Subgroups — C₁₃₉×#37305 #48031901

Order 35584.

2694 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#535×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2858×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2858×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2714×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2678×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2676×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2670×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2657×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2640×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2548×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2545×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2544×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2541×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2435×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2433×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2432×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2431×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2298×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
22	#542×C₁₃₉	—	2	8	no	—
23	#535×C₁₃₉	—	2	8	no	—
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×#126×C₁₃₉	C₂²	1	2	yes	complemented
32	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
35	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×#124×C₁₃₉	C₂²	1	4	yes	complemented
41	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
42	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
44	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
45	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
46	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂×#121×C₁₃₉	C₂²	1	4	yes	complemented
48	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
49	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
50	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
51	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
54	#397×C₁₃₉	C₂²	1	4	yes	complemented
55	#396×C₁₃₉	C₂²	1	4	yes	complemented
56	#394×C₁₃₉	C₂²	1	4	yes	—
57	#394×C₁₃₉	C₂²	1	4	yes	—
58	#394×C₁₃₉	C₂²	1	4	yes	complemented
59	#394×C₁₃₉	C₂²	1	4	yes	complemented
60	#393×C₁₃₉	C₂²	1	4	yes	complemented
61	#392×C₁₃₉	C₂²	1	4	yes	—
62	#392×C₁₃₉	C₂²	1	4	yes	—
63	#392×C₁₃₉	C₂²	1	4	yes	complemented
64	#392×C₁₃₉	C₂²	1	4	yes	complemented
65	#392×C₁₃₉	C₂²	1	4	yes	complemented
66	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
67	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
68	#390×C₁₃₉	C₂²	1	1	yes	characteristic
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, complemented
73	#390×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
74	#390×C₁₃₉	C₂²	1	4	yes	complemented
75	#390×C₁₃₉	C₂²	1	4	yes	complemented
76	#390×C₁₃₉	C₂²	1	4	yes	complemented
77	#390×C₁₃₉	C₂²	1	4	yes	complemented
78	#388×C₁₃₉	C₂²	1	2	yes	—
79	#388×C₁₃₉	C₂²	1	2	yes	—
80	#388×C₁₃₉	C₂²	1	4	yes	complemented
81	#387×C₁₃₉	C₂²	1	2	yes	complemented
82	#387×C₁₃₉	C₂²	1	2	yes	complemented
83	#386×C₁₃₉	C₂²	1	4	yes	complemented
84	#386×C₁₃₉	C₂²	1	4	yes	complemented
85	#385×C₁₃₉	C₂²	1	4	yes	complemented
86	#379×C₁₃₉	C₂²	1	4	yes	—
87	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
88	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
89	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
91	#376×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
92	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
93	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
94	C₂×#41×C₁₃₉	—	2	4	no	—
95	C₂×#41×C₁₃₉	—	4	2	no	—
96	C₂×#41×C₁₃₉	—	4	2	no	—
97	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
100	C₂²×D₄×C₁₃₉	—	2	4	no	—
101	C₂²×D₄×C₁₃₉	—	4	2	no	—
102	C₂²×D₄×C₁₃₉	—	4	2	no	—
103	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
116	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
121	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
122	#127×C₁₃₉	—	2	4	no	—
123	#127×C₁₃₉	—	2	4	no	—
124	#127×C₁₃₉	—	4	2	no	—
125	#127×C₁₃₉	—	4	2	no	—
126	#127×C₁₃₉	—	4	2	no	—
127	#126×C₁₃₉	—	2	8	no	—
128	#124×C₁₃₉	—	2	8	no	—
129	#124×C₁₃₉	—	2	4	no	—
130	#124×C₁₃₉	—	2	4	no	—
131	#124×C₁₃₉	—	2	4	no	—
132	#124×C₁₃₉	—	4	8	no	—
133	#124×C₁₃₉	—	4	2	no	—
134	#124×C₁₃₉	—	4	2	no	—
135	#124×C₁₃₉	—	4	2	no	—
136	#124×C₁₃₉	—	4	2	no	—
137	#123×C₁₃₉	—	2	8	no	—
138	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
139	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
140	#121×C₁₃₉	—	2	4	no	—
141	#121×C₁₃₉	—	2	8	no	—
142	#121×C₁₃₉	—	2	8	no	—
143	#121×C₁₃₉	—	4	8	no	—
144	#120×C₁₃₉	—	2	8	no	—
145	#120×C₁₃₉	—	2	8	no	—
146	#120×C₁₃₉	—	4	8	no	—
147	C₄×Q₈×C₁₃₉	—	2	4	no	—
148	C₄×D₄×C₁₃₉	—	2	4	no	—
149	#117×C₁₃₉	D₄	1	8	yes	complemented
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	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	4	yes	—
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
174	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
176	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
177	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
178	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
179	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
180	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
191	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
192	#95×C₁₃₉	C₂³	1	4	yes	—
193	#95×C₁₃₉	C₂³	1	2	yes	—
194	#95×C₁₃₉	C₂³	1	4	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	C₂⁴×C₁₃₉	—	2	4	no	—
201	C₂⁴×C₁₃₉	—	4	2	no	—
202	C₂⁴×C₁₃₉	—	4	2	no	—
203	C₂⁴×C₁₃₉	—	4	4	no	—
204	C₂⁴×C₁₃₉	—	4	4	no	—
205	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
206	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
207	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
209	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
210	#41×C₁₃₉	—	4	16	no	—
211	C₂×Q₈×C₁₃₉	—	2	2	no	—
212	C₂×Q₈×C₁₃₉	—	2	2	no	—
213	C₂×Q₈×C₁₃₉	—	2	4	no	—
214	C₂×Q₈×C₁₃₉	—	2	2	no	—
215	C₂×Q₈×C₁₃₉	—	2	2	no	—
216	C₂×Q₈×C₁₃₉	—	2	2	no	—
217	C₂×Q₈×C₁₃₉	—	2	2	no	—
218	C₂×Q₈×C₁₃₉	—	4	4	no	—
219	C₂×D₄×C₁₃₉	—	2	4	no	—
220	C₂×D₄×C₁₃₉	—	2	4	no	—
221	C₂×D₄×C₁₃₉	—	2	2	no	—
222	C₂×D₄×C₁₃₉	—	2	4	no	—
223	C₂×D₄×C₁₃₉	—	2	2	no	—
224	C₂×D₄×C₁₃₉	—	2	2	no	—
225	C₂×D₄×C₁₃₉	—	2	2	no	—
226	C₂×D₄×C₁₃₉	—	2	4	no	—
227	C₂×D₄×C₁₃₉	—	2	4	no	—
228	C₂×D₄×C₁₃₉	—	2	4	no	—
229	C₂×D₄×C₁₃₉	—	2	4	no	—
230	C₂×D₄×C₁₃₉	—	2	2	no	—
231	C₂×D₄×C₁₃₉	—	2	2	no	—
232	C₂×D₄×C₁₃₉	—	2	2	no	—
233	C₂×D₄×C₁₃₉	—	2	2	no	—
234	C₂×D₄×C₁₃₉	—	2	2	no	—
235	C₂×D₄×C₁₃₉	—	2	2	no	—
236	C₂×D₄×C₁₃₉	—	2	2	no	—
237	C₂×D₄×C₁₃₉	—	2	2	no	—
238	C₂×D₄×C₁₃₉	—	2	8	no	—
239	C₂×D₄×C₁₃₉	—	4	2	no	—
240	C₂×D₄×C₁₃₉	—	4	2	no	—
241	C₂×D₄×C₁₃₉	—	4	2	no	—
242	C₂×D₄×C₁₃₉	—	4	2	no	—
243	C₂×D₄×C₁₃₉	—	4	16	no	—
244	C₂×D₄×C₁₃₉	—	4	4	no	—
245	C₂×D₄×C₁₃₉	—	4	4	no	—
246	C₂×D₄×C₁₃₉	—	4	4	no	—
247	C₂×D₄×C₁₃₉	—	4	4	no	—
248	C₂×D₄×C₁₃₉	—	4	4	no	—
249	C₂×D₄×C₁₃₉	—	4	4	no	—
250	C₂×D₄×C₁₃₉	—	4	4	no	—
251	C₂×D₄×C₁₃₉	—	4	4	no	—
252	C₂×D₄×C₁₃₉	—	4	4	no	—
253	C₂×D₄×C₁₃₉	—	4	4	no	—
254	C₂×D₄×C₁₃₉	—	4	4	no	—
255	C₂×D₄×C₁₃₉	—	4	4	no	—
256	C₂×D₄×C₁₃₉	—	4	4	no	—
257	C₂²×C₄×C₁₃₉	—	2	2	no	—
258	C₂²×C₄×C₁₃₉	—	2	2	no	—
259	C₂²×C₄×C₁₃₉	—	2	4	no	—
260	C₂²×C₄×C₁₃₉	—	2	4	no	—
261	C₂²×C₄×C₁₃₉	—	4	2	no	—
262	C₂²×C₄×C₁₃₉	—	4	2	no	—
263	C₂²×C₄×C₁₃₉	—	4	4	no	—
264	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
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	1	yes	characteristic
273	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
278	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
279	C₄⋊C₄×C₁₃₉	—	2	2	no	—
280	C₄⋊C₄×C₁₃₉	—	2	2	no	—
281	C₄⋊C₄×C₁₃₉	—	2	4	no	—
282	C₄⋊C₄×C₁₃₉	—	2	4	no	—
283	C₄⋊C₄×C₁₃₉	—	2	4	no	—
284	C₄⋊C₄×C₁₃₉	—	2	4	no	—
285	C₄⋊C₄×C₁₃₉	—	4	2	no	—
286	C₄⋊C₄×C₁₃₉	—	4	4	no	—
287	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
288	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
289	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
290	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
291	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
292	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
293	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
294	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
295	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
296	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
297	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
298	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
299	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
300	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
301	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
302	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
303	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
304	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
305	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
306	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
307	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
308	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
309	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
310	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
311	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
312	C₄²×C₁₃₉	—	2	4	no	—
313	C₄²×C₁₃₉	—	2	4	no	—
314	C₄²×C₁₃₉	—	2	2	no	—
315	C₄²×C₁₃₉	—	2	2	no	—
316	C₄²×C₁₃₉	—	2	2	no	—
317	C₄²×C₁₃₉	—	2	2	no	—
318	C₄²×C₁₃₉	—	4	2	no	—
319	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
320	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
321	C₂³×C₁₃₉	—	2	2	no	—
322	C₂³×C₁₃₉	—	2	1	no	—
323	C₂³×C₁₃₉	—	2	1	no	—
324	C₂³×C₁₃₉	—	2	2	no	—
325	C₂³×C₁₃₉	—	2	2	no	—
326	C₂³×C₁₃₉	—	2	2	no	—
327	C₂³×C₁₃₉	—	2	2	no	—
328	C₂³×C₁₃₉	—	2	2	no	—
329	C₂³×C₁₃₉	—	2	4	no	—
330	C₂³×C₁₃₉	—	2	4	no	—
331	C₂³×C₁₃₉	—	2	2	no	—
332	C₂³×C₁₃₉	—	2	2	no	—
333	C₂³×C₁₃₉	—	2	2	no	—
334	C₂³×C₁₃₉	—	2	2	no	—
335	C₂³×C₁₃₉	—	2	4	no	—
336	C₂³×C₁₃₉	—	2	2	no	—
337	C₂³×C₁₃₉	—	2	4	no	—
338	C₂³×C₁₃₉	—	2	2	no	—
339	C₂³×C₁₃₉	—	2	2	no	—
340	C₂³×C₁₃₉	—	2	2	no	—
341	C₂³×C₁₃₉	—	2	4	no	—
342	C₂³×C₁₃₉	—	2	4	no	—
343	C₂³×C₁₃₉	—	2	4	no	—
344	C₂³×C₁₃₉	—	2	4	no	—
345	C₂³×C₁₃₉	—	4	8	no	—
346	C₂³×C₁₃₉	—	8	4	no	—
347	C₂³×C₁₃₉	—	8	4	no	—
348	C₂³×C₁₃₉	—	8	8	no	—
349	C₂³×C₁₃₉	—	8	8	no	—
350	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
351	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
352	Q₈×C₁₃₉	—	4	4	no	—
353	Q₈×C₁₃₉	—	4	4	no	—
354	Q₈×C₁₃₉	—	8	4	no	—
355	D₄×C₁₃₉	—	4	8	no	—
356	D₄×C₁₃₉	—	4	8	no	—
357	D₄×C₁₃₉	—	4	4	no	—
358	D₄×C₁₃₉	—	4	4	no	—
359	D₄×C₁₃₉	—	4	4	no	—
360	D₄×C₁₃₉	—	4	4	no	—
361	D₄×C₁₃₉	—	8	4	no	—
362	D₄×C₁₃₉	—	8	4	no	—
363	D₄×C₁₃₉	—	8	4	no	—
364	D₄×C₁₃₉	—	8	4	no	—
365	D₄×C₁₃₉	—	8	8	no	—
366	D₄×C₁₃₉	—	8	4	no	—
367	D₄×C₁₃₉	—	8	8	no	—
368	D₄×C₁₃₉	—	8	8	no	—
369	C₂×C₄×C₁₃₉	—	2	2	no	—
370	C₂×C₄×C₁₃₉	—	2	2	no	—
371	C₂×C₄×C₁₃₉	—	2	2	no	—
372	C₂×C₄×C₁₃₉	—	2	1	no	—
373	C₂×C₄×C₁₃₉	—	2	1	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	8	no	—
378	C₂×C₄×C₁₃₉	—	2	2	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	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	4	no	—
387	C₂×C₄×C₁₃₉	—	2	2	no	—
388	C₂×C₄×C₁₃₉	—	2	4	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	—	2	2	no	—
396	C₂×C₄×C₁₃₉	—	2	2	no	—
397	C₂×C₄×C₁₃₉	—	4	8	no	—
398	C₂×C₄×C₁₃₉	—	8	4	no	—
399	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
406	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
407	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
408	C₂²×C₁₃₉	—	2	2	no	—
409	C₂²×C₁₃₉	—	2	2	no	—
410	C₂²×C₁₃₉	—	2	2	no	—
411	C₂²×C₁₃₉	—	4	2	no	—
412	C₂²×C₁₃₉	—	4	2	no	—
413	C₂²×C₁₃₉	—	4	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	—	4	2	no	—
422	C₂²×C₁₃₉	—	4	2	no	—
423	C₂²×C₁₃₉	—	4	2	no	—
424	C₂²×C₁₃₉	—	4	2	no	—
425	C₂²×C₁₃₉	—	4	4	no	—
426	C₂²×C₁₃₉	—	4	4	no	—
427	C₂²×C₁₃₉	—	4	4	no	—
428	C₂²×C₁₃₉	—	4	4	no	—
429	C₂²×C₁₃₉	—	4	4	no	—
430	C₂²×C₁₃₉	—	4	4	no	—
431	C₂²×C₁₃₉	—	4	4	no	—
432	C₂²×C₁₃₉	—	4	4	no	—
433	C₂²×C₁₃₉	—	8	16	no	—
434	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
435	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
436	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
437	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
438	C₂²×C₁₃₉	#585	1	2	yes	—
439	C₄×C₁₃₉	—	2	2	no	—
440	C₄×C₁₃₉	—	2	2	no	—
441	C₄×C₁₃₉	—	2	2	no	—
442	C₄×C₁₃₉	—	2	2	no	—
443	C₄×C₁₃₉	—	2	2	no	—
444	C₄×C₁₃₉	—	2	4	no	—
445	C₄×C₁₃₉	—	4	2	no	—
446	C₄×C₁₃₉	—	4	2	no	—
447	C₄×C₁₃₉	—	4	2	no	—
448	C₄×C₁₃₉	—	4	2	no	—
449	C₄×C₁₃₉	—	4	2	no	—
450	C₄×C₁₃₉	—	4	2	no	—
451	C₄×C₁₃₉	—	4	2	no	—
452	C₄×C₁₃₉	#535	1	4	yes	—
453	C₂×C₁₃₉	—	4	2	no	—
454	C₂×C₁₃₉	—	8	2	no	—
455	C₂×C₁₃₉	—	8	2	no	—
456	C₂×C₁₃₉	—	8	2	no	—
457	C₂×C₁₃₉	—	8	2	no	—
458	C₂×C₁₃₉	C₂×#535	1	1	yes	characteristic
459	C₂×C₁₃₉	#3498	1	1	yes	characteristic
460	C₂×C₁₃₉	#3500	1	1	yes	characteristic
461	C₂×C₁₃₉	#3546	1	2	yes	—
462	C₂×C₁₃₉	#3558	1	2	yes	—
463	#37305	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
464	C₁₃₉	#37305	1	1	yes	characteristic, direct product factor, Sylow
465	C₂×#542	C₂×C₁₃₉	1	1	yes	characteristic, complemented
466	C₂×#535	C₂×C₁₃₉	1	1	yes	characteristic, complemented
467	#2858	C₂×C₁₃₉	1	1	yes	characteristic, complemented
468	#2858	C₂×C₁₃₉	1	1	yes	characteristic, complemented
469	#2714	C₂×C₁₃₉	1	4	yes	complemented
470	#2678	C₂×C₁₃₉	1	4	yes	complemented
471	#2676	C₂×C₁₃₉	1	4	yes	complemented
472	#2670	C₂×C₁₃₉	1	4	yes	complemented
473	#2657	C₂×C₁₃₉	1	1	yes	characteristic, complemented
474	#2640	C₂×C₁₃₉	1	1	yes	characteristic, complemented
475	#2548	C₂×C₁₃₉	1	1	yes	characteristic, complemented
476	#2545	C₂×C₁₃₉	1	1	yes	characteristic, complemented
477	#2544	C₂×C₁₃₉	1	1	yes	characteristic, complemented
478	#2541	C₂×C₁₃₉	1	1	yes	characteristic, complemented
479	#2435	C₂×C₁₃₉	1	1	yes	characteristic, complemented
480	#2433	C₂×C₁₃₉	1	1	yes	characteristic, complemented
481	#2432	C₂×C₁₃₉	1	1	yes	characteristic, complemented
482	#2431	C₂×C₁₃₉	1	1	yes	characteristic, complemented
483	#2298	C₂×C₁₃₉	1	1	yes	characteristic, complemented
484	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
485	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
486	#542	—	2	8	no	—
487	#535	—	2	8	no	—
488	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
489	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
490	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
491	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
492	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
493	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
494	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
495	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
496	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
497	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
498	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
499	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
500	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
501	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
502	C₂×#124	C₂²×C₁₃₉	1	4	yes	complemented
503	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
504	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
505	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
506	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
507	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
508	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
509	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
510	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
511	C₂×#121	C₂²×C₁₃₉	1	4	yes	complemented
512	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
513	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
514	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
515	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
516	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
517	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
518	#397	C₂²×C₁₃₉	1	4	yes	complemented
519	#396	C₂²×C₁₃₉	1	4	yes	complemented
520	#394	C₂²×C₁₃₉	1	4	yes	—
521	#394	C₂²×C₁₃₉	1	4	yes	—
522	#394	C₂²×C₁₃₉	1	4	yes	complemented
523	#394	C₂²×C₁₃₉	1	4	yes	complemented
524	#393	C₂²×C₁₃₉	1	4	yes	complemented
525	#392	C₂²×C₁₃₉	1	4	yes	—
526	#392	C₂²×C₁₃₉	1	4	yes	—
527	#392	C₂²×C₁₃₉	1	4	yes	complemented
528	#392	C₂²×C₁₃₉	1	4	yes	complemented
529	#392	C₂²×C₁₃₉	1	4	yes	complemented
530	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
531	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
532	#390	C₂²×C₁₃₉	1	1	yes	characteristic
533	#390	C₂²×C₁₃₉	1	1	yes	characteristic
534	#390	C₂²×C₁₃₉	1	1	yes	characteristic
535	#390	C₂²×C₁₃₉	1	1	yes	characteristic
536	#390	C₂²×C₁₃₉	1	4	yes	complemented
537	#390	C₂²×C₁₃₉	1	4	yes	complemented
538	#390	C₂²×C₁₃₉	1	4	yes	complemented
539	#390	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
540	#390	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
541	#390	C₂²×C₁₃₉	1	4	yes	complemented
542	#388	C₂²×C₁₃₉	1	2	yes	—
543	#388	C₂²×C₁₃₉	1	2	yes	—
544	#388	C₂²×C₁₃₉	1	4	yes	complemented
545	#387	C₂²×C₁₃₉	1	2	yes	complemented
546	#387	C₂²×C₁₃₉	1	2	yes	complemented
547	#386	C₂²×C₁₃₉	1	4	yes	complemented
548	#386	C₂²×C₁₃₉	1	4	yes	complemented
549	#385	C₂²×C₁₃₉	1	4	yes	complemented
550	#379	C₂²×C₁₃₉	1	4	yes	—
551	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
552	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
553	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
554	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
555	#376	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
556	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
557	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
558	C₂×#41	—	2	4	no	—
559	C₂×#41	—	4	2	no	—
560	C₂×#41	—	4	2	no	—
561	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
562	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
563	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
564	C₂²×D₄	—	2	4	no	—
565	C₂²×D₄	—	4	2	no	—
566	C₂²×D₄	—	4	2	no	—
567	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
568	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
570	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
571	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
572	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
573	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
574	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
575	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
576	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
578	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
579	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
580	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
581	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
582	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
583	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
584	C₄⋊Q₈	—	2	4	no	—
585	C₄⋊Q₈	—	4	2	no	—
586	#127	—	2	4	no	—
587	#127	—	2	4	no	—
588	#127	—	4	2	no	—
589	#127	—	4	2	no	—
590	#127	—	4	2	no	—
591	#126	—	2	8	no	—
592	#124	—	2	8	no	—
593	#124	—	2	4	no	—
594	#124	—	2	4	no	—
595	#124	—	2	4	no	—
596	#124	—	4	8	no	—
597	#124	—	4	2	no	—
598	#124	—	4	2	no	—
599	#124	—	4	2	no	—
600	#124	—	4	2	no	—
601	#123	—	2	8	no	—
602	C₂²⋊Q₈	—	2	4	no	—
603	C₂²⋊Q₈	—	2	8	no	—
604	#121	—	2	4	no	—
605	#121	—	2	8	no	—
606	#121	—	2	8	no	—
607	#121	—	4	8	no	—
608	#120	—	2	8	no	—
609	#120	—	2	8	no	—
610	#120	—	4	8	no	—
611	C₄×Q₈	—	2	4	no	—
612	C₄×D₄	—	2	4	no	—
613	#117	D₄×C₁₃₉	1	8	yes	complemented
614	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	4	yes	—
621	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
626	C₂×C₂²⋊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	4	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	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	4	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
648	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
651	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
654	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
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	4	yes	—
663	#95	C₂³×C₁₃₉	1	4	yes	—
664	C₂⁴	—	2	4	no	—
665	C₂⁴	—	4	2	no	—
666	C₂⁴	—	4	2	no	—
667	C₂⁴	—	4	4	no	—
668	C₂⁴	—	4	4	no	—
669	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
670	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
671	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
672	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
673	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
674	#41	—	4	16	no	—
675	C₂×Q₈	—	2	2	no	—
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	—	2	2	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×Q₈	—	4	4	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	4	no	—
693	C₂×D₄	—	2	4	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	8	no	—
703	C₂×D₄	—	4	2	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	2	no	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	4	16	no	—
708	C₂×D₄	—	4	4	no	—
709	C₂×D₄	—	4	4	no	—
710	C₂×D₄	—	4	4	no	—
711	C₂×D₄	—	4	4	no	—
712	C₂×D₄	—	4	4	no	—
713	C₂×D₄	—	4	4	no	—
714	C₂×D₄	—	4	4	no	—
715	C₂×D₄	—	4	4	no	—
716	C₂×D₄	—	4	4	no	—
717	C₂×D₄	—	4	4	no	—
718	C₂×D₄	—	4	4	no	—
719	C₂×D₄	—	4	4	no	—
720	C₂×D₄	—	4	4	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	4	4	no	—
728	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
729	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	4	2	no	—
750	C₄⋊C₄	—	4	4	no	—
751	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
752	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	8	no	—
764	C₂²⋊C₄	—	2	8	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	4	no	—
767	C₂²⋊C₄	—	4	4	no	—
768	C₂²⋊C₄	—	4	4	no	—
769	C₂²⋊C₄	—	4	4	no	—
770	C₂²⋊C₄	—	4	4	no	—
771	C₂²⋊C₄	—	4	4	no	—
772	C₂²⋊C₄	—	4	4	no	—
773	C₂²⋊C₄	—	4	4	no	—
774	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
775	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
776	C₄²	—	2	4	no	—
777	C₄²	—	2	4	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	4	2	no	—
783	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
784	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
785	C₂³	—	2	2	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	4	no	—
794	C₂³	—	2	4	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	4	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	4	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	4	no	—
806	C₂³	—	2	4	no	—
807	C₂³	—	2	4	no	—
808	C₂³	—	2	4	no	—
809	C₂³	—	4	8	no	—
810	C₂³	—	8	4	no	—
811	C₂³	—	8	4	no	—
812	C₂³	—	8	8	no	—
813	C₂³	—	8	8	no	—
814	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
815	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
816	Q₈	—	4	4	no	—
817	Q₈	—	4	4	no	—
818	Q₈	—	8	4	no	—
819	D₄	—	4	8	no	—
820	D₄	—	4	8	no	—
821	D₄	—	4	4	no	—
822	D₄	—	4	4	no	—
823	D₄	—	4	4	no	—
824	D₄	—	4	4	no	—
825	D₄	—	8	8	no	—
826	D₄	—	8	4	no	—
827	D₄	—	8	4	no	—
828	D₄	—	8	4	no	—
829	D₄	—	8	4	no	—
830	D₄	—	8	4	no	—
831	D₄	—	8	8	no	—
832	D₄	—	8	8	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	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	8	no	—
842	C₂×C₄	—	2	2	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	4	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	4	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	4	8	no	—
862	C₂×C₄	—	8	4	no	—
863	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
864	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
865	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
866	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
867	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
868	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
869	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
870	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
871	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	4	no	—
878	C₂²	—	4	4	no	—
879	C₂²	—	4	4	no	—
880	C₂²	—	4	4	no	—
881	C₂²	—	4	4	no	—
882	C₂²	—	4	4	no	—
883	C₂²	—	4	4	no	—
884	C₂²	—	4	4	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	8	16	no	—
898	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
899	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
900	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
901	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
902	C₂²	#585×C₁₃₉	1	2	yes	—
903	C₄	—	2	4	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	2	no	—
907	C₄	—	2	2	no	—
908	C₄	—	2	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	2	no	—
915	C₄	—	4	2	no	—
916	C₄	#535×C₁₃₉	1	4	yes	—
917	C₂	—	4	2	no	—
918	C₂	—	8	2	no	—
919	C₂	—	8	2	no	—
920	C₂	—	8	2	no	—
921	C₂	—	8	2	no	—
922	C₂	C₂×#535×C₁₃₉	1	1	yes	characteristic
923	C₂	#3498×C₁₃₉	1	1	yes	characteristic
924	C₂	#3500×C₁₃₉	1	1	yes	characteristic
925	C₂	#3546×C₁₃₉	1	2	yes	—
926	C₂	#3558×C₁₃₉	1	2	yes	—

	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×#542×C₁₃₉	C₂	semidirect
2. C₂×#535×C₁₃₉	C₂	semidirect
3. #2858×C₁₃₉	C₂	semidirect
4. #2858×C₁₃₉	C₂	semidirect
5. #2714×C₁₃₉	C₂	semidirect
6. #2678×C₁₃₉	C₂	semidirect
7. #2676×C₁₃₉	C₂	semidirect
8. #2670×C₁₃₉	C₂	semidirect
9. #2657×C₁₃₉	C₂	semidirect
10. #2640×C₁₃₉	C₂	semidirect
11. #2548×C₁₃₉	C₂	semidirect
12. #2545×C₁₃₉	C₂	semidirect
13. #2544×C₁₃₉	C₂	semidirect
14. #2541×C₁₃₉	C₂	semidirect
15. #2435×C₁₃₉	C₂	semidirect
16. #2433×C₁₃₉	C₂	semidirect
17. #2432×C₁₃₉	C₂	semidirect
18. #2431×C₁₃₉	C₂	semidirect
19. #2298×C₁₃₉	C₂	semidirect
24. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
25. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
30. C₂×#127×C₁₃₉	C₂²	semidirect
31. C₂×#126×C₁₃₉	C₂²	semidirect
37. C₂×#124×C₁₃₉	C₂²	semidirect
38. C₂×#124×C₁₃₉	C₂²	semidirect
39. C₂×#124×C₁₃₉	C₂²	semidirect
40. C₂×#124×C₁₃₉	C₂²	semidirect
43. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
47. C₂×#121×C₁₃₉	C₂²	semidirect
51. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
52. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
54. #397×C₁₃₉	C₂²	semidirect
55. #396×C₁₃₉	C₂²	semidirect
58. #394×C₁₃₉	C₂²	semidirect
59. #394×C₁₃₉	C₂²	semidirect
60. #393×C₁₃₉	C₂²	semidirect
63. #392×C₁₃₉	C₂²	semidirect
64. #392×C₁₃₉	C₂²	semidirect
65. #392×C₁₃₉	C₂²	semidirect
66. #391×C₁₃₉	C₂²	semidirect
67. #391×C₁₃₉	C₂²	semidirect
72. #390×C₁₃₉	C₂²	semidirect
73. #390×C₁₃₉	C₂²	semidirect
74. #390×C₁₃₉	C₂²	semidirect
75. #390×C₁₃₉	C₂²	semidirect
76. #390×C₁₃₉	C₂²	semidirect
77. #390×C₁₃₉	C₂²	semidirect
80. #388×C₁₃₉	C₂²	semidirect
81. #387×C₁₃₉	C₂²	semidirect
82. #387×C₁₃₉	C₂²	semidirect
83. #386×C₁₃₉	C₂²	semidirect
84. #386×C₁₃₉	C₂²	semidirect
85. #385×C₁₃₉	C₂²	semidirect
87. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
88. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
91. #376×C₁₃₉	C₂²	semidirect
92. C₄³×C₁₃₉	C₂²	semidirect
149. #117×C₁₃₉	D₄	semidirect
463. #37305	C₁₃₉	direct (N × H)
464. C₁₃₉	#37305	direct (N × H)
465. C₂×#542	C₂×C₁₃₉	semidirect
466. C₂×#535	C₂×C₁₃₉	semidirect
467. #2858	C₂×C₁₃₉	semidirect
468. #2858	C₂×C₁₃₉	semidirect
469. #2714	C₂×C₁₃₉	semidirect
470. #2678	C₂×C₁₃₉	semidirect
471. #2676	C₂×C₁₃₉	semidirect
472. #2670	C₂×C₁₃₉	semidirect
473. #2657	C₂×C₁₃₉	semidirect
474. #2640	C₂×C₁₃₉	semidirect
475. #2548	C₂×C₁₃₉	semidirect
476. #2545	C₂×C₁₃₉	semidirect
477. #2544	C₂×C₁₃₉	semidirect
478. #2541	C₂×C₁₃₉	semidirect
479. #2435	C₂×C₁₃₉	semidirect
480. #2433	C₂×C₁₃₉	semidirect
481. #2432	C₂×C₁₃₉	semidirect
482. #2431	C₂×C₁₃₉	semidirect
483. #2298	C₂×C₁₃₉	semidirect
488. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
489. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
494. C₂×#127	C₂²×C₁₃₉	semidirect
495. C₂×#126	C₂²×C₁₃₉	semidirect
501. C₂×#124	C₂²×C₁₃₉	semidirect
502. C₂×#124	C₂²×C₁₃₉	semidirect
503. C₂×#124	C₂²×C₁₃₉	semidirect
504. C₂×#124	C₂²×C₁₃₉	semidirect
507. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
511. C₂×#121	C₂²×C₁₃₉	semidirect
515. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
516. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
518. #397	C₂²×C₁₃₉	semidirect
519. #396	C₂²×C₁₃₉	semidirect
522. #394	C₂²×C₁₃₉	semidirect
523. #394	C₂²×C₁₃₉	semidirect
524. #393	C₂²×C₁₃₉	semidirect
527. #392	C₂²×C₁₃₉	semidirect
528. #392	C₂²×C₁₃₉	semidirect
529. #392	C₂²×C₁₃₉	semidirect
530. #391	C₂²×C₁₃₉	semidirect
531. #391	C₂²×C₁₃₉	semidirect
536. #390	C₂²×C₁₃₉	semidirect
537. #390	C₂²×C₁₃₉	semidirect
538. #390	C₂²×C₁₃₉	semidirect
539. #390	C₂²×C₁₃₉	semidirect
540. #390	C₂²×C₁₃₉	semidirect
541. #390	C₂²×C₁₃₉	semidirect
544. #388	C₂²×C₁₃₉	semidirect
545. #387	C₂²×C₁₃₉	semidirect
546. #387	C₂²×C₁₃₉	semidirect
547. #386	C₂²×C₁₃₉	semidirect
548. #386	C₂²×C₁₃₉	semidirect
549. #385	C₂²×C₁₃₉	semidirect
551. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
552. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
555. #376	C₂²×C₁₃₉	semidirect
556. C₄³	C₂²×C₁₃₉	semidirect
613. #117	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#542×C₁₃₉	2
C₂×#535×C₁₃₉	2
#2858×C₁₃₉	2
#2714×C₁₃₉	2
#2678×C₁₃₉	2
#2676×C₁₃₉	2
#2670×C₁₃₉	2
#2657×C₁₃₉	2
#2640×C₁₃₉	2
#2548×C₁₃₉	2
#2545×C₁₃₉	2
#2544×C₁₃₉	2
#2541×C₁₃₉	2
#2435×C₁₃₉	2
#2433×C₁₃₉	2
#2432×C₁₃₉	2
#2431×C₁₃₉	2
#2298×C₁₃₉	2
#37305	139

Subgroups — C139×#37305 #48031901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37305 #48031901