Subgroups — C₁₃₉×#36275 #48030871

Order 35584.

2532 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	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	#2567×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2487×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2453×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2449×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2441×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2438×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2417×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×C₄⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2339×C₁₃₉	C₂	1	2	yes	maximal
16	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#389×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
19	#554×C₁₃₉	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
26	C₄×#41×C₁₃₉	—	2	8	no	—
27	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
37	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
40	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
41	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
42	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
43	#400×C₁₃₉	C₂²	1	4	yes	—
44	#399×C₁₃₉	C₂²	1	4	yes	—
45	#398×C₁₃₉	C₂²	1	4	yes	—
46	#398×C₁₃₉	C₂²	1	4	yes	—
47	#396×C₁₃₉	C₂²	1	4	yes	—
48	#395×C₁₃₉	C₂²	1	4	yes	—
49	#391×C₁₃₉	C₂²	1	1	yes	characteristic
50	#391×C₁₃₉	C₂²	1	2	yes	—
51	#391×C₁₃₉	C₂²	1	2	yes	—
52	#391×C₁₃₉	C₂²	1	2	yes	—
53	#391×C₁₃₉	C₂²	1	2	yes	—
54	#389×C₁₃₉	C₂²	1	1	yes	characteristic
55	#389×C₁₃₉	C₂²	1	2	yes	—
56	#389×C₁₃₉	C₂²	1	2	yes	—
57	#389×C₁₃₉	C₂²	1	2	yes	—
58	#389×C₁₃₉	C₂²	1	4	yes	—
59	#389×C₁₃₉	C₂²	1	4	yes	—
60	#389×C₁₃₉	C₂²	1	2	yes	—
61	#389×C₁₃₉	C₂²	1	2	yes	—
62	#389×C₁₃₉	C₂²	1	2	yes	—
63	#389×C₁₃₉	C₂²	1	2	yes	—
64	#387×C₁₃₉	C₂²	1	2	yes	—
65	#387×C₁₃₉	C₂²	1	4	yes	—
66	#387×C₁₃₉	C₂²	1	4	yes	—
67	#386×C₁₃₉	C₂²	1	4	yes	—
68	#386×C₁₃₉	C₂²	1	4	yes	—
69	#385×C₁₃₉	C₂²	1	2	yes	—
70	#385×C₁₃₉	C₂²	1	4	yes	—
71	#385×C₁₃₉	C₂²	1	4	yes	—
72	#385×C₁₃₉	C₂²	1	4	yes	—
73	#384×C₁₃₉	C₂²	1	2	yes	—
74	#384×C₁₃₉	C₂²	1	1	yes	characteristic
75	#381×C₁₃₉	C₂²	1	4	yes	—
76	#380×C₁₃₉	C₂²	1	1	yes	characteristic
77	#380×C₁₃₉	C₂²	1	2	yes	—
78	#380×C₁₃₉	C₂²	1	2	yes	—
79	#380×C₁₃₉	C₂²	1	2	yes	—
80	#380×C₁₃₉	C₂²	1	4	yes	—
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
82	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	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	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
97	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
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	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
102	#125×C₁₃₉	—	2	8	no	—
103	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
104	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
105	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
106	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
107	C₄×Q₈×C₁₃₉	—	2	4	no	—
108	C₄×Q₈×C₁₃₉	—	2	4	no	—
109	C₄×Q₈×C₁₃₉	—	2	4	no	—
110	C₄×D₄×C₁₃₉	—	2	4	no	—
111	C₄×D₄×C₁₃₉	—	2	8	no	—
112	C₄×D₄×C₁₃₉	—	2	8	no	—
113	C₄×D₄×C₁₃₉	—	2	8	no	—
114	C₄×D₄×C₁₃₉	—	2	8	no	—
115	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
116	#117×C₁₃₉	—	2	4	no	—
117	#117×C₁₃₉	—	2	8	no	—
118	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
119	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
120	C₂×C₄⋊C₄×C₁₃₉	—	4	8	no	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄²×C₁₃₉	—	2	8	no	—
152	C₂×C₄²×C₁₃₉	—	2	4	no	—
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	1	yes	characteristic
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	2	yes	—
161	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
162	#95×C₁₃₉	C₂³	1	2	yes	—
163	#95×C₁₃₉	C₂³	1	4	yes	—
164	#95×C₁₃₉	C₂³	1	4	yes	—
165	#95×C₁₃₉	C₂³	1	4	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	4	yes	—
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	4	yes	—
173	#95×C₁₃₉	C₂³	1	2	yes	—
174	#95×C₁₃₉	C₂³	1	2	yes	—
175	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
176	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
177	#41×C₁₃₉	—	2	32	no	—
178	C₂×Q₈×C₁₃₉	—	2	2	no	—
179	C₂×Q₈×C₁₃₉	—	2	2	no	—
180	C₂×Q₈×C₁₃₉	—	2	4	no	—
181	C₂×Q₈×C₁₃₉	—	2	2	no	—
182	C₂×Q₈×C₁₃₉	—	2	2	no	—
183	C₂×Q₈×C₁₃₉	—	2	2	no	—
184	C₂×Q₈×C₁₃₉	—	4	2	no	—
185	C₂×Q₈×C₁₃₉	—	4	2	no	—
186	C₂×Q₈×C₁₃₉	C₂×Q₈	1	4	yes	—
187	C₂×D₄×C₁₃₉	—	2	4	no	—
188	C₂×D₄×C₁₃₉	—	2	4	no	—
189	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
190	C₂×D₄×C₁₃₉	C₂×Q₈	1	8	yes	—
191	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
192	C₂×D₄×C₁₃₉	#41	1	4	yes	—
193	C₂²×C₄×C₁₃₉	—	2	4	no	—
194	C₂²×C₄×C₁₃₉	—	2	4	no	—
195	C₂²×C₄×C₁₃₉	—	2	2	no	—
196	C₂²×C₄×C₁₃₉	—	2	4	no	—
197	C₂²×C₄×C₁₃₉	—	2	2	no	—
198	C₂²×C₄×C₁₃₉	—	2	4	no	—
199	C₂²×C₄×C₁₃₉	—	2	4	no	—
200	C₂²×C₄×C₁₃₉	—	2	8	no	—
201	C₂²×C₄×C₁₃₉	—	2	8	no	—
202	C₂²×C₄×C₁₃₉	—	2	2	no	—
203	C₂²×C₄×C₁₃₉	—	2	2	no	—
204	C₂²×C₄×C₁₃₉	—	2	8	no	—
205	C₂²×C₄×C₁₃₉	—	2	2	no	—
206	C₂²×C₄×C₁₃₉	—	2	4	no	—
207	C₂²×C₄×C₁₃₉	—	2	2	no	—
208	C₂²×C₄×C₁₃₉	—	2	2	no	—
209	C₂²×C₄×C₁₃₉	—	4	4	no	—
210	C₂²×C₄×C₁₃₉	—	4	1	no	—
211	C₂²×C₄×C₁₃₉	—	4	2	no	—
212	C₂²×C₄×C₁₃₉	—	4	4	no	—
213	C₂²×C₄×C₁₃₉	—	4	4	no	—
214	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
215	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
216	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
217	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
232	C₄⋊C₄×C₁₃₉	—	2	2	no	—
233	C₄⋊C₄×C₁₃₉	—	2	8	no	—
234	C₄⋊C₄×C₁₃₉	—	2	4	no	—
235	C₄⋊C₄×C₁₃₉	—	2	4	no	—
236	C₄⋊C₄×C₁₃₉	—	2	4	no	—
237	C₄⋊C₄×C₁₃₉	—	2	2	no	—
238	C₄⋊C₄×C₁₃₉	—	2	4	no	—
239	C₄⋊C₄×C₁₃₉	—	2	4	no	—
240	C₄⋊C₄×C₁₃₉	—	2	8	no	—
241	C₄⋊C₄×C₁₃₉	—	2	8	no	—
242	C₄⋊C₄×C₁₃₉	—	2	4	no	—
243	C₄⋊C₄×C₁₃₉	—	2	4	no	—
244	C₄⋊C₄×C₁₃₉	—	2	4	no	—
245	C₄⋊C₄×C₁₃₉	—	2	4	no	—
246	C₄⋊C₄×C₁₃₉	—	2	8	no	—
247	C₄⋊C₄×C₁₃₉	—	2	2	no	—
248	C₄⋊C₄×C₁₃₉	—	4	4	no	—
249	C₄⋊C₄×C₁₃₉	—	4	4	no	—
250	C₄⋊C₄×C₁₃₉	—	4	4	no	—
251	C₄⋊C₄×C₁₃₉	—	4	2	no	—
252	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
253	C₄⋊C₄×C₁₃₉	#41	1	4	yes	complemented
254	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
255	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
256	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
257	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
259	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
260	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
261	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
262	C₄²×C₁₃₉	—	2	2	no	—
263	C₄²×C₁₃₉	—	2	4	no	—
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	4	no	—
269	C₄²×C₁₃₉	—	2	4	no	—
270	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
271	C₂³×C₁₃₉	—	2	2	no	—
272	C₂³×C₁₃₉	—	2	2	no	—
273	C₂³×C₁₃₉	—	2	2	no	—
274	C₂³×C₁₃₉	—	2	2	no	—
275	C₂³×C₁₃₉	—	2	1	no	—
276	C₂³×C₁₃₉	—	2	1	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	C₂²×D₄	1	4	yes	—
282	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
283	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
284	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
285	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
286	Q₈×C₁₃₉	—	2	8	no	—
287	Q₈×C₁₃₉	—	4	4	no	—
288	Q₈×C₁₃₉	—	8	4	no	—
289	D₄×C₁₃₉	—	2	16	no	—
290	D₄×C₁₃₉	C₂²⋊Q₈	1	16	yes	complemented
291	C₂×C₄×C₁₃₉	—	2	16	no	—
292	C₂×C₄×C₁₃₉	—	2	1	no	—
293	C₂×C₄×C₁₃₉	—	2	1	no	—
294	C₂×C₄×C₁₃₉	—	2	2	no	—
295	C₂×C₄×C₁₃₉	—	2	2	no	—
296	C₂×C₄×C₁₃₉	—	2	2	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	1	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	2	1	no	—
303	C₂×C₄×C₁₃₉	—	2	1	no	—
304	C₂×C₄×C₁₃₉	—	2	8	no	—
305	C₂×C₄×C₁₃₉	—	2	16	no	—
306	C₂×C₄×C₁₃₉	—	2	1	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	2	2	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	4	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	1	no	—
315	C₂×C₄×C₁₃₉	—	2	4	no	—
316	C₂×C₄×C₁₃₉	—	2	4	no	—
317	C₂×C₄×C₁₃₉	—	2	4	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	2	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	1	no	—
322	C₂×C₄×C₁₃₉	—	2	2	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	4	no	—
327	C₂×C₄×C₁₃₉	—	4	4	no	—
328	C₂×C₄×C₁₃₉	—	4	16	no	—
329	C₂×C₄×C₁₃₉	—	4	8	no	—
330	C₂×C₄×C₁₃₉	—	4	4	no	—
331	C₂×C₄×C₁₃₉	—	8	8	no	—
332	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
333	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
337	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
338	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
339	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
340	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
341	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
342	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
343	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
344	C₂²×C₁₃₉	—	2	4	no	—
345	C₂²×C₁₃₉	—	2	4	no	—
346	C₂²×C₁₃₉	—	2	4	no	—
347	C₂²×C₁₃₉	—	2	4	no	—
348	C₂²×C₁₃₉	—	2	4	no	—
349	C₂²×C₁₃₉	—	2	4	no	—
350	C₂²×C₁₃₉	—	2	2	no	—
351	C₂²×C₁₃₉	—	2	2	no	—
352	C₂²×C₁₃₉	—	2	2	no	—
353	C₂²×C₁₃₉	—	4	1	no	—
354	C₂²×C₁₃₉	—	4	1	no	—
355	C₂²×C₁₃₉	—	4	1	no	—
356	C₂²×C₁₃₉	—	4	1	no	—
357	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	8	yes	—
358	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
359	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
360	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
361	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
362	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
364	C₂²×C₁₃₉	#585	1	1	yes	characteristic
365	C₄×C₁₃₉	—	2	2	no	—
366	C₄×C₁₃₉	—	2	4	no	—
367	C₄×C₁₃₉	—	2	4	no	—
368	C₄×C₁₃₉	—	2	4	no	—
369	C₄×C₁₃₉	—	2	2	no	—
370	C₄×C₁₃₉	—	2	2	no	—
371	C₄×C₁₃₉	—	4	1	no	—
372	C₄×C₁₃₉	—	4	2	no	—
373	C₄×C₁₃₉	—	4	4	no	—
374	C₄×C₁₃₉	—	4	2	no	—
375	C₄×C₁₃₉	—	4	2	no	—
376	C₄×C₁₃₉	—	4	4	no	—
377	C₄×C₁₃₉	—	4	2	no	—
378	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	4	yes	—
379	C₄×C₁₃₉	#547	1	4	yes	—
380	C₂×C₁₃₉	—	2	8	no	—
381	C₂×C₁₃₉	—	4	2	no	—
382	C₂×C₁₃₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
383	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
384	C₂×C₁₃₉	Q₈×#41	1	1	yes	characteristic
385	C₂×C₁₃₉	#3481	1	1	yes	characteristic
386	C₂×C₁₃₉	#3488	1	1	yes	characteristic
387	C₂×C₁₃₉	#3503	1	1	yes	characteristic
388	C₂×C₁₃₉	#3515	1	1	yes	characteristic
389	#36275	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
390	C₁₃₉	#36275	1	1	yes	characteristic, direct product factor, Sylow
391	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic, complemented
392	C₂×C₄×#41	C₂×C₁₃₉	1	1	yes	characteristic
393	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
394	#2855	C₂×C₁₃₉	1	2	yes	complemented
395	#2582	C₂×C₁₃₉	1	1	yes	characteristic, complemented
396	#2567	C₂×C₁₃₉	1	1	yes	characteristic, complemented
397	#2487	C₂×C₁₃₉	1	2	yes	complemented
398	#2453	C₂×C₁₃₉	1	2	yes	complemented
399	#2449	C₂×C₁₃₉	1	4	yes	complemented
400	#2441	C₂×C₁₃₉	1	2	yes	complemented
401	#2438	C₂×C₁₃₉	1	4	yes	complemented
402	#2417	C₂×C₁₃₉	1	2	yes	complemented
403	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
404	D₄×C₄⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
405	#2339	C₂×C₁₃₉	1	2	yes	—
406	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
407	C₂×#389	C₂×C₁₃₉	1	2	yes	complemented
408	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
409	#554	—	2	8	no	—
410	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
411	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
412	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
413	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
414	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
415	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
416	C₄×#41	—	2	8	no	—
417	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
418	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
419	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
420	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
421	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
422	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
423	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
424	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
425	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
426	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
427	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
428	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
429	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
430	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
431	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
432	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
433	#400	C₂²×C₁₃₉	1	4	yes	—
434	#399	C₂²×C₁₃₉	1	4	yes	—
435	#398	C₂²×C₁₃₉	1	4	yes	—
436	#398	C₂²×C₁₃₉	1	4	yes	—
437	#396	C₂²×C₁₃₉	1	4	yes	—
438	#395	C₂²×C₁₃₉	1	4	yes	—
439	#391	C₂²×C₁₃₉	1	2	yes	—
440	#391	C₂²×C₁₃₉	1	2	yes	—
441	#391	C₂²×C₁₃₉	1	2	yes	—
442	#391	C₂²×C₁₃₉	1	1	yes	characteristic
443	#391	C₂²×C₁₃₉	1	2	yes	—
444	#389	C₂²×C₁₃₉	1	2	yes	—
445	#389	C₂²×C₁₃₉	1	2	yes	—
446	#389	C₂²×C₁₃₉	1	2	yes	—
447	#389	C₂²×C₁₃₉	1	2	yes	—
448	#389	C₂²×C₁₃₉	1	2	yes	—
449	#389	C₂²×C₁₃₉	1	2	yes	—
450	#389	C₂²×C₁₃₉	1	2	yes	—
451	#389	C₂²×C₁₃₉	1	4	yes	—
452	#389	C₂²×C₁₃₉	1	4	yes	—
453	#389	C₂²×C₁₃₉	1	1	yes	characteristic
454	#387	C₂²×C₁₃₉	1	4	yes	—
455	#387	C₂²×C₁₃₉	1	4	yes	—
456	#387	C₂²×C₁₃₉	1	2	yes	—
457	#386	C₂²×C₁₃₉	1	4	yes	—
458	#386	C₂²×C₁₃₉	1	4	yes	—
459	#385	C₂²×C₁₃₉	1	4	yes	—
460	#385	C₂²×C₁₃₉	1	4	yes	—
461	#385	C₂²×C₁₃₉	1	4	yes	—
462	#385	C₂²×C₁₃₉	1	2	yes	—
463	#384	C₂²×C₁₃₉	1	2	yes	—
464	#384	C₂²×C₁₃₉	1	1	yes	characteristic
465	#381	C₂²×C₁₃₉	1	4	yes	—
466	#380	C₂²×C₁₃₉	1	2	yes	—
467	#380	C₂²×C₁₃₉	1	2	yes	—
468	#380	C₂²×C₁₃₉	1	2	yes	—
469	#380	C₂²×C₁₃₉	1	4	yes	—
470	#380	C₂²×C₁₃₉	1	1	yes	characteristic
471	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
472	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
473	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
474	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
475	C₂×#41	—	2	4	no	—
476	C₂×#41	—	2	4	no	—
477	C₂×#41	Q₈×C₁₃₉	1	8	yes	complemented
478	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
479	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
480	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
481	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
482	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
485	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
486	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
488	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
489	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
491	C₄⋊Q₈	—	2	4	no	—
492	#125	—	2	8	no	—
493	C₂²⋊Q₈	—	2	8	no	—
494	C₂²⋊Q₈	—	2	4	no	—
495	C₂²⋊Q₈	—	2	16	no	—
496	C₂²⋊Q₈	—	4	4	no	—
497	C₄×Q₈	—	2	4	no	—
498	C₄×Q₈	—	2	4	no	—
499	C₄×Q₈	—	2	4	no	—
500	C₄×D₄	—	2	4	no	—
501	C₄×D₄	—	2	8	no	—
502	C₄×D₄	—	2	8	no	—
503	C₄×D₄	—	2	8	no	—
504	C₄×D₄	—	2	8	no	—
505	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
506	#117	—	2	4	no	—
507	#117	—	2	8	no	—
508	C₂×C₄⋊C₄	—	2	8	no	—
509	C₂×C₄⋊C₄	—	2	8	no	—
510	C₂×C₄⋊C₄	—	4	8	no	—
511	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
514	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	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	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	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	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	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	2	yes	—
541	C₂×C₄²	—	2	8	no	—
542	C₂×C₄²	—	2	4	no	—
543	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
551	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
552	#95	C₂³×C₁₃₉	1	2	yes	—
553	#95	C₂³×C₁₃₉	1	4	yes	—
554	#95	C₂³×C₁₃₉	1	4	yes	—
555	#95	C₂³×C₁₃₉	1	4	yes	—
556	#95	C₂³×C₁₃₉	1	2	yes	—
557	#95	C₂³×C₁₃₉	1	2	yes	—
558	#95	C₂³×C₁₃₉	1	2	yes	—
559	#95	C₂³×C₁₃₉	1	2	yes	—
560	#95	C₂³×C₁₃₉	1	4	yes	—
561	#95	C₂³×C₁₃₉	1	4	yes	—
562	#95	C₂³×C₁₃₉	1	4	yes	—
563	#95	C₂³×C₁₃₉	1	4	yes	—
564	#95	C₂³×C₁₃₉	1	4	yes	—
565	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
566	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
567	#41	—	2	32	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	—	2	2	no	—
570	C₂×Q₈	—	2	4	no	—
571	C₂×Q₈	—	2	2	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	4	2	no	—
575	C₂×Q₈	—	4	2	no	—
576	C₂×Q₈	C₂×Q₈×C₁₃₉	1	4	yes	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
580	C₂×D₄	C₂×Q₈×C₁₃₉	1	8	yes	—
581	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
582	C₂×D₄	#41×C₁₃₉	1	4	yes	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	8	no	—
591	C₂²×C₄	—	2	8	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	8	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	4	4	no	—
600	C₂²×C₄	—	4	1	no	—
601	C₂²×C₄	—	4	2	no	—
602	C₂²×C₄	—	4	4	no	—
603	C₂²×C₄	—	4	4	no	—
604	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
605	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
606	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
607	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
611	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
613	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	8	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	8	no	—
631	C₄⋊C₄	—	2	8	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	8	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	4	4	no	—
639	C₄⋊C₄	—	4	4	no	—
640	C₄⋊C₄	—	4	4	no	—
641	C₄⋊C₄	—	4	2	no	—
642	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
643	C₄⋊C₄	#41×C₁₃₉	1	4	yes	complemented
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	8	no	—
646	C₂²⋊C₄	—	2	8	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	4	4	no	—
651	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
652	C₄²	—	2	2	no	—
653	C₄²	—	2	4	no	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	4	no	—
660	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
672	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
673	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
674	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
675	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
676	Q₈	—	2	8	no	—
677	Q₈	—	4	4	no	—
678	Q₈	—	8	4	no	—
679	D₄	—	2	16	no	—
680	D₄	C₂²⋊Q₈×C₁₃₉	1	16	yes	complemented
681	C₂×C₄	—	2	16	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	8	no	—
695	C₂×C₄	—	2	16	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	16	no	—
719	C₂×C₄	—	4	8	no	—
720	C₂×C₄	—	4	4	no	—
721	C₂×C₄	—	8	8	no	—
722	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
723	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
724	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
725	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
726	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
727	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
728	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
729	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
730	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
731	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
732	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
733	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
734	C₂²	—	2	4	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	4	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	2	4	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	8	yes	—
748	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
749	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
750	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
751	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
752	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
753	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
754	C₂²	#585×C₁₃₉	1	1	yes	characteristic
755	C₄	—	2	2	no	—
756	C₄	—	2	4	no	—
757	C₄	—	2	4	no	—
758	C₄	—	2	4	no	—
759	C₄	—	2	2	no	—
760	C₄	—	2	2	no	—
761	C₄	—	4	1	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	4	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	4	no	—
767	C₄	—	4	2	no	—
768	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	4	yes	—
769	C₄	#547×C₁₃₉	1	4	yes	—
770	C₂	—	2	8	no	—
771	C₂	—	4	2	no	—
772	C₂	C₂²×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
773	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
774	C₂	Q₈×#41×C₁₃₉	1	1	yes	characteristic
775	C₂	#3481×C₁₃₉	1	1	yes	characteristic
776	C₂	#3488×C₁₃₉	1	1	yes	characteristic
777	C₂	#3503×C₁₃₉	1	1	yes	characteristic
778	C₂	#3515×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×#554×C₁₃₉	C₂	semidirect
3. #2857×C₁₃₉	C₂	semidirect
4. #2855×C₁₃₉	C₂	semidirect
5. #2582×C₁₃₉	C₂	semidirect
6. #2567×C₁₃₉	C₂	semidirect
7. #2487×C₁₃₉	C₂	semidirect
8. #2453×C₁₃₉	C₂	semidirect
9. #2449×C₁₃₉	C₂	semidirect
10. #2441×C₁₃₉	C₂	semidirect
11. #2438×C₁₃₉	C₂	semidirect
12. #2417×C₁₃₉	C₂	semidirect
13. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
14. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
16. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
17. C₂×#389×C₁₃₉	C₂	semidirect
87. C₂×#41×C₁₃₉	Q₈	semidirect
253. C₄⋊C₄×C₁₃₉	#41	semidirect
290. D₄×C₁₃₉	C₂²⋊Q₈	semidirect
389. #36275	C₁₃₉	direct (N × H)
390. C₁₃₉	#36275	direct (N × H)
391. C₂×#554	C₂×C₁₃₉	semidirect
393. #2857	C₂×C₁₃₉	semidirect
394. #2855	C₂×C₁₃₉	semidirect
395. #2582	C₂×C₁₃₉	semidirect
396. #2567	C₂×C₁₃₉	semidirect
397. #2487	C₂×C₁₃₉	semidirect
398. #2453	C₂×C₁₃₉	semidirect
399. #2449	C₂×C₁₃₉	semidirect
400. #2441	C₂×C₁₃₉	semidirect
401. #2438	C₂×C₁₃₉	semidirect
402. #2417	C₂×C₁₃₉	semidirect
403. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
404. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
406. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
407. C₂×#389	C₂×C₁₃₉	semidirect
477. C₂×#41	Q₈×C₁₃₉	semidirect
643. C₄⋊C₄	#41×C₁₃₉	semidirect
680. 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×#554×C₁₃₉	2
C₂×C₄×#41×C₁₃₉	2
#2857×C₁₃₉	2
#2855×C₁₃₉	2
#2582×C₁₃₉	2
#2567×C₁₃₉	2
#2487×C₁₃₉	2
#2453×C₁₃₉	2
#2449×C₁₃₉	2
#2441×C₁₃₉	2
#2438×C₁₃₉	2
#2417×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
#2339×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
C₂×#389×C₁₃₉	2
#36275	139

Subgroups — C139×#36275 #48030871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36275 #48030871