Subgroups — #532×D₁₃₉ #31819681

Order 17792.

1728 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₃₉	C₂	1	2	yes	maximal, complemented
2	#22581504	C₂	1	1	yes	maximal, characteristic, complemented
3	#22581503	C₂	1	1	yes	maximal, characteristic, complemented
4	#22581502	C₂	1	2	yes	maximal, complemented
5	#22581501	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581500	C₂	1	4	yes	maximal, complemented
7	#22581499	C₂	1	2	yes	maximal, complemented
8	#22581498	C₂	1	4	yes	maximal, complemented
9	C₄⋊Q₈×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#127×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#124×D₁₃₉	C₂	1	2	yes	maximal, complemented
12	#121×D₁₃₉	C₂	1	4	yes	maximal, complemented
13	C₄×D₄×D₁₃₉	C₂	1	4	yes	maximal, complemented
14	C₂×C₄²×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#532×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14555786	C₂²	1	2	yes	complemented
17	C₂×#14555785	C₂²	1	2	yes	complemented
18	C₂×#14555785	C₂²	1	4	yes	complemented
19	C₂×#14555784	C₂²	1	4	yes	complemented
20	C₂×#14555784	C₂²	1	2	yes	complemented
21	#41×D₁₃₉	—	2	16	no	—
22	C₂×Q₈×D₁₃₉	C₂²	1	2	yes	—
23	C₂×D₄×D₁₃₉	C₂²	1	4	yes	—
24	C₂×D₄×D₁₃₉	C₂²	1	2	yes	—
25	C₂×D₄×D₁₃₉	C₂²	1	4	yes	—
26	C₂²×C₄×D₁₃₉	C₂²	1	4	yes	—
27	C₂²×C₄×D₁₃₉	C₂²	1	2	yes	—
28	C₂²×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
29	#17984842	C₂²	1	1	yes	characteristic, complemented
30	#17984841	C₂²	1	4	yes	complemented
31	#17984840	C₂²	1	2	yes	complemented
32	#17984839	C₂²	1	1	yes	characteristic, complemented
33	#17984838	C₂²	1	4	yes	complemented
34	#17984838	C₂²	1	2	yes	complemented
35	#17984831	C₂²	1	2	yes	complemented
36	#17984830	C₂²	1	2	yes	complemented
37	#17984829	C₂²	1	2	yes	complemented
38	#17984828	C₂²	1	8	yes	complemented
39	#17984817	C₂²	1	4	yes	complemented
40	#17984816	C₂²	1	4	yes	complemented
41	#17984815	C₂²	1	8	yes	complemented
42	#17984814	C₂²	1	8	yes	complemented
43	#17984813	C₂²	1	4	yes	complemented
44	C₄×D₅₅₆	C₂²	1	4	yes	complemented
45	D₄×Dic₁₃₉	C₂²	1	4	yes	complemented
46	#17984804	C₂²	1	4	yes	complemented
47	C₄×C₂²⋊D₁₃₉	C₂²	1	8	yes	complemented
48	(C₂²⋊D₁₃₉)⋊C₄	C₂²	1	8	yes	complemented
49	C₄⋊C₄×D₁₃₉	C₂²	1	4	yes	—
50	C₂²⋊C₄×D₁₃₉	C₂²	1	8	yes	—
51	C₂×C₄×Dic₁₃₉	C₂²	1	2	yes	complemented
52	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic, complemented
53	C₄²×D₁₃₉	C₂²	1	2	yes	—
54	C₄²×D₁₃₉	C₂²	1	1	yes	characteristic
55	C₄²×D₁₃₉	C₂²	1	1	yes	characteristic
56	C₄²×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
57	C₄²×D₁₃₉	C₂²	1	2	yes	complemented
58	C₄²×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
59	C₂×#41×C₁₃₉	C₂²	1	2	yes	complemented
60	C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
61	#127×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
62	#124×C₁₃₉	C₂²	1	2	yes	complemented
63	#121×C₁₃₉	C₂²	1	4	yes	complemented
64	C₄×D₄×C₁₃₉	C₂²	1	4	yes	complemented
65	C₂×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
66	C₂³×D₁₃₉	C₂³	1	4	yes	—
67	C₂³×D₁₃₉	C₂³	1	1	yes	characteristic
68	#14555786	—	2	8	no	—
69	#14555785	—	2	16	no	—
70	#14555785	—	2	8	no	—
71	#14555784	—	2	16	no	—
72	#14555784	—	2	8	no	—
73	C₂×Dic₂₇₈	C₂³	1	4	yes	—
74	C₂×Dic₂₇₈	C₂³	1	2	yes	—
75	Q₈×D₁₃₉	—	2	8	no	—
76	C₂×D₅₅₆	C₂³	1	4	yes	—
77	C₂×D₅₅₆	C₂³	1	4	yes	—
78	C₂×D₅₅₆	C₂³	1	2	yes	—
79	C₂×C₂²⋊D₁₃₉	C₂³	1	8	yes	—
80	C₂×C₂²⋊D₁₃₉	C₂³	1	4	yes	—
81	C₂×C₂²⋊D₁₃₉	C₂³	1	4	yes	—
82	C₂×C₂²⋊D₁₃₉	C₂³	1	4	yes	—
83	D₄×D₁₃₉	—	2	16	no	—
84	D₄×D₁₃₉	—	2	8	no	—
85	D₄×D₁₃₉	—	2	16	no	—
86	C₂²×Dic₁₃₉	C₂³	1	2	yes	—
87	C₂²×Dic₁₃₉	C₂³	1	4	yes	—
88	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
89	C₂×C₄×D₁₃₉	—	2	16	no	—
90	C₂×C₄×D₁₃₉	—	2	8	no	—
91	C₂×C₄×D₁₃₉	D₄	1	8	yes	complemented
92	C₂×C₄×D₁₃₉	C₂³	1	2	yes	—
93	C₂×C₄×D₁₃₉	C₂³	1	2	yes	—
94	C₂×C₄×D₁₃₉	C₂³	1	2	yes	—
95	C₂×C₄×D₁₃₉	C₂³	1	4	yes	—
96	C₂×C₄×D₁₃₉	C₂³	1	4	yes	—
97	C₂×C₄×D₁₃₉	C₂³	1	4	yes	—
98	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₁₃₉	C₂³	1	2	yes	—
103	C₄⋊Dic₁₃₉	C₂³	1	4	yes	—
104	Dic₁₃₉⋊C₄	C₂³	1	8	yes	—
105	C₂²⋊Dic₁₃₉	C₂³	1	8	yes	—
106	(C₂×D₁₃₉)⋊C₄	C₂³	1	8	yes	—
107	(C₂×D₁₃₉)⋊C₄	C₂³	1	8	yes	—
108	C₄×Dic₁₃₉	C₂³	1	2	yes	—
109	C₄×Dic₁₃₉	C₂³	1	2	yes	—
110	C₄×Dic₁₃₉	C₂³	1	2	yes	—
111	C₄×Dic₁₃₉	C₂³	1	2	yes	—
112	C₄×Dic₁₃₉	C₂³	1	1	yes	characteristic
113	C₄×Dic₁₃₉	C₂³	1	1	yes	characteristic
114	C₄×Dic₁₃₉	C₂³	1	2	yes	—
115	#41×C₁₃₉	—	2	8	no	—
116	C₂×Q₈×C₁₃₉	C₂³	1	2	yes	—
117	C₂×D₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×D₄×C₁₃₉	C₂³	1	4	yes	—
119	C₂×D₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂²×C₄×C₁₃₉	C₂³	1	2	yes	—
121	C₂²×C₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
123	C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
124	C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
125	C₄²×C₁₃₉	C₂³	1	2	yes	—
126	C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂²×D₁₃₉	—	2	4	no	—
129	C₂²×D₁₃₉	—	2	8	no	—
130	C₂²×D₁₃₉	—	2	16	no	—
131	C₂²×D₁₃₉	C₂×D₄	1	4	yes	—
132	C₂²×D₁₃₉	C₂⁴	1	4	yes	—
133	C₂²×D₁₃₉	C₂⁴	1	1	yes	characteristic
134	C₂²×D₁₃₉	C₂⁴	1	1	yes	characteristic
135	Dic₂₇₈	—	2	4	no	—
136	Dic₂₇₈	—	2	8	no	—
137	D₅₅₆	—	2	8	no	—
138	D₅₅₆	—	2	4	no	—
139	D₅₅₆	—	2	8	no	—
140	C₂²⋊D₁₃₉	—	2	8	no	—
141	C₂²⋊D₁₃₉	—	2	8	no	—
142	C₂²⋊D₁₃₉	—	2	8	no	—
143	C₂²⋊D₁₃₉	—	2	16	no	—
144	C₂×Dic₁₃₉	—	2	8	no	—
145	C₂×Dic₁₃₉	—	2	4	no	—
146	C₂×Dic₁₃₉	C₂×D₄	1	4	yes	complemented
147	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
148	C₂×Dic₁₃₉	C₂⁴	1	4	yes	—
149	C₂×Dic₁₃₉	C₂⁴	1	1	yes	characteristic
150	C₂×Dic₁₃₉	C₂⁴	1	1	yes	characteristic
151	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
152	C₄×D₁₃₉	—	2	8	no	—
153	C₄×D₁₃₉	—	2	4	no	—
154	C₄×D₁₃₉	—	2	8	no	—
155	C₄×D₁₃₉	—	2	4	no	—
156	C₄×D₁₃₉	—	2	8	no	—
157	C₄×D₁₃₉	—	2	4	no	—
158	C₄×D₁₃₉	C₂×D₄	1	4	yes	—
159	C₄×D₁₃₉	C₂×D₄	1	4	yes	—
160	C₄×D₁₃₉	C₂×D₄	1	4	yes	complemented
161	C₄×D₁₃₉	C₂×D₄	1	4	yes	complemented
162	C₄×D₁₃₉	#41	1	8	yes	complemented
163	C₂³×C₁₃₉	C₂⁴	1	4	yes	—
164	C₂³×C₁₃₉	C₂⁴	1	1	yes	characteristic
165	Q₈×C₁₃₉	—	2	4	no	—
166	D₄×C₁₃₉	—	2	8	no	—
167	D₄×C₁₃₉	—	2	4	no	—
168	D₄×C₁₃₉	—	2	8	no	—
169	C₂×C₄×C₁₃₉	—	2	8	no	—
170	C₂×C₄×C₁₃₉	—	2	4	no	—
171	C₂×C₄×C₁₃₉	C₂×D₄	1	4	yes	complemented
172	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
173	C₂×C₄×C₁₃₉	C₂⁴	1	4	yes	—
174	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
176	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
177	C₂²×C₁₃₉	—	2	2	no	—
178	C₂²×C₁₃₉	—	2	4	no	—
179	C₂²×C₁₃₉	—	2	8	no	—
180	C₂²×C₁₃₉	C₂²×D₄	1	2	yes	—
181	C₂²×C₁₃₉	C₂⁵	1	1	yes	characteristic
182	C₂×D₁₃₉	—	2	2	no	—
183	C₂×D₁₃₉	—	2	8	no	—
184	C₂×D₁₃₉	—	2	4	no	—
185	C₂×D₁₃₉	—	2	8	no	—
186	C₂×D₁₃₉	—	4	16	no	—
187	C₂×D₁₃₉	C₂²×D₄	1	2	yes	—
188	C₂×D₁₃₉	C₂²×D₄	1	2	yes	—
189	C₂×D₁₃₉	C₂×#41	1	4	yes	—
190	C₄×C₁₃₉	—	2	4	no	—
191	C₄×C₁₃₉	—	2	2	no	—
192	C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
193	C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
194	C₄×C₁₃₉	C₂×#41	1	4	yes	complemented
195	Dic₁₃₉	—	2	4	no	—
196	Dic₁₃₉	—	2	2	no	—
197	Dic₁₃₉	C₂²×D₄	1	2	yes	—
198	Dic₁₃₉	C₂²×D₄	1	2	yes	—
199	Dic₁₃₉	C₂×#41	1	4	yes	complemented
200	C₂×C₁₃₉	—	2	2	no	—
201	C₂×C₁₃₉	—	4	4	no	—
202	C₂×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
203	C₂×C₁₃₉	C₂²×#41	1	2	yes	—
204	D₁₃₉	—	2	2	no	—
205	D₁₃₉	—	4	4	no	—
206	D₁₃₉	#532	1	4	yes	direct product factor
207	C₁₃₉	C₂×#532	1	1	yes	characteristic, complemented, Sylow
208	C₂×#532	—	139	1	no	maximal, Sylow
209	C₂²×#41	—	139	2	no	—
210	#532	—	139	2	no	—
211	#532	—	139	1	no	—
212	#532	—	139	1	no	—
213	#532	—	139	2	no	—
214	#532	—	139	4	no	—
215	#532	—	139	4	no	—
216	#532	—	139	1	no	—
217	#532	D₁₃₉	1	1	yes	characteristic, direct product factor
218	C₂×C₄⋊Q₈	—	139	1	no	—
219	C₂×#127	—	139	1	no	—
220	C₂×#124	—	139	2	no	—
221	C₂×#121	—	139	4	no	—
222	C₂×C₄×D₄	—	139	4	no	—
223	C₂²×C₄²	—	139	1	no	—
224	C₂×#41	—	278	16	no	—
225	C₂×#41	—	139	2	no	—
226	C₂×#41	—	139	2	no	—
227	C₂×#41	—	139	4	no	—
228	C₂×#41	—	139	2	no	—
229	C₂×#41	—	139	4	no	—
230	C₂×#41	C₂×D₁₃₉	1	2	yes	complemented
231	C₂²×Q₈	—	139	2	no	—
232	C₂²×D₄	—	139	4	no	—
233	C₂²×D₄	—	139	4	no	—
234	C₂²×D₄	—	139	2	no	—
235	C₂³×C₄	—	139	4	no	—
236	C₂³×C₄	—	139	2	no	—
237	C₂³×C₄	—	139	1	no	—
238	C₄⋊Q₈	—	139	2	no	—
239	C₄⋊Q₈	—	139	4	no	—
240	C₄⋊Q₈	—	139	1	no	—
241	C₄⋊Q₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
242	#127	—	139	2	no	—
243	#127	—	139	4	no	—
244	#127	—	139	1	no	—
245	#127	C₂×D₁₃₉	1	1	yes	characteristic, complemented
246	#124	—	139	2	no	—
247	#124	—	139	2	no	—
248	#124	—	139	8	no	—
249	#124	—	139	2	no	—
250	#124	C₂×D₁₃₉	1	2	yes	complemented
251	#121	—	139	4	no	—
252	#121	—	139	8	no	—
253	#121	—	139	4	no	—
254	#121	—	139	4	no	—
255	#121	—	139	8	no	—
256	#121	C₂×D₁₃₉	1	4	yes	complemented
257	C₄×D₄	—	139	4	no	—
258	C₄×D₄	—	139	8	no	—
259	C₄×D₄	—	139	4	no	—
260	C₄×D₄	—	139	8	no	—
261	C₄×D₄	—	139	4	no	—
262	C₄×D₄	C₂×D₁₃₉	1	4	yes	complemented
263	C₂×C₄⋊C₄	—	139	4	no	—
264	C₂×C₂²⋊C₄	—	139	8	no	—
265	C₂×C₄²	—	139	2	no	—
266	C₂×C₄²	—	139	1	no	—
267	C₂×C₄²	—	139	2	no	—
268	C₂×C₄²	—	139	1	no	—
269	C₂×C₄²	—	139	1	no	—
270	C₂×C₄²	—	139	1	no	—
271	C₂×C₄²	—	139	1	no	—
272	C₂×C₄²	—	139	2	no	—
273	C₂×C₄²	C₂×D₁₃₉	1	1	yes	characteristic, complemented
274	C₂⁴	—	139	4	no	—
275	C₂⁴	—	139	1	no	—
276	#41	—	2	8	no	—
277	#41	—	278	16	no	—
278	#41	—	278	16	no	—
279	#41	—	278	8	no	—
280	#41	—	278	8	no	—
281	#41	—	278	8	no	—
282	C₂×Q₈	—	278	8	no	—
283	C₂×Q₈	—	139	2	no	—
284	C₂×Q₈	—	139	4	no	—
285	C₂×Q₈	C₂²×D₁₃₉	1	2	yes	—
286	C₂×D₄	—	278	16	no	—
287	C₂×D₄	—	278	16	no	—
288	C₂×D₄	—	278	8	no	—
289	C₂×D₄	—	139	8	no	—
290	C₂×D₄	—	139	4	no	—
291	C₂×D₄	—	139	4	no	—
292	C₂×D₄	—	139	4	no	—
293	C₂×D₄	—	139	4	no	—
294	C₂×D₄	—	139	4	no	—
295	C₂×D₄	—	139	2	no	—
296	C₂×D₄	C₂²×D₁₃₉	1	4	yes	—
297	C₂×D₄	C₂²×D₁₃₉	1	4	yes	—
298	C₂×D₄	C₂²×D₁₃₉	1	2	yes	—
299	C₂²×C₄	—	278	8	no	—
300	C₂²×C₄	—	278	16	no	—
301	C₂²×C₄	—	139	2	no	—
302	C₂²×C₄	—	139	4	no	—
303	C₂²×C₄	—	139	2	no	—
304	C₂²×C₄	—	139	2	no	—
305	C₂²×C₄	—	139	2	no	—
306	C₂²×C₄	—	139	4	no	—
307	C₂²×C₄	—	139	4	no	—
308	C₂²×C₄	—	139	4	no	—
309	C₂²×C₄	—	139	1	no	—
310	C₂²×C₄	—	139	8	no	—
311	C₂²×C₄	—	139	2	no	—
312	C₂²×C₄	—	139	1	no	—
313	C₂²×C₄	—	139	1	no	—
314	C₂²×C₄	—	139	1	no	—
315	C₂²×C₄	—	139	1	no	—
316	C₂²×C₄	C₂²×D₁₃₉	1	2	yes	—
317	C₂²×C₄	C₂²×D₁₃₉	1	4	yes	—
318	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
319	C₄⋊C₄	—	139	8	no	—
320	C₄⋊C₄	—	139	4	no	—
321	C₄⋊C₄	C₂²×D₁₃₉	1	4	yes	—
322	C₂²⋊C₄	—	139	8	no	—
323	C₂²⋊C₄	—	139	8	no	—
324	C₂²⋊C₄	—	139	8	no	—
325	C₂²⋊C₄	C₂²×D₁₃₉	1	8	yes	—
326	C₄²	—	139	2	no	—
327	C₄²	—	139	2	no	—
328	C₄²	—	139	1	no	—
329	C₄²	—	139	2	no	—
330	C₄²	—	139	1	no	—
331	C₄²	—	139	2	no	—
332	C₄²	—	139	2	no	—
333	C₄²	C₂²×D₁₃₉	1	1	yes	characteristic
334	C₄²	C₂²×D₁₃₉	1	1	yes	characteristic
335	C₄²	C₂²×D₁₃₉	1	2	yes	—
336	C₂³	—	278	4	no	—
337	C₂³	—	278	8	no	—
338	C₂³	—	278	16	no	—
339	C₂³	—	139	4	no	—
340	C₂³	—	139	4	no	—
341	C₂³	—	139	1	no	—
342	C₂³	—	139	1	no	—
343	C₂³	C₂³×D₁₃₉	1	4	yes	—
344	C₂³	C₂³×D₁₃₉	1	1	yes	characteristic
345	Q₈	—	2	4	no	—
346	Q₈	—	278	8	no	—
347	Q₈	—	278	4	no	—
348	D₄	—	2	8	no	—
349	D₄	—	2	4	no	—
350	D₄	—	2	8	no	—
351	D₄	—	278	8	no	—
352	D₄	—	278	8	no	—
353	D₄	—	278	8	no	—
354	D₄	—	278	8	no	—
355	D₄	—	278	16	no	—
356	D₄	—	278	4	no	—
357	D₄	—	278	8	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	278	8	no	—
361	C₂×C₄	—	278	4	no	—
362	C₂×C₄	—	278	8	no	—
363	C₂×C₄	—	278	4	no	—
364	C₂×C₄	—	278	8	no	—
365	C₂×C₄	—	278	4	no	—
366	C₂×C₄	—	278	8	no	—
367	C₂×C₄	—	278	4	no	—
368	C₂×C₄	—	139	2	no	—
369	C₂×C₄	—	139	4	no	—
370	C₂×C₄	—	139	4	no	—
371	C₂×C₄	—	139	2	no	—
372	C₂×C₄	—	139	1	no	—
373	C₂×C₄	—	139	1	no	—
374	C₂×C₄	—	139	4	no	—
375	C₂×C₄	—	139	4	no	—
376	C₂×C₄	—	139	4	no	—
377	C₂×C₄	—	139	4	no	—
378	C₂×C₄	—	139	8	no	—
379	C₂×C₄	D₄×D₁₃₉	1	4	yes	complemented
380	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
381	C₂×C₄	C₂³×D₁₃₉	1	4	yes	—
382	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
383	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
384	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
385	C₂²	—	2	2	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	2	8	no	—
388	C₂²	—	278	8	no	—
389	C₂²	—	278	2	no	—
390	C₂²	—	278	4	no	—
391	C₂²	—	278	8	no	—
392	C₂²	—	556	16	no	—
393	C₂²	—	139	2	no	—
394	C₂²	—	139	2	no	—
395	C₂²	—	139	4	no	—
396	C₂²	C₂×D₄×D₁₃₉	1	2	yes	—
397	C₂²	C₂⁴×D₁₃₉	1	1	yes	characteristic
398	C₄	—	2	4	no	—
399	C₄	—	2	2	no	—
400	C₄	—	278	4	no	—
401	C₄	—	278	2	no	—
402	C₄	—	139	2	no	—
403	C₄	—	139	2	no	—
404	C₄	—	139	4	no	—
405	C₄	C₂×D₄×D₁₃₉	1	2	yes	—
406	C₄	C₂×D₄×D₁₃₉	1	2	yes	—
407	C₄	#41×D₁₃₉	1	4	yes	complemented
408	C₂	—	2	2	no	—
409	C₂	—	4	4	no	—
410	C₂	—	278	2	no	—
411	C₂	—	556	4	no	—
412	C₂	—	139	4	no	—
413	C₂	C₂²×D₄×D₁₃₉	1	1	yes	characteristic
414	C₂	C₂×#41×D₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₃₉
commutator, socle, cosocle	C₂²×C₁₃₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₃₉
Fitting	#532×C₁₃₉	C₂
hypercenter	#532	D₁₃₉
hypocenter	C₁₃₉	C₂×#532
LCS	G ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂×C₄ ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₃₉	C₂	semidirect
2. #22581504	C₂	semidirect
3. #22581503	C₂	semidirect
4. #22581502	C₂	semidirect
5. #22581501	C₂	semidirect
6. #22581500	C₂	semidirect
7. #22581499	C₂	semidirect
8. #22581498	C₂	semidirect
9. C₄⋊Q₈×D₁₃₉	C₂	semidirect
10. #127×D₁₃₉	C₂	semidirect
11. #124×D₁₃₉	C₂	semidirect
12. #121×D₁₃₉	C₂	semidirect
13. C₄×D₄×D₁₃₉	C₂	semidirect
14. C₂×C₄²×D₁₃₉	C₂	semidirect
15. #532×C₁₃₉	C₂	semidirect
16. C₂×#14555786	C₂²	semidirect
17. C₂×#14555785	C₂²	semidirect
18. C₂×#14555785	C₂²	semidirect
19. C₂×#14555784	C₂²	semidirect
20. C₂×#14555784	C₂²	semidirect
29. #17984842	C₂²	semidirect
30. #17984841	C₂²	semidirect
31. #17984840	C₂²	semidirect
32. #17984839	C₂²	semidirect
33. #17984838	C₂²	semidirect
34. #17984838	C₂²	semidirect
35. #17984831	C₂²	semidirect
36. #17984830	C₂²	semidirect
37. #17984829	C₂²	semidirect
38. #17984828	C₂²	semidirect
39. #17984817	C₂²	semidirect
40. #17984816	C₂²	semidirect
41. #17984815	C₂²	semidirect
42. #17984814	C₂²	semidirect
43. #17984813	C₂²	semidirect
44. C₄×D₅₅₆	C₂²	semidirect
45. D₄×Dic₁₃₉	C₂²	semidirect
46. #17984804	C₂²	semidirect
47. C₄×C₂²⋊D₁₃₉	C₂²	semidirect
48. (C₂²⋊D₁₃₉)⋊C₄	C₂²	semidirect
51. C₂×C₄×Dic₁₃₉	C₂²	semidirect
52. C₂×C₄×Dic₁₃₉	C₂²	semidirect
56. C₄²×D₁₃₉	C₂²	semidirect
57. C₄²×D₁₃₉	C₂²	semidirect
58. C₄²×D₁₃₉	C₂²	semidirect
59. C₂×#41×C₁₃₉	C₂²	semidirect
60. C₄⋊Q₈×C₁₃₉	C₂²	semidirect
61. #127×C₁₃₉	C₂²	semidirect
62. #124×C₁₃₉	C₂²	semidirect
63. #121×C₁₃₉	C₂²	semidirect
64. C₄×D₄×C₁₃₉	C₂²	semidirect
65. C₂×C₄²×C₁₃₉	C₂²	semidirect
91. C₂×C₄×D₁₃₉	D₄	semidirect
146. C₂×Dic₁₃₉	C₂×D₄	semidirect
160. C₄×D₁₃₉	C₂×D₄	semidirect
161. C₄×D₁₃₉	C₂×D₄	semidirect
162. C₄×D₁₃₉	#41	semidirect
171. C₂×C₄×C₁₃₉	C₂×D₄	semidirect
194. C₄×C₁₃₉	C₂×#41	semidirect
199. Dic₁₃₉	C₂×#41	semidirect
206. D₁₃₉	#532	direct (N × H)
207. C₁₃₉	C₂×#532	semidirect
217. #532	D₁₃₉	direct (N × H)
230. C₂×#41	C₂×D₁₃₉	semidirect
241. C₄⋊Q₈	C₂×D₁₃₉	semidirect
245. #127	C₂×D₁₃₉	semidirect
250. #124	C₂×D₁₃₉	semidirect
256. #121	C₂×D₁₃₉	semidirect
262. C₄×D₄	C₂×D₁₃₉	semidirect
273. C₂×C₄²	C₂×D₁₃₉	semidirect
379. C₂×C₄	D₄×D₁₃₉	semidirect
407. C₄	#41×D₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₁₃₉	2
#22581504	2
#22581503	2
#22581502	2
#22581501	2
#22581500	2
#22581499	2
#22581498	2
C₄⋊Q₈×D₁₃₉	2
#127×D₁₃₉	2
#124×D₁₃₉	2
#121×D₁₃₉	2
C₄×D₄×D₁₃₉	2
C₂×C₄²×D₁₃₉	2
#532×C₁₃₉	2
C₂×#532	139

Subgroups — #532×D139 #31819681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #532×D₁₃₉ #31819681