Subgroups — C₁₃₉×#36160 #48030756

Order 35584.

3004 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#555×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2847×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2563×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2537×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2485×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2472×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2459×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2420×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2414×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2408×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2363×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2354×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2352×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	C₄×#121×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2280×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
20	#555×C₁₃₉	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×#124×C₁₃₉	C₂²	1	4	yes	complemented
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
28	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₁₃₉	—	2	8	no	—
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
40	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
41	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
42	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
44	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
45	#397×C₁₃₉	C₂²	1	4	yes	complemented
46	#394×C₁₃₉	C₂²	1	4	yes	—
47	#394×C₁₃₉	C₂²	1	4	yes	complemented
48	#394×C₁₃₉	C₂²	1	4	yes	complemented
49	#393×C₁₃₉	C₂²	1	4	yes	complemented
50	#392×C₁₃₉	C₂²	1	4	yes	—
51	#391×C₁₃₉	C₂²	1	2	yes	complemented
52	#390×C₁₃₉	C₂²	1	2	yes	—
53	#390×C₁₃₉	C₂²	1	2	yes	—
54	#390×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
55	#390×C₁₃₉	C₂²	1	4	yes	complemented
56	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
57	#389×C₁₃₉	C₂²	1	2	yes	complemented
58	#389×C₁₃₉	C₂²	1	2	yes	complemented
59	#388×C₁₃₉	C₂²	1	2	yes	complemented
60	#388×C₁₃₉	C₂²	1	4	yes	complemented
61	#388×C₁₃₉	C₂²	1	4	yes	complemented
62	#388×C₁₃₉	C₂²	1	4	yes	complemented
63	#387×C₁₃₉	C₂²	1	4	yes	complemented
64	#386×C₁₃₉	C₂²	1	2	yes	—
65	#386×C₁₃₉	C₂²	1	4	yes	—
66	#386×C₁₃₉	C₂²	1	4	yes	complemented
67	#386×C₁₃₉	C₂²	1	4	yes	complemented
68	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
69	#382×C₁₃₉	C₂²	1	2	yes	complemented
70	#381×C₁₃₉	C₂²	1	4	yes	complemented
71	#380×C₁₃₉	C₂²	1	1	yes	characteristic
72	#380×C₁₃₉	C₂²	1	2	yes	—
73	#380×C₁₃₉	C₂²	1	2	yes	—
74	#380×C₁₃₉	C₂²	1	2	yes	complemented
75	#380×C₁₃₉	C₂²	1	2	yes	complemented
76	#380×C₁₃₉	C₂²	1	2	yes	complemented
77	#380×C₁₃₉	C₂²	1	2	yes	complemented
78	#380×C₁₃₉	C₂²	1	2	yes	complemented
79	#379×C₁₃₉	C₂²	1	4	yes	—
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
85	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
86	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
87	C₂²×D₄×C₁₃₉	—	2	4	no	—
88	C₂²×D₄×C₁₃₉	—	2	4	no	—
89	C₂²×D₄×C₁₃₉	—	2	4	no	—
90	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
97	C₂³×C₄×C₁₃₉	—	2	8	no	—
98	C₂³×C₄×C₁₃₉	—	2	8	no	—
99	C₂³×C₄×C₁₃₉	—	4	4	no	—
100	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
110	#124×C₁₃₉	—	2	16	no	—
111	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
112	#121×C₁₃₉	—	2	8	no	—
113	#121×C₁₃₉	—	2	8	no	—
114	#121×C₁₃₉	—	2	8	no	—
115	#121×C₁₃₉	—	2	4	no	—
116	#121×C₁₃₉	—	4	4	no	—
117	#120×C₁₃₉	—	4	8	no	—
118	C₄×D₄×C₁₃₉	—	2	4	no	—
119	C₄×D₄×C₁₃₉	—	2	8	no	—
120	C₄×D₄×C₁₃₉	—	2	8	no	—
121	C₄×D₄×C₁₃₉	—	2	4	no	—
122	C₄×D₄×C₁₃₉	—	2	8	no	—
123	C₄×D₄×C₁₃₉	—	2	4	no	—
124	C₄×D₄×C₁₃₉	—	2	4	no	—
125	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
126	#117×C₁₃₉	—	2	8	no	—
127	#117×C₁₃₉	—	2	8	no	—
128	#117×C₁₃₉	—	4	4	no	—
129	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃₉	—	2	4	no	—
163	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
167	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
169	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	4	yes	—
172	#95×C₁₃₉	C₂³	1	4	yes	—
173	#95×C₁₃₉	C₂³	1	4	yes	—
174	#95×C₁₃₉	C₂³	1	2	yes	—
175	#95×C₁₃₉	C₂³	1	4	yes	—
176	#95×C₁₃₉	C₂³	1	4	yes	—
177	#95×C₁₃₉	C₂³	1	2	yes	—
178	#95×C₁₃₉	C₂³	1	4	yes	—
179	C₂⁴×C₁₃₉	—	2	4	no	—
180	C₂⁴×C₁₃₉	—	2	4	no	—
181	C₂⁴×C₁₃₉	—	2	4	no	—
182	C₂⁴×C₁₃₉	—	2	4	no	—
183	C₂⁴×C₁₃₉	—	2	4	no	—
184	C₂⁴×C₁₃₉	—	4	2	no	—
185	C₂⁴×C₁₃₉	—	4	2	no	—
186	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
187	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
188	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
189	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
190	C₂×Q₈×C₁₃₉	—	2	4	no	—
191	C₂×Q₈×C₁₃₉	—	4	2	no	—
192	C₂×Q₈×C₁₃₉	—	4	2	no	—
193	C₂×D₄×C₁₃₉	—	2	32	no	—
194	C₂×D₄×C₁₃₉	—	2	4	no	—
195	C₂×D₄×C₁₃₉	—	2	4	no	—
196	C₂×D₄×C₁₃₉	—	2	4	no	—
197	C₂×D₄×C₁₃₉	—	2	4	no	—
198	C₂×D₄×C₁₃₉	—	2	4	no	—
199	C₂×D₄×C₁₃₉	—	2	8	no	—
200	C₂×D₄×C₁₃₉	—	2	8	no	—
201	C₂×D₄×C₁₃₉	—	2	2	no	—
202	C₂×D₄×C₁₃₉	—	2	2	no	—
203	C₂×D₄×C₁₃₉	—	2	4	no	—
204	C₂×D₄×C₁₃₉	—	2	2	no	—
205	C₂×D₄×C₁₃₉	—	2	2	no	—
206	C₂×D₄×C₁₃₉	—	2	2	no	—
207	C₂×D₄×C₁₃₉	—	2	2	no	—
208	C₂×D₄×C₁₃₉	—	2	2	no	—
209	C₂×D₄×C₁₃₉	—	4	4	no	—
210	C₂×D₄×C₁₃₉	—	4	4	no	—
211	C₂×D₄×C₁₃₉	—	4	4	no	—
212	C₂×D₄×C₁₃₉	—	4	4	no	—
213	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
214	C₂×D₄×C₁₃₉	#41	1	4	yes	—
215	C₂²×C₄×C₁₃₉	—	2	2	no	—
216	C₂²×C₄×C₁₃₉	—	2	2	no	—
217	C₂²×C₄×C₁₃₉	—	2	4	no	—
218	C₂²×C₄×C₁₃₉	—	2	2	no	—
219	C₂²×C₄×C₁₃₉	—	2	4	no	—
220	C₂²×C₄×C₁₃₉	—	2	2	no	—
221	C₂²×C₄×C₁₃₉	—	2	4	no	—
222	C₂²×C₄×C₁₃₉	—	2	4	no	—
223	C₂²×C₄×C₁₃₉	—	2	2	no	—
224	C₂²×C₄×C₁₃₉	—	2	2	no	—
225	C₂²×C₄×C₁₃₉	—	2	4	no	—
226	C₂²×C₄×C₁₃₉	—	2	4	no	—
227	C₂²×C₄×C₁₃₉	—	2	4	no	—
228	C₂²×C₄×C₁₃₉	—	2	4	no	—
229	C₂²×C₄×C₁₃₉	—	2	4	no	—
230	C₂²×C₄×C₁₃₉	—	2	4	no	—
231	C₂²×C₄×C₁₃₉	—	2	4	no	—
232	C₂²×C₄×C₁₃₉	—	2	4	no	—
233	C₂²×C₄×C₁₃₉	—	2	4	no	—
234	C₂²×C₄×C₁₃₉	—	2	4	no	—
235	C₂²×C₄×C₁₃₉	—	4	2	no	—
236	C₂²×C₄×C₁₃₉	—	4	2	no	—
237	C₂²×C₄×C₁₃₉	—	4	2	no	—
238	C₂²×C₄×C₁₃₉	—	4	1	no	—
239	C₂²×C₄×C₁₃₉	—	4	32	no	—
240	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
241	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
242	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
243	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
248	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
256	C₄⋊C₄×C₁₃₉	—	2	4	no	—
257	C₄⋊C₄×C₁₃₉	—	2	2	no	—
258	C₄⋊C₄×C₁₃₉	—	2	2	no	—
259	C₄⋊C₄×C₁₃₉	—	2	4	no	—
260	C₄⋊C₄×C₁₃₉	—	2	4	no	—
261	C₄⋊C₄×C₁₃₉	—	2	4	no	—
262	C₄⋊C₄×C₁₃₉	—	2	4	no	—
263	C₄⋊C₄×C₁₃₉	—	2	2	no	—
264	C₄⋊C₄×C₁₃₉	—	2	2	no	—
265	C₄⋊C₄×C₁₃₉	—	2	4	no	—
266	C₄⋊C₄×C₁₃₉	—	4	2	no	—
267	C₄⋊C₄×C₁₃₉	—	4	4	no	—
268	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
269	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
270	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
271	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
272	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
273	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
274	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
275	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
276	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
277	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
278	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
279	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
280	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
281	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
282	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
283	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
284	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
285	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
286	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
287	C₄²×C₁₃₉	—	2	2	no	—
288	C₄²×C₁₃₉	—	2	2	no	—
289	C₄²×C₁₃₉	—	2	2	no	—
290	C₄²×C₁₃₉	—	2	8	no	—
291	C₄²×C₁₃₉	—	2	4	no	—
292	C₄²×C₁₃₉	—	4	4	no	—
293	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
294	C₂³×C₁₃₉	—	2	1	no	—
295	C₂³×C₁₃₉	—	2	1	no	—
296	C₂³×C₁₃₉	—	2	1	no	—
297	C₂³×C₁₃₉	—	2	1	no	—
298	C₂³×C₁₃₉	—	2	16	no	—
299	C₂³×C₁₃₉	—	2	2	no	—
300	C₂³×C₁₃₉	—	2	2	no	—
301	C₂³×C₁₃₉	—	2	2	no	—
302	C₂³×C₁₃₉	—	2	2	no	—
303	C₂³×C₁₃₉	—	2	2	no	—
304	C₂³×C₁₃₉	—	2	2	no	—
305	C₂³×C₁₃₉	—	2	2	no	—
306	C₂³×C₁₃₉	—	2	2	no	—
307	C₂³×C₁₃₉	—	2	2	no	—
308	C₂³×C₁₃₉	—	2	2	no	—
309	C₂³×C₁₃₉	—	2	2	no	—
310	C₂³×C₁₃₉	—	2	2	no	—
311	C₂³×C₁₃₉	—	2	2	no	—
312	C₂³×C₁₃₉	—	2	2	no	—
313	C₂³×C₁₃₉	—	2	2	no	—
314	C₂³×C₁₃₉	—	2	2	no	—
315	C₂³×C₁₃₉	—	2	2	no	—
316	C₂³×C₁₃₉	—	2	2	no	—
317	C₂³×C₁₃₉	—	2	2	no	—
318	C₂³×C₁₃₉	—	4	8	no	—
319	C₂³×C₁₃₉	—	4	8	no	—
320	C₂³×C₁₃₉	—	4	8	no	—
321	C₂³×C₁₃₉	—	4	8	no	—
322	C₂³×C₁₃₉	—	4	8	no	—
323	C₂³×C₁₃₉	—	4	8	no	—
324	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
325	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
326	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
327	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
328	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
329	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
330	Q₈×C₁₃₉	—	8	4	no	—
331	D₄×C₁₃₉	—	2	16	no	—
332	D₄×C₁₃₉	—	2	8	no	—
333	D₄×C₁₃₉	—	2	8	no	—
334	D₄×C₁₃₉	—	4	8	no	—
335	D₄×C₁₃₉	—	4	4	no	—
336	D₄×C₁₃₉	—	8	8	no	—
337	D₄×C₁₃₉	—	8	8	no	—
338	C₂×C₄×C₁₃₉	—	2	1	no	—
339	C₂×C₄×C₁₃₉	—	2	1	no	—
340	C₂×C₄×C₁₃₉	—	2	2	no	—
341	C₂×C₄×C₁₃₉	—	2	1	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	2	1	no	—
344	C₂×C₄×C₁₃₉	—	2	1	no	—
345	C₂×C₄×C₁₃₉	—	2	1	no	—
346	C₂×C₄×C₁₃₉	—	2	8	no	—
347	C₂×C₄×C₁₃₉	—	2	8	no	—
348	C₂×C₄×C₁₃₉	—	2	16	no	—
349	C₂×C₄×C₁₃₉	—	2	1	no	—
350	C₂×C₄×C₁₃₉	—	2	2	no	—
351	C₂×C₄×C₁₃₉	—	2	4	no	—
352	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
357	C₂×C₄×C₁₃₉	—	2	2	no	—
358	C₂×C₄×C₁₃₉	—	2	4	no	—
359	C₂×C₄×C₁₃₉	—	2	2	no	—
360	C₂×C₄×C₁₃₉	—	2	2	no	—
361	C₂×C₄×C₁₃₉	—	2	4	no	—
362	C₂×C₄×C₁₃₉	—	2	4	no	—
363	C₂×C₄×C₁₃₉	—	2	4	no	—
364	C₂×C₄×C₁₃₉	—	2	2	no	—
365	C₂×C₄×C₁₃₉	—	2	2	no	—
366	C₂×C₄×C₁₃₉	—	2	1	no	—
367	C₂×C₄×C₁₃₉	—	2	2	no	—
368	C₂×C₄×C₁₃₉	—	2	1	no	—
369	C₂×C₄×C₁₃₉	—	2	4	no	—
370	C₂×C₄×C₁₃₉	—	4	8	no	—
371	C₂×C₄×C₁₃₉	—	4	4	no	—
372	C₂×C₄×C₁₃₉	—	4	8	no	—
373	C₂×C₄×C₁₃₉	—	4	8	no	—
374	C₂×C₄×C₁₃₉	—	4	8	no	—
375	C₂×C₄×C₁₃₉	—	4	8	no	—
376	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
377	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
381	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
382	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
383	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
384	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
385	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
386	C₂²×C₁₃₉	—	2	2	no	—
387	C₂²×C₁₃₉	—	2	2	no	—
388	C₂²×C₁₃₉	—	2	2	no	—
389	C₂²×C₁₃₉	—	2	2	no	—
390	C₂²×C₁₃₉	—	2	2	no	—
391	C₂²×C₁₃₉	—	2	2	no	—
392	C₂²×C₁₃₉	—	2	4	no	—
393	C₂²×C₁₃₉	—	2	4	no	—
394	C₂²×C₁₃₉	—	2	4	no	—
395	C₂²×C₁₃₉	—	2	4	no	—
396	C₂²×C₁₃₉	—	2	4	no	—
397	C₂²×C₁₃₉	—	2	4	no	—
398	C₂²×C₁₃₉	—	4	32	no	—
399	C₂²×C₁₃₉	—	4	2	no	—
400	C₂²×C₁₃₉	—	4	2	no	—
401	C₂²×C₁₃₉	—	4	2	no	—
402	C₂²×C₁₃₉	—	4	2	no	—
403	C₂²×C₁₃₉	—	4	2	no	—
404	C₂²×C₁₃₉	—	4	2	no	—
405	C₂²×C₁₃₉	—	4	2	no	—
406	C₂²×C₁₃₉	—	4	2	no	—
407	C₂²×C₁₃₉	—	4	2	no	—
408	C₂²×C₁₃₉	—	4	2	no	—
409	C₂²×C₁₃₉	—	4	2	no	—
410	C₂²×C₁₃₉	—	4	2	no	—
411	C₂²×C₁₃₉	—	4	2	no	—
412	C₂²×C₁₃₉	—	4	2	no	—
413	C₂²×C₁₃₉	—	4	2	no	—
414	C₂²×C₁₃₉	#555	1	4	yes	complemented
415	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
416	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
417	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
418	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
419	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
420	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
421	C₂²×C₁₃₉	#585	1	1	yes	characteristic
422	C₄×C₁₃₉	—	2	2	no	—
423	C₄×C₁₃₉	—	2	2	no	—
424	C₄×C₁₃₉	—	2	4	no	—
425	C₄×C₁₃₉	—	2	2	no	—
426	C₄×C₁₃₉	—	4	2	no	—
427	C₄×C₁₃₉	—	4	2	no	—
428	C₄×C₁₃₉	—	4	2	no	—
429	C₄×C₁₃₉	—	4	1	no	—
430	C₄×C₁₃₉	—	4	4	no	—
431	C₄×C₁₃₉	—	4	2	no	—
432	C₄×C₁₃₉	—	4	4	no	—
433	C₄×C₁₃₉	#525	1	4	yes	—
434	C₄×C₁₃₉	#546	1	4	yes	—
435	C₂×C₁₃₉	—	2	4	no	—
436	C₂×C₁₃₉	—	4	4	no	—
437	C₂×C₁₃₉	—	4	4	no	—
438	C₂×C₁₃₉	—	8	2	no	—
439	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
440	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
441	C₂×C₁₃₉	C₂×#555	1	1	yes	characteristic
442	C₂×C₁₃₉	#3475	1	1	yes	characteristic
443	C₂×C₁₃₉	#3488	1	1	yes	characteristic
444	C₂×C₁₃₉	#3506	1	1	yes	characteristic
445	C₂×C₁₃₉	#3519	1	1	yes	characteristic
446	#36160	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₁₃₉	#36160	1	1	yes	characteristic, direct product factor, Sylow
448	C₂×#555	C₂×C₁₃₉	1	1	yes	characteristic, complemented
449	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
450	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
451	#2847	C₂×C₁₃₉	1	2	yes	complemented
452	#2563	C₂×C₁₃₉	1	1	yes	characteristic, complemented
453	#2537	C₂×C₁₃₉	1	1	yes	characteristic, complemented
454	#2485	C₂×C₁₃₉	1	2	yes	complemented
455	#2472	C₂×C₁₃₉	1	4	yes	complemented
456	#2459	C₂×C₁₃₉	1	4	yes	complemented
457	#2420	C₂×C₁₃₉	1	2	yes	complemented
458	#2414	C₂×C₁₃₉	1	2	yes	complemented
459	#2408	C₂×C₁₃₉	1	2	yes	complemented
460	#2363	C₂×C₁₃₉	1	2	yes	complemented
461	#2354	C₂×C₁₃₉	1	1	yes	characteristic, complemented
462	#2352	C₂×C₁₃₉	1	2	yes	complemented
463	C₄×#121	C₂×C₁₃₉	1	1	yes	characteristic, complemented
464	#2280	C₂×C₁₃₉	1	2	yes	complemented
465	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
466	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
467	#555	—	2	8	no	—
468	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
469	C₂×#124	C₂²×C₁₃₉	1	4	yes	complemented
470	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
471	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
472	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
473	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
474	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
475	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
476	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
477	C₂×C₄×D₄	—	2	8	no	—
478	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
479	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
480	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
481	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
482	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
483	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
484	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
485	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
486	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
487	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
488	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
489	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
490	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
491	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
492	#397	C₂²×C₁₃₉	1	4	yes	complemented
493	#394	C₂²×C₁₃₉	1	4	yes	—
494	#394	C₂²×C₁₃₉	1	4	yes	complemented
495	#394	C₂²×C₁₃₉	1	4	yes	complemented
496	#393	C₂²×C₁₃₉	1	4	yes	complemented
497	#392	C₂²×C₁₃₉	1	4	yes	—
498	#391	C₂²×C₁₃₉	1	2	yes	complemented
499	#390	C₂²×C₁₃₉	1	2	yes	—
500	#390	C₂²×C₁₃₉	1	2	yes	—
501	#390	C₂²×C₁₃₉	1	4	yes	complemented
502	#390	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
503	#389	C₂²×C₁₃₉	1	2	yes	complemented
504	#389	C₂²×C₁₃₉	1	2	yes	complemented
505	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
506	#388	C₂²×C₁₃₉	1	4	yes	complemented
507	#388	C₂²×C₁₃₉	1	4	yes	complemented
508	#388	C₂²×C₁₃₉	1	4	yes	complemented
509	#388	C₂²×C₁₃₉	1	2	yes	complemented
510	#387	C₂²×C₁₃₉	1	4	yes	complemented
511	#386	C₂²×C₁₃₉	1	4	yes	—
512	#386	C₂²×C₁₃₉	1	2	yes	—
513	#386	C₂²×C₁₃₉	1	4	yes	complemented
514	#386	C₂²×C₁₃₉	1	4	yes	complemented
515	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
516	#382	C₂²×C₁₃₉	1	2	yes	complemented
517	#381	C₂²×C₁₃₉	1	4	yes	complemented
518	#380	C₂²×C₁₃₉	1	2	yes	—
519	#380	C₂²×C₁₃₉	1	2	yes	—
520	#380	C₂²×C₁₃₉	1	1	yes	characteristic
521	#380	C₂²×C₁₃₉	1	2	yes	complemented
522	#380	C₂²×C₁₃₉	1	2	yes	complemented
523	#380	C₂²×C₁₃₉	1	2	yes	complemented
524	#380	C₂²×C₁₃₉	1	2	yes	complemented
525	#380	C₂²×C₁₃₉	1	2	yes	complemented
526	#379	C₂²×C₁₃₉	1	4	yes	—
527	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
528	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
529	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
530	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
531	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
532	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
533	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
534	C₂²×D₄	—	2	4	no	—
535	C₂²×D₄	—	2	4	no	—
536	C₂²×D₄	—	2	4	no	—
537	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
540	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
541	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
542	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
543	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
544	C₂³×C₄	—	2	8	no	—
545	C₂³×C₄	—	2	8	no	—
546	C₂³×C₄	—	4	4	no	—
547	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
548	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
551	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
552	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
553	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
554	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
556	C₄⋊Q₈	—	2	4	no	—
557	#124	—	2	16	no	—
558	C₂²⋊Q₈	—	4	4	no	—
559	#121	—	2	8	no	—
560	#121	—	2	8	no	—
561	#121	—	2	8	no	—
562	#121	—	2	4	no	—
563	#121	—	4	4	no	—
564	#120	—	4	8	no	—
565	C₄×D₄	—	2	4	no	—
566	C₄×D₄	—	2	8	no	—
567	C₄×D₄	—	2	8	no	—
568	C₄×D₄	—	2	4	no	—
569	C₄×D₄	—	2	8	no	—
570	C₄×D₄	—	2	4	no	—
571	C₄×D₄	—	2	4	no	—
572	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
573	#117	—	2	8	no	—
574	#117	—	2	8	no	—
575	#117	—	4	4	no	—
576	C₂×C₄⋊C₄	—	2	4	no	—
577	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
590	C₂×C₂²⋊C₄	—	2	8	no	—
591	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
609	C₂×C₄²	—	2	4	no	—
610	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
611	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
615	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
616	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
617	#95	C₂³×C₁₃₉	1	4	yes	—
618	#95	C₂³×C₁₃₉	1	4	yes	—
619	#95	C₂³×C₁₃₉	1	2	yes	—
620	#95	C₂³×C₁₃₉	1	4	yes	—
621	#95	C₂³×C₁₃₉	1	2	yes	—
622	#95	C₂³×C₁₃₉	1	4	yes	—
623	#95	C₂³×C₁₃₉	1	2	yes	—
624	#95	C₂³×C₁₃₉	1	4	yes	—
625	#95	C₂³×C₁₃₉	1	4	yes	—
626	C₂⁴	—	2	4	no	—
627	C₂⁴	—	2	4	no	—
628	C₂⁴	—	2	4	no	—
629	C₂⁴	—	2	4	no	—
630	C₂⁴	—	2	4	no	—
631	C₂⁴	—	4	2	no	—
632	C₂⁴	—	4	2	no	—
633	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
634	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
635	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
636	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
637	C₂×Q₈	—	2	4	no	—
638	C₂×Q₈	—	4	2	no	—
639	C₂×Q₈	—	4	2	no	—
640	C₂×D₄	—	2	32	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	4	no	—
646	C₂×D₄	—	2	8	no	—
647	C₂×D₄	—	2	8	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	4	4	no	—
657	C₂×D₄	—	4	4	no	—
658	C₂×D₄	—	4	4	no	—
659	C₂×D₄	—	4	4	no	—
660	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
661	C₂×D₄	#41×C₁₃₉	1	4	yes	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	2	4	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	4	1	no	—
686	C₂²×C₄	—	4	32	no	—
687	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
688	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
689	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
690	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
695	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
696	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	4	2	no	—
714	C₄⋊C₄	—	4	4	no	—
715	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	8	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	8	no	—
720	C₂²⋊C₄	—	2	8	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	8	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	4	2	no	—
728	C₂²⋊C₄	—	4	4	no	—
729	C₂²⋊C₄	—	4	4	no	—
730	C₂²⋊C₄	—	4	4	no	—
731	C₂²⋊C₄	—	4	4	no	—
732	C₂²⋊C₄	—	4	4	no	—
733	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
734	C₄²	—	2	2	no	—
735	C₄²	—	2	2	no	—
736	C₄²	—	2	2	no	—
737	C₄²	—	2	8	no	—
738	C₄²	—	2	4	no	—
739	C₄²	—	4	4	no	—
740	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
741	C₂³	—	2	1	no	—
742	C₂³	—	2	1	no	—
743	C₂³	—	2	1	no	—
744	C₂³	—	2	1	no	—
745	C₂³	—	2	16	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	4	8	no	—
766	C₂³	—	4	8	no	—
767	C₂³	—	4	8	no	—
768	C₂³	—	4	8	no	—
769	C₂³	—	4	8	no	—
770	C₂³	—	4	8	no	—
771	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
772	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
773	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
774	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
775	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
776	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
777	Q₈	—	8	4	no	—
778	D₄	—	2	16	no	—
779	D₄	—	2	8	no	—
780	D₄	—	2	8	no	—
781	D₄	—	4	8	no	—
782	D₄	—	4	4	no	—
783	D₄	—	8	8	no	—
784	D₄	—	8	8	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	8	no	—
794	C₂×C₄	—	2	8	no	—
795	C₂×C₄	—	2	16	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	4	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	4	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	2	4	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	4	no	—
817	C₂×C₄	—	4	8	no	—
818	C₂×C₄	—	4	8	no	—
819	C₂×C₄	—	4	8	no	—
820	C₂×C₄	—	4	4	no	—
821	C₂×C₄	—	4	8	no	—
822	C₂×C₄	—	4	8	no	—
823	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
824	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
825	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
826	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
827	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
828	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
829	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
830	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
831	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
832	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	4	no	—
840	C₂²	—	2	4	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	2	4	no	—
843	C₂²	—	2	4	no	—
844	C₂²	—	2	4	no	—
845	C₂²	—	4	32	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	#555×C₁₃₉	1	4	yes	complemented
862	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
863	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
864	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
865	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
866	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
867	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
868	C₂²	#585×C₁₃₉	1	1	yes	characteristic
869	C₄	—	2	2	no	—
870	C₄	—	2	2	no	—
871	C₄	—	2	4	no	—
872	C₄	—	2	2	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	4	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	4	no	—
880	C₄	#525×C₁₃₉	1	4	yes	—
881	C₄	#546×C₁₃₉	1	4	yes	—
882	C₂	—	2	4	no	—
883	C₂	—	4	4	no	—
884	C₂	—	4	4	no	—
885	C₂	—	8	2	no	—
886	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
887	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
888	C₂	C₂×#555×C₁₃₉	1	1	yes	characteristic
889	C₂	#3475×C₁₃₉	1	1	yes	characteristic
890	C₂	#3488×C₁₃₉	1	1	yes	characteristic
891	C₂	#3506×C₁₃₉	1	1	yes	characteristic
892	C₂	#3519×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
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×#555×C₁₃₉	C₂	semidirect
2. C₂²×C₄×D₄×C₁₃₉	C₂	semidirect
3. #2857×C₁₃₉	C₂	semidirect
4. #2847×C₁₃₉	C₂	semidirect
5. #2563×C₁₃₉	C₂	semidirect
6. #2537×C₁₃₉	C₂	semidirect
7. #2485×C₁₃₉	C₂	semidirect
8. #2472×C₁₃₉	C₂	semidirect
9. #2459×C₁₃₉	C₂	semidirect
10. #2420×C₁₃₉	C₂	semidirect
11. #2414×C₁₃₉	C₂	semidirect
12. #2408×C₁₃₉	C₂	semidirect
13. #2363×C₁₃₉	C₂	semidirect
14. #2354×C₁₃₉	C₂	semidirect
15. #2352×C₁₃₉	C₂	semidirect
16. C₄×#121×C₁₃₉	C₂	semidirect
17. #2280×C₁₃₉	C₂	semidirect
21. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
22. C₂×#124×C₁₃₉	C₂²	semidirect
27. C₂×#121×C₁₃₉	C₂²	semidirect
28. C₂×#121×C₁₃₉	C₂²	semidirect
38. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
39. C₂×#117×C₁₃₉	C₂²	semidirect
40. C₂×#117×C₁₃₉	C₂²	semidirect
41. C₂×#117×C₁₃₉	C₂²	semidirect
45. #397×C₁₃₉	C₂²	semidirect
47. #394×C₁₃₉	C₂²	semidirect
48. #394×C₁₃₉	C₂²	semidirect
49. #393×C₁₃₉	C₂²	semidirect
51. #391×C₁₃₉	C₂²	semidirect
54. #390×C₁₃₉	C₂²	semidirect
55. #390×C₁₃₉	C₂²	semidirect
56. #389×C₁₃₉	C₂²	semidirect
57. #389×C₁₃₉	C₂²	semidirect
58. #389×C₁₃₉	C₂²	semidirect
59. #388×C₁₃₉	C₂²	semidirect
60. #388×C₁₃₉	C₂²	semidirect
61. #388×C₁₃₉	C₂²	semidirect
62. #388×C₁₃₉	C₂²	semidirect
63. #387×C₁₃₉	C₂²	semidirect
66. #386×C₁₃₉	C₂²	semidirect
67. #386×C₁₃₉	C₂²	semidirect
68. #384×C₁₃₉	C₂²	semidirect
69. #382×C₁₃₉	C₂²	semidirect
70. #381×C₁₃₉	C₂²	semidirect
74. #380×C₁₃₉	C₂²	semidirect
75. #380×C₁₃₉	C₂²	semidirect
76. #380×C₁₃₉	C₂²	semidirect
77. #380×C₁₃₉	C₂²	semidirect
78. #380×C₁₃₉	C₂²	semidirect
80. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
81. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
125. C₄×D₄×C₁₃₉	D₄	semidirect
414. C₂²×C₁₃₉	#555	semidirect
446. #36160	C₁₃₉	direct (N × H)
447. C₁₃₉	#36160	direct (N × H)
448. C₂×#555	C₂×C₁₃₉	semidirect
449. C₂²×C₄×D₄	C₂×C₁₃₉	semidirect
450. #2857	C₂×C₁₃₉	semidirect
451. #2847	C₂×C₁₃₉	semidirect
452. #2563	C₂×C₁₃₉	semidirect
453. #2537	C₂×C₁₃₉	semidirect
454. #2485	C₂×C₁₃₉	semidirect
455. #2472	C₂×C₁₃₉	semidirect
456. #2459	C₂×C₁₃₉	semidirect
457. #2420	C₂×C₁₃₉	semidirect
458. #2414	C₂×C₁₃₉	semidirect
459. #2408	C₂×C₁₃₉	semidirect
460. #2363	C₂×C₁₃₉	semidirect
461. #2354	C₂×C₁₃₉	semidirect
462. #2352	C₂×C₁₃₉	semidirect
463. C₄×#121	C₂×C₁₃₉	semidirect
464. #2280	C₂×C₁₃₉	semidirect
468. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
469. C₂×#124	C₂²×C₁₃₉	semidirect
474. C₂×#121	C₂²×C₁₃₉	semidirect
475. C₂×#121	C₂²×C₁₃₉	semidirect
485. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
486. C₂×#117	C₂²×C₁₃₉	semidirect
487. C₂×#117	C₂²×C₁₃₉	semidirect
488. C₂×#117	C₂²×C₁₃₉	semidirect
492. #397	C₂²×C₁₃₉	semidirect
494. #394	C₂²×C₁₃₉	semidirect
495. #394	C₂²×C₁₃₉	semidirect
496. #393	C₂²×C₁₃₉	semidirect
498. #391	C₂²×C₁₃₉	semidirect
501. #390	C₂²×C₁₃₉	semidirect
502. #390	C₂²×C₁₃₉	semidirect
503. #389	C₂²×C₁₃₉	semidirect
504. #389	C₂²×C₁₃₉	semidirect
505. #389	C₂²×C₁₃₉	semidirect
506. #388	C₂²×C₁₃₉	semidirect
507. #388	C₂²×C₁₃₉	semidirect
508. #388	C₂²×C₁₃₉	semidirect
509. #388	C₂²×C₁₃₉	semidirect
510. #387	C₂²×C₁₃₉	semidirect
513. #386	C₂²×C₁₃₉	semidirect
514. #386	C₂²×C₁₃₉	semidirect
515. #384	C₂²×C₁₃₉	semidirect
516. #382	C₂²×C₁₃₉	semidirect
517. #381	C₂²×C₁₃₉	semidirect
521. #380	C₂²×C₁₃₉	semidirect
522. #380	C₂²×C₁₃₉	semidirect
523. #380	C₂²×C₁₃₉	semidirect
524. #380	C₂²×C₁₃₉	semidirect
525. #380	C₂²×C₁₃₉	semidirect
527. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
528. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
530. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
531. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
572. C₄×D₄	D₄×C₁₃₉	semidirect
861. C₂²	#555×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#555×C₁₃₉	2
C₂²×C₄×D₄×C₁₃₉	2
#2857×C₁₃₉	2
#2847×C₁₃₉	2
#2563×C₁₃₉	2
#2537×C₁₃₉	2
#2485×C₁₃₉	2
#2472×C₁₃₉	2
#2459×C₁₃₉	2
#2420×C₁₃₉	2
#2414×C₁₃₉	2
#2408×C₁₃₉	2
#2363×C₁₃₉	2
#2354×C₁₃₉	2
#2352×C₁₃₉	2
C₄×#121×C₁₃₉	2
#2280×C₁₃₉	2
#36160	139

Subgroups — C139×#36160 #48030756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36160 #48030756