Subgroups — C₁₃₉×#37327 #48031923

Order 35584.

1672 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2868×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2861×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2795×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2793×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2790×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2731×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2729×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2718×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2716×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2674×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2629×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2620×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	#2512×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2511×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2492×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2491×C₁₃₉	C₂	1	1	yes	maximal, characteristic
17	#2452×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2451×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2423×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#2422×C₁₃₉	C₂	1	1	yes	maximal, characteristic
21	#2330×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#2326×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#2298×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
35	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
39	#400×C₁₃₉	C₂²	1	2	yes	—
40	#400×C₁₃₉	C₂²	1	2	yes	—
41	#400×C₁₃₉	C₂²	1	2	yes	—
42	#399×C₁₃₉	C₂²	1	2	yes	—
43	#398×C₁₃₉	C₂²	1	2	yes	—
44	#398×C₁₃₉	C₂²	1	2	yes	—
45	#398×C₁₃₉	C₂²	1	2	yes	—
46	#398×C₁₃₉	C₂²	1	2	yes	—
47	#397×C₁₃₉	C₂²	1	2	yes	—
48	#397×C₁₃₉	C₂²	1	2	yes	—
49	#396×C₁₃₉	C₂²	1	2	yes	—
50	#396×C₁₃₉	C₂²	1	2	yes	—
51	#396×C₁₃₉	C₂²	1	2	yes	—
52	#396×C₁₃₉	C₂²	1	2	yes	—
53	#396×C₁₃₉	C₂²	1	2	yes	—
54	#396×C₁₃₉	C₂²	1	2	yes	—
55	#395×C₁₃₉	C₂²	1	2	yes	—
56	#394×C₁₃₉	C₂²	1	2	yes	—
57	#394×C₁₃₉	C₂²	1	2	yes	—
58	#394×C₁₃₉	C₂²	1	2	yes	—
59	#394×C₁₃₉	C₂²	1	2	yes	—
60	#393×C₁₃₉	C₂²	1	2	yes	—
61	#393×C₁₃₉	C₂²	1	2	yes	—
62	#393×C₁₃₉	C₂²	1	2	yes	—
63	#391×C₁₃₉	C₂²	1	1	yes	characteristic
64	#391×C₁₃₉	C₂²	1	1	yes	characteristic
65	#391×C₁₃₉	C₂²	1	1	yes	characteristic
66	#391×C₁₃₉	C₂²	1	1	yes	characteristic
67	#391×C₁₃₉	C₂²	1	2	yes	—
68	#391×C₁₃₉	C₂²	1	2	yes	—
69	#390×C₁₃₉	C₂²	1	1	yes	characteristic
70	#390×C₁₃₉	C₂²	1	1	yes	characteristic
71	#390×C₁₃₉	C₂²	1	1	yes	characteristic
72	#390×C₁₃₉	C₂²	1	1	yes	characteristic
73	#389×C₁₃₉	C₂²	1	1	yes	characteristic
74	#389×C₁₃₉	C₂²	1	1	yes	characteristic
75	#389×C₁₃₉	C₂²	1	2	yes	—
76	#389×C₁₃₉	C₂²	1	1	yes	characteristic
77	#389×C₁₃₉	C₂²	1	1	yes	characteristic
78	#389×C₁₃₉	C₂²	1	2	yes	—
79	#388×C₁₃₉	C₂²	1	2	yes	—
80	#388×C₁₃₉	C₂²	1	2	yes	—
81	#388×C₁₃₉	C₂²	1	2	yes	—
82	#388×C₁₃₉	C₂²	1	2	yes	—
83	#388×C₁₃₉	C₂²	1	2	yes	—
84	#388×C₁₃₉	C₂²	1	1	yes	characteristic
85	#388×C₁₃₉	C₂²	1	2	yes	—
86	#388×C₁₃₉	C₂²	1	2	yes	—
87	#388×C₁₃₉	C₂²	1	2	yes	—
88	#388×C₁₃₉	C₂²	1	1	yes	characteristic
89	#388×C₁₃₉	C₂²	1	1	yes	characteristic
90	#388×C₁₃₉	C₂²	1	1	yes	characteristic
91	#388×C₁₃₉	C₂²	1	2	yes	—
92	#388×C₁₃₉	C₂²	1	2	yes	—
93	#387×C₁₃₉	C₂²	1	2	yes	—
94	#387×C₁₃₉	C₂²	1	2	yes	—
95	#387×C₁₃₉	C₂²	1	1	yes	characteristic
96	#387×C₁₃₉	C₂²	1	1	yes	characteristic
97	#387×C₁₃₉	C₂²	1	2	yes	—
98	#387×C₁₃₉	C₂²	1	2	yes	—
99	#387×C₁₃₉	C₂²	1	2	yes	—
100	#387×C₁₃₉	C₂²	1	2	yes	—
101	#387×C₁₃₉	C₂²	1	1	yes	characteristic
102	#387×C₁₃₉	C₂²	1	1	yes	characteristic
103	#385×C₁₃₉	C₂²	1	2	yes	—
104	#385×C₁₃₉	C₂²	1	2	yes	—
105	#385×C₁₃₉	C₂²	1	2	yes	—
106	#385×C₁₃₉	C₂²	1	2	yes	—
107	#384×C₁₃₉	C₂²	1	1	yes	characteristic
108	#384×C₁₃₉	C₂²	1	1	yes	characteristic
109	#384×C₁₃₉	C₂²	1	2	yes	—
110	#384×C₁₃₉	C₂²	1	2	yes	—
111	#384×C₁₃₉	C₂²	1	1	yes	characteristic
112	#384×C₁₃₉	C₂²	1	1	yes	characteristic
113	#380×C₁₃₉	C₂²	1	1	yes	characteristic
114	#380×C₁₃₉	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
121	#376×C₁₃₉	C₂²	1	1	yes	characteristic
122	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
125	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
126	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
131	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
132	C₄⋊Q₈×C₁₃₉	—	4	4	no	—
133	C₄⋊Q₈×C₁₃₉	—	4	4	no	—
134	#126×C₁₃₉	—	4	4	no	—
135	#125×C₁₃₉	—	2	4	no	—
136	#124×C₁₃₉	—	2	4	no	—
137	#124×C₁₃₉	—	4	4	no	—
138	#123×C₁₃₉	—	4	4	no	—
139	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
140	C₂²⋊Q₈×C₁₃₉	—	4	2	no	—
141	#121×C₁₃₉	—	4	2	no	—
142	C₄×Q₈×C₁₃₉	—	4	2	no	—
143	C₄×D₄×C₁₃₉	—	4	2	no	—
144	#117×C₁₃₉	—	2	4	no	—
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
196	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
206	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
207	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
208	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
209	#95×C₁₃₉	C₂³	1	2	yes	—
210	#95×C₁₃₉	C₂³	1	2	yes	—
211	#95×C₁₃₉	C₂³	1	2	yes	—
212	#95×C₁₃₉	C₂³	1	2	yes	—
213	#95×C₁₃₉	C₂³	1	2	yes	—
214	#95×C₁₃₉	C₂³	1	2	yes	—
215	#95×C₁₃₉	C₂³	1	2	yes	—
216	#95×C₁₃₉	C₂³	1	1	yes	characteristic
217	#95×C₁₃₉	C₂³	1	1	yes	characteristic
218	#95×C₁₃₉	C₂³	1	2	yes	—
219	#95×C₁₃₉	C₂³	1	2	yes	—
220	#95×C₁₃₉	C₂³	1	2	yes	—
221	#95×C₁₃₉	C₂³	1	1	yes	characteristic
222	#95×C₁₃₉	C₂³	1	1	yes	characteristic
223	#95×C₁₃₉	C₂³	1	2	yes	—
224	#95×C₁₃₉	C₂³	1	2	yes	—
225	#95×C₁₃₉	C₂³	1	2	yes	—
226	#95×C₁₃₉	C₂³	1	1	yes	characteristic
227	#95×C₁₃₉	C₂³	1	1	yes	characteristic
228	#95×C₁₃₉	C₂³	1	2	yes	—
229	#95×C₁₃₉	C₂³	1	2	yes	—
230	#95×C₁₃₉	C₂³	1	2	yes	—
231	#95×C₁₃₉	C₂³	1	1	yes	characteristic
232	#95×C₁₃₉	C₂³	1	1	yes	characteristic
233	#95×C₁₃₉	C₂³	1	1	yes	characteristic
234	#95×C₁₃₉	C₂³	1	1	yes	characteristic
235	#95×C₁₃₉	C₂³	1	1	yes	characteristic
236	#95×C₁₃₉	C₂³	1	1	yes	characteristic
237	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
238	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
239	C₂×Q₈×C₁₃₉	—	2	2	no	—
240	C₂×Q₈×C₁₃₉	—	2	2	no	—
241	C₂×Q₈×C₁₃₉	—	2	4	no	—
242	C₂×Q₈×C₁₃₉	—	2	4	no	—
243	C₂×Q₈×C₁₃₉	—	2	2	no	—
244	C₂×Q₈×C₁₃₉	—	4	2	no	—
245	C₂×Q₈×C₁₃₉	—	4	2	no	—
246	C₂×Q₈×C₁₃₉	—	4	2	no	—
247	C₂×Q₈×C₁₃₉	—	4	2	no	—
248	C₂×D₄×C₁₃₉	—	2	2	no	—
249	C₂×D₄×C₁₃₉	—	2	2	no	—
250	C₂×D₄×C₁₃₉	—	2	2	no	—
251	C₂×D₄×C₁₃₉	—	4	2	no	—
252	C₂×D₄×C₁₃₉	—	4	2	no	—
253	C₂×D₄×C₁₃₉	—	4	2	no	—
254	C₂²×C₄×C₁₃₉	—	2	2	no	—
255	C₂²×C₄×C₁₃₉	—	2	2	no	—
256	C₂²×C₄×C₁₃₉	—	2	2	no	—
257	C₂²×C₄×C₁₃₉	—	4	2	no	—
258	C₂²×C₄×C₁₃₉	—	4	2	no	—
259	C₂²×C₄×C₁₃₉	—	4	2	no	—
260	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
281	C₄⋊C₄×C₁₃₉	—	2	2	no	—
282	C₄⋊C₄×C₁₃₉	—	2	2	no	—
283	C₄⋊C₄×C₁₃₉	—	2	4	no	—
284	C₄⋊C₄×C₁₃₉	—	2	4	no	—
285	C₄⋊C₄×C₁₃₉	—	2	2	no	—
286	C₄⋊C₄×C₁₃₉	—	2	2	no	—
287	C₄⋊C₄×C₁₃₉	—	2	2	no	—
288	C₄⋊C₄×C₁₃₉	—	2	2	no	—
289	C₄⋊C₄×C₁₃₉	—	2	2	no	—
290	C₄⋊C₄×C₁₃₉	—	2	2	no	—
291	C₄⋊C₄×C₁₃₉	—	2	2	no	—
292	C₄⋊C₄×C₁₃₉	—	2	4	no	—
293	C₄⋊C₄×C₁₃₉	—	2	2	no	—
294	C₄⋊C₄×C₁₃₉	—	2	4	no	—
295	C₄⋊C₄×C₁₃₉	—	2	2	no	—
296	C₄⋊C₄×C₁₃₉	—	2	2	no	—
297	C₄⋊C₄×C₁₃₉	—	4	2	no	—
298	C₄⋊C₄×C₁₃₉	—	4	2	no	—
299	C₄⋊C₄×C₁₃₉	—	4	2	no	—
300	C₄⋊C₄×C₁₃₉	—	4	2	no	—
301	C₄⋊C₄×C₁₃₉	—	4	2	no	—
302	C₄⋊C₄×C₁₃₉	—	4	2	no	—
303	C₄⋊C₄×C₁₃₉	—	4	2	no	—
304	C₄⋊C₄×C₁₃₉	—	4	2	no	—
305	C₄⋊C₄×C₁₃₉	—	4	2	no	—
306	C₄⋊C₄×C₁₃₉	—	4	2	no	—
307	C₄⋊C₄×C₁₃₉	—	4	2	no	—
308	C₄⋊C₄×C₁₃₉	—	4	2	no	—
309	C₄⋊C₄×C₁₃₉	—	4	2	no	—
310	C₄⋊C₄×C₁₃₉	—	4	2	no	—
311	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
312	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
313	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
314	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
315	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
316	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
317	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
318	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
319	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
320	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
321	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
322	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
323	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
324	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
325	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
326	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
327	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
328	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
329	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
330	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
331	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
332	C₄²×C₁₃₉	—	2	2	no	—
333	C₄²×C₁₃₉	—	2	2	no	—
334	C₄²×C₁₃₉	—	2	2	no	—
335	C₄²×C₁₃₉	—	2	2	no	—
336	C₄²×C₁₃₉	—	2	2	no	—
337	C₄²×C₁₃₉	—	2	2	no	—
338	C₄²×C₁₃₉	—	2	2	no	—
339	C₄²×C₁₃₉	—	2	2	no	—
340	C₄²×C₁₃₉	—	2	2	no	—
341	C₄²×C₁₃₉	—	4	2	no	—
342	C₄²×C₁₃₉	—	4	2	no	—
343	C₄²×C₁₃₉	—	4	2	no	—
344	C₄²×C₁₃₉	#41	1	4	yes	—
345	C₂³×C₁₃₉	—	2	1	no	—
346	C₂³×C₁₃₉	—	2	2	no	—
347	C₂³×C₁₃₉	—	2	2	no	—
348	C₂³×C₁₃₉	—	2	2	no	—
349	C₂³×C₁₃₉	—	2	1	no	—
350	C₂³×C₁₃₉	—	2	1	no	—
351	C₂³×C₁₃₉	—	2	1	no	—
352	C₂³×C₁₃₉	—	2	2	no	—
353	C₂³×C₁₃₉	—	2	1	no	—
354	C₂³×C₁₃₉	—	2	2	no	—
355	C₂³×C₁₃₉	—	2	1	no	—
356	C₂³×C₁₃₉	—	2	2	no	—
357	C₂³×C₁₃₉	—	2	1	no	—
358	C₂³×C₁₃₉	—	2	2	no	—
359	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
360	Q₈×C₁₃₉	—	4	4	no	—
361	Q₈×C₁₃₉	—	8	4	no	—
362	Q₈×C₁₃₉	—	8	4	no	—
363	D₄×C₁₃₉	—	4	4	no	—
364	D₄×C₁₃₉	—	8	4	no	—
365	C₂×C₄×C₁₃₉	—	2	1	no	—
366	C₂×C₄×C₁₃₉	—	2	1	no	—
367	C₂×C₄×C₁₃₉	—	2	1	no	—
368	C₂×C₄×C₁₃₉	—	2	1	no	—
369	C₂×C₄×C₁₃₉	—	2	1	no	—
370	C₂×C₄×C₁₃₉	—	2	1	no	—
371	C₂×C₄×C₁₃₉	—	2	1	no	—
372	C₂×C₄×C₁₃₉	—	2	1	no	—
373	C₂×C₄×C₁₃₉	—	2	1	no	—
374	C₂×C₄×C₁₃₉	—	2	1	no	—
375	C₂×C₄×C₁₃₉	—	2	1	no	—
376	C₂×C₄×C₁₃₉	—	2	1	no	—
377	C₂×C₄×C₁₃₉	—	2	1	no	—
378	C₂×C₄×C₁₃₉	—	2	1	no	—
379	C₂×C₄×C₁₃₉	—	2	2	no	—
380	C₂×C₄×C₁₃₉	—	2	2	no	—
381	C₂×C₄×C₁₃₉	—	2	2	no	—
382	C₂×C₄×C₁₃₉	—	2	1	no	—
383	C₂×C₄×C₁₃₉	—	2	1	no	—
384	C₂×C₄×C₁₃₉	—	2	1	no	—
385	C₂×C₄×C₁₃₉	—	2	1	no	—
386	C₂×C₄×C₁₃₉	—	2	1	no	—
387	C₂×C₄×C₁₃₉	—	2	2	no	—
388	C₂×C₄×C₁₃₉	—	2	2	no	—
389	C₂×C₄×C₁₃₉	—	2	2	no	—
390	C₂×C₄×C₁₃₉	—	2	2	no	—
391	C₂×C₄×C₁₃₉	—	2	2	no	—
392	C₂×C₄×C₁₃₉	—	2	2	no	—
393	C₂×C₄×C₁₃₉	—	2	1	no	—
394	C₂×C₄×C₁₃₉	—	2	1	no	—
395	C₂×C₄×C₁₃₉	—	2	1	no	—
396	C₂×C₄×C₁₃₉	—	2	1	no	—
397	C₂×C₄×C₁₃₉	—	2	2	no	—
398	C₂×C₄×C₁₃₉	—	2	2	no	—
399	C₂×C₄×C₁₃₉	—	2	2	no	—
400	C₂×C₄×C₁₃₉	—	2	2	no	—
401	C₂×C₄×C₁₃₉	—	2	2	no	—
402	C₂×C₄×C₁₃₉	—	2	2	no	—
403	C₂×C₄×C₁₃₉	—	2	2	no	—
404	C₂×C₄×C₁₃₉	—	2	1	no	—
405	C₂×C₄×C₁₃₉	—	2	2	no	—
406	C₂×C₄×C₁₃₉	—	2	2	no	—
407	C₂×C₄×C₁₃₉	—	2	1	no	—
408	C₂×C₄×C₁₃₉	—	2	1	no	—
409	C₂×C₄×C₁₃₉	—	2	2	no	—
410	C₂×C₄×C₁₃₉	—	2	2	no	—
411	C₂×C₄×C₁₃₉	—	2	1	no	—
412	C₂×C₄×C₁₃₉	—	2	1	no	—
413	C₂×C₄×C₁₃₉	—	2	1	no	—
414	C₂×C₄×C₁₃₉	—	2	1	no	—
415	C₂×C₄×C₁₃₉	—	2	1	no	—
416	C₂×C₄×C₁₃₉	—	2	1	no	—
417	C₂×C₄×C₁₃₉	—	2	1	no	—
418	C₂×C₄×C₁₃₉	—	2	2	no	—
419	C₂×C₄×C₁₃₉	—	4	4	no	—
420	C₂×C₄×C₁₃₉	—	8	4	no	—
421	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
422	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
423	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
424	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
425	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
426	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
427	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
428	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
429	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
430	C₂²×C₁₃₉	—	4	1	no	—
431	C₂²×C₁₃₉	—	4	2	no	—
432	C₂²×C₁₃₉	—	4	1	no	—
433	C₂²×C₁₃₉	—	4	1	no	—
434	C₂²×C₁₃₉	—	4	2	no	—
435	C₂²×C₁₃₉	—	4	2	no	—
436	C₂²×C₁₃₉	—	4	2	no	—
437	C₂²×C₁₃₉	—	4	1	no	—
438	C₂²×C₁₃₉	—	4	2	no	—
439	C₂²×C₁₃₉	—	4	1	no	—
440	C₂²×C₁₃₉	—	4	2	no	—
441	C₂²×C₁₃₉	—	4	1	no	—
442	C₂²×C₁₃₉	—	4	1	no	—
443	C₂²×C₁₃₉	—	4	2	no	—
444	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
445	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
446	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
447	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
449	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
450	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
451	C₄×C₁₃₉	—	2	2	no	—
452	C₄×C₁₃₉	—	2	2	no	—
453	C₄×C₁₃₉	—	2	2	no	—
454	C₄×C₁₃₉	—	2	2	no	—
455	C₄×C₁₃₉	—	2	2	no	—
456	C₄×C₁₃₉	—	2	2	no	—
457	C₄×C₁₃₉	—	4	1	no	—
458	C₄×C₁₃₉	—	4	2	no	—
459	C₄×C₁₃₉	—	4	1	no	—
460	C₄×C₁₃₉	—	4	1	no	—
461	C₄×C₁₃₉	—	4	2	no	—
462	C₄×C₁₃₉	—	4	2	no	—
463	C₄×C₁₃₉	—	4	1	no	—
464	C₄×C₁₃₉	—	4	2	no	—
465	C₄×C₁₃₉	—	4	2	no	—
466	C₄×C₁₃₉	—	4	2	no	—
467	C₄×C₁₃₉	—	4	2	no	—
468	C₄×C₁₃₉	—	4	1	no	—
469	C₄×C₁₃₉	—	4	1	no	—
470	C₄×C₁₃₉	—	4	1	no	—
471	C₄×C₁₃₉	#542	1	4	yes	—
472	C₂×C₁₃₉	—	8	1	no	—
473	C₂×C₁₃₉	—	8	2	no	—
474	C₂×C₁₃₉	C₂×#542	1	1	yes	characteristic
475	C₂×C₁₃₉	#3511	1	1	yes	characteristic
476	C₂×C₁₃₉	#3511	1	1	yes	characteristic
477	C₂×C₁₃₉	#3543	1	1	yes	characteristic
478	C₂×C₁₃₉	#3544	1	1	yes	characteristic
479	C₂×C₁₃₉	#3552	1	1	yes	characteristic
480	C₂×C₁₃₉	#3552	1	1	yes	characteristic
481	#37327	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
482	C₁₃₉	#37327	1	1	yes	characteristic, direct product factor, Sylow
483	#2868	C₂×C₁₃₉	1	1	yes	characteristic, complemented
484	#2861	C₂×C₁₃₉	1	1	yes	characteristic, complemented
485	#2795	C₂×C₁₃₉	1	2	yes	complemented
486	#2793	C₂×C₁₃₉	1	2	yes	complemented
487	#2790	C₂×C₁₃₉	1	2	yes	complemented
488	#2731	C₂×C₁₃₉	1	2	yes	complemented
489	#2729	C₂×C₁₃₉	1	2	yes	complemented
490	#2718	C₂×C₁₃₉	1	2	yes	complemented
491	#2716	C₂×C₁₃₉	1	2	yes	complemented
492	#2674	C₂×C₁₃₉	1	2	yes	complemented
493	#2629	C₂×C₁₃₉	1	1	yes	characteristic, complemented
494	#2620	C₂×C₁₃₉	1	1	yes	characteristic
495	#2512	C₂×C₁₃₉	1	1	yes	characteristic, complemented
496	#2511	C₂×C₁₃₉	1	1	yes	characteristic, complemented
497	#2492	C₂×C₁₃₉	1	1	yes	characteristic, complemented
498	#2491	C₂×C₁₃₉	1	1	yes	characteristic
499	#2452	C₂×C₁₃₉	1	1	yes	characteristic, complemented
500	#2451	C₂×C₁₃₉	1	1	yes	characteristic, complemented
501	#2423	C₂×C₁₃₉	1	1	yes	characteristic, complemented
502	#2422	C₂×C₁₃₉	1	1	yes	characteristic
503	#2330	C₂×C₁₃₉	1	1	yes	characteristic, complemented
504	#2326	C₂×C₁₃₉	1	1	yes	characteristic, complemented
505	#2298	C₂×C₁₃₉	1	1	yes	characteristic, complemented
506	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
507	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
508	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
509	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
510	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
511	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
512	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
513	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
514	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
515	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
516	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
517	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
518	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
519	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
520	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
521	#400	C₂²×C₁₃₉	1	2	yes	—
522	#400	C₂²×C₁₃₉	1	2	yes	—
523	#400	C₂²×C₁₃₉	1	2	yes	—
524	#399	C₂²×C₁₃₉	1	2	yes	—
525	#398	C₂²×C₁₃₉	1	2	yes	—
526	#398	C₂²×C₁₃₉	1	2	yes	—
527	#398	C₂²×C₁₃₉	1	2	yes	—
528	#398	C₂²×C₁₃₉	1	2	yes	—
529	#397	C₂²×C₁₃₉	1	2	yes	—
530	#397	C₂²×C₁₃₉	1	2	yes	—
531	#396	C₂²×C₁₃₉	1	2	yes	—
532	#396	C₂²×C₁₃₉	1	2	yes	—
533	#396	C₂²×C₁₃₉	1	2	yes	—
534	#396	C₂²×C₁₃₉	1	2	yes	—
535	#396	C₂²×C₁₃₉	1	2	yes	—
536	#396	C₂²×C₁₃₉	1	2	yes	—
537	#395	C₂²×C₁₃₉	1	2	yes	—
538	#394	C₂²×C₁₃₉	1	2	yes	—
539	#394	C₂²×C₁₃₉	1	2	yes	—
540	#394	C₂²×C₁₃₉	1	2	yes	—
541	#394	C₂²×C₁₃₉	1	2	yes	—
542	#393	C₂²×C₁₃₉	1	2	yes	—
543	#393	C₂²×C₁₃₉	1	2	yes	—
544	#393	C₂²×C₁₃₉	1	2	yes	—
545	#391	C₂²×C₁₃₉	1	1	yes	characteristic
546	#391	C₂²×C₁₃₉	1	1	yes	characteristic
547	#391	C₂²×C₁₃₉	1	1	yes	characteristic
548	#391	C₂²×C₁₃₉	1	1	yes	characteristic
549	#391	C₂²×C₁₃₉	1	2	yes	—
550	#391	C₂²×C₁₃₉	1	2	yes	—
551	#390	C₂²×C₁₃₉	1	1	yes	characteristic
552	#390	C₂²×C₁₃₉	1	1	yes	characteristic
553	#390	C₂²×C₁₃₉	1	1	yes	characteristic
554	#390	C₂²×C₁₃₉	1	1	yes	characteristic
555	#389	C₂²×C₁₃₉	1	2	yes	—
556	#389	C₂²×C₁₃₉	1	1	yes	characteristic
557	#389	C₂²×C₁₃₉	1	1	yes	characteristic
558	#389	C₂²×C₁₃₉	1	2	yes	—
559	#389	C₂²×C₁₃₉	1	1	yes	characteristic
560	#389	C₂²×C₁₃₉	1	1	yes	characteristic
561	#388	C₂²×C₁₃₉	1	2	yes	—
562	#388	C₂²×C₁₃₉	1	2	yes	—
563	#388	C₂²×C₁₃₉	1	2	yes	—
564	#388	C₂²×C₁₃₉	1	2	yes	—
565	#388	C₂²×C₁₃₉	1	2	yes	—
566	#388	C₂²×C₁₃₉	1	2	yes	—
567	#388	C₂²×C₁₃₉	1	1	yes	characteristic
568	#388	C₂²×C₁₃₉	1	2	yes	—
569	#388	C₂²×C₁₃₉	1	1	yes	characteristic
570	#388	C₂²×C₁₃₉	1	2	yes	—
571	#388	C₂²×C₁₃₉	1	2	yes	—
572	#388	C₂²×C₁₃₉	1	1	yes	characteristic
573	#388	C₂²×C₁₃₉	1	2	yes	—
574	#388	C₂²×C₁₃₉	1	1	yes	characteristic
575	#387	C₂²×C₁₃₉	1	2	yes	—
576	#387	C₂²×C₁₃₉	1	2	yes	—
577	#387	C₂²×C₁₃₉	1	2	yes	—
578	#387	C₂²×C₁₃₉	1	2	yes	—
579	#387	C₂²×C₁₃₉	1	2	yes	—
580	#387	C₂²×C₁₃₉	1	1	yes	characteristic
581	#387	C₂²×C₁₃₉	1	1	yes	characteristic
582	#387	C₂²×C₁₃₉	1	2	yes	—
583	#387	C₂²×C₁₃₉	1	1	yes	characteristic
584	#387	C₂²×C₁₃₉	1	1	yes	characteristic
585	#385	C₂²×C₁₃₉	1	2	yes	—
586	#385	C₂²×C₁₃₉	1	2	yes	—
587	#385	C₂²×C₁₃₉	1	2	yes	—
588	#385	C₂²×C₁₃₉	1	2	yes	—
589	#384	C₂²×C₁₃₉	1	1	yes	characteristic
590	#384	C₂²×C₁₃₉	1	1	yes	characteristic
591	#384	C₂²×C₁₃₉	1	1	yes	characteristic
592	#384	C₂²×C₁₃₉	1	1	yes	characteristic
593	#384	C₂²×C₁₃₉	1	2	yes	—
594	#384	C₂²×C₁₃₉	1	2	yes	—
595	#380	C₂²×C₁₃₉	1	1	yes	characteristic
596	#380	C₂²×C₁₃₉	1	1	yes	characteristic
597	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
598	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
599	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
600	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
601	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
602	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
603	#376	C₂²×C₁₃₉	1	1	yes	characteristic
604	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
605	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
606	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
607	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
608	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
609	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
610	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
612	C₄⋊Q₈	—	4	2	no	—
613	C₄⋊Q₈	—	4	2	no	—
614	C₄⋊Q₈	—	4	4	no	—
615	C₄⋊Q₈	—	4	4	no	—
616	#126	—	4	4	no	—
617	#125	—	2	4	no	—
618	#124	—	2	4	no	—
619	#124	—	4	4	no	—
620	#123	—	4	4	no	—
621	C₂²⋊Q₈	—	4	4	no	—
622	C₂²⋊Q₈	—	4	2	no	—
623	#121	—	4	2	no	—
624	C₄×Q₈	—	4	2	no	—
625	C₄×D₄	—	4	2	no	—
626	#117	—	2	4	no	—
627	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
661	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
663	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
666	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
678	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
682	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
688	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
689	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
690	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
691	#95	C₂³×C₁₃₉	1	1	yes	characteristic
692	#95	C₂³×C₁₃₉	1	1	yes	characteristic
693	#95	C₂³×C₁₃₉	1	1	yes	characteristic
694	#95	C₂³×C₁₃₉	1	1	yes	characteristic
695	#95	C₂³×C₁₃₉	1	1	yes	characteristic
696	#95	C₂³×C₁₃₉	1	1	yes	characteristic
697	#95	C₂³×C₁₃₉	1	1	yes	characteristic
698	#95	C₂³×C₁₃₉	1	1	yes	characteristic
699	#95	C₂³×C₁₃₉	1	1	yes	characteristic
700	#95	C₂³×C₁₃₉	1	1	yes	characteristic
701	#95	C₂³×C₁₃₉	1	1	yes	characteristic
702	#95	C₂³×C₁₃₉	1	1	yes	characteristic
703	#95	C₂³×C₁₃₉	1	2	yes	—
704	#95	C₂³×C₁₃₉	1	2	yes	—
705	#95	C₂³×C₁₃₉	1	2	yes	—
706	#95	C₂³×C₁₃₉	1	2	yes	—
707	#95	C₂³×C₁₃₉	1	2	yes	—
708	#95	C₂³×C₁₃₉	1	2	yes	—
709	#95	C₂³×C₁₃₉	1	2	yes	—
710	#95	C₂³×C₁₃₉	1	2	yes	—
711	#95	C₂³×C₁₃₉	1	2	yes	—
712	#95	C₂³×C₁₃₉	1	2	yes	—
713	#95	C₂³×C₁₃₉	1	2	yes	—
714	#95	C₂³×C₁₃₉	1	2	yes	—
715	#95	C₂³×C₁₃₉	1	2	yes	—
716	#95	C₂³×C₁₃₉	1	2	yes	—
717	#95	C₂³×C₁₃₉	1	2	yes	—
718	#95	C₂³×C₁₃₉	1	2	yes	—
719	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
720	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
721	C₂×Q₈	—	2	2	no	—
722	C₂×Q₈	—	2	2	no	—
723	C₂×Q₈	—	2	4	no	—
724	C₂×Q₈	—	2	4	no	—
725	C₂×Q₈	—	2	2	no	—
726	C₂×Q₈	—	4	2	no	—
727	C₂×Q₈	—	4	2	no	—
728	C₂×Q₈	—	4	2	no	—
729	C₂×Q₈	—	4	2	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	4	2	no	—
734	C₂×D₄	—	4	2	no	—
735	C₂×D₄	—	4	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	4	2	no	—
740	C₂²×C₄	—	4	2	no	—
741	C₂²×C₄	—	4	2	no	—
742	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	4	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	4	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	—	4	2	no	—
789	C₄⋊C₄	—	4	2	no	—
790	C₄⋊C₄	—	4	2	no	—
791	C₄⋊C₄	—	4	2	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	—	4	2	no	—
808	C₂²⋊C₄	—	4	2	no	—
809	C₂²⋊C₄	—	4	2	no	—
810	C₂²⋊C₄	—	4	2	no	—
811	C₂²⋊C₄	—	4	2	no	—
812	C₂²⋊C₄	—	4	2	no	—
813	C₂²⋊C₄	—	4	2	no	—
814	C₄²	—	2	2	no	—
815	C₄²	—	2	2	no	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	4	2	no	—
824	C₄²	—	4	2	no	—
825	C₄²	—	4	2	no	—
826	C₄²	#41×C₁₃₉	1	4	yes	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	2	no	—
841	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
842	Q₈	—	4	4	no	—
843	Q₈	—	8	4	no	—
844	Q₈	—	8	4	no	—
845	D₄	—	4	4	no	—
846	D₄	—	8	4	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	8	4	no	—
903	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
904	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
905	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
906	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
907	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
908	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
909	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
910	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
911	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	2	no	—
917	C₂²	—	4	1	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
927	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
928	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
929	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
930	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
931	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
932	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
933	C₄	—	2	2	no	—
934	C₄	—	2	2	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	2	2	no	—
938	C₄	—	2	2	no	—
939	C₄	—	4	1	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	2	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	2	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	1	no	—
946	C₄	—	4	1	no	—
947	C₄	—	4	1	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	1	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	2	no	—
953	C₄	#542×C₁₃₉	1	4	yes	—
954	C₂	—	8	2	no	—
955	C₂	—	8	1	no	—
956	C₂	C₂×#542×C₁₃₉	1	1	yes	characteristic
957	C₂	#3511×C₁₃₉	1	1	yes	characteristic
958	C₂	#3511×C₁₃₉	1	1	yes	characteristic
959	C₂	#3543×C₁₃₉	1	1	yes	characteristic
960	C₂	#3544×C₁₃₉	1	1	yes	characteristic
961	C₂	#3552×C₁₃₉	1	1	yes	characteristic
962	C₂	#3552×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. #2868×C₁₃₉	C₂	semidirect
2. #2861×C₁₃₉	C₂	semidirect
3. #2795×C₁₃₉	C₂	semidirect
4. #2793×C₁₃₉	C₂	semidirect
5. #2790×C₁₃₉	C₂	semidirect
6. #2731×C₁₃₉	C₂	semidirect
7. #2729×C₁₃₉	C₂	semidirect
8. #2718×C₁₃₉	C₂	semidirect
9. #2716×C₁₃₉	C₂	semidirect
10. #2674×C₁₃₉	C₂	semidirect
11. #2629×C₁₃₉	C₂	semidirect
13. #2512×C₁₃₉	C₂	semidirect
14. #2511×C₁₃₉	C₂	semidirect
15. #2492×C₁₃₉	C₂	semidirect
17. #2452×C₁₃₉	C₂	semidirect
18. #2451×C₁₃₉	C₂	semidirect
19. #2423×C₁₃₉	C₂	semidirect
21. #2330×C₁₃₉	C₂	semidirect
22. #2326×C₁₃₉	C₂	semidirect
23. #2298×C₁₃₉	C₂	semidirect
481. #37327	C₁₃₉	direct (N × H)
482. C₁₃₉	#37327	direct (N × H)
483. #2868	C₂×C₁₃₉	semidirect
484. #2861	C₂×C₁₃₉	semidirect
485. #2795	C₂×C₁₃₉	semidirect
486. #2793	C₂×C₁₃₉	semidirect
487. #2790	C₂×C₁₃₉	semidirect
488. #2731	C₂×C₁₃₉	semidirect
489. #2729	C₂×C₁₃₉	semidirect
490. #2718	C₂×C₁₃₉	semidirect
491. #2716	C₂×C₁₃₉	semidirect
492. #2674	C₂×C₁₃₉	semidirect
493. #2629	C₂×C₁₃₉	semidirect
495. #2512	C₂×C₁₃₉	semidirect
496. #2511	C₂×C₁₃₉	semidirect
497. #2492	C₂×C₁₃₉	semidirect
499. #2452	C₂×C₁₃₉	semidirect
500. #2451	C₂×C₁₃₉	semidirect
501. #2423	C₂×C₁₃₉	semidirect
503. #2330	C₂×C₁₃₉	semidirect
504. #2326	C₂×C₁₃₉	semidirect
505. #2298	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2868×C₁₃₉	2
#2861×C₁₃₉	2
#2795×C₁₃₉	2
#2793×C₁₃₉	2
#2790×C₁₃₉	2
#2731×C₁₃₉	2
#2729×C₁₃₉	2
#2718×C₁₃₉	2
#2716×C₁₃₉	2
#2674×C₁₃₉	2
#2629×C₁₃₉	2
#2620×C₁₃₉	2
#2512×C₁₃₉	2
#2511×C₁₃₉	2
#2492×C₁₃₉	2
#2491×C₁₃₉	2
#2452×C₁₃₉	2
#2451×C₁₃₉	2
#2423×C₁₃₉	2
#2422×C₁₃₉	2
#2330×C₁₃₉	2
#2326×C₁₃₉	2
#2298×C₁₃₉	2
#37327	139

Subgroups — C139×#37327 #48031923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37327 #48031923