Subgroups — C₁₃₉×#36742 #48031338

Order 35584.

2038 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#544×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#539×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2850×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#2721×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2719×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2716×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2713×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2694×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2690×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2677×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2674×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2659×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2639×C₁₃₉	C₂	1	1	yes	maximal, characteristic
15	#2564×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2498×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2498×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2417×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	C₂×#387×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#544×C₁₃₉	—	2	8	no	—
21	#539×C₁₃₉	—	2	8	no	—
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
37	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
38	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
40	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
41	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
44	#400×C₁₃₉	C₂²	1	2	yes	—
45	#400×C₁₃₉	C₂²	1	2	yes	—
46	#400×C₁₃₉	C₂²	1	2	yes	—
47	#400×C₁₃₉	C₂²	1	2	yes	—
48	#399×C₁₃₉	C₂²	1	2	yes	—
49	#399×C₁₃₉	C₂²	1	2	yes	—
50	#399×C₁₃₉	C₂²	1	2	yes	—
51	#398×C₁₃₉	C₂²	1	2	yes	—
52	#398×C₁₃₉	C₂²	1	2	yes	—
53	#398×C₁₃₉	C₂²	1	2	yes	—
54	#398×C₁₃₉	C₂²	1	2	yes	—
55	#398×C₁₃₉	C₂²	1	2	yes	—
56	#398×C₁₃₉	C₂²	1	2	yes	—
57	#397×C₁₃₉	C₂²	1	2	yes	—
58	#397×C₁₃₉	C₂²	1	2	yes	—
59	#397×C₁₃₉	C₂²	1	2	yes	—
60	#396×C₁₃₉	C₂²	1	2	yes	—
61	#396×C₁₃₉	C₂²	1	2	yes	—
62	#395×C₁₃₉	C₂²	1	2	yes	—
63	#395×C₁₃₉	C₂²	1	2	yes	—
64	#395×C₁₃₉	C₂²	1	2	yes	—
65	#394×C₁₃₉	C₂²	1	2	yes	—
66	#393×C₁₃₉	C₂²	1	2	yes	—
67	#393×C₁₃₉	C₂²	1	2	yes	—
68	#391×C₁₃₉	C₂²	1	1	yes	characteristic
69	#391×C₁₃₉	C₂²	1	1	yes	characteristic
70	#391×C₁₃₉	C₂²	1	1	yes	characteristic
71	#391×C₁₃₉	C₂²	1	2	yes	—
72	#390×C₁₃₉	C₂²	1	1	yes	characteristic
73	#389×C₁₃₉	C₂²	1	2	yes	—
74	#389×C₁₃₉	C₂²	1	2	yes	—
75	#389×C₁₃₉	C₂²	1	2	yes	—
76	#388×C₁₃₉	C₂²	1	2	yes	—
77	#388×C₁₃₉	C₂²	1	2	yes	—
78	#388×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	#387×C₁₃₉	C₂²	1	2	yes	—
83	#387×C₁₃₉	C₂²	1	2	yes	—
84	#387×C₁₃₉	C₂²	1	2	yes	—
85	#387×C₁₃₉	C₂²	1	2	yes	—
86	#387×C₁₃₉	C₂²	1	2	yes	—
87	#387×C₁₃₉	C₂²	1	2	yes	—
88	#387×C₁₃₉	C₂²	1	2	yes	—
89	#387×C₁₃₉	C₂²	1	2	yes	—
90	#387×C₁₃₉	C₂²	1	2	yes	—
91	#387×C₁₃₉	C₂²	1	2	yes	—
92	#386×C₁₃₉	C₂²	1	2	yes	—
93	#386×C₁₃₉	C₂²	1	2	yes	—
94	#386×C₁₃₉	C₂²	1	2	yes	—
95	#386×C₁₃₉	C₂²	1	2	yes	—
96	#385×C₁₃₉	C₂²	1	2	yes	—
97	#385×C₁₃₉	C₂²	1	2	yes	—
98	#384×C₁₃₉	C₂²	1	1	yes	characteristic
99	#382×C₁₃₉	C₂²	1	1	yes	characteristic
100	#380×C₁₃₉	C₂²	1	2	yes	—
101	#380×C₁₃₉	C₂²	1	2	yes	—
102	#380×C₁₃₉	C₂²	1	2	yes	—
103	#380×C₁₃₉	C₂²	1	2	yes	—
104	#380×C₁₃₉	C₂²	1	2	yes	—
105	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
106	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
108	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
112	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
123	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
124	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
125	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
126	#126×C₁₃₉	—	2	8	no	—
127	#125×C₁₃₉	—	2	8	no	—
128	#125×C₁₃₉	—	2	8	no	—
129	#125×C₁₃₉	—	2	8	no	—
130	#124×C₁₃₉	—	4	2	no	—
131	#123×C₁₃₉	—	2	8	no	—
132	#123×C₁₃₉	—	2	8	no	—
133	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
134	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
135	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
136	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
137	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
138	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
139	#121×C₁₃₉	—	2	4	no	—
140	C₄×D₄×C₁₃₉	—	2	8	no	—
141	#117×C₁₃₉	—	2	8	no	—
142	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
143	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
183	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃₉	—	4	2	no	—
187	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
190	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
192	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
194	#95×C₁₃₉	C₂³	1	2	yes	—
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	#95×C₁₃₉	C₂³	1	2	yes	—
197	#95×C₁₃₉	C₂³	1	2	yes	—
198	#95×C₁₃₉	C₂³	1	2	yes	—
199	#95×C₁₃₉	C₂³	1	2	yes	—
200	#95×C₁₃₉	C₂³	1	2	yes	—
201	#95×C₁₃₉	C₂³	1	2	yes	—
202	#95×C₁₃₉	C₂³	1	2	yes	—
203	#95×C₁₃₉	C₂³	1	2	yes	—
204	#95×C₁₃₉	C₂³	1	2	yes	—
205	#95×C₁₃₉	C₂³	1	2	yes	—
206	#95×C₁₃₉	C₂³	1	2	yes	—
207	#95×C₁₃₉	C₂³	1	2	yes	—
208	#95×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
217	#95×C₁₃₉	C₂³	1	2	yes	—
218	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
219	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
220	C₂×Q₈×C₁₃₉	—	2	2	no	—
221	C₂×Q₈×C₁₃₉	—	2	4	no	—
222	C₂×Q₈×C₁₃₉	—	2	2	no	—
223	C₂×Q₈×C₁₃₉	—	2	2	no	—
224	C₂×Q₈×C₁₃₉	—	4	2	no	—
225	C₂×Q₈×C₁₃₉	—	4	1	no	—
226	C₂×Q₈×C₁₃₉	—	4	1	no	—
227	C₂×Q₈×C₁₃₉	—	4	1	no	—
228	C₂×Q₈×C₁₃₉	—	4	2	no	—
229	C₂×Q₈×C₁₃₉	—	4	1	no	—
230	C₂×Q₈×C₁₃₉	—	4	1	no	—
231	C₂×Q₈×C₁₃₉	—	4	1	no	—
232	C₂×D₄×C₁₃₉	—	2	4	no	—
233	C₂×D₄×C₁₃₉	—	2	4	no	—
234	C₂×D₄×C₁₃₉	—	2	4	no	—
235	C₂×D₄×C₁₃₉	—	2	2	no	—
236	C₂×D₄×C₁₃₉	—	4	1	no	—
237	C₂×D₄×C₁₃₉	—	4	1	no	—
238	C₂²×C₄×C₁₃₉	—	2	2	no	—
239	C₂²×C₄×C₁₃₉	—	2	2	no	—
240	C₂²×C₄×C₁₃₉	—	2	2	no	—
241	C₂²×C₄×C₁₃₉	—	2	2	no	—
242	C₂²×C₄×C₁₃₉	—	2	2	no	—
243	C₂²×C₄×C₁₃₉	—	2	2	no	—
244	C₂²×C₄×C₁₃₉	—	2	2	no	—
245	C₂²×C₄×C₁₃₉	—	2	2	no	—
246	C₂²×C₄×C₁₃₉	—	2	4	no	—
247	C₂²×C₄×C₁₃₉	—	4	1	no	—
248	C₂²×C₄×C₁₃₉	—	4	1	no	—
249	C₂²×C₄×C₁₃₉	—	4	1	no	—
250	C₂²×C₄×C₁₃₉	—	4	1	no	—
251	C₂²×C₄×C₁₃₉	—	4	1	no	—
252	C₂²×C₄×C₁₃₉	—	4	1	no	—
253	C₂²×C₄×C₁₃₉	—	4	1	no	—
254	C₂²×C₄×C₁₃₉	—	4	2	no	—
255	C₂²×C₄×C₁₃₉	—	4	2	no	—
256	C₂²×C₄×C₁₃₉	—	4	1	no	—
257	C₂²×C₄×C₁₃₉	—	4	1	no	—
258	C₂²×C₄×C₁₃₉	—	4	1	no	—
259	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
260	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
261	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
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	2	yes	—
266	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	2	yes	—
277	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
279	C₄⋊C₄×C₁₃₉	—	2	4	no	—
280	C₄⋊C₄×C₁₃₉	—	2	4	no	—
281	C₄⋊C₄×C₁₃₉	—	2	4	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	4	no	—
286	C₄⋊C₄×C₁₃₉	—	2	2	no	—
287	C₄⋊C₄×C₁₃₉	—	2	2	no	—
288	C₄⋊C₄×C₁₃₉	—	2	4	no	—
289	C₄⋊C₄×C₁₃₉	—	2	4	no	—
290	C₄⋊C₄×C₁₃₉	—	2	4	no	—
291	C₄⋊C₄×C₁₃₉	—	2	4	no	—
292	C₄⋊C₄×C₁₃₉	—	2	2	no	—
293	C₄⋊C₄×C₁₃₉	—	2	4	no	—
294	C₄⋊C₄×C₁₃₉	—	2	4	no	—
295	C₄⋊C₄×C₁₃₉	—	2	4	no	—
296	C₄⋊C₄×C₁₃₉	—	2	4	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	C₂×D₄	1	8	yes	—
305	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
306	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
307	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
308	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
309	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
310	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
311	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
312	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
313	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
314	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
315	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
316	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
317	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
318	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
319	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
320	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
321	C₄²×C₁₃₉	—	2	4	no	—
322	C₄²×C₁₃₉	—	2	4	no	—
323	C₄²×C₁₃₉	—	2	4	no	—
324	C₄²×C₁₃₉	—	2	2	no	—
325	C₄²×C₁₃₉	—	2	2	no	—
326	C₄²×C₁₃₉	—	4	1	no	—
327	C₄²×C₁₃₉	—	4	1	no	—
328	C₂³×C₁₃₉	—	2	1	no	—
329	C₂³×C₁₃₉	—	2	1	no	—
330	C₂³×C₁₃₉	—	2	1	no	—
331	C₂³×C₁₃₉	—	2	1	no	—
332	C₂³×C₁₃₉	—	2	2	no	—
333	C₂³×C₁₃₉	—	2	2	no	—
334	C₂³×C₁₃₉	—	2	2	no	—
335	C₂³×C₁₃₉	—	2	2	no	—
336	C₂³×C₁₃₉	—	2	2	no	—
337	C₂³×C₁₃₉	—	2	2	no	—
338	C₂³×C₁₃₉	—	2	2	no	—
339	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
340	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
341	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
342	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
343	Q₈×C₁₃₉	—	8	4	no	—
344	Q₈×C₁₃₉	—	8	2	no	—
345	Q₈×C₁₃₉	—	8	2	no	—
346	Q₈×C₁₃₉	—	8	2	no	—
347	D₄×C₁₃₉	—	4	8	no	—
348	D₄×C₁₃₉	—	8	2	no	—
349	C₂×C₄×C₁₃₉	—	2	8	no	—
350	C₂×C₄×C₁₃₉	—	2	1	no	—
351	C₂×C₄×C₁₃₉	—	2	1	no	—
352	C₂×C₄×C₁₃₉	—	2	1	no	—
353	C₂×C₄×C₁₃₉	—	2	2	no	—
354	C₂×C₄×C₁₃₉	—	2	2	no	—
355	C₂×C₄×C₁₃₉	—	2	2	no	—
356	C₂×C₄×C₁₃₉	—	2	1	no	—
357	C₂×C₄×C₁₃₉	—	2	1	no	—
358	C₂×C₄×C₁₃₉	—	2	1	no	—
359	C₂×C₄×C₁₃₉	—	2	2	no	—
360	C₂×C₄×C₁₃₉	—	2	1	no	—
361	C₂×C₄×C₁₃₉	—	2	1	no	—
362	C₂×C₄×C₁₃₉	—	2	2	no	—
363	C₂×C₄×C₁₃₉	—	2	2	no	—
364	C₂×C₄×C₁₃₉	—	2	2	no	—
365	C₂×C₄×C₁₃₉	—	2	2	no	—
366	C₂×C₄×C₁₃₉	—	2	2	no	—
367	C₂×C₄×C₁₃₉	—	2	2	no	—
368	C₂×C₄×C₁₃₉	—	2	2	no	—
369	C₂×C₄×C₁₃₉	—	2	1	no	—
370	C₂×C₄×C₁₃₉	—	2	1	no	—
371	C₂×C₄×C₁₃₉	—	2	2	no	—
372	C₂×C₄×C₁₃₉	—	2	2	no	—
373	C₂×C₄×C₁₃₉	—	2	2	no	—
374	C₂×C₄×C₁₃₉	—	2	2	no	—
375	C₂×C₄×C₁₃₉	—	2	2	no	—
376	C₂×C₄×C₁₃₉	—	2	2	no	—
377	C₂×C₄×C₁₃₉	—	2	2	no	—
378	C₂×C₄×C₁₃₉	—	2	1	no	—
379	C₂×C₄×C₁₃₉	—	2	2	no	—
380	C₂×C₄×C₁₃₉	—	2	1	no	—
381	C₂×C₄×C₁₃₉	—	2	1	no	—
382	C₂×C₄×C₁₃₉	—	2	2	no	—
383	C₂×C₄×C₁₃₉	—	2	2	no	—
384	C₂×C₄×C₁₃₉	—	2	2	no	—
385	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
394	C₂×C₄×C₁₃₉	—	2	2	no	—
395	C₂×C₄×C₁₃₉	—	4	4	no	—
396	C₂×C₄×C₁₃₉	—	4	4	no	—
397	C₂×C₄×C₁₃₉	—	4	4	no	—
398	C₂×C₄×C₁₃₉	—	4	4	no	—
399	C₂×C₄×C₁₃₉	—	8	4	no	—
400	C₂×C₄×C₁₃₉	—	8	2	no	—
401	C₂×C₄×C₁₃₉	—	8	2	no	—
402	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
403	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
404	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
407	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
408	C₂²×C₁₃₉	—	2	2	no	—
409	C₂²×C₁₃₉	—	2	2	no	—
410	C₂²×C₁₃₉	—	2	2	no	—
411	C₂²×C₁₃₉	—	2	2	no	—
412	C₂²×C₁₃₉	—	2	2	no	—
413	C₂²×C₁₃₉	—	2	2	no	—
414	C₂²×C₁₃₉	—	4	2	no	—
415	C₂²×C₁₃₉	—	4	2	no	—
416	C₂²×C₁₃₉	—	4	2	no	—
417	C₂²×C₁₃₉	—	4	2	no	—
418	C₂²×C₁₃₉	—	4	2	no	—
419	C₂²×C₁₃₉	—	4	2	no	—
420	C₂²×C₁₃₉	—	4	2	no	—
421	C₂²×C₁₃₉	#536	1	4	yes	—
422	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
423	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
424	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
425	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
426	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
427	C₂²×C₁₃₉	#585	1	1	yes	characteristic
428	C₂²×C₁₃₉	#585	1	1	yes	characteristic
429	C₄×C₁₃₉	—	2	4	no	—
430	C₄×C₁₃₉	—	2	4	no	—
431	C₄×C₁₃₉	—	2	2	no	—
432	C₄×C₁₃₉	—	2	2	no	—
433	C₄×C₁₃₉	—	2	2	no	—
434	C₄×C₁₃₉	—	2	2	no	—
435	C₄×C₁₃₉	—	4	2	no	—
436	C₄×C₁₃₉	—	4	2	no	—
437	C₄×C₁₃₉	—	4	2	no	—
438	C₄×C₁₃₉	—	4	2	no	—
439	C₄×C₁₃₉	—	4	2	no	—
440	C₄×C₁₃₉	—	4	2	no	—
441	C₄×C₁₃₉	—	4	2	no	—
442	C₄×C₁₃₉	—	4	1	no	—
443	C₄×C₁₃₉	—	4	2	no	—
444	C₄×C₁₃₉	—	4	1	no	—
445	C₄×C₁₃₉	—	4	2	no	—
446	C₂×C₁₃₉	—	2	4	no	—
447	C₂×C₁₃₉	—	8	2	no	—
448	C₂×C₁₃₉	C₂×#536	1	1	yes	characteristic
449	C₂×C₁₃₉	#3496	1	1	yes	characteristic
450	C₂×C₁₃₉	#3497	1	1	yes	characteristic
451	C₂×C₁₃₉	#3535	1	1	yes	characteristic
452	C₂×C₁₃₉	#3538	1	1	yes	characteristic
453	C₂×C₁₃₉	#3563	1	1	yes	characteristic
454	C₂×C₁₃₉	#3564	1	1	yes	characteristic
455	#36742	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
456	C₁₃₉	#36742	1	1	yes	characteristic, direct product factor, Sylow
457	C₂×#544	C₂×C₁₃₉	1	1	yes	characteristic, complemented
458	C₂×#539	C₂×C₁₃₉	1	1	yes	characteristic
459	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
460	#2850	C₂×C₁₃₉	1	1	yes	characteristic
461	#2721	C₂×C₁₃₉	1	2	yes	complemented
462	#2719	C₂×C₁₃₉	1	2	yes	complemented
463	#2716	C₂×C₁₃₉	1	2	yes	complemented
464	#2713	C₂×C₁₃₉	1	2	yes	complemented
465	#2694	C₂×C₁₃₉	1	2	yes	complemented
466	#2690	C₂×C₁₃₉	1	2	yes	complemented
467	#2677	C₂×C₁₃₉	1	2	yes	complemented
468	#2674	C₂×C₁₃₉	1	2	yes	complemented
469	#2659	C₂×C₁₃₉	1	1	yes	characteristic, complemented
470	#2639	C₂×C₁₃₉	1	1	yes	characteristic
471	#2564	C₂×C₁₃₉	1	2	yes	complemented
472	#2498	C₂×C₁₃₉	1	2	yes	complemented
473	#2498	C₂×C₁₃₉	1	2	yes	complemented
474	#2417	C₂×C₁₃₉	1	2	yes	complemented
475	C₂×#387	C₂×C₁₃₉	1	1	yes	characteristic, complemented
476	#544	—	2	8	no	—
477	#539	—	2	8	no	—
478	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
479	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
480	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
481	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
482	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
483	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
484	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
485	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
486	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
487	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
488	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
489	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
490	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
491	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
492	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
493	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
494	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
495	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
496	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
497	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
498	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
499	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
500	#400	C₂²×C₁₃₉	1	2	yes	—
501	#400	C₂²×C₁₃₉	1	2	yes	—
502	#400	C₂²×C₁₃₉	1	2	yes	—
503	#400	C₂²×C₁₃₉	1	2	yes	—
504	#399	C₂²×C₁₃₉	1	2	yes	—
505	#399	C₂²×C₁₃₉	1	2	yes	—
506	#399	C₂²×C₁₃₉	1	2	yes	—
507	#398	C₂²×C₁₃₉	1	2	yes	—
508	#398	C₂²×C₁₃₉	1	2	yes	—
509	#398	C₂²×C₁₃₉	1	2	yes	—
510	#398	C₂²×C₁₃₉	1	2	yes	—
511	#398	C₂²×C₁₃₉	1	2	yes	—
512	#398	C₂²×C₁₃₉	1	2	yes	—
513	#397	C₂²×C₁₃₉	1	2	yes	—
514	#397	C₂²×C₁₃₉	1	2	yes	—
515	#397	C₂²×C₁₃₉	1	2	yes	—
516	#396	C₂²×C₁₃₉	1	2	yes	—
517	#396	C₂²×C₁₃₉	1	2	yes	—
518	#395	C₂²×C₁₃₉	1	2	yes	—
519	#395	C₂²×C₁₃₉	1	2	yes	—
520	#395	C₂²×C₁₃₉	1	2	yes	—
521	#394	C₂²×C₁₃₉	1	2	yes	—
522	#393	C₂²×C₁₃₉	1	2	yes	—
523	#393	C₂²×C₁₃₉	1	2	yes	—
524	#391	C₂²×C₁₃₉	1	1	yes	characteristic
525	#391	C₂²×C₁₃₉	1	1	yes	characteristic
526	#391	C₂²×C₁₃₉	1	1	yes	characteristic
527	#391	C₂²×C₁₃₉	1	2	yes	—
528	#390	C₂²×C₁₃₉	1	1	yes	characteristic
529	#389	C₂²×C₁₃₉	1	2	yes	—
530	#389	C₂²×C₁₃₉	1	2	yes	—
531	#389	C₂²×C₁₃₉	1	2	yes	—
532	#388	C₂²×C₁₃₉	1	2	yes	—
533	#388	C₂²×C₁₃₉	1	2	yes	—
534	#388	C₂²×C₁₃₉	1	2	yes	—
535	#388	C₂²×C₁₃₉	1	2	yes	—
536	#388	C₂²×C₁₃₉	1	2	yes	—
537	#388	C₂²×C₁₃₉	1	2	yes	—
538	#387	C₂²×C₁₃₉	1	2	yes	—
539	#387	C₂²×C₁₃₉	1	2	yes	—
540	#387	C₂²×C₁₃₉	1	2	yes	—
541	#387	C₂²×C₁₃₉	1	2	yes	—
542	#387	C₂²×C₁₃₉	1	2	yes	—
543	#387	C₂²×C₁₃₉	1	2	yes	—
544	#387	C₂²×C₁₃₉	1	2	yes	—
545	#387	C₂²×C₁₃₉	1	2	yes	—
546	#387	C₂²×C₁₃₉	1	2	yes	—
547	#387	C₂²×C₁₃₉	1	2	yes	—
548	#386	C₂²×C₁₃₉	1	2	yes	—
549	#386	C₂²×C₁₃₉	1	2	yes	—
550	#386	C₂²×C₁₃₉	1	2	yes	—
551	#386	C₂²×C₁₃₉	1	2	yes	—
552	#385	C₂²×C₁₃₉	1	2	yes	—
553	#385	C₂²×C₁₃₉	1	2	yes	—
554	#384	C₂²×C₁₃₉	1	1	yes	characteristic
555	#382	C₂²×C₁₃₉	1	1	yes	characteristic
556	#380	C₂²×C₁₃₉	1	2	yes	—
557	#380	C₂²×C₁₃₉	1	2	yes	—
558	#380	C₂²×C₁₃₉	1	2	yes	—
559	#380	C₂²×C₁₃₉	1	2	yes	—
560	#380	C₂²×C₁₃₉	1	2	yes	—
561	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
562	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
563	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
564	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
565	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
566	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
567	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
568	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
570	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
572	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
573	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
575	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
576	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
579	C₄⋊Q₈	—	2	8	no	—
580	C₄⋊Q₈	—	2	8	no	—
581	C₄⋊Q₈	—	4	2	no	—
582	#126	—	2	8	no	—
583	#125	—	2	8	no	—
584	#125	—	2	8	no	—
585	#125	—	2	8	no	—
586	#124	—	4	2	no	—
587	#123	—	2	8	no	—
588	#123	—	2	8	no	—
589	C₂²⋊Q₈	—	2	4	no	—
590	C₂²⋊Q₈	—	2	8	no	—
591	C₂²⋊Q₈	—	2	4	no	—
592	C₂²⋊Q₈	—	2	4	no	—
593	C₂²⋊Q₈	—	2	8	no	—
594	C₂²⋊Q₈	—	4	4	no	—
595	#121	—	2	4	no	—
596	C₄×D₄	—	2	8	no	—
597	#117	—	2	8	no	—
598	C₂×C₄⋊C₄	—	4	2	no	—
599	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	—
600	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
642	C₂×C₄²	—	4	2	no	—
643	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
644	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
645	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
646	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
650	#95	C₂³×C₁₃₉	1	2	yes	—
651	#95	C₂³×C₁₃₉	1	2	yes	—
652	#95	C₂³×C₁₃₉	1	2	yes	—
653	#95	C₂³×C₁₃₉	1	2	yes	—
654	#95	C₂³×C₁₃₉	1	2	yes	—
655	#95	C₂³×C₁₃₉	1	2	yes	—
656	#95	C₂³×C₁₃₉	1	2	yes	—
657	#95	C₂³×C₁₃₉	1	2	yes	—
658	#95	C₂³×C₁₃₉	1	2	yes	—
659	#95	C₂³×C₁₃₉	1	2	yes	—
660	#95	C₂³×C₁₃₉	1	2	yes	—
661	#95	C₂³×C₁₃₉	1	2	yes	—
662	#95	C₂³×C₁₃₉	1	2	yes	—
663	#95	C₂³×C₁₃₉	1	2	yes	—
664	#95	C₂³×C₁₃₉	1	2	yes	—
665	#95	C₂³×C₁₃₉	1	2	yes	—
666	#95	C₂³×C₁₃₉	1	2	yes	—
667	#95	C₂³×C₁₃₉	1	2	yes	—
668	#95	C₂³×C₁₃₉	1	2	yes	—
669	#95	C₂³×C₁₃₉	1	2	yes	—
670	#95	C₂³×C₁₃₉	1	2	yes	—
671	#95	C₂³×C₁₃₉	1	2	yes	—
672	#95	C₂³×C₁₃₉	1	2	yes	—
673	#95	C₂³×C₁₃₉	1	2	yes	—
674	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
675	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
676	C₂×Q₈	—	2	2	no	—
677	C₂×Q₈	—	2	4	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	2	2	no	—
680	C₂×Q₈	—	4	2	no	—
681	C₂×Q₈	—	4	1	no	—
682	C₂×Q₈	—	4	1	no	—
683	C₂×Q₈	—	4	1	no	—
684	C₂×Q₈	—	4	2	no	—
685	C₂×Q₈	—	4	1	no	—
686	C₂×Q₈	—	4	1	no	—
687	C₂×Q₈	—	4	1	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	4	1	no	—
693	C₂×D₄	—	4	1	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	4	1	no	—
704	C₂²×C₄	—	4	1	no	—
705	C₂²×C₄	—	4	1	no	—
706	C₂²×C₄	—	4	1	no	—
707	C₂²×C₄	—	4	1	no	—
708	C₂²×C₄	—	4	1	no	—
709	C₂²×C₄	—	4	1	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	—	4	1	no	—
713	C₂²×C₄	—	4	1	no	—
714	C₂²×C₄	—	4	1	no	—
715	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
716	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
717	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
718	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	4	2	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₄⋊C₄	—	4	2	no	—
756	C₄⋊C₄	—	4	2	no	—
757	C₄⋊C₄	—	4	2	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
761	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₄²	—	2	4	no	—
778	C₄²	—	2	4	no	—
779	C₄²	—	2	4	no	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	4	1	no	—
783	C₄²	—	4	1	no	—
784	C₂³	—	2	1	no	—
785	C₂³	—	2	1	no	—
786	C₂³	—	2	1	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
796	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
797	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
798	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
799	Q₈	—	8	4	no	—
800	Q₈	—	8	2	no	—
801	Q₈	—	8	2	no	—
802	Q₈	—	8	2	no	—
803	D₄	—	4	8	no	—
804	D₄	—	8	2	no	—
805	C₂×C₄	—	2	8	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	4	4	no	—
852	C₂×C₄	—	4	4	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	4	no	—
855	C₂×C₄	—	8	4	no	—
856	C₂×C₄	—	8	2	no	—
857	C₂×C₄	—	8	2	no	—
858	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
859	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
860	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
861	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
862	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
863	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	#536×C₁₃₉	1	4	yes	—
878	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
879	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
880	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
881	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
882	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
883	C₂²	#585×C₁₃₉	1	1	yes	characteristic
884	C₂²	#585×C₁₃₉	1	1	yes	characteristic
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	4	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	4	1	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₂	—	2	4	no	—
903	C₂	—	8	2	no	—
904	C₂	C₂×#536×C₁₃₉	1	1	yes	characteristic
905	C₂	#3496×C₁₃₉	1	1	yes	characteristic
906	C₂	#3497×C₁₃₉	1	1	yes	characteristic
907	C₂	#3535×C₁₃₉	1	1	yes	characteristic
908	C₂	#3538×C₁₃₉	1	1	yes	characteristic
909	C₂	#3563×C₁₃₉	1	1	yes	characteristic
910	C₂	#3564×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. C₂×#544×C₁₃₉	C₂	semidirect
3. #2857×C₁₃₉	C₂	semidirect
5. #2721×C₁₃₉	C₂	semidirect
6. #2719×C₁₃₉	C₂	semidirect
7. #2716×C₁₃₉	C₂	semidirect
8. #2713×C₁₃₉	C₂	semidirect
9. #2694×C₁₃₉	C₂	semidirect
10. #2690×C₁₃₉	C₂	semidirect
11. #2677×C₁₃₉	C₂	semidirect
12. #2674×C₁₃₉	C₂	semidirect
13. #2659×C₁₃₉	C₂	semidirect
15. #2564×C₁₃₉	C₂	semidirect
16. #2498×C₁₃₉	C₂	semidirect
17. #2498×C₁₃₉	C₂	semidirect
18. #2417×C₁₃₉	C₂	semidirect
19. C₂×#387×C₁₃₉	C₂	semidirect
455. #36742	C₁₃₉	direct (N × H)
456. C₁₃₉	#36742	direct (N × H)
457. C₂×#544	C₂×C₁₃₉	semidirect
459. #2857	C₂×C₁₃₉	semidirect
461. #2721	C₂×C₁₃₉	semidirect
462. #2719	C₂×C₁₃₉	semidirect
463. #2716	C₂×C₁₃₉	semidirect
464. #2713	C₂×C₁₃₉	semidirect
465. #2694	C₂×C₁₃₉	semidirect
466. #2690	C₂×C₁₃₉	semidirect
467. #2677	C₂×C₁₃₉	semidirect
468. #2674	C₂×C₁₃₉	semidirect
469. #2659	C₂×C₁₃₉	semidirect
471. #2564	C₂×C₁₃₉	semidirect
472. #2498	C₂×C₁₃₉	semidirect
473. #2498	C₂×C₁₃₉	semidirect
474. #2417	C₂×C₁₃₉	semidirect
475. C₂×#387	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#544×C₁₃₉	2
C₂×#539×C₁₃₉	2
#2857×C₁₃₉	2
#2850×C₁₃₉	2
#2721×C₁₃₉	2
#2719×C₁₃₉	2
#2716×C₁₃₉	2
#2713×C₁₃₉	2
#2694×C₁₃₉	2
#2690×C₁₃₉	2
#2677×C₁₃₉	2
#2674×C₁₃₉	2
#2659×C₁₃₉	2
#2639×C₁₃₉	2
#2564×C₁₃₉	2
#2498×C₁₃₉	2
#2417×C₁₃₉	2
C₂×#387×C₁₃₉	2
#36742	139

Subgroups — C139×#36742 #48031338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36742 #48031338