃₉	2
#2851×C₁₃₉	2
#2589×C₁₃₉	2
#2563×C₁₃₉	2
#2552×C₁₃₉	2
#2509×C₁₃₉	2
#2497×C₁₃₉	2
#2487×C₁₃₉	2
#2454×C₁₃₉	2
#2450×C₁₃₉	2
#2369×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
#2345×C₁₃₉	2
C₄×#121×C₁₃₉	2
C₂×C₄×C₄⋊C₄×C₁₃₉	2
#36551	139

Subgroups — C139×#36551 #48031147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36551 #48031147