Subgroups — C₁₃₉×#35680 #48030276

Order 35584.

6056 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×H(5,𝔽₂)×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄²×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2615×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2613×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2433×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2431×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2430×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2410×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2408×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2407×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2404×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2403×C₁₃₉	C₂	1	4	yes	maximal, complemented
14	#2388×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#392×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2339×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂×H(5,𝔽₂)×C₁₃₉	—	2	8	no	—
19	C₂×H(5,𝔽₂)×C₁₃₉	—	2	16	no	—
20	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
22	C₂²×#41×C₁₃₉	C₂²	1	2	yes	complemented
23	C₂²×#41×C₁₃₉	C₂²	1	2	yes	complemented
24	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
25	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	complemented
26	C₂³×D₄×C₁₃₉	C₂²	1	4	yes	complemented
27	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
28	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
29	C₂³×D₄×C₁₃₉	C₂²	1	4	yes	complemented
30	#546×C₁₃₉	—	2	8	no	—
31	D₄²×C₁₃₉	—	2	16	no	—
32	C₂×#127×C₁₃₉	C₂²	1	2	yes	complemented
33	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
35	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
37	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
39	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
40	C₂×#121×C₁₃₉	C₂²	1	4	yes	complemented
41	C₂×#120×C₁₃₉	C₂²	1	4	yes	complemented
42	C₂×#120×C₁₃₉	C₂²	1	2	yes	complemented
43	C₂×#120×C₁₃₉	C₂²	1	4	yes	complemented
44	C₂×#120×C₁₃₉	C₂²	1	2	yes	complemented
45	C₂×#120×C₁₃₉	C₂²	1	4	yes	complemented
46	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
48	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
49	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
51	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
52	#395×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
53	#394×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
54	#394×C₁₃₉	C₂²	1	4	yes	complemented
55	#394×C₁₃₉	C₂²	1	2	yes	complemented
56	#394×C₁₃₉	C₂²	1	2	yes	complemented
57	#393×C₁₃₉	C₂²	1	2	yes	complemented
58	#393×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
59	#392×C₁₃₉	C₂²	1	2	yes	complemented
60	#392×C₁₃₉	C₂²	1	4	yes	complemented
61	#392×C₁₃₉	C₂²	1	2	yes	complemented
62	#392×C₁₃₉	C₂²	1	4	yes	complemented
63	#392×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
64	#392×C₁₃₉	C₂²	1	4	yes	complemented
65	#392×C₁₃₉	C₂²	1	2	yes	complemented
66	#392×C₁₃₉	C₂²	1	4	yes	complemented
67	#392×C₁₃₉	C₂²	1	2	yes	complemented
68	#392×C₁₃₉	C₂²	1	2	yes	complemented
69	#391×C₁₃₉	C₂²	1	2	yes	complemented
70	#390×C₁₃₉	C₂²	1	2	yes	complemented
71	#390×C₁₃₉	C₂²	1	2	yes	complemented
72	#386×C₁₃₉	C₂²	1	4	yes	complemented
73	#386×C₁₃₉	C₂²	1	4	yes	complemented
74	#386×C₁₃₉	C₂²	1	4	yes	complemented
75	#386×C₁₃₉	C₂²	1	4	yes	complemented
76	#386×C₁₃₉	C₂²	1	4	yes	complemented
77	#386×C₁₃₉	C₂²	1	4	yes	complemented
78	#385×C₁₃₉	C₂²	1	4	yes	complemented
79	#381×C₁₃₉	C₂²	1	2	yes	complemented
80	#380×C₁₃₉	C₂²	1	2	yes	complemented
81	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
82	#379×C₁₃₉	C₂²	1	4	yes	complemented
83	#379×C₁₃₉	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
86	C₂×#95×C₁₃₉	C₂²	1	2	yes	complemented
87	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
88	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
89	C₂⁵×C₁₃₉	C₂³	1	4	yes	—
90	H(5,𝔽₂)×C₁₃₉	—	2	128	no	—
91	C₂×#41×C₁₃₉	—	2	8	no	—
92	C₂×#41×C₁₃₉	—	2	8	no	—
93	C₂×#41×C₁₃₉	—	2	16	no	—
94	C₂×#41×C₁₃₉	—	2	8	no	—
95	C₂×#41×C₁₃₉	—	2	8	no	—
96	C₂×#41×C₁₃₉	—	2	4	no	—
97	C₂×#41×C₁₃₉	—	2	8	no	—
98	C₂×#41×C₁₃₉	—	2	8	no	—
99	C₂×#41×C₁₃₉	D₄	1	8	yes	complemented
100	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₁₃₉	—	2	16	no	—
103	C₂²×D₄×C₁₃₉	—	2	16	no	—
104	C₂²×D₄×C₁₃₉	—	2	8	no	—
105	C₂²×D₄×C₁₃₉	—	2	8	no	—
106	C₂²×D₄×C₁₃₉	—	2	16	no	—
107	C₂²×D₄×C₁₃₉	—	2	16	no	—
108	C₂²×D₄×C₁₃₉	—	2	8	no	—
109	C₂²×D₄×C₁₃₉	—	2	16	no	—
110	C₂²×D₄×C₁₃₉	—	2	8	no	—
111	C₂²×D₄×C₁₃₉	—	2	4	no	—
112	C₂²×D₄×C₁₃₉	—	2	8	no	—
113	C₂²×D₄×C₁₃₉	—	2	4	no	—
114	C₂²×D₄×C₁₃₉	—	4	8	no	—
115	C₂²×D₄×C₁₃₉	—	4	8	no	—
116	C₂²×D₄×C₁₃₉	D₄	1	16	yes	complemented
117	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
126	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
127	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
132	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
133	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
136	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
141	#127×C₁₃₉	—	2	8	no	—
142	#124×C₁₃₉	—	2	4	no	—
143	#123×C₁₃₉	—	2	8	no	—
144	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
145	#121×C₁₃₉	—	2	8	no	—
146	#121×C₁₃₉	—	2	16	no	—
147	#121×C₁₃₉	—	2	8	no	—
148	#121×C₁₃₉	—	2	8	no	—
149	#121×C₁₃₉	—	2	4	no	—
150	#120×C₁₃₉	—	2	16	no	—
151	#120×C₁₃₉	—	2	16	no	—
152	#120×C₁₃₉	—	2	8	no	—
153	#120×C₁₃₉	—	4	8	no	—
154	#120×C₁₃₉	—	4	4	no	—
155	C₄×D₄×C₁₃₉	—	2	8	no	—
156	C₄×D₄×C₁₃₉	—	2	4	no	—
157	C₄×D₄×C₁₃₉	—	2	8	no	—
158	C₄×D₄×C₁₃₉	—	2	4	no	—
159	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
165	C₂×C₂²⋊C₄×C₁₃₉	—	4	8	no	—
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	2	yes	—
174	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	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	4	yes	—
182	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
183	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
185	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
186	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
189	#95×C₁₃₉	C₂³	1	1	yes	characteristic
190	#95×C₁₃₉	C₂³	1	2	yes	—
191	#95×C₁₃₉	C₂³	1	2	yes	—
192	#95×C₁₃₉	C₂³	1	4	yes	—
193	#95×C₁₃₉	C₂³	1	1	yes	characteristic
194	#95×C₁₃₉	C₂³	1	2	yes	—
195	#95×C₁₃₉	C₂³	1	4	yes	—
196	#95×C₁₃₉	C₂³	1	4	yes	—
197	C₂⁴×C₁₃₉	—	2	8	no	—
198	C₂⁴×C₁₃₉	—	2	4	no	—
199	C₂⁴×C₁₃₉	—	2	8	no	—
200	C₂⁴×C₁₃₉	—	2	8	no	—
201	C₂⁴×C₁₃₉	—	2	4	no	—
202	C₂⁴×C₁₃₉	—	2	4	no	—
203	C₂⁴×C₁₃₉	—	2	8	no	—
204	C₂⁴×C₁₃₉	—	4	4	no	—
205	C₂⁴×C₁₃₉	—	4	4	no	—
206	C₂⁴×C₁₃₉	—	4	4	no	—
207	C₂⁴×C₁₃₉	—	4	4	no	—
208	C₂⁴×C₁₃₉	—	4	4	no	—
209	C₂⁴×C₁₃₉	—	4	2	no	—
210	C₂⁴×C₁₃₉	—	4	4	no	—
211	C₂⁴×C₁₃₉	—	4	2	no	—
212	C₂⁴×C₁₃₉	—	4	2	no	—
213	C₂⁴×C₁₃₉	C₂×D₄	1	16	yes	complemented
214	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
215	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
216	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
217	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
218	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
219	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
220	#41×C₁₃₉	—	2	64	no	—
221	#41×C₁₃₉	—	2	64	no	—
222	#41×C₁₃₉	—	2	32	no	—
223	#41×C₁₃₉	—	2	32	no	—
224	C₂×Q₈×C₁₃₉	—	2	4	no	—
225	C₂×Q₈×C₁₃₉	—	2	2	no	—
226	C₂×Q₈×C₁₃₉	—	2	4	no	—
227	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	complemented
228	C₂×D₄×C₁₃₉	—	2	128	no	—
229	C₂×D₄×C₁₃₉	—	2	64	no	—
230	C₂×D₄×C₁₃₉	—	2	32	no	—
231	C₂×D₄×C₁₃₉	—	2	4	no	—
232	C₂×D₄×C₁₃₉	—	2	8	no	—
233	C₂×D₄×C₁₃₉	—	2	8	no	—
234	C₂×D₄×C₁₃₉	—	2	4	no	—
235	C₂×D₄×C₁₃₉	—	2	8	no	—
236	C₂×D₄×C₁₃₉	—	2	4	no	—
237	C₂×D₄×C₁₃₉	—	2	4	no	—
238	C₂×D₄×C₁₃₉	—	2	8	no	—
239	C₂×D₄×C₁₃₉	—	2	8	no	—
240	C₂×D₄×C₁₃₉	—	2	8	no	—
241	C₂×D₄×C₁₃₉	—	2	4	no	—
242	C₂×D₄×C₁₃₉	—	2	64	no	—
243	C₂×D₄×C₁₃₉	—	2	2	no	—
244	C₂×D₄×C₁₃₉	—	2	8	no	—
245	C₂×D₄×C₁₃₉	—	2	8	no	—
246	C₂×D₄×C₁₃₉	—	2	8	no	—
247	C₂×D₄×C₁₃₉	—	2	4	no	—
248	C₂×D₄×C₁₃₉	—	2	8	no	—
249	C₂×D₄×C₁₃₉	—	2	2	no	—
250	C₂×D₄×C₁₃₉	—	2	8	no	—
251	C₂×D₄×C₁₃₉	—	2	8	no	—
252	C₂×D₄×C₁₃₉	—	2	4	no	—
253	C₂×D₄×C₁₃₉	—	2	8	no	—
254	C₂×D₄×C₁₃₉	—	2	4	no	—
255	C₂×D₄×C₁₃₉	—	2	2	no	—
256	C₂×D₄×C₁₃₉	—	2	4	no	—
257	C₂×D₄×C₁₃₉	—	2	4	no	—
258	C₂×D₄×C₁₃₉	—	2	4	no	—
259	C₂×D₄×C₁₃₉	—	2	2	no	—
260	C₂×D₄×C₁₃₉	—	2	4	no	—
261	C₂×D₄×C₁₃₉	—	2	4	no	—
262	C₂×D₄×C₁₃₉	—	2	8	no	—
263	C₂×D₄×C₁₃₉	—	4	4	no	—
264	C₂×D₄×C₁₃₉	—	4	4	no	—
265	C₂×D₄×C₁₃₉	—	4	4	no	—
266	C₂×D₄×C₁₃₉	—	4	4	no	—
267	C₂×D₄×C₁₃₉	—	4	1	no	—
268	C₂×D₄×C₁₃₉	—	4	4	no	—
269	C₂×D₄×C₁₃₉	—	4	4	no	—
270	C₂×D₄×C₁₃₉	—	4	4	no	—
271	C₂×D₄×C₁₃₉	—	4	64	no	—
272	C₂×D₄×C₁₃₉	—	4	16	no	—
273	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
274	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
275	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	complemented
276	C₂×D₄×C₁₃₉	C₂×D₄	1	16	yes	complemented
277	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	complemented
278	C₂²×C₄×C₁₃₉	—	2	8	no	—
279	C₂²×C₄×C₁₃₉	—	2	8	no	—
280	C₂²×C₄×C₁₃₉	—	2	8	no	—
281	C₂²×C₄×C₁₃₉	—	2	8	no	—
282	C₂²×C₄×C₁₃₉	—	2	4	no	—
283	C₂²×C₄×C₁₃₉	—	2	4	no	—
284	C₂²×C₄×C₁₃₉	—	2	4	no	—
285	C₂²×C₄×C₁₃₉	—	2	8	no	—
286	C₂²×C₄×C₁₃₉	—	2	4	no	—
287	C₂²×C₄×C₁₃₉	—	2	4	no	—
288	C₂²×C₄×C₁₃₉	—	2	2	no	—
289	C₂²×C₄×C₁₃₉	—	2	8	no	—
290	C₂²×C₄×C₁₃₉	—	4	4	no	—
291	C₂²×C₄×C₁₃₉	—	4	4	no	—
292	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	complemented
293	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	complemented
294	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	complemented
295	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
297	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₁₃₉	—	2	4	no	—
307	C₄⋊C₄×C₁₃₉	—	2	4	no	—
308	C₄⋊C₄×C₁₃₉	—	2	2	no	—
309	C₄⋊C₄×C₁₃₉	—	2	2	no	—
310	C₄⋊C₄×C₁₃₉	—	2	4	no	—
311	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
312	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
313	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
314	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
315	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
316	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
317	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
318	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
319	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
320	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
321	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
322	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
323	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
324	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
325	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
326	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
327	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
328	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
329	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
330	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
331	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
332	C₄²×C₁₃₉	—	2	2	no	—
333	C₄²×C₁₃₉	—	2	4	no	—
334	C₂³×C₁₃₉	—	2	4	no	—
335	C₂³×C₁₃₉	—	2	2	no	—
336	C₂³×C₁₃₉	—	2	2	no	—
337	C₂³×C₁₃₉	—	2	16	no	—
338	C₂³×C₁₃₉	—	2	1	no	—
339	C₂³×C₁₃₉	—	2	2	no	—
340	C₂³×C₁₃₉	—	2	4	no	—
341	C₂³×C₁₃₉	—	2	2	no	—
342	C₂³×C₁₃₉	—	2	2	no	—
343	C₂³×C₁₃₉	—	2	4	no	—
344	C₂³×C₁₃₉	—	2	2	no	—
345	C₂³×C₁₃₉	—	2	2	no	—
346	C₂³×C₁₃₉	—	2	4	no	—
347	C₂³×C₁₃₉	—	2	2	no	—
348	C₂³×C₁₃₉	—	2	1	no	—
349	C₂³×C₁₃₉	—	2	4	no	—
350	C₂³×C₁₃₉	—	2	4	no	—
351	C₂³×C₁₃₉	—	2	2	no	—
352	C₂³×C₁₃₉	—	2	2	no	—
353	C₂³×C₁₃₉	—	2	2	no	—
354	C₂³×C₁₃₉	—	2	2	no	—
355	C₂³×C₁₃₉	—	2	1	no	—
356	C₂³×C₁₃₉	—	2	1	no	—
357	C₂³×C₁₃₉	—	2	4	no	—
358	C₂³×C₁₃₉	—	2	32	no	—
359	C₂³×C₁₃₉	—	2	2	no	—
360	C₂³×C₁₃₉	—	2	4	no	—
361	C₂³×C₁₃₉	—	2	4	no	—
362	C₂³×C₁₃₉	—	2	2	no	—
363	C₂³×C₁₃₉	—	2	2	no	—
364	C₂³×C₁₃₉	—	4	16	no	—
365	C₂³×C₁₃₉	—	4	16	no	—
366	C₂³×C₁₃₉	—	4	16	no	—
367	C₂³×C₁₃₉	—	4	8	no	—
368	C₂³×C₁₃₉	—	4	8	no	—
369	C₂³×C₁₃₉	—	8	8	no	—
370	C₂³×C₁₃₉	—	8	8	no	—
371	C₂³×C₁₃₉	—	8	8	no	—
372	C₂³×C₁₃₉	—	8	8	no	—
373	C₂³×C₁₃₉	—	8	8	no	—
374	C₂³×C₁₃₉	—	8	4	no	—
375	C₂³×C₁₃₉	—	8	8	no	—
376	C₂³×C₁₃₉	—	8	4	no	—
377	C₂³×C₁₃₉	—	8	8	no	—
378	C₂³×C₁₃₉	—	8	4	no	—
379	C₂³×C₁₃₉	C₂²×D₄	1	8	yes	—
380	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
381	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
382	C₂³×C₁₃₉	C₂²×D₄	1	8	yes	—
383	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
384	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	complemented
385	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
386	Q₈×C₁₃₉	—	2	8	no	—
387	Q₈×C₁₃₉	—	2	8	no	—
388	D₄×C₁₃₉	—	2	32	no	—
389	D₄×C₁₃₉	—	2	16	no	—
390	D₄×C₁₃₉	—	2	16	no	—
391	D₄×C₁₃₉	—	2	8	no	—
392	D₄×C₁₃₉	—	2	16	no	—
393	D₄×C₁₃₉	—	2	16	no	—
394	D₄×C₁₃₉	—	2	32	no	—
395	D₄×C₁₃₉	—	2	16	no	—
396	D₄×C₁₃₉	—	4	16	no	—
397	D₄×C₁₃₉	—	4	4	no	—
398	D₄×C₁₃₉	—	4	16	no	—
399	D₄×C₁₃₉	—	4	16	no	—
400	D₄×C₁₃₉	—	4	8	no	—
401	D₄×C₁₃₉	—	4	4	no	—
402	D₄×C₁₃₉	—	8	8	no	—
403	D₄×C₁₃₉	—	8	4	no	—
404	D₄×C₁₃₉	#120	1	16	yes	complemented
405	C₂×C₄×C₁₃₉	—	2	32	no	—
406	C₂×C₄×C₁₃₉	—	2	16	no	—
407	C₂×C₄×C₁₃₉	—	2	2	no	—
408	C₂×C₄×C₁₃₉	—	2	4	no	—
409	C₂×C₄×C₁₃₉	—	2	2	no	—
410	C₂×C₄×C₁₃₉	—	2	2	no	—
411	C₂×C₄×C₁₃₉	—	2	2	no	—
412	C₂×C₄×C₁₃₉	—	2	2	no	—
413	C₂×C₄×C₁₃₉	—	2	8	no	—
414	C₂×C₄×C₁₃₉	—	2	16	no	—
415	C₂×C₄×C₁₃₉	—	2	1	no	—
416	C₂×C₄×C₁₃₉	—	2	1	no	—
417	C₂×C₄×C₁₃₉	—	2	2	no	—
418	C₂×C₄×C₁₃₉	—	2	2	no	—
419	C₂×C₄×C₁₃₉	—	2	2	no	—
420	C₂×C₄×C₁₃₉	—	2	4	no	—
421	C₂×C₄×C₁₃₉	—	2	1	no	—
422	C₂×C₄×C₁₃₉	—	2	2	no	—
423	C₂×C₄×C₁₃₉	—	2	4	no	—
424	C₂×C₄×C₁₃₉	—	2	2	no	—
425	C₂×C₄×C₁₃₉	—	2	1	no	—
426	C₂×C₄×C₁₃₉	—	2	4	no	—
427	C₂×C₄×C₁₃₉	—	2	4	no	—
428	C₂×C₄×C₁₃₉	—	2	1	no	—
429	C₂×C₄×C₁₃₉	—	2	2	no	—
430	C₂×C₄×C₁₃₉	—	4	16	no	—
431	C₂×C₄×C₁₃₉	—	4	4	no	—
432	C₂×C₄×C₁₃₉	—	8	4	no	—
433	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
434	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
435	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
437	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
438	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	complemented
439	C₂²×C₁₃₉	—	2	8	no	—
440	C₂²×C₁₃₉	—	2	4	no	—
441	C₂²×C₁₃₉	—	2	8	no	—
442	C₂²×C₁₃₉	—	2	4	no	—
443	C₂²×C₁₃₉	—	2	8	no	—
444	C₂²×C₁₃₉	—	2	4	no	—
445	C₂²×C₁₃₉	—	2	2	no	—
446	C₂²×C₁₃₉	—	2	4	no	—
447	C₂²×C₁₃₉	—	2	4	no	—
448	C₂²×C₁₃₉	—	2	8	no	—
449	C₂²×C₁₃₉	—	2	2	no	—
450	C₂²×C₁₃₉	—	2	2	no	—
451	C₂²×C₁₃₉	—	2	8	no	—
452	C₂²×C₁₃₉	—	2	4	no	—
453	C₂²×C₁₃₉	—	2	2	no	—
454	C₂²×C₁₃₉	—	4	1	no	—
455	C₂²×C₁₃₉	—	4	2	no	—
456	C₂²×C₁₃₉	—	4	4	no	—
457	C₂²×C₁₃₉	—	4	2	no	—
458	C₂²×C₁₃₉	—	4	4	no	—
459	C₂²×C₁₃₉	—	4	2	no	—
460	C₂²×C₁₃₉	—	4	2	no	—
461	C₂²×C₁₃₉	—	4	2	no	—
462	C₂²×C₁₃₉	—	4	4	no	—
463	C₂²×C₁₃₉	—	4	2	no	—
464	C₂²×C₁₃₉	—	4	1	no	—
465	C₂²×C₁₃₉	—	4	2	no	—
466	C₂²×C₁₃₉	—	4	4	no	—
467	C₂²×C₁₃₉	—	4	2	no	—
468	C₂²×C₁₃₉	—	4	4	no	—
469	C₂²×C₁₃₉	—	4	2	no	—
470	C₂²×C₁₃₉	—	4	4	no	—
471	C₂²×C₁₃₉	—	4	2	no	—
472	C₂²×C₁₃₉	—	8	32	no	—
473	C₂²×C₁₃₉	—	8	16	no	—
474	C₂²×C₁₃₉	—	8	16	no	—
475	C₂²×C₁₃₉	C₂×#120	1	8	yes	—
476	C₂²×C₁₃₉	C₂³×D₄	1	2	yes	—
477	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
478	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
479	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
480	C₂²×C₁₃₉	#585	1	1	yes	characteristic
481	C₄×C₁₃₉	—	2	4	no	—
482	C₄×C₁₃₉	—	2	4	no	—
483	C₄×C₁₃₉	—	2	2	no	—
484	C₄×C₁₃₉	—	2	4	no	—
485	C₄×C₁₃₉	—	4	1	no	—
486	C₄×C₁₃₉	—	4	4	no	—
487	C₄×C₁₃₉	—	4	1	no	—
488	C₄×C₁₃₉	—	4	2	no	—
489	C₄×C₁₃₉	—	4	1	no	—
490	C₄×C₁₃₉	—	4	2	no	—
491	C₄×C₁₃₉	C₂×#120	1	4	yes	—
492	C₂×C₁₃₉	—	2	8	no	—
493	C₂×C₁₃₉	—	4	4	no	—
494	C₂×C₁₃₉	—	4	8	no	—
495	C₂×C₁₃₉	—	4	2	no	—
496	C₂×C₁₃₉	—	4	2	no	—
497	C₂×C₁₃₉	—	8	2	no	—
498	C₂×C₁₃₉	C₂²×#120	1	1	yes	characteristic
499	C₂×C₁₃₉	#3484	1	2	yes	—
500	C₂×C₁₃₉	#3488	1	1	yes	characteristic
501	C₂×C₁₃₉	#3496	1	2	yes	—
502	C₂×C₁₃₉	#3498	1	1	yes	characteristic
503	#35680	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
504	C₁₃₉	#35680	1	1	yes	characteristic, direct product factor, Sylow
505	C₂²×H(5,𝔽₂)	C₂×C₁₃₉	1	1	yes	characteristic, complemented
506	C₂×#546	C₂×C₁₃₉	1	1	yes	characteristic, complemented
507	C₂×D₄²	C₂×C₁₃₉	1	2	yes	complemented
508	#2615	C₂×C₁₃₉	1	1	yes	characteristic, complemented
509	#2613	C₂×C₁₃₉	1	2	yes	complemented
510	#2433	C₂×C₁₃₉	1	1	yes	characteristic, complemented
511	#2431	C₂×C₁₃₉	1	2	yes	complemented
512	#2430	C₂×C₁₃₉	1	2	yes	complemented
513	#2410	C₂×C₁₃₉	1	4	yes	complemented
514	#2408	C₂×C₁₃₉	1	1	yes	characteristic, complemented
515	#2407	C₂×C₁₃₉	1	2	yes	complemented
516	#2404	C₂×C₁₃₉	1	2	yes	complemented
517	#2403	C₂×C₁₃₉	1	4	yes	complemented
518	#2388	C₂×C₁₃₉	1	1	yes	characteristic, complemented
519	C₂×#392	C₂×C₁₃₉	1	2	yes	complemented
520	#2339	C₂×C₁₃₉	1	1	yes	characteristic, complemented
521	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
522	C₂×H(5,𝔽₂)	—	2	8	no	—
523	C₂×H(5,𝔽₂)	—	2	16	no	—
524	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
525	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
526	C₂²×#41	C₂²×C₁₃₉	1	2	yes	complemented
527	C₂²×#41	C₂²×C₁₃₉	1	2	yes	complemented
528	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
529	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	complemented
530	C₂³×D₄	C₂²×C₁₃₉	1	4	yes	complemented
531	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
532	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
533	C₂³×D₄	C₂²×C₁₃₉	1	4	yes	complemented
534	#546	—	2	8	no	—
535	D₄²	—	2	16	no	—
536	C₂×#127	C₂²×C₁₃₉	1	2	yes	complemented
537	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
538	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
539	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
540	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
541	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
542	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
543	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
544	C₂×#121	C₂²×C₁₃₉	1	4	yes	complemented
545	C₂×#120	C₂²×C₁₃₉	1	4	yes	complemented
546	C₂×#120	C₂²×C₁₃₉	1	2	yes	complemented
547	C₂×#120	C₂²×C₁₃₉	1	4	yes	complemented
548	C₂×#120	C₂²×C₁₃₉	1	2	yes	complemented
549	C₂×#120	C₂²×C₁₃₉	1	4	yes	complemented
550	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
551	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
552	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
553	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
554	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
555	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
556	#395	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
557	#394	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
558	#394	C₂²×C₁₃₉	1	4	yes	complemented
559	#394	C₂²×C₁₃₉	1	2	yes	complemented
560	#394	C₂²×C₁₃₉	1	2	yes	complemented
561	#393	C₂²×C₁₃₉	1	2	yes	complemented
562	#393	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
563	#392	C₂²×C₁₃₉	1	2	yes	complemented
564	#392	C₂²×C₁₃₉	1	4	yes	complemented
565	#392	C₂²×C₁₃₉	1	2	yes	complemented
566	#392	C₂²×C₁₃₉	1	4	yes	complemented
567	#392	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
568	#392	C₂²×C₁₃₉	1	4	yes	complemented
569	#392	C₂²×C₁₃₉	1	2	yes	complemented
570	#392	C₂²×C₁₃₉	1	4	yes	complemented
571	#392	C₂²×C₁₃₉	1	2	yes	complemented
572	#392	C₂²×C₁₃₉	1	2	yes	complemented
573	#391	C₂²×C₁₃₉	1	2	yes	complemented
574	#390	C₂²×C₁₃₉	1	2	yes	complemented
575	#390	C₂²×C₁₃₉	1	2	yes	complemented
576	#386	C₂²×C₁₃₉	1	4	yes	complemented
577	#386	C₂²×C₁₃₉	1	4	yes	complemented
578	#386	C₂²×C₁₃₉	1	4	yes	complemented
579	#386	C₂²×C₁₃₉	1	4	yes	complemented
580	#386	C₂²×C₁₃₉	1	4	yes	complemented
581	#386	C₂²×C₁₃₉	1	4	yes	complemented
582	#385	C₂²×C₁₃₉	1	4	yes	complemented
583	#381	C₂²×C₁₃₉	1	2	yes	complemented
584	#380	C₂²×C₁₃₉	1	2	yes	complemented
585	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
586	#379	C₂²×C₁₃₉	1	4	yes	complemented
587	#379	C₂²×C₁₃₉	1	2	yes	complemented
588	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
589	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
590	C₂×#95	C₂²×C₁₃₉	1	2	yes	complemented
591	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
592	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
593	C₂⁵	C₂³×C₁₃₉	1	4	yes	—
594	H(5,𝔽₂)	—	2	128	no	—
595	C₂×#41	—	2	8	no	—
596	C₂×#41	—	2	8	no	—
597	C₂×#41	—	2	16	no	—
598	C₂×#41	—	2	8	no	—
599	C₂×#41	—	2	8	no	—
600	C₂×#41	—	2	4	no	—
601	C₂×#41	—	2	8	no	—
602	C₂×#41	—	2	8	no	—
603	C₂×#41	D₄×C₁₃₉	1	8	yes	complemented
604	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
605	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
606	C₂²×D₄	—	2	16	no	—
607	C₂²×D₄	—	2	16	no	—
608	C₂²×D₄	—	2	8	no	—
609	C₂²×D₄	—	2	8	no	—
610	C₂²×D₄	—	2	16	no	—
611	C₂²×D₄	—	2	16	no	—
612	C₂²×D₄	—	2	8	no	—
613	C₂²×D₄	—	2	16	no	—
614	C₂²×D₄	—	2	8	no	—
615	C₂²×D₄	—	2	4	no	—
616	C₂²×D₄	—	2	8	no	—
617	C₂²×D₄	—	2	4	no	—
618	C₂²×D₄	—	4	8	no	—
619	C₂²×D₄	—	4	8	no	—
620	C₂²×D₄	D₄×C₁₃₉	1	16	yes	complemented
621	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
622	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
623	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
624	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
625	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
626	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
627	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
628	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
629	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
630	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
631	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
632	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
633	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
634	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
635	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
636	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
637	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
638	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
639	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
640	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
641	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
642	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
643	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
644	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
645	#127	—	2	8	no	—
646	#124	—	2	4	no	—
647	#123	—	2	8	no	—
648	C₂²⋊Q₈	—	2	4	no	—
649	#121	—	2	8	no	—
650	#121	—	2	16	no	—
651	#121	—	2	8	no	—
652	#121	—	2	8	no	—
653	#121	—	2	4	no	—
654	#120	—	2	16	no	—
655	#120	—	2	16	no	—
656	#120	—	2	8	no	—
657	#120	—	4	8	no	—
658	#120	—	4	4	no	—
659	C₄×D₄	—	2	8	no	—
660	C₄×D₄	—	2	4	no	—
661	C₄×D₄	—	2	8	no	—
662	C₄×D₄	—	2	4	no	—
663	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
668	C₂×C₂²⋊C₄	—	2	8	no	—
669	C₂×C₂²⋊C₄	—	4	8	no	—
670	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
671	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
681	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
691	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
693	#95	C₂³×C₁₃₉	1	1	yes	characteristic
694	#95	C₂³×C₁₃₉	1	2	yes	—
695	#95	C₂³×C₁₃₉	1	4	yes	—
696	#95	C₂³×C₁₃₉	1	1	yes	characteristic
697	#95	C₂³×C₁₃₉	1	2	yes	—
698	#95	C₂³×C₁₃₉	1	2	yes	—
699	#95	C₂³×C₁₃₉	1	4	yes	—
700	#95	C₂³×C₁₃₉	1	4	yes	—
701	C₂⁴	—	2	8	no	—
702	C₂⁴	—	2	4	no	—
703	C₂⁴	—	2	8	no	—
704	C₂⁴	—	2	8	no	—
705	C₂⁴	—	2	4	no	—
706	C₂⁴	—	2	4	no	—
707	C₂⁴	—	2	8	no	—
708	C₂⁴	—	4	4	no	—
709	C₂⁴	—	4	4	no	—
710	C₂⁴	—	4	4	no	—
711	C₂⁴	—	4	4	no	—
712	C₂⁴	—	4	4	no	—
713	C₂⁴	—	4	2	no	—
714	C₂⁴	—	4	4	no	—
715	C₂⁴	—	4	2	no	—
716	C₂⁴	—	4	2	no	—
717	C₂⁴	C₂×D₄×C₁₃₉	1	16	yes	complemented
718	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
719	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
720	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
721	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
722	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
723	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
724	#41	—	2	64	no	—
725	#41	—	2	64	no	—
726	#41	—	2	32	no	—
727	#41	—	2	32	no	—
728	C₂×Q₈	—	2	4	no	—
729	C₂×Q₈	—	2	2	no	—
730	C₂×Q₈	—	2	4	no	—
731	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	complemented
732	C₂×D₄	—	2	128	no	—
733	C₂×D₄	—	2	64	no	—
734	C₂×D₄	—	2	32	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	8	no	—
737	C₂×D₄	—	2	8	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	8	no	—
740	C₂×D₄	—	2	4	no	—
741	C₂×D₄	—	2	4	no	—
742	C₂×D₄	—	2	8	no	—
743	C₂×D₄	—	2	8	no	—
744	C₂×D₄	—	2	8	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	2	64	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	8	no	—
749	C₂×D₄	—	2	8	no	—
750	C₂×D₄	—	2	8	no	—
751	C₂×D₄	—	2	4	no	—
752	C₂×D₄	—	2	8	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	8	no	—
755	C₂×D₄	—	2	8	no	—
756	C₂×D₄	—	2	4	no	—
757	C₂×D₄	—	2	8	no	—
758	C₂×D₄	—	2	4	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	4	no	—
761	C₂×D₄	—	2	4	no	—
762	C₂×D₄	—	2	4	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	4	no	—
765	C₂×D₄	—	2	4	no	—
766	C₂×D₄	—	2	8	no	—
767	C₂×D₄	—	4	4	no	—
768	C₂×D₄	—	4	4	no	—
769	C₂×D₄	—	4	4	no	—
770	C₂×D₄	—	4	4	no	—
771	C₂×D₄	—	4	1	no	—
772	C₂×D₄	—	4	4	no	—
773	C₂×D₄	—	4	4	no	—
774	C₂×D₄	—	4	4	no	—
775	C₂×D₄	—	4	64	no	—
776	C₂×D₄	—	4	16	no	—
777	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
778	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
779	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	complemented
780	C₂×D₄	C₂×D₄×C₁₃₉	1	16	yes	complemented
781	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	complemented
782	C₂²×C₄	—	2	8	no	—
783	C₂²×C₄	—	2	8	no	—
784	C₂²×C₄	—	2	8	no	—
785	C₂²×C₄	—	2	8	no	—
786	C₂²×C₄	—	2	4	no	—
787	C₂²×C₄	—	2	4	no	—
788	C₂²×C₄	—	2	4	no	—
789	C₂²×C₄	—	2	8	no	—
790	C₂²×C₄	—	2	4	no	—
791	C₂²×C₄	—	2	4	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	8	no	—
794	C₂²×C₄	—	4	4	no	—
795	C₂²×C₄	—	4	4	no	—
796	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	complemented
797	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	complemented
798	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	complemented
799	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
801	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
804	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
807	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
809	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
810	C₄⋊C₄	—	2	4	no	—
811	C₄⋊C₄	—	2	4	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	8	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	8	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	8	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	8	no	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	4	4	no	—
831	C₂²⋊C₄	—	4	4	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	4	no	—
834	C₂²⋊C₄	—	4	4	no	—
835	C₂²⋊C₄	—	4	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	4	no	—
838	C₂³	—	2	4	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	16	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	4	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	4	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	4	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	4	no	—
854	C₂³	—	2	4	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	4	no	—
862	C₂³	—	2	32	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	4	no	—
865	C₂³	—	2	4	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	4	16	no	—
869	C₂³	—	4	16	no	—
870	C₂³	—	4	16	no	—
871	C₂³	—	4	8	no	—
872	C₂³	—	4	8	no	—
873	C₂³	—	8	8	no	—
874	C₂³	—	8	8	no	—
875	C₂³	—	8	8	no	—
876	C₂³	—	8	8	no	—
877	C₂³	—	8	8	no	—
878	C₂³	—	8	4	no	—
879	C₂³	—	8	8	no	—
880	C₂³	—	8	4	no	—
881	C₂³	—	8	8	no	—
882	C₂³	—	8	4	no	—
883	C₂³	C₂²×D₄×C₁₃₉	1	8	yes	—
884	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
885	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
886	C₂³	C₂²×D₄×C₁₃₉	1	8	yes	—
887	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
888	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	complemented
889	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
890	Q₈	—	2	8	no	—
891	Q₈	—	2	8	no	—
892	D₄	—	2	32	no	—
893	D₄	—	2	16	no	—
894	D₄	—	2	16	no	—
895	D₄	—	2	8	no	—
896	D₄	—	2	16	no	—
897	D₄	—	2	16	no	—
898	D₄	—	2	32	no	—
899	D₄	—	2	16	no	—
900	D₄	—	4	16	no	—
901	D₄	—	4	16	no	—
902	D₄	—	4	4	no	—
903	D₄	—	4	16	no	—
904	D₄	—	4	8	no	—
905	D₄	—	4	4	no	—
906	D₄	—	8	8	no	—
907	D₄	—	8	4	no	—
908	D₄	#120×C₁₃₉	1	16	yes	complemented
909	C₂×C₄	—	2	32	no	—
910	C₂×C₄	—	2	16	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	4	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	8	no	—
918	C₂×C₄	—	2	16	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	4	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	4	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	4	no	—
931	C₂×C₄	—	2	4	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	4	16	no	—
935	C₂×C₄	—	4	4	no	—
936	C₂×C₄	—	8	4	no	—
937	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
938	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
939	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
940	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
941	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
942	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	complemented
943	C₂²	—	2	8	no	—
944	C₂²	—	2	4	no	—
945	C₂²	—	2	8	no	—
946	C₂²	—	2	4	no	—
947	C₂²	—	2	8	no	—
948	C₂²	—	2	4	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	4	no	—
951	C₂²	—	2	4	no	—
952	C₂²	—	2	8	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	2	no	—
955	C₂²	—	2	8	no	—
956	C₂²	—	2	4	no	—
957	C₂²	—	2	2	no	—
958	C₂²	—	4	1	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	4	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	4	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	2	no	—
966	C₂²	—	4	4	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	1	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	4	no	—
971	C₂²	—	4	2	no	—
972	C₂²	—	4	4	no	—
973	C₂²	—	4	2	no	—
974	C₂²	—	4	4	no	—
975	C₂²	—	4	2	no	—
976	C₂²	—	8	32	no	—
977	C₂²	—	8	16	no	—
978	C₂²	—	8	16	no	—
979	C₂²	C₂×#120×C₁₃₉	1	8	yes	—
980	C₂²	C₂³×D₄×C₁₃₉	1	2	yes	—
981	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
982	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
983	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
984	C₂²	#585×C₁₃₉	1	1	yes	characteristic
985	C₄	—	2	4	no	—
986	C₄	—	2	4	no	—
987	C₄	—	2	2	no	—
988	C₄	—	2	4	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	4	no	—
991	C₄	—	4	1	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	2	no	—
995	C₄	C₂×#120×C₁₃₉	1	4	yes	—
996	C₂	—	2	8	no	—
997	C₂	—	4	4	no	—
998	C₂	—	4	8	no	—
999	C₂	—	4	2	no	—
1000	C₂	—	4	2	no	—
1001	C₂	—	8	2	no	—
1002	C₂	C₂²×#120×C₁₃₉	1	1	yes	characteristic
1003	C₂	#3484×C₁₃₉	1	2	yes	—
1004	C₂	#3488×C₁₃₉	1	1	yes	characteristic
1005	C₂	#3496×C₁₃₉	1	2	yes	—
1006	C₂	#3498×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. C₂²×H(5,𝔽₂)×C₁₃₉	C₂	semidirect
2. C₂×#546×C₁₃₉	C₂	semidirect
3. C₂×D₄²×C₁₃₉	C₂	semidirect
4. #2615×C₁₃₉	C₂	semidirect
5. #2613×C₁₃₉	C₂	semidirect
6. #2433×C₁₃₉	C₂	semidirect
7. #2431×C₁₃₉	C₂	semidirect
8. #2430×C₁₃₉	C₂	semidirect
9. #2410×C₁₃₉	C₂	semidirect
10. #2408×C₁₃₉	C₂	semidirect
11. #2407×C₁₃₉	C₂	semidirect
12. #2404×C₁₃₉	C₂	semidirect
13. #2403×C₁₃₉	C₂	semidirect
14. #2388×C₁₃₉	C₂	semidirect
15. C₂×#392×C₁₃₉	C₂	semidirect
16. #2339×C₁₃₉	C₂	semidirect
17. D₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
21. C₂²×#41×C₁₃₉	C₂²	semidirect
22. C₂²×#41×C₁₃₉	C₂²	semidirect
23. C₂²×#41×C₁₃₉	C₂²	semidirect
25. C₂³×D₄×C₁₃₉	C₂²	semidirect
26. C₂³×D₄×C₁₃₉	C₂²	semidirect
27. C₂³×D₄×C₁₃₉	C₂²	semidirect
28. C₂³×D₄×C₁₃₉	C₂²	semidirect
29. C₂³×D₄×C₁₃₉	C₂²	semidirect
32. C₂×#127×C₁₃₉	C₂²	semidirect
33. C₂×#124×C₁₃₉	C₂²	semidirect
34. C₂×#123×C₁₃₉	C₂²	semidirect
35. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
36. C₂×#121×C₁₃₉	C₂²	semidirect
37. C₂×#121×C₁₃₉	C₂²	semidirect
38. C₂×#121×C₁₃₉	C₂²	semidirect
39. C₂×#121×C₁₃₉	C₂²	semidirect
40. C₂×#121×C₁₃₉	C₂²	semidirect
41. C₂×#120×C₁₃₉	C₂²	semidirect
42. C₂×#120×C₁₃₉	C₂²	semidirect
43. C₂×#120×C₁₃₉	C₂²	semidirect
44. C₂×#120×C₁₃₉	C₂²	semidirect
45. C₂×#120×C₁₃₉	C₂²	semidirect
46. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
47. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
48. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
49. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
50. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
51. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
52. #395×C₁₃₉	C₂²	semidirect
53. #394×C₁₃₉	C₂²	semidirect
54. #394×C₁₃₉	C₂²	semidirect
55. #394×C₁₃₉	C₂²	semidirect
56. #394×C₁₃₉	C₂²	semidirect
57. #393×C₁₃₉	C₂²	semidirect
58. #393×C₁₃₉	C₂²	semidirect
59. #392×C₁₃₉	C₂²	semidirect
60. #392×C₁₃₉	C₂²	semidirect
61. #392×C₁₃₉	C₂²	semidirect
62. #392×C₁₃₉	C₂²	semidirect
63. #392×C₁₃₉	C₂²	semidirect
64. #392×C₁₃₉	C₂²	semidirect
65. #392×C₁₃₉	C₂²	semidirect
66. #392×C₁₃₉	C₂²	semidirect
67. #392×C₁₃₉	C₂²	semidirect
68. #392×C₁₃₉	C₂²	semidirect
69. #391×C₁₃₉	C₂²	semidirect
70. #390×C₁₃₉	C₂²	semidirect
71. #390×C₁₃₉	C₂²	semidirect
72. #386×C₁₃₉	C₂²	semidirect
73. #386×C₁₃₉	C₂²	semidirect
74. #386×C₁₃₉	C₂²	semidirect
75. #386×C₁₃₉	C₂²	semidirect
76. #386×C₁₃₉	C₂²	semidirect
77. #386×C₁₃₉	C₂²	semidirect
78. #385×C₁₃₉	C₂²	semidirect
79. #381×C₁₃₉	C₂²	semidirect
80. #380×C₁₃₉	C₂²	semidirect
81. #380×C₁₃₉	C₂²	semidirect
82. #379×C₁₃₉	C₂²	semidirect
83. #379×C₁₃₉	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
85. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
86. C₂×#95×C₁₃₉	C₂²	semidirect
99. C₂×#41×C₁₃₉	D₄	semidirect
116. C₂²×D₄×C₁₃₉	D₄	semidirect
213. C₂⁴×C₁₃₉	C₂×D₄	semidirect
227. C₂×Q₈×C₁₃₉	C₂×D₄	semidirect
275. C₂×D₄×C₁₃₉	C₂×D₄	semidirect
276. C₂×D₄×C₁₃₉	C₂×D₄	semidirect
277. C₂×D₄×C₁₃₉	C₂×D₄	semidirect
292. C₂²×C₄×C₁₃₉	C₂×D₄	semidirect
293. C₂²×C₄×C₁₃₉	C₂×D₄	semidirect
294. C₂²×C₄×C₁₃₉	C₂×D₄	semidirect
384. C₂³×C₁₃₉	H(5,𝔽₂)	semidirect
404. D₄×C₁₃₉	#120	semidirect
438. C₂×C₄×C₁₃₉	H(5,𝔽₂)	semidirect
503. #35680	C₁₃₉	direct (N × H)
504. C₁₃₉	#35680	direct (N × H)
505. C₂²×H(5,𝔽₂)	C₂×C₁₃₉	semidirect
506. C₂×#546	C₂×C₁₃₉	semidirect
507. C₂×D₄²	C₂×C₁₃₉	semidirect
508. #2615	C₂×C₁₃₉	semidirect
509. #2613	C₂×C₁₃₉	semidirect
510. #2433	C₂×C₁₃₉	semidirect
511. #2431	C₂×C₁₃₉	semidirect
512. #2430	C₂×C₁₃₉	semidirect
513. #2410	C₂×C₁₃₉	semidirect
514. #2408	C₂×C₁₃₉	semidirect
515. #2407	C₂×C₁₃₉	semidirect
516. #2404	C₂×C₁₃₉	semidirect
517. #2403	C₂×C₁₃₉	semidirect
518. #2388	C₂×C₁₃₉	semidirect
519. C₂×#392	C₂×C₁₃₉	semidirect
520. #2339	C₂×C₁₃₉	semidirect
521. D₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
525. C₂²×#41	C₂²×C₁₃₉	semidirect
526. C₂²×#41	C₂²×C₁₃₉	semidirect
527. C₂²×#41	C₂²×C₁₃₉	semidirect
529. C₂³×D₄	C₂²×C₁₃₉	semidirect
530. C₂³×D₄	C₂²×C₁₃₉	semidirect
531. C₂³×D₄	C₂²×C₁₃₉	semidirect
532. C₂³×D₄	C₂²×C₁₃₉	semidirect
533. C₂³×D₄	C₂²×C₁₃₉	semidirect
536. C₂×#127	C₂²×C₁₃₉	semidirect
537. C₂×#124	C₂²×C₁₃₉	semidirect
538. C₂×#123	C₂²×C₁₃₉	semidirect
539. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
540. C₂×#121	C₂²×C₁₃₉	semidirect
541. C₂×#121	C₂²×C₁₃₉	semidirect
542. C₂×#121	C₂²×C₁₃₉	semidirect
543. C₂×#121	C₂²×C₁₃₉	semidirect
544. C₂×#121	C₂²×C₁₃₉	semidirect
545. C₂×#120	C₂²×C₁₃₉	semidirect
546. C₂×#120	C₂²×C₁₃₉	semidirect
547. C₂×#120	C₂²×C₁₃₉	semidirect
548. C₂×#120	C₂²×C₁₃₉	semidirect
549. C₂×#120	C₂²×C₁₃₉	semidirect
550. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
551. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
552. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
553. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
554. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
555. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
556. #395	C₂²×C₁₃₉	semidirect
557. #394	C₂²×C₁₃₉	semidirect
558. #394	C₂²×C₁₃₉	semidirect
559. #394	C₂²×C₁₃₉	semidirect
560. #394	C₂²×C₁₃₉	semidirect
561. #393	C₂²×C₁₃₉	semidirect
562. #393	C₂²×C₁₃₉	semidirect
563. #392	C₂²×C₁₃₉	semidirect
564. #392	C₂²×C₁₃₉	semidirect
565. #392	C₂²×C₁₃₉	semidirect
566. #392	C₂²×C₁₃₉	semidirect
567. #392	C₂²×C₁₃₉	semidirect
568. #392	C₂²×C₁₃₉	semidirect
569. #392	C₂²×C₁₃₉	semidirect
570. #392	C₂²×C₁₃₉	semidirect
571. #392	C₂²×C₁₃₉	semidirect
572. #392	C₂²×C₁₃₉	semidirect
573. #391	C₂²×C₁₃₉	semidirect
574. #390	C₂²×C₁₃₉	semidirect
575. #390	C₂²×C₁₃₉	semidirect
576. #386	C₂²×C₁₃₉	semidirect
577. #386	C₂²×C₁₃₉	semidirect
578. #386	C₂²×C₁₃₉	semidirect
579. #386	C₂²×C₁₃₉	semidirect
580. #386	C₂²×C₁₃₉	semidirect
581. #386	C₂²×C₁₃₉	semidirect
582. #385	C₂²×C₁₃₉	semidirect
583. #381	C₂²×C₁₃₉	semidirect
584. #380	C₂²×C₁₃₉	semidirect
585. #380	C₂²×C₁₃₉	semidirect
586. #379	C₂²×C₁₃₉	semidirect
587. #379	C₂²×C₁₃₉	semidirect
588. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
589. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
590. C₂×#95	C₂²×C₁₃₉	semidirect
603. C₂×#41	D₄×C₁₃₉	semidirect
620. C₂²×D₄	D₄×C₁₃₉	semidirect
717. C₂⁴	C₂×D₄×C₁₃₉	semidirect
731. C₂×Q₈	C₂×D₄×C₁₃₉	semidirect
779. C₂×D₄	C₂×D₄×C₁₃₉	semidirect
780. C₂×D₄	C₂×D₄×C₁₃₉	semidirect
781. C₂×D₄	C₂×D₄×C₁₃₉	semidirect
796. C₂²×C₄	C₂×D₄×C₁₃₉	semidirect
797. C₂²×C₄	C₂×D₄×C₁₃₉	semidirect
798. C₂²×C₄	C₂×D₄×C₁₃₉	semidirect
888. C₂³	H(5,𝔽₂)×C₁₃₉	semidirect
908. D₄	#120×C₁₃₉	semidirect
942. C₂×C₄	H(5,𝔽₂)×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×H(5,𝔽₂)×C₁₃₉	2
C₂×#546×C₁₃₉	2
C₂×D₄²×C₁₃₉	2
#2615×C₁₃₉	2
#2613×C₁₃₉	2
#2433×C₁₃₉	2
#2431×C₁₃₉	2
#2430×C₁₃₉	2
#2410×C₁₃₉	2
#2408×C₁₃₉	2
#2407×C₁₃₉	2
#2404×C₁₃₉	2
#2403×C₁₃₉	2
#2388×C₁₃₉	2
C₂×#392×C₁₃₉	2
#2339×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
#35680	139

Subgroups — C139×#35680 #48030276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35680 #48030276