Subgroups — C₂×#2428×C₁₃₉ #48029274

Order 35584.

5062 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle	C₂⁴×C₁₃₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂²×#127×C₁₃₉	C₂	semidirect
2. C₂²×#121×C₁₃₉	C₂	semidirect
3. C₂²×#121×C₁₃₉	C₂	semidirect
4. C₂²×#121×C₁₃₉	C₂	semidirect
5. C₂²×C₄×D₄×C₁₃₉	C₂	semidirect
6. #2428×C₁₃₉	C₂	direct (N × H)
7. C₂×#394×C₁₃₉	C₂	semidirect
8. C₂×#392×C₁₃₉	C₂	semidirect
9. C₂×#390×C₁₃₉	C₂	semidirect
10. C₂×#389×C₁₃₉	C₂	semidirect
11. C₂×#386×C₁₃₉	C₂	semidirect
12. C₂×C₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
22. C₂×#127×C₁₃₉	C₂²	semidirect
26. C₂×#121×C₁₃₉	C₂²	semidirect
27. C₂×#121×C₁₃₉	C₂²	semidirect
28. C₂×#121×C₁₃₉	C₂²	semidirect
30. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
43. #394×C₁₃₉	C₂²	semidirect
44. #392×C₁₃₉	C₂²	semidirect
45. #390×C₁₃₉	C₂²	semidirect
46. #389×C₁₃₉	C₂²	semidirect
47. #386×C₁₃₉	C₂²	semidirect
48. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
72. C₂²×D₄×C₁₃₉	D₄	semidirect
102. C₂×C₄⋊C₄×C₁₃₉	D₄	semidirect
112. C₂×C₂²⋊C₄×C₁₃₉	D₄	semidirect
175. C₂×D₄×C₁₃₉	C₂×D₄	semidirect
218. C₄⋊C₄×C₁₃₉	C₂×D₄	semidirect
225. C₂²⋊C₄×C₁₃₉	C₂×D₄	semidirect
310. C₂×C₄×C₁₃₉	#121	semidirect
363. C₄×C₁₃₉	C₂×#121	semidirect
367. C₂×C₁₃₉	#2428	direct (N × H)
375. C₂×#2428	C₁₃₉	direct (N × H)
376. C₁₃₉	C₂×#2428	direct (N × H)
377. C₂²×#127	C₂×C₁₃₉	semidirect
378. C₂²×#121	C₂×C₁₃₉	semidirect
379. C₂²×#121	C₂×C₁₃₉	semidirect
380. C₂²×#121	C₂×C₁₃₉	semidirect
381. C₂²×C₄×D₄	C₂×C₁₃₉	semidirect
382. #2428	C₂×C₁₃₉	direct (N × H)
383. C₂×#394	C₂×C₁₃₉	semidirect
384. C₂×#392	C₂×C₁₃₉	semidirect
385. C₂×#390	C₂×C₁₃₉	semidirect
386. C₂×#389	C₂×C₁₃₉	semidirect
387. C₂×#386	C₂×C₁₃₉	semidirect
388. C₂×C₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
398. C₂×#127	C₂²×C₁₃₉	semidirect
402. C₂×#121	C₂²×C₁₃₉	semidirect
403. C₂×#121	C₂²×C₁₃₉	semidirect
404. C₂×#121	C₂²×C₁₃₉	semidirect
406. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
419. #394	C₂²×C₁₃₉	semidirect
420. #392	C₂²×C₁₃₉	semidirect
421. #390	C₂²×C₁₃₉	semidirect
422. #389	C₂²×C₁₃₉	semidirect
423. #386	C₂²×C₁₃₉	semidirect
424. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
448. C₂²×D₄	D₄×C₁₃₉	semidirect
478. C₂×C₄⋊C₄	D₄×C₁₃₉	semidirect
488. C₂×C₂²⋊C₄	D₄×C₁₃₉	semidirect
551. C₂×D₄	C₂×D₄×C₁₃₉	semidirect
594. C₄⋊C₄	C₂×D₄×C₁₃₉	semidirect
601. C₂²⋊C₄	C₂×D₄×C₁₃₉	semidirect
686. C₂×C₄	#121×C₁₃₉	semidirect
739. C₄	C₂×#121×C₁₃₉	semidirect
743. C₂	#2428×C₁₃₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#127×C₁₃₉	2
C₂²×#121×C₁₃₉	2
C₂²×C₄×D₄×C₁₃₉	2
#2428×C₁₃₉	2
C₂×#394×C₁₃₉	2
C₂×#392×C₁₃₉	2
C₂×#390×C₁₃₉	2
C₂×#389×C₁₃₉	2
C₂×#386×C₁₃₉	2
C₂×C₄×C₂²⋊C₄×C₁₃₉	2
C₂×#2428	139

Subgroups — C2×#2428×C139 #48029274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2428×C₁₃₉ #48029274