Subgroups — C₁₃₉×#36121 #48030717

Order 35584.

3966 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#546×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	C₂×#532×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#127×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2858×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2544×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2445×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2435×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2431×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2428×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2408×C₁₃₉	C₂	1	4	yes	maximal, complemented
13	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	4	yes	maximal, complemented
14	C₄×#127×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₃₉	C₂²	1	2	yes	complemented
17	C₂³×D₄×C₁₃₉	C₂²	1	4	yes	—
18	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
19	#546×C₁₃₉	—	2	16	no	—
20	#532×C₁₃₉	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×#127×C₁₃₉	—	2	8	no	—
23	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#127×C₁₃₉	C₂²	1	4	yes	—
26	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#124×C₁₃₉	C₂²	1	2	yes	complemented
28	C₂×#124×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×#124×C₁₃₉	C₂²	1	2	yes	complemented
30	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
31	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
33	C₂×#121×C₁₃₉	C₂²	1	4	yes	complemented
34	C₂×#121×C₁₃₉	C₂²	1	4	yes	complemented
35	C₂×#121×C₁₃₉	C₂²	1	4	yes	complemented
36	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	complemented
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	complemented
42	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
43	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
45	#394×C₁₃₉	C₂²	1	8	yes	complemented
46	#394×C₁₃₉	C₂²	1	8	yes	complemented
47	#392×C₁₃₉	C₂²	1	8	yes	complemented
48	#391×C₁₃₉	C₂²	1	2	yes	complemented
49	#390×C₁₃₉	C₂²	1	2	yes	complemented
50	#390×C₁₃₉	C₂²	1	4	yes	complemented
51	#390×C₁₃₉	C₂²	1	2	yes	complemented
52	#390×C₁₃₉	C₂²	1	4	yes	complemented
53	#390×C₁₃₉	C₂²	1	4	yes	complemented
54	#390×C₁₃₉	C₂²	1	4	yes	complemented
55	#389×C₁₃₉	C₂²	1	4	yes	complemented
56	#386×C₁₃₉	C₂²	1	8	yes	complemented
57	#386×C₁₃₉	C₂²	1	8	yes	complemented
58	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
59	#380×C₁₃₉	C₂²	1	4	yes	—
60	#379×C₁₃₉	C₂²	1	8	yes	—
61	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
62	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
67	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
68	C₂⁵×C₁₃₉	C₂³	1	4	yes	—
69	C₂×#41×C₁₃₉	—	2	8	no	—
70	C₂×#41×C₁₃₉	—	2	8	no	—
71	C₂×#41×C₁₃₉	—	4	4	no	—
72	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃₉	—	2	16	no	—
74	C₂²×D₄×C₁₃₉	—	2	8	no	—
75	C₂²×D₄×C₁₃₉	—	2	8	no	—
76	C₂²×D₄×C₁₃₉	—	2	16	no	—
77	C₂²×D₄×C₁₃₉	—	4	8	no	—
78	C₂²×D₄×C₁₃₉	—	4	4	no	—
79	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
80	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
81	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
82	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
83	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
84	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
86	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
87	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
88	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
90	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
94	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
95	#127×C₁₃₉	—	2	16	no	—
96	#127×C₁₃₉	—	2	8	no	—
97	#127×C₁₃₉	—	2	4	no	—
98	#127×C₁₃₉	D₄	1	8	yes	complemented
99	#124×C₁₃₉	—	2	8	no	—
100	#124×C₁₃₉	—	2	8	no	—
101	#124×C₁₃₉	—	4	4	no	—
102	#123×C₁₃₉	—	2	16	no	—
103	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
104	#121×C₁₃₉	—	2	16	no	—
105	#121×C₁₃₉	—	2	8	no	—
106	#121×C₁₃₉	—	2	16	no	—
107	#121×C₁₃₉	—	4	8	no	—
108	#120×C₁₃₉	—	2	16	no	—
109	C₄×D₄×C₁₃₉	—	2	16	no	—
110	C₄×D₄×C₁₃₉	—	2	8	no	—
111	C₄×D₄×C₁₃₉	—	2	8	no	—
112	C₄×D₄×C₁₃₉	—	4	8	no	—
113	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₁₃₉	—	2	16	no	—
121	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
130	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
131	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
132	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₃₉	—	2	4	no	—
135	C₂×C₄²×C₁₃₉	—	2	4	no	—
136	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
145	#95×C₁₃₉	C₂³	1	2	yes	—
146	#95×C₁₃₉	C₂³	1	2	yes	—
147	#95×C₁₃₉	C₂³	1	2	yes	—
148	#95×C₁₃₉	C₂³	1	8	yes	—
149	C₂⁴×C₁₃₉	—	2	8	no	—
150	C₂⁴×C₁₃₉	—	2	8	no	—
151	C₂⁴×C₁₃₉	—	2	16	no	—
152	C₂⁴×C₁₃₉	—	4	8	no	—
153	C₂⁴×C₁₃₉	—	4	4	no	—
154	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
155	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
156	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
157	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
158	#41×C₁₃₉	—	4	32	no	—
159	C₂×Q₈×C₁₃₉	—	2	4	no	—
160	C₂×Q₈×C₁₃₉	—	2	4	no	—
161	C₂×Q₈×C₁₃₉	—	2	4	no	—
162	C₂×D₄×C₁₃₉	—	2	4	no	—
163	C₂×D₄×C₁₃₉	—	2	8	no	—
164	C₂×D₄×C₁₃₉	—	2	8	no	—
165	C₂×D₄×C₁₃₉	—	2	8	no	—
166	C₂×D₄×C₁₃₉	—	2	16	no	—
167	C₂×D₄×C₁₃₉	—	2	8	no	—
168	C₂×D₄×C₁₃₉	—	2	4	no	—
169	C₂×D₄×C₁₃₉	—	2	8	no	—
170	C₂×D₄×C₁₃₉	—	2	4	no	—
171	C₂×D₄×C₁₃₉	—	2	4	no	—
172	C₂×D₄×C₁₃₉	—	2	8	no	—
173	C₂×D₄×C₁₃₉	—	2	8	no	—
174	C₂×D₄×C₁₃₉	—	2	16	no	—
175	C₂×D₄×C₁₃₉	—	2	8	no	—
176	C₂×D₄×C₁₃₉	—	2	8	no	—
177	C₂×D₄×C₁₃₉	—	2	4	no	—
178	C₂×D₄×C₁₃₉	—	2	8	no	—
179	C₂×D₄×C₁₃₉	—	2	4	no	—
180	C₂×D₄×C₁₃₉	—	4	32	no	—
181	C₂×D₄×C₁₃₉	—	4	64	no	—
182	C₂×D₄×C₁₃₉	—	4	8	no	—
183	C₂×D₄×C₁₃₉	—	4	4	no	—
184	C₂×D₄×C₁₃₉	—	4	4	no	—
185	C₂×D₄×C₁₃₉	—	4	8	no	—
186	C₂×D₄×C₁₃₉	C₂×D₄	1	16	yes	—
187	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
188	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
189	C₂²×C₄×C₁₃₉	—	2	2	no	—
190	C₂²×C₄×C₁₃₉	—	2	4	no	—
191	C₂²×C₄×C₁₃₉	—	2	2	no	—
192	C₂²×C₄×C₁₃₉	—	2	2	no	—
193	C₂²×C₄×C₁₃₉	—	2	4	no	—
194	C₂²×C₄×C₁₃₉	—	2	2	no	—
195	C₂²×C₄×C₁₃₉	—	2	8	no	—
196	C₂²×C₄×C₁₃₉	—	2	4	no	—
197	C₂²×C₄×C₁₃₉	—	2	8	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	—	4	4	no	—
202	C₂²×C₄×C₁₃₉	—	4	8	no	—
203	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	complemented
205	C₂²×C₄×C₁₃₉	#41	1	8	yes	complemented
206	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
217	C₄⋊C₄×C₁₃₉	—	2	4	no	—
218	C₄⋊C₄×C₁₃₉	—	2	8	no	—
219	C₄⋊C₄×C₁₃₉	—	2	8	no	—
220	C₄⋊C₄×C₁₃₉	—	2	4	no	—
221	C₄⋊C₄×C₁₃₉	—	2	8	no	—
222	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	complemented
223	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
224	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
225	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
226	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
227	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
228	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
229	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
230	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
231	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
232	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
233	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
234	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
235	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	complemented
236	C₄²×C₁₃₉	—	2	4	no	—
237	C₄²×C₁₃₉	—	2	2	no	—
238	C₄²×C₁₃₉	—	2	2	no	—
239	C₄²×C₁₃₉	—	2	4	no	—
240	C₄²×C₁₃₉	—	2	4	no	—
241	C₄²×C₁₃₉	—	2	4	no	—
242	C₄²×C₁₃₉	—	2	2	no	—
243	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
244	C₄²×C₁₃₉	C₂×D₄	1	4	yes	complemented
245	C₂³×C₁₃₉	—	2	1	no	—
246	C₂³×C₁₃₉	—	2	1	no	—
247	C₂³×C₁₃₉	—	2	2	no	—
248	C₂³×C₁₃₉	—	2	4	no	—
249	C₂³×C₁₃₉	—	2	1	no	—
250	C₂³×C₁₃₉	—	2	2	no	—
251	C₂³×C₁₃₉	—	2	8	no	—
252	C₂³×C₁₃₉	—	2	8	no	—
253	C₂³×C₁₃₉	—	2	1	no	—
254	C₂³×C₁₃₉	—	2	2	no	—
255	C₂³×C₁₃₉	—	2	4	no	—
256	C₂³×C₁₃₉	—	2	4	no	—
257	C₂³×C₁₃₉	—	2	4	no	—
258	C₂³×C₁₃₉	—	2	8	no	—
259	C₂³×C₁₃₉	—	2	4	no	—
260	C₂³×C₁₃₉	—	2	8	no	—
261	C₂³×C₁₃₉	—	4	16	no	—
262	C₂³×C₁₃₉	—	4	32	no	—
263	C₂³×C₁₃₉	—	4	16	no	—
264	C₂³×C₁₃₉	—	8	8	no	—
265	C₂³×C₁₃₉	—	8	16	no	—
266	C₂³×C₁₃₉	C₂²×D₄	1	8	yes	—
267	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
268	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
269	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
270	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
271	Q₈×C₁₃₉	—	4	8	no	—
272	D₄×C₁₃₉	—	2	8	no	—
273	D₄×C₁₃₉	—	2	16	no	—
274	D₄×C₁₃₉	—	2	32	no	—
275	D₄×C₁₃₉	—	4	16	no	—
276	D₄×C₁₃₉	—	4	32	no	—
277	D₄×C₁₃₉	—	4	16	no	—
278	D₄×C₁₃₉	—	4	8	no	—
279	D₄×C₁₃₉	—	4	16	no	—
280	D₄×C₁₃₉	—	8	8	no	—
281	C₂×C₄×C₁₃₉	—	2	1	no	—
282	C₂×C₄×C₁₃₉	—	2	1	no	—
283	C₂×C₄×C₁₃₉	—	2	2	no	—
284	C₂×C₄×C₁₃₉	—	2	2	no	—
285	C₂×C₄×C₁₃₉	—	2	2	no	—
286	C₂×C₄×C₁₃₉	—	2	1	no	—
287	C₂×C₄×C₁₃₉	—	2	1	no	—
288	C₂×C₄×C₁₃₉	—	2	2	no	—
289	C₂×C₄×C₁₃₉	—	2	8	no	—
290	C₂×C₄×C₁₃₉	—	2	8	no	—
291	C₂×C₄×C₁₃₉	—	2	16	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	4	no	—
294	C₂×C₄×C₁₃₉	—	2	4	no	—
295	C₂×C₄×C₁₃₉	—	2	4	no	—
296	C₂×C₄×C₁₃₉	—	2	2	no	—
297	C₂×C₄×C₁₃₉	—	2	2	no	—
298	C₂×C₄×C₁₃₉	—	2	2	no	—
299	C₂×C₄×C₁₃₉	—	2	2	no	—
300	C₂×C₄×C₁₃₉	—	2	2	no	—
301	C₂×C₄×C₁₃₉	—	2	8	no	—
302	C₂×C₄×C₁₃₉	—	2	4	no	—
303	C₂×C₄×C₁₃₉	—	4	16	no	—
304	C₂×C₄×C₁₃₉	—	4	8	no	—
305	C₂×C₄×C₁₃₉	—	8	8	no	—
306	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
307	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
308	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
310	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
313	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
314	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
315	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
316	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
317	C₂²×C₁₃₉	—	2	2	no	—
318	C₂²×C₁₃₉	—	2	4	no	—
319	C₂²×C₁₃₉	—	2	2	no	—
320	C₂²×C₁₃₉	—	2	4	no	—
321	C₂²×C₁₃₉	—	2	2	no	—
322	C₂²×C₁₃₉	—	2	2	no	—
323	C₂²×C₁₃₉	—	2	8	no	—
324	C₂²×C₁₃₉	—	2	16	no	—
325	C₂²×C₁₃₉	—	2	2	no	—
326	C₂²×C₁₃₉	—	4	4	no	—
327	C₂²×C₁₃₉	—	4	2	no	—
328	C₂²×C₁₃₉	—	4	4	no	—
329	C₂²×C₁₃₉	—	4	2	no	—
330	C₂²×C₁₃₉	—	4	8	no	—
331	C₂²×C₁₃₉	—	4	4	no	—
332	C₂²×C₁₃₉	—	4	4	no	—
333	C₂²×C₁₃₉	—	4	8	no	—
334	C₂²×C₁₃₉	—	4	4	no	—
335	C₂²×C₁₃₉	—	4	8	no	—
336	C₂²×C₁₃₉	—	8	32	no	—
337	C₂²×C₁₃₉	#532	1	4	yes	complemented
338	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
339	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
340	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
341	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
342	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
343	C₄×C₁₃₉	—	2	2	no	—
344	C₄×C₁₃₉	—	2	2	no	—
345	C₄×C₁₃₉	—	2	2	no	—
346	C₄×C₁₃₉	—	2	4	no	—
347	C₄×C₁₃₉	—	2	2	no	—
348	C₄×C₁₃₉	—	4	4	no	—
349	C₄×C₁₃₉	—	4	2	no	—
350	C₄×C₁₃₉	—	4	4	no	—
351	C₄×C₁₃₉	—	4	2	no	—
352	C₄×C₁₃₉	D₄²	1	4	yes	—
353	C₄×C₁₃₉	#546	1	8	yes	complemented
354	C₂×C₁₃₉	—	2	4	no	—
355	C₂×C₁₃₉	—	4	2	no	—
356	C₂×C₁₃₉	—	4	8	no	—
357	C₂×C₁₃₉	—	8	4	no	—
358	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
359	C₂×C₁₃₉	C₂×D₄²	1	1	yes	characteristic
360	C₂×C₁₃₉	C₂×#546	1	2	yes	—
361	C₂×C₁₃₉	#3498	1	1	yes	characteristic
362	C₂×C₁₃₉	#3508	1	2	yes	—
363	#36121	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
364	C₁₃₉	#36121	1	1	yes	characteristic, direct product factor, Sylow
365	C₂×#546	C₂×C₁₃₉	1	2	yes	complemented
366	C₂×#532	C₂×C₁₃₉	1	1	yes	characteristic, complemented
367	C₂²×#127	C₂×C₁₃₉	1	1	yes	characteristic, complemented
368	#2858	C₂×C₁₃₉	1	1	yes	characteristic, complemented
369	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
370	#2856	C₂×C₁₃₉	1	1	yes	characteristic, complemented
371	#2544	C₂×C₁₃₉	1	2	yes	complemented
372	#2445	C₂×C₁₃₉	1	4	yes	complemented
373	#2435	C₂×C₁₃₉	1	2	yes	complemented
374	#2431	C₂×C₁₃₉	1	2	yes	complemented
375	#2428	C₂×C₁₃₉	1	4	yes	complemented
376	#2408	C₂×C₁₃₉	1	4	yes	complemented
377	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	4	yes	complemented
378	C₄×#127	C₂×C₁₃₉	1	1	yes	characteristic, complemented
379	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
380	C₂²×#41	C₂²×C₁₃₉	1	2	yes	complemented
381	C₂³×D₄	C₂²×C₁₃₉	1	4	yes	—
382	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
383	#546	—	2	16	no	—
384	#532	—	2	8	no	—
385	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
386	C₂×#127	—	2	8	no	—
387	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
388	C₂×#127	C₂²×C₁₃₉	1	4	yes	—
389	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
390	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
391	C₂×#124	C₂²×C₁₃₉	1	2	yes	complemented
392	C₂×#124	C₂²×C₁₃₉	1	2	yes	complemented
393	C₂×#124	C₂²×C₁₃₉	1	2	yes	complemented
394	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
395	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
396	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
397	C₂×#121	C₂²×C₁₃₉	1	4	yes	complemented
398	C₂×#121	C₂²×C₁₃₉	1	4	yes	complemented
399	C₂×#121	C₂²×C₁₃₉	1	4	yes	complemented
400	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
401	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
402	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
403	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
404	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	complemented
405	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	complemented
406	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
407	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
408	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
409	#394	C₂²×C₁₃₉	1	8	yes	complemented
410	#394	C₂²×C₁₃₉	1	8	yes	complemented
411	#392	C₂²×C₁₃₉	1	8	yes	complemented
412	#391	C₂²×C₁₃₉	1	2	yes	complemented
413	#390	C₂²×C₁₃₉	1	4	yes	complemented
414	#390	C₂²×C₁₃₉	1	2	yes	complemented
415	#390	C₂²×C₁₃₉	1	4	yes	complemented
416	#390	C₂²×C₁₃₉	1	4	yes	complemented
417	#390	C₂²×C₁₃₉	1	2	yes	complemented
418	#390	C₂²×C₁₃₉	1	4	yes	complemented
419	#389	C₂²×C₁₃₉	1	4	yes	complemented
420	#386	C₂²×C₁₃₉	1	8	yes	complemented
421	#386	C₂²×C₁₃₉	1	8	yes	complemented
422	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
423	#380	C₂²×C₁₃₉	1	4	yes	—
424	#379	C₂²×C₁₃₉	1	8	yes	—
425	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
426	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
427	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
428	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
429	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
430	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
431	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
432	C₂⁵	C₂³×C₁₃₉	1	4	yes	—
433	C₂×#41	—	2	8	no	—
434	C₂×#41	—	2	8	no	—
435	C₂×#41	—	4	4	no	—
436	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
437	C₂²×D₄	—	2	16	no	—
438	C₂²×D₄	—	2	8	no	—
439	C₂²×D₄	—	2	8	no	—
440	C₂²×D₄	—	2	16	no	—
441	C₂²×D₄	—	4	8	no	—
442	C₂²×D₄	—	4	4	no	—
443	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
444	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
445	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
446	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
447	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
448	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
449	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
450	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
451	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
452	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
453	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
454	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
456	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
457	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
458	C₄⋊Q₈	—	2	4	no	—
459	#127	—	2	16	no	—
460	#127	—	2	8	no	—
461	#127	—	2	4	no	—
462	#127	D₄×C₁₃₉	1	8	yes	complemented
463	#124	—	2	8	no	—
464	#124	—	2	8	no	—
465	#124	—	4	4	no	—
466	#123	—	2	16	no	—
467	C₂²⋊Q₈	—	2	8	no	—
468	#121	—	2	16	no	—
469	#121	—	2	8	no	—
470	#121	—	2	16	no	—
471	#121	—	4	8	no	—
472	#120	—	2	16	no	—
473	C₄×D₄	—	2	16	no	—
474	C₄×D₄	—	2	8	no	—
475	C₄×D₄	—	2	8	no	—
476	C₄×D₄	—	4	8	no	—
477	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
478	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
481	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
482	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
483	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	—	2	16	no	—
485	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
498	C₂×C₄²	—	2	4	no	—
499	C₂×C₄²	—	2	4	no	—
500	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
501	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
502	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
503	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
506	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
509	#95	C₂³×C₁₃₉	1	2	yes	—
510	#95	C₂³×C₁₃₉	1	2	yes	—
511	#95	C₂³×C₁₃₉	1	2	yes	—
512	#95	C₂³×C₁₃₉	1	8	yes	—
513	C₂⁴	—	2	8	no	—
514	C₂⁴	—	2	8	no	—
515	C₂⁴	—	2	16	no	—
516	C₂⁴	—	4	8	no	—
517	C₂⁴	—	4	4	no	—
518	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
519	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
520	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
521	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
522	#41	—	4	32	no	—
523	C₂×Q₈	—	2	4	no	—
524	C₂×Q₈	—	2	4	no	—
525	C₂×Q₈	—	2	4	no	—
526	C₂×D₄	—	2	4	no	—
527	C₂×D₄	—	2	8	no	—
528	C₂×D₄	—	2	8	no	—
529	C₂×D₄	—	2	8	no	—
530	C₂×D₄	—	2	16	no	—
531	C₂×D₄	—	2	8	no	—
532	C₂×D₄	—	2	4	no	—
533	C₂×D₄	—	2	8	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	8	no	—
537	C₂×D₄	—	2	8	no	—
538	C₂×D₄	—	2	16	no	—
539	C₂×D₄	—	2	8	no	—
540	C₂×D₄	—	2	8	no	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	2	8	no	—
543	C₂×D₄	—	2	4	no	—
544	C₂×D₄	—	4	32	no	—
545	C₂×D₄	—	4	64	no	—
546	C₂×D₄	—	4	8	no	—
547	C₂×D₄	—	4	4	no	—
548	C₂×D₄	—	4	4	no	—
549	C₂×D₄	—	4	8	no	—
550	C₂×D₄	C₂×D₄×C₁₃₉	1	16	yes	—
551	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
552	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	4	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	8	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	2	8	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	8	no	—
565	C₂²×C₄	—	4	4	no	—
566	C₂²×C₄	—	4	8	no	—
567	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
568	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	complemented
569	C₂²×C₄	#41×C₁₃₉	1	8	yes	complemented
570	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
572	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
573	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
574	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
575	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
576	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
577	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	8	no	—
583	C₄⋊C₄	—	2	8	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	8	no	—
586	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	complemented
587	C₂²⋊C₄	—	2	8	no	—
588	C₂²⋊C₄	—	2	16	no	—
589	C₂²⋊C₄	—	2	4	no	—
590	C₂²⋊C₄	—	2	8	no	—
591	C₂²⋊C₄	—	2	8	no	—
592	C₂²⋊C₄	—	2	8	no	—
593	C₂²⋊C₄	—	2	8	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	4	8	no	—
596	C₂²⋊C₄	—	4	8	no	—
597	C₂²⋊C₄	—	4	8	no	—
598	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
599	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	complemented
600	C₄²	—	2	4	no	—
601	C₄²	—	2	2	no	—
602	C₄²	—	2	2	no	—
603	C₄²	—	2	4	no	—
604	C₄²	—	2	4	no	—
605	C₄²	—	2	4	no	—
606	C₄²	—	2	2	no	—
607	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
608	C₄²	C₂×D₄×C₁₃₉	1	4	yes	complemented
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	4	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	2	8	no	—
616	C₂³	—	2	8	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	4	no	—
620	C₂³	—	2	4	no	—
621	C₂³	—	2	4	no	—
622	C₂³	—	2	8	no	—
623	C₂³	—	2	4	no	—
624	C₂³	—	2	8	no	—
625	C₂³	—	4	16	no	—
626	C₂³	—	4	32	no	—
627	C₂³	—	4	16	no	—
628	C₂³	—	8	8	no	—
629	C₂³	—	8	16	no	—
630	C₂³	C₂²×D₄×C₁₃₉	1	8	yes	—
631	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
632	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
633	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
634	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
635	Q₈	—	4	8	no	—
636	D₄	—	2	8	no	—
637	D₄	—	2	16	no	—
638	D₄	—	2	32	no	—
639	D₄	—	4	16	no	—
640	D₄	—	4	32	no	—
641	D₄	—	4	16	no	—
642	D₄	—	4	8	no	—
643	D₄	—	4	16	no	—
644	D₄	—	8	8	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	8	no	—
654	C₂×C₄	—	2	8	no	—
655	C₂×C₄	—	2	16	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	8	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	4	16	no	—
668	C₂×C₄	—	4	8	no	—
669	C₂×C₄	—	8	8	no	—
670	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
671	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
672	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
673	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
674	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
675	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
676	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
677	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
678	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
679	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
680	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	4	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	4	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	8	no	—
688	C₂²	—	2	16	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	4	4	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	4	no	—
693	C₂²	—	4	8	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	4	no	—
696	C₂²	—	4	4	no	—
697	C₂²	—	4	8	no	—
698	C₂²	—	4	4	no	—
699	C₂²	—	4	8	no	—
700	C₂²	—	8	32	no	—
701	C₂²	#532×C₁₃₉	1	4	yes	complemented
702	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
703	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
704	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
705	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
706	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
707	C₄	—	2	2	no	—
708	C₄	—	2	2	no	—
709	C₄	—	2	2	no	—
710	C₄	—	2	4	no	—
711	C₄	—	2	2	no	—
712	C₄	—	4	4	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	4	no	—
715	C₄	—	4	2	no	—
716	C₄	D₄²×C₁₃₉	1	4	yes	—
717	C₄	#546×C₁₃₉	1	8	yes	complemented
718	C₂	—	2	4	no	—
719	C₂	—	4	8	no	—
720	C₂	—	4	2	no	—
721	C₂	—	8	4	no	—
722	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
723	C₂	C₂×D₄²×C₁₃₉	1	1	yes	characteristic
724	C₂	C₂×#546×C₁₃₉	1	2	yes	—
725	C₂	#3498×C₁₃₉	1	1	yes	characteristic
726	C₂	#3508×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×#546×C₁₃₉	C₂	semidirect
2. C₂×#532×C₁₃₉	C₂	semidirect
3. C₂²×#127×C₁₃₉	C₂	semidirect
4. #2858×C₁₃₉	C₂	semidirect
5. #2857×C₁₃₉	C₂	semidirect
6. #2856×C₁₃₉	C₂	semidirect
7. #2544×C₁₃₉	C₂	semidirect
8. #2445×C₁₃₉	C₂	semidirect
9. #2435×C₁₃₉	C₂	semidirect
10. #2431×C₁₃₉	C₂	semidirect
11. #2428×C₁₃₉	C₂	semidirect
12. #2408×C₁₃₉	C₂	semidirect
13. D₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
14. C₄×#127×C₁₃₉	C₂	semidirect
15. C₄²×D₄×C₁₃₉	C₂	semidirect
16. C₂²×#41×C₁₃₉	C₂²	semidirect
21. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
27. C₂×#124×C₁₃₉	C₂²	semidirect
28. C₂×#124×C₁₃₉	C₂²	semidirect
29. C₂×#124×C₁₃₉	C₂²	semidirect
30. C₂×#123×C₁₃₉	C₂²	semidirect
32. C₂×#121×C₁₃₉	C₂²	semidirect
33. C₂×#121×C₁₃₉	C₂²	semidirect
34. C₂×#121×C₁₃₉	C₂²	semidirect
35. C₂×#121×C₁₃₉	C₂²	semidirect
39. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
40. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
41. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
44. C₂²×C₄²×C₁₃₉	C₂²	semidirect
45. #394×C₁₃₉	C₂²	semidirect
46. #394×C₁₃₉	C₂²	semidirect
47. #392×C₁₃₉	C₂²	semidirect
48. #391×C₁₃₉	C₂²	semidirect
49. #390×C₁₃₉	C₂²	semidirect
50. #390×C₁₃₉	C₂²	semidirect
51. #390×C₁₃₉	C₂²	semidirect
52. #390×C₁₃₉	C₂²	semidirect
53. #390×C₁₃₉	C₂²	semidirect
54. #390×C₁₃₉	C₂²	semidirect
55. #389×C₁₃₉	C₂²	semidirect
56. #386×C₁₃₉	C₂²	semidirect
57. #386×C₁₃₉	C₂²	semidirect
58. #384×C₁₃₉	C₂²	semidirect
61. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
62. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
65. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
66. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
67. C₄³×C₁₃₉	C₂²	semidirect
98. #127×C₁₃₉	D₄	semidirect
113. C₄×D₄×C₁₃₉	D₄	semidirect
204. C₂²×C₄×C₁₃₉	C₂×D₄	semidirect
205. C₂²×C₄×C₁₃₉	#41	semidirect
222. C₄⋊C₄×C₁₃₉	C₂×D₄	semidirect
235. C₂²⋊C₄×C₁₃₉	C₂×D₄	semidirect
244. C₄²×C₁₃₉	C₂×D₄	semidirect
337. C₂²×C₁₃₉	#532	semidirect
353. C₄×C₁₃₉	#546	semidirect
363. #36121	C₁₃₉	direct (N × H)
364. C₁₃₉	#36121	direct (N × H)
365. C₂×#546	C₂×C₁₃₉	semidirect
366. C₂×#532	C₂×C₁₃₉	semidirect
367. C₂²×#127	C₂×C₁₃₉	semidirect
368. #2858	C₂×C₁₃₉	semidirect
369. #2857	C₂×C₁₃₉	semidirect
370. #2856	C₂×C₁₃₉	semidirect
371. #2544	C₂×C₁₃₉	semidirect
372. #2445	C₂×C₁₃₉	semidirect
373. #2435	C₂×C₁₃₉	semidirect
374. #2431	C₂×C₁₃₉	semidirect
375. #2428	C₂×C₁₃₉	semidirect
376. #2408	C₂×C₁₃₉	semidirect
377. D₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
378. C₄×#127	C₂×C₁₃₉	semidirect
379. C₄²×D₄	C₂×C₁₃₉	semidirect
380. C₂²×#41	C₂²×C₁₃₉	semidirect
385. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
391. C₂×#124	C₂²×C₁₃₉	semidirect
392. C₂×#124	C₂²×C₁₃₉	semidirect
393. C₂×#124	C₂²×C₁₃₉	semidirect
394. C₂×#123	C₂²×C₁₃₉	semidirect
396. C₂×#121	C₂²×C₁₃₉	semidirect
397. C₂×#121	C₂²×C₁₃₉	semidirect
398. C₂×#121	C₂²×C₁₃₉	semidirect
399. C₂×#121	C₂²×C₁₃₉	semidirect
403. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
404. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
405. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
408. C₂²×C₄²	C₂²×C₁₃₉	semidirect
409. #394	C₂²×C₁₃₉	semidirect
410. #394	C₂²×C₁₃₉	semidirect
411. #392	C₂²×C₁₃₉	semidirect
412. #391	C₂²×C₁₃₉	semidirect
413. #390	C₂²×C₁₃₉	semidirect
414. #390	C₂²×C₁₃₉	semidirect
415. #390	C₂²×C₁₃₉	semidirect
416. #390	C₂²×C₁₃₉	semidirect
417. #390	C₂²×C₁₃₉	semidirect
418. #390	C₂²×C₁₃₉	semidirect
419. #389	C₂²×C₁₃₉	semidirect
420. #386	C₂²×C₁₃₉	semidirect
421. #386	C₂²×C₁₃₉	semidirect
422. #384	C₂²×C₁₃₉	semidirect
425. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
426. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
429. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
430. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
431. C₄³	C₂²×C₁₃₉	semidirect
462. #127	D₄×C₁₃₉	semidirect
477. C₄×D₄	D₄×C₁₃₉	semidirect
568. C₂²×C₄	C₂×D₄×C₁₃₉	semidirect
569. C₂²×C₄	#41×C₁₃₉	semidirect
586. C₄⋊C₄	C₂×D₄×C₁₃₉	semidirect
599. C₂²⋊C₄	C₂×D₄×C₁₃₉	semidirect
608. C₄²	C₂×D₄×C₁₃₉	semidirect
701. C₂²	#532×C₁₃₉	semidirect
717. C₄	#546×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#546×C₁₃₉	2
C₂×#532×C₁₃₉	2
C₂²×#127×C₁₃₉	2
#2858×C₁₃₉	2
#2857×C₁₃₉	2
#2856×C₁₃₉	2
#2544×C₁₃₉	2
#2445×C₁₃₉	2
#2435×C₁₃₉	2
#2431×C₁₃₉	2
#2428×C₁₃₉	2
#2408×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
C₄×#127×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36121	139

Subgroups — C139×#36121 #48030717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36121 #48030717