Subgroups — #31809278

Order 17792.

548 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×D₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#22580850	C₂	1	1	yes	maximal, characteristic, complemented
3	#22580848	C₂	1	1	yes	maximal, characteristic, complemented
4	#22580839	C₂	1	1	yes	maximal, characteristic, complemented
5	#22580838	C₂	1	1	yes	maximal, characteristic, complemented
6	#22580836	C₂	1	1	yes	maximal, characteristic, complemented
7	#22580812	C₂	1	1	yes	maximal, characteristic
8	#22580812	C₂	1	1	yes	maximal, characteristic
9	#22580810	C₂	1	1	yes	maximal, characteristic
10	C₄×Dic₁₃₉⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	#22580804	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×(C₂×D₁₃₉)⋊C₄	C₂	1	1	yes	maximal, characteristic
13	#22580800	C₂	1	1	yes	maximal, characteristic
14	#22580800	C₂	1	1	yes	maximal, characteristic
15	#387×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
27	C₄⋊C₄×D₁₃₉	C₄	1	8	yes	complemented
28	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
37	C₁₃₉⋊#95	C₂²	1	1	yes	characteristic
38	C₁₃₉⋊#95	C₂²	1	1	yes	characteristic
39	C₁₃₉⋊#95	C₂²	1	1	yes	characteristic
40	C₁₃₉⋊#95	C₂²	1	1	yes	characteristic
41	C₁₃₉⋊#95	C₂²	1	1	yes	characteristic
42	C₁₃₉⋊#95	C₂²	1	1	yes	characteristic
43	C₁₃₉⋊#95	C₂²	1	1	yes	characteristic
44	C₁₃₉⋊#95	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
48	#95×C₁₃₉	C₂²	1	1	yes	characteristic
49	#95×C₁₃₉	C₂²	1	1	yes	characteristic
50	#95×C₁₃₉	C₂²	1	1	yes	characteristic
51	#95×C₁₃₉	C₂²	1	1	yes	characteristic
52	C₂³×D₁₃₉	C₂³	1	1	yes	characteristic
53	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
54	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
55	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
56	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
57	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
58	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
59	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
60	C₂×C₄×D₁₃₉	—	2	2	no	—
61	C₂×C₄×D₁₃₉	—	2	2	no	—
62	C₂×C₄×D₁₃₉	—	4	1	no	—
63	C₂×C₄×D₁₃₉	—	4	1	no	—
64	C₂×C₄×D₁₃₉	—	4	1	no	—
65	C₂×C₄×D₁₃₉	—	4	1	no	—
66	C₂×C₄×D₁₃₉	C₂×C₄	1	4	yes	—
67	C₂×C₄×D₁₃₉	C₂×C₄	1	4	yes	—
68	C₂×C₄×D₁₃₉	C₂×C₄	1	4	yes	—
69	C₄⋊Dic₁₃₉	—	4	1	no	—
70	C₄⋊Dic₁₃₉	C₂×C₄	1	4	yes	—
71	Dic₁₃₉⋊C₄	—	2	2	no	—
72	Dic₁₃₉⋊C₄	—	2	2	no	—
73	Dic₁₃₉⋊C₄	—	4	1	no	—
74	Dic₁₃₉⋊C₄	—	4	1	no	—
75	Dic₁₃₉⋊C₄	C₂×C₄	1	4	yes	—
76	Dic₁₃₉⋊C₄	C₂×C₄	1	4	yes	—
77	(C₂×D₁₃₉)⋊C₄	—	2	2	no	—
78	(C₂×D₁₃₉)⋊C₄	—	2	2	no	—
79	(C₂×D₁₃₉)⋊C₄	—	2	2	no	—
80	(C₂×D₁₃₉)⋊C₄	Q₈	1	4	yes	—
81	C₄×Dic₁₃₉	—	2	2	no	—
82	C₄×Dic₁₃₉	—	2	2	no	—
83	C₄×Dic₁₃₉	—	4	1	no	—
84	C₄×Dic₁₃₉	—	4	1	no	—
85	C₄×Dic₁₃₉	—	4	1	no	—
86	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₄×C₁₃₉	—	4	1	no	—
94	C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
95	C₄²×C₁₃₉	—	4	1	no	—
96	C₂²×D₁₃₉	—	2	1	no	—
97	C₂²×D₁₃₉	—	2	1	no	—
98	C₂²×D₁₃₉	—	2	1	no	—
99	C₂²×D₁₃₉	—	2	1	no	—
100	C₂²×D₁₃₉	C₂²×C₄	1	2	yes	—
101	C₂²×D₁₃₉	C₂×Q₈	1	2	yes	—
102	C₂²×D₁₃₉	#41	1	2	yes	—
103	C₂×Dic₁₃₉	—	2	1	no	—
104	C₂×Dic₁₃₉	—	2	1	no	—
105	C₂×Dic₁₃₉	—	2	1	no	—
106	C₂×Dic₁₃₉	—	2	1	no	—
107	C₂×Dic₁₃₉	—	2	1	no	—
108	C₂×Dic₁₃₉	—	2	1	no	—
109	C₂×Dic₁₃₉	—	2	1	no	—
110	C₂×Dic₁₃₉	—	2	1	no	—
111	C₂×Dic₁₃₉	—	2	1	no	—
112	C₂×Dic₁₃₉	—	2	1	no	—
113	C₂×Dic₁₃₉	—	2	1	no	—
114	C₂×Dic₁₃₉	—	2	1	no	—
115	C₂×Dic₁₃₉	—	2	1	no	—
116	C₂×Dic₁₃₉	—	2	1	no	—
117	C₂×Dic₁₃₉	—	2	1	no	—
118	C₂×Dic₁₃₉	C₂²×C₄	1	2	yes	—
119	C₂×Dic₁₃₉	C₂²×C₄	1	2	yes	—
120	C₂×Dic₁₃₉	C₂²×C₄	1	2	yes	—
121	C₂×Dic₁₃₉	C₂×Q₈	1	2	yes	—
122	C₂×Dic₁₃₉	#41	1	2	yes	—
123	C₂×Dic₁₃₉	#41	1	2	yes	—
124	C₄×D₁₃₉	—	2	8	no	—
125	C₄×D₁₃₉	—	4	4	no	—
126	C₄×D₁₃₉	—	4	4	no	—
127	C₂³×C₁₃₉	C₂⁴	1	1	yes	characteristic
128	C₂×C₄×C₁₃₉	—	2	1	no	—
129	C₂×C₄×C₁₃₉	—	2	1	no	—
130	C₂×C₄×C₁₃₉	—	2	1	no	—
131	C₂×C₄×C₁₃₉	—	2	1	no	—
132	C₂×C₄×C₁₃₉	—	2	1	no	—
133	C₂×C₄×C₁₃₉	—	2	1	no	—
134	C₂×C₄×C₁₃₉	—	2	1	no	—
135	C₂×C₄×C₁₃₉	—	2	1	no	—
136	C₂×C₄×C₁₃₉	—	2	1	no	—
137	C₂×C₄×C₁₃₉	—	2	1	no	—
138	C₂×C₄×C₁₃₉	—	2	1	no	—
139	C₂×C₄×C₁₃₉	—	2	1	no	—
140	C₂×C₄×C₁₃₉	—	2	1	no	—
141	C₂×C₄×C₁₃₉	—	2	1	no	—
142	C₂×C₄×C₁₃₉	—	2	1	no	—
143	C₂×C₄×C₁₃₉	—	2	1	no	—
144	C₂×C₄×C₁₃₉	—	2	1	no	—
145	C₂×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
146	C₂×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
147	C₂×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
148	C₂×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
149	C₂²×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
150	C₂²×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
151	C₂²×C₁₃₉	C₂×#41	1	1	yes	characteristic
152	C₂²×C₁₃₉	C₂×#41	1	1	yes	characteristic
153	C₂²×C₁₃₉	C₂×#41	1	1	yes	characteristic
154	C₂²×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
155	C₂²×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
156	C₂×D₁₃₉	—	2	2	no	—
157	C₂×D₁₃₉	—	2	2	no	—
158	C₂×D₁₃₉	—	2	2	no	—
159	C₂×D₁₃₉	—	2	2	no	—
160	C₂×D₁₃₉	—	2	2	no	—
161	C₂×D₁₃₉	—	2	2	no	—
162	C₂×D₁₃₉	C₄×Q₈	1	4	yes	—
163	C₄×C₁₃₉	—	2	2	no	—
164	C₄×C₁₃₉	—	2	2	no	—
165	C₄×C₁₃₉	—	2	2	no	—
166	C₄×C₁₃₉	—	2	2	no	—
167	C₄×C₁₃₉	—	4	1	no	—
168	C₄×C₁₃₉	—	4	1	no	—
169	C₄×C₁₃₉	—	4	1	no	—
170	Dic₁₃₉	—	2	2	no	—
171	Dic₁₃₉	—	2	2	no	—
172	Dic₁₃₉	—	2	2	no	—
173	Dic₁₃₉	—	4	1	no	—
174	Dic₁₃₉	—	4	1	no	—
175	Dic₁₃₉	—	4	1	no	—
176	Dic₁₃₉	#117	1	4	yes	—
177	C₂×C₁₃₉	C₂×#117	1	1	yes	characteristic
178	C₂×C₁₃₉	C₂×C₄×Q₈	1	1	yes	characteristic
179	C₂×C₁₃₉	#518	1	1	yes	characteristic
180	C₂×C₁₃₉	#553	1	1	yes	characteristic
181	C₂×C₁₃₉	#553	1	1	yes	characteristic
182	C₂×C₁₃₉	#554	1	1	yes	characteristic
183	C₂×C₁₃₉	#554	1	1	yes	characteristic
184	D₁₃₉	—	2	4	no	—
185	C₁₃₉	#2345	1	1	yes	characteristic, complemented, Sylow
186	#2345	—	139	1	no	maximal, Sylow
187	C₂²×C₄⋊C₄	—	139	1	no	—
188	#389	—	139	1	no	—
189	#389	—	139	1	no	—
190	#387	—	139	1	no	—
191	#387	—	139	1	no	—
192	#387	—	139	1	no	—
193	#387	D₁₃₉	1	1	yes	characteristic, complemented
194	#380	—	139	1	no	—
195	#380	—	139	1	no	—
196	#380	—	139	1	no	—
197	C₄×C₄⋊C₄	—	139	1	no	—
198	C₄×C₄⋊C₄	—	139	1	no	—
199	C₄×C₂²⋊C₄	—	139	1	no	—
200	C₄×C₂²⋊C₄	—	139	1	no	—
201	C₄×C₂²⋊C₄	—	139	1	no	—
202	C₂³×C₄	—	139	1	no	—
203	C₂³×C₄	—	139	1	no	—
204	C₂³×C₄	—	139	1	no	—
205	C₂×C₄⋊C₄	—	139	1	no	—
206	C₂×C₄⋊C₄	—	139	1	no	—
207	C₂×C₄⋊C₄	—	139	1	no	—
208	C₂×C₄⋊C₄	—	139	1	no	—
209	C₂×C₄⋊C₄	—	139	1	no	—
210	C₂×C₄⋊C₄	—	139	1	no	—
211	C₂×C₄⋊C₄	—	139	1	no	—
212	C₂×C₄⋊C₄	—	139	1	no	—
213	C₂×C₄⋊C₄	—	139	8	no	—
214	C₂×C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
215	C₂×C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
216	C₂×C₂²⋊C₄	—	139	1	no	—
217	C₂×C₂²⋊C₄	—	139	1	no	—
218	C₂×C₂²⋊C₄	—	139	1	no	—
219	C₂×C₂²⋊C₄	—	139	1	no	—
220	C₂×C₄²	—	139	1	no	—
221	C₂×C₄²	—	139	1	no	—
222	C₂×C₄²	—	139	1	no	—
223	C₂×C₄²	—	139	1	no	—
224	C₂×C₄²	—	139	1	no	—
225	C₂×C₄²	C₂×D₁₃₉	1	1	yes	characteristic
226	#95	—	139	1	no	—
227	#95	—	139	1	no	—
228	#95	—	139	1	no	—
229	#95	—	139	1	no	—
230	#95	—	139	1	no	—
231	#95	—	139	1	no	—
232	#95	—	139	1	no	—
233	#95	—	139	1	no	—
234	#95	C₂×D₁₃₉	1	1	yes	characteristic
235	#95	C₂×D₁₃₉	1	1	yes	characteristic
236	#95	C₂×D₁₃₉	1	1	yes	characteristic
237	#95	C₂×D₁₃₉	1	1	yes	characteristic
238	C₂⁴	—	139	1	no	—
239	C₂²×C₄	—	278	2	no	—
240	C₂²×C₄	—	278	2	no	—
241	C₂²×C₄	—	556	1	no	—
242	C₂²×C₄	—	556	1	no	—
243	C₂²×C₄	—	556	1	no	—
244	C₂²×C₄	—	556	1	no	—
245	C₂²×C₄	—	139	1	no	—
246	C₂²×C₄	—	139	1	no	—
247	C₂²×C₄	—	139	1	no	—
248	C₂²×C₄	—	139	1	no	—
249	C₂²×C₄	—	139	1	no	—
250	C₂²×C₄	—	139	1	no	—
251	C₂²×C₄	—	139	4	no	—
252	C₂²×C₄	—	139	4	no	—
253	C₂²×C₄	—	139	4	no	—
254	C₂²×C₄	—	139	1	no	—
255	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
256	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
257	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
258	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
259	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
260	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
261	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
262	C₄⋊C₄	—	4	1	no	—
263	C₄⋊C₄	—	278	2	no	—
264	C₄⋊C₄	—	278	2	no	—
265	C₄⋊C₄	—	556	1	no	—
266	C₄⋊C₄	—	556	1	no	—
267	C₄⋊C₄	—	556	1	no	—
268	C₄⋊C₄	—	139	4	no	—
269	C₄⋊C₄	—	139	4	no	—
270	C₄⋊C₄	—	139	4	no	—
271	C₄⋊C₄	C₄×D₁₃₉	1	4	yes	—
272	C₂²⋊C₄	—	278	2	no	—
273	C₂²⋊C₄	—	278	2	no	—
274	C₂²⋊C₄	—	278	2	no	—
275	C₂²⋊C₄	—	139	4	no	—
276	C₄²	—	4	1	no	—
277	C₄²	—	278	2	no	—
278	C₄²	—	278	2	no	—
279	C₄²	—	556	1	no	—
280	C₄²	—	556	1	no	—
281	C₄²	—	556	1	no	—
282	C₂³	—	278	1	no	—
283	C₂³	—	278	1	no	—
284	C₂³	—	278	1	no	—
285	C₂³	—	278	1	no	—
286	C₂³	—	139	2	no	—
287	C₂³	—	139	2	no	—
288	C₂³	—	139	2	no	—
289	C₂³	C₂³×D₁₃₉	1	1	yes	characteristic
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	278	8	no	—
308	C₂×C₄	—	278	1	no	—
309	C₂×C₄	—	278	1	no	—
310	C₂×C₄	—	278	1	no	—
311	C₂×C₄	—	278	1	no	—
312	C₂×C₄	—	278	1	no	—
313	C₂×C₄	—	278	1	no	—
314	C₂×C₄	—	278	1	no	—
315	C₂×C₄	—	278	1	no	—
316	C₂×C₄	—	278	1	no	—
317	C₂×C₄	—	278	1	no	—
318	C₂×C₄	—	278	1	no	—
319	C₂×C₄	—	278	1	no	—
320	C₂×C₄	—	278	1	no	—
321	C₂×C₄	—	278	1	no	—
322	C₂×C₄	—	278	1	no	—
323	C₂×C₄	—	556	4	no	—
324	C₂×C₄	—	556	4	no	—
325	C₂×C₄	—	139	2	no	—
326	C₂×C₄	—	139	2	no	—
327	C₂×C₄	—	139	2	no	—
328	C₂×C₄	—	139	2	no	—
329	C₂×C₄	—	139	2	no	—
330	C₂×C₄	—	139	2	no	—
331	C₂×C₄	C₂×C₄×D₁₃₉	1	2	yes	—
332	C₂×C₄	C₂×C₄×D₁₃₉	1	2	yes	—
333	C₂×C₄	C₂×C₄×D₁₃₉	1	2	yes	—
334	C₂×C₄	Q₈×D₁₃₉	1	2	yes	—
335	C₂²	—	278	2	no	—
336	C₂²	—	278	2	no	—
337	C₂²	—	278	2	no	—
338	C₂²	—	278	2	no	—
339	C₂²	—	278	2	no	—
340	C₂²	—	278	2	no	—
341	C₂²	—	139	4	no	—
342	C₂²	C₂²×C₄×D₁₃₉	1	1	yes	characteristic
343	C₂²	C₂×Q₈×D₁₃₉	1	1	yes	characteristic
344	C₂²	#41×D₁₃₉	1	1	yes	characteristic
345	C₂²	#41×D₁₃₉	1	1	yes	characteristic
346	C₂²	#41×D₁₃₉	1	1	yes	characteristic
347	C₂²	#17984887	1	1	yes	characteristic
348	C₂²	#17984888	1	1	yes	characteristic
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	2	no	—
352	C₄	—	2	2	no	—
353	C₄	—	4	1	no	—
354	C₄	—	4	1	no	—
355	C₄	—	4	1	no	—
356	C₄	—	278	2	no	—
357	C₄	—	278	2	no	—
358	C₄	—	278	2	no	—
359	C₄	—	556	1	no	—
360	C₄	—	556	1	no	—
361	C₄	—	556	1	no	—
362	C₄	—	139	4	no	—
363	C₂	—	278	4	no	—
364	C₂	#117×D₁₃₉	1	1	yes	characteristic
365	C₂	C₄×Q₈×D₁₃₉	1	1	yes	characteristic
366	C₂	#22581425	1	1	yes	characteristic
367	C₂	#22581648	1	1	yes	characteristic
368	C₂	#22581654	1	1	yes	characteristic
369	C₂	#22581657	1	1	yes	characteristic
370	C₂	#22581659	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃₉
commutator	C₂²×C₁₃₉	C₂³×C₄
Fitting	#387×C₁₃₉	C₂
socle, cosocle	C₂³×C₁₃₉	C₂⁴
prime radical	C₂³×D₁₃₉	C₂³
hypercenter	#387	D₁₃₉
hypocenter	C₁₃₉	#2345
LCS	G ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂³ ◁ #387

Complements

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

N	H ≅ G/N	type
2. #22580850	C₂	semidirect
3. #22580848	C₂	semidirect
4. #22580839	C₂	semidirect
5. #22580838	C₂	semidirect
6. #22580836	C₂	semidirect
10. C₄×Dic₁₃₉⋊C₄	C₂	semidirect
11. #22580804	C₂	semidirect
15. #387×C₁₃₉	C₂	semidirect
27. C₄⋊C₄×D₁₃₉	C₄	semidirect
185. C₁₃₉	#2345	semidirect
193. #387	D₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₄×D₁₃₉	2
#22580850	2
#22580848	2
#22580839	2
#22580838	2
#22580836	2
#22580812	2
#22580810	2
C₄×Dic₁₃₉⋊C₄	2
#22580804	2
C₄×(C₂×D₁₃₉)⋊C₄	2
#22580800	2
#387×C₁₃₉	2
#2345	139