Subgroups — #31818215

Order 17792.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22581604	C₂	1	1	yes	maximal, characteristic, complemented
2	#22581587	C₂	1	1	yes	maximal, characteristic, complemented
3	#22581298	C₂	1	1	yes	maximal, characteristic, complemented
4	#22581268	C₂	1	1	yes	maximal, characteristic, complemented
5	#22581232	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581190	C₂	1	1	yes	maximal, characteristic, complemented
7	#22581187	C₂	1	1	yes	maximal, characteristic, complemented
8	#22581147	C₂	1	1	yes	maximal, characteristic, complemented
9	#22581089	C₂	1	1	yes	maximal, characteristic, complemented
10	#22581088	C₂	1	1	yes	maximal, characteristic, complemented
11	#22581035	C₂	1	1	yes	maximal, characteristic, complemented
12	(C₂²⋊D₁₃₉)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#17984762	C₂	1	1	yes	maximal, characteristic, complemented
14	#102×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#480×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14555785	—	2	1	no	—
17	C₂²×D₅₅₆	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₁₃₉	—	2	1	no	—
19	C₂×D₄×D₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×D₁₁₁₂	C₂²	1	1	yes	characteristic
21	C₂×D₁₁₁₂	C₂²	1	1	yes	characteristic, complemented
22	C₂×#14555770	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₈×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
25	#17984841	C₂²	1	1	yes	characteristic, complemented
26	#17984838	C₂²	1	1	yes	characteristic
27	#17984827	—	2	1	no	—
28	#17984825	—	2	1	no	—
29	#17984820	—	2	1	no	—
30	#17984817	C₂²	1	1	yes	characteristic
31	#17984817	C₂²	1	1	yes	characteristic, complemented
32	#17984816	C₂²	1	1	yes	characteristic, complemented
33	#17984815	—	2	1	no	—
34	#17984812	—	2	1	no	—
35	#17984810	—	2	1	no	—
36	#17984804	C₂²	1	1	yes	characteristic
37	#17984804	C₂²	1	1	yes	characteristic, complemented
38	C₄×C₂²⋊D₁₃₉	C₂²	1	1	yes	characteristic
39	C₄⋊C₄×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
40	#17984775	C₂²	1	1	yes	characteristic, complemented
41	Dic₁₃₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	#17984764	C₂²	1	1	yes	characteristic
43	#17984764	C₂²	1	1	yes	characteristic, complemented
44	#17984763	C₂²	1	1	yes	characteristic, complemented
45	#17984762	C₂²	1	1	yes	characteristic
46	#17984762	C₂²	1	1	yes	characteristic
47	#17984762	C₂²	1	1	yes	characteristic, complemented
48	#17984762	C₂²	1	1	yes	characteristic, complemented
49	#17984762	C₂²	1	1	yes	characteristic, complemented
50	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	C₈×Dic₁₃₉	C₂²	1	1	yes	characteristic, complemented
52	#121×C₁₃₉	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
54	#107×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
55	#107×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
56	#102×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
57	#102×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₁₃₉	—	2	1	no	—
60	C₂³×D₁₃₉	—	2	1	no	—
61	#14555785	—	4	4	no	—
62	C₂×Dic₂₇₈	—	2	1	no	—
63	C₂×D₅₅₆	—	2	2	no	—
64	C₂×D₅₅₆	—	2	1	no	—
65	C₂×D₅₅₆	—	2	1	no	—
66	C₂×D₅₅₆	—	2	1	no	—
67	C₂×D₅₅₆	—	4	1	no	—
68	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
69	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
70	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
72	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
73	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
74	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
75	C₂×C₂²⋊D₁₃₉	D₄	1	1	yes	characteristic
76	D₄×D₁₃₉	—	2	2	no	—
77	D₄×D₁₃₉	—	4	1	no	—
78	D₄×D₁₃₉	—	4	4	no	—
79	C₂×C₄×D₁₃₉	—	2	1	no	—
80	C₂×C₄×D₁₃₉	—	2	1	no	—
81	C₂×C₄×D₁₃₉	—	2	1	no	—
82	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
83	D₁₁₁₂	—	2	2	no	—
84	D₁₁₁₂	—	4	1	no	—
85	#14555770	—	4	1	no	—
86	C₂×C₁₃₉⋊C₈	—	4	1	no	—
87	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
88	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
89	C₈×D₁₃₉	—	4	1	no	—
90	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
91	Dic₁₃₉⋊C₄	—	2	1	no	—
92	Dic₁₃₉⋊C₄	—	2	1	no	—
93	Dic₁₃₉⋊C₄	D₄	1	1	yes	characteristic
94	C₂²⋊Dic₁₃₉	D₄	1	1	yes	characteristic
95	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
96	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
97	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
98	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
99	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
100	(C₂×D₁₃₉)⋊C₄	D₄	1	1	yes	characteristic
101	C₄×Dic₁₃₉	C₂³	1	1	yes	characteristic
102	C₂×D₄×C₁₃₉	—	2	1	no	—
103	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₉	—	2	1	no	—
105	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₄⋊C₄×C₁₃₉	—	2	1	no	—
109	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
113	C₂²×D₁₃₉	—	2	1	no	—
114	C₂²×D₁₃₉	—	2	1	no	—
115	C₂²×D₁₃₉	—	2	1	no	—
116	C₂²×D₁₃₉	—	4	2	no	—
117	C₂²×D₁₃₉	—	4	2	no	—
118	C₂²×D₁₃₉	—	4	2	no	—
119	C₂²×D₁₃₉	—	4	2	no	—
120	C₂²×D₁₃₉	—	8	1	no	—
121	C₂²×D₁₃₉	—	8	1	no	—
122	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
123	Dic₂₇₈	—	4	2	no	—
124	D₅₅₆	—	2	1	no	—
125	D₅₅₆	—	2	1	no	—
126	D₅₅₆	—	2	1	no	—
127	D₅₅₆	—	2	1	no	—
128	D₅₅₆	—	2	1	no	—
129	D₅₅₆	—	4	2	no	—
130	D₅₅₆	—	4	2	no	—
131	D₅₅₆	—	4	2	no	—
132	D₅₅₆	#41	1	2	yes	complemented
133	C₂²⋊D₁₃₉	—	4	2	no	—
134	C₂²⋊D₁₃₉	—	4	2	no	—
135	C₂²⋊D₁₃₉	—	4	2	no	—
136	C₂²⋊D₁₃₉	—	8	1	no	—
137	C₂²⋊D₁₃₉	D₈	1	4	yes	complemented
138	C₂×Dic₁₃₉	—	2	1	no	—
139	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
140	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
141	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
142	C₄×D₁₃₉	—	2	1	no	—
143	C₄×D₁₃₉	—	2	1	no	—
144	C₄×D₁₃₉	—	4	2	no	—
145	C₄×D₁₃₉	—	4	2	no	—
146	C₄×D₁₃₉	—	4	2	no	—
147	C₁₃₉⋊C₈	—	2	1	no	—
148	C₁₃₉⋊C₈	—	2	1	no	—
149	C₂³×C₁₃₉	—	2	1	no	—
150	C₂³×C₁₃₉	C₂×D₄	1	1	yes	characteristic
151	D₄×C₁₃₉	—	2	1	no	—
152	D₄×C₁₃₉	—	2	1	no	—
153	D₄×C₁₃₉	—	4	2	no	—
154	C₂×C₄×C₁₃₉	—	2	1	no	—
155	C₂×C₄×C₁₃₉	—	2	1	no	—
156	C₂×C₄×C₁₃₉	—	2	1	no	—
157	C₂×C₄×C₁₃₉	—	2	1	no	—
158	C₂×C₄×C₁₃₉	—	2	1	no	—
159	C₂×C₄×C₁₃₉	—	4	2	no	—
160	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
162	C₈×C₁₃₉	—	2	1	no	—
163	C₈×C₁₃₉	—	2	1	no	—
164	C₂²×C₁₃₉	—	2	1	no	—
165	C₂²×C₁₃₉	—	2	1	no	—
166	C₂²×C₁₃₉	—	4	1	no	—
167	C₂²×C₁₃₉	—	4	1	no	—
168	C₂²×C₁₃₉	—	4	1	no	—
169	C₂²×C₁₃₉	C₂×D₈	1	2	yes	—
170	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×D₁₃₉	—	2	1	no	—
172	C₂×D₁₃₉	—	2	1	no	—
173	C₂×D₁₃₉	—	2	2	no	—
174	C₂×D₁₃₉	—	4	1	no	—
175	C₂×D₁₃₉	—	4	1	no	—
176	C₂×D₁₃₉	—	4	1	no	—
177	C₂×D₁₃₉	—	4	1	no	—
178	C₂×D₁₃₉	—	4	1	no	—
179	C₂×D₁₃₉	—	4	1	no	—
180	C₂×D₁₃₉	—	4	1	no	—
181	C₂×D₁₃₉	—	4	1	no	—
182	C₂×D₁₃₉	—	8	4	no	—
183	C₂×D₁₃₉	—	8	4	no	—
184	C₂×D₁₃₉	C₂×D₈	1	2	yes	—
185	C₄×C₁₃₉	—	2	1	no	—
186	C₄×C₁₃₉	—	4	1	no	—
187	C₄×C₁₃₉	—	4	1	no	—
188	C₄×C₁₃₉	—	4	1	no	—
189	C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
190	C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
191	Dic₁₃₉	—	2	1	no	—
192	Dic₁₃₉	—	2	1	no	—
193	Dic₁₃₉	—	4	1	no	—
194	Dic₁₃₉	C₂×D₈	1	2	yes	—
195	C₂×C₁₃₉	—	2	2	no	—
196	C₂×C₁₃₉	—	8	1	no	—
197	C₂×C₁₃₉	#546	1	1	yes	characteristic
198	C₂×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
199	C₂×C₁₃₉	#577	1	1	yes	characteristic
200	D₁₃₉	—	2	2	no	—
201	D₁₃₉	—	4	2	no	—
202	D₁₃₉	—	8	1	no	—
203	D₁₃₉	—	8	1	no	—
204	C₁₃₉	#3294	1	1	yes	characteristic, complemented, Sylow
205	#3294	—	139	1	no	maximal, Sylow
206	#547	—	139	1	no	—
207	D₄²	—	139	1	no	—
208	#486	—	139	1	no	—
209	#480	—	139	1	no	—
210	#480	D₁₃₉	1	1	yes	characteristic, complemented
211	#474	—	139	1	no	—
212	#466	—	139	1	no	—
213	#466	—	139	1	no	—
214	#459	—	139	1	no	—
215	#447	—	139	1	no	—
216	#447	—	139	1	no	—
217	C₄×D₈	—	139	1	no	—
218	C₈×D₄	—	139	1	no	—
219	C₂×#102	—	139	1	no	—
220	C₂×#102	—	139	1	no	—
221	C₂×#41	—	278	1	no	—
222	C₂²×D₄	—	278	1	no	—
223	C₂²×D₄	—	139	1	no	—
224	C₂²×D₄	—	139	1	no	—
225	C₂×D₈	—	139	1	no	—
226	C₂×D₈	—	139	1	no	—
227	C₂×D₈	—	139	1	no	—
228	C₂²×C₈	—	139	1	no	—
229	C₂²×C₈	—	139	1	no	—
230	C₄⋊Q₈	—	139	1	no	—
231	#127	—	139	1	no	—
232	#123	—	278	1	no	—
233	#123	—	278	1	no	—
234	C₂²⋊Q₈	—	278	1	no	—
235	#121	—	278	1	no	—
236	#121	—	139	1	no	—
237	#121	—	139	1	no	—
238	#121	—	139	1	no	—
239	#121	C₂×D₁₃₉	1	1	yes	characteristic
240	#120	—	278	1	no	—
241	#120	—	278	1	no	—
242	C₄×D₄	—	139	1	no	—
243	C₄×D₄	—	139	1	no	—
244	C₄×D₄	—	139	1	no	—
245	C₂×C₄⋊C₄	—	139	1	no	—
246	C₂×C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic, complemented
247	#107	—	139	1	no	—
248	#107	C₂×D₁₃₉	1	1	yes	characteristic, complemented
249	#107	C₂×D₁₃₉	1	1	yes	characteristic, complemented
250	C₄⋊C₈	—	139	1	no	—
251	#102	—	139	1	no	—
252	#102	—	139	1	no	—
253	#102	—	139	1	no	—
254	#102	—	139	1	no	—
255	#102	—	139	1	no	—
256	#102	—	139	1	no	—
257	#102	—	139	1	no	—
258	#102	—	139	1	no	—
259	#102	C₂×D₁₃₉	1	1	yes	characteristic, complemented
260	#102	C₂×D₁₃₉	1	1	yes	characteristic, complemented
261	C₂²⋊C₈	—	139	1	no	—
262	C₂²⋊C₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
263	C₄×C₈	—	139	1	no	—
264	C₂⁴	—	278	1	no	—
265	C₂⁴	—	278	1	no	—
266	#41	—	556	4	no	—
267	C₂×Q₈	—	278	1	no	—
268	C₂×D₄	—	2	1	no	—
269	C₂×D₄	—	278	2	no	—
270	C₂×D₄	—	278	1	no	—
271	C₂×D₄	—	278	1	no	—
272	C₂×D₄	—	278	2	no	—
273	C₂×D₄	—	278	1	no	—
274	C₂×D₄	—	278	1	no	—
275	C₂×D₄	—	278	1	no	—
276	C₂×D₄	—	278	1	no	—
277	C₂×D₄	—	278	1	no	—
278	C₂×D₄	—	556	1	no	—
279	C₂×D₄	—	556	1	no	—
280	C₂×D₄	—	556	4	no	—
281	C₂×D₄	—	139	1	no	—
282	C₂×D₄	—	139	1	no	—
283	C₂×D₄	—	139	1	no	—
284	C₂×D₄	—	139	1	no	—
285	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	278	1	no	—
288	C₂²×C₄	—	278	1	no	—
289	C₂²×C₄	—	278	1	no	—
290	C₂²×C₄	—	139	1	no	—
291	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
292	D₈	—	278	2	no	—
293	D₈	—	556	1	no	—
294	D₈	—	556	1	no	—
295	C₂×C₈	—	556	1	no	—
296	C₂×C₈	—	556	1	no	—
297	C₂×C₈	—	139	1	no	—
298	C₂×C₈	—	139	1	no	—
299	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
300	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	278	1	no	—
303	C₄⋊C₄	—	278	1	no	—
304	C₄⋊C₄	—	139	1	no	—
305	C₄⋊C₄	—	139	1	no	—
306	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
307	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
308	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
309	C₂²⋊C₄	—	2	1	no	—
310	C₂²⋊C₄	—	278	1	no	—
311	C₂²⋊C₄	—	278	1	no	—
312	C₂²⋊C₄	—	278	1	no	—
313	C₂²⋊C₄	—	278	1	no	—
314	C₂²⋊C₄	—	278	1	no	—
315	C₂²⋊C₄	—	139	1	no	—
316	C₂²⋊C₄	—	139	1	no	—
317	C₄²	—	139	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	278	1	no	—
320	C₂³	—	278	1	no	—
321	C₂³	—	278	1	no	—
322	C₂³	—	556	2	no	—
323	C₂³	—	556	2	no	—
324	C₂³	—	556	2	no	—
325	C₂³	—	556	2	no	—
326	C₂³	—	1112	1	no	—
327	C₂³	—	1112	1	no	—
328	C₂³	—	139	1	no	—
329	C₂³	D₄×D₁₃₉	1	1	yes	characteristic
330	Q₈	—	556	2	no	—
331	D₄	—	2	1	no	—
332	D₄	—	2	1	no	—
333	D₄	—	4	2	no	—
334	D₄	—	278	1	no	—
335	D₄	—	278	1	no	—
336	D₄	—	278	1	no	—
337	D₄	—	278	1	no	—
338	D₄	—	278	1	no	—
339	D₄	—	556	2	no	—
340	D₄	—	556	2	no	—
341	D₄	—	556	2	no	—
342	D₄	—	556	2	no	—
343	D₄	—	556	2	no	—
344	D₄	—	556	2	no	—
345	D₄	—	1112	1	no	—
346	D₄	—	139	4	no	—
347	D₄	—	139	2	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	278	1	no	—
355	C₂×C₄	—	278	1	no	—
356	C₂×C₄	—	278	1	no	—
357	C₂×C₄	—	556	2	no	—
358	C₂×C₄	—	556	2	no	—
359	C₂×C₄	—	556	2	no	—
360	C₂×C₄	—	139	1	no	—
361	C₂×C₄	—	139	1	no	—
362	C₂×C₄	—	139	1	no	—
363	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
364	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
365	C₈	—	2	1	no	—
366	C₈	—	2	1	no	—
367	C₈	—	278	1	no	—
368	C₈	—	278	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	278	1	no	—
375	C₂²	—	278	1	no	—
376	C₂²	—	278	2	no	—
377	C₂²	—	556	1	no	—
378	C₂²	—	556	1	no	—
379	C₂²	—	556	1	no	—
380	C₂²	—	556	1	no	—
381	C₂²	—	556	1	no	—
382	C₂²	—	556	1	no	—
383	C₂²	—	556	1	no	—
384	C₂²	—	556	1	no	—
385	C₂²	—	1112	4	no	—
386	C₂²	—	1112	4	no	—
387	C₂²	—	139	2	no	—
388	C₂²	D₈×D₁₃₉	1	2	yes	—
389	C₂²	C₂×D₄×D₁₃₉	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	1	no	—
394	C₄	—	278	1	no	—
395	C₄	—	278	1	no	—
396	C₄	—	556	1	no	—
397	C₄	—	139	2	no	—
398	C₄	#41×D₁₃₉	1	1	yes	characteristic
399	C₄	#17984888	1	1	yes	characteristic
400	C₂	—	2	2	no	—
401	C₂	—	8	1	no	—
402	C₂	—	278	2	no	—
403	C₂	—	556	2	no	—
404	C₂	—	1112	1	no	—
405	C₂	—	1112	1	no	—
406	C₂	#22581595	1	1	yes	characteristic
407	C₂	C₂×D₈×D₁₃₉	1	1	yes	characteristic
408	C₂	#22581762	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃₉
commutator, cosocle	C₂×C₄×C₁₃₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₃₉
Fitting	#480×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂²×D₄
hypercenter	#480	D₁₃₉
hypocenter	C₁₃₉	#3294
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #480

Complements

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

N	H ≅ G/N	type
1. #22581604	C₂	semidirect
2. #22581587	C₂	semidirect
3. #22581298	C₂	semidirect
4. #22581268	C₂	semidirect
5. #22581232	C₂	semidirect
6. #22581190	C₂	semidirect
7. #22581187	C₂	semidirect
8. #22581147	C₂	semidirect
9. #22581089	C₂	semidirect
10. #22581088	C₂	semidirect
11. #22581035	C₂	semidirect
12. (C₂²⋊D₁₃₉)⋊C₈	C₂	semidirect
13. C₂×#17984762	C₂	semidirect
14. #102×D₁₃₉	C₂	semidirect
15. #480×C₁₃₉	C₂	semidirect
21. C₂×D₁₁₁₂	C₂²	semidirect
22. C₂×#14555770	C₂²	semidirect
23. C₂²×C₁₃₉⋊C₈	C₂²	semidirect
24. C₂×C₈×D₁₃₉	C₂²	semidirect
25. #17984841	C₂²	semidirect
31. #17984817	C₂²	semidirect
32. #17984816	C₂²	semidirect
37. #17984804	C₂²	semidirect
39. C₄⋊C₄×D₁₃₉	C₂²	semidirect
40. #17984775	C₂²	semidirect
41. Dic₁₃₉⋊C₈	C₂²	semidirect
43. #17984764	C₂²	semidirect
44. #17984763	C₂²	semidirect
47. #17984762	C₂²	semidirect
48. #17984762	C₂²	semidirect
49. #17984762	C₂²	semidirect
50. (C₂×D₁₃₉)⋊C₈	C₂²	semidirect
51. C₈×Dic₁₃₉	C₂²	semidirect
53. C₂×C₄⋊C₄×C₁₃₉	C₂²	semidirect
54. #107×C₁₃₉	C₂²	semidirect
55. #107×C₁₃₉	C₂²	semidirect
56. #102×C₁₃₉	C₂²	semidirect
57. #102×C₁₃₉	C₂²	semidirect
58. C₂²⋊C₈×C₁₃₉	C₂²	semidirect
132. D₅₅₆	#41	semidirect
137. C₂²⋊D₁₃₉	D₈	semidirect
204. C₁₃₉	#3294	semidirect
210. #480	D₁₃₉	semidirect
246. C₂×C₄⋊C₄	C₂×D₁₃₉	semidirect
248. #107	C₂×D₁₃₉	semidirect
249. #107	C₂×D₁₃₉	semidirect
259. #102	C₂×D₁₃₉	semidirect
260. #102	C₂×D₁₃₉	semidirect
262. C₂²⋊C₈	C₂×D₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#22581604	2
#22581587	2
#22581298	2
#22581268	2
#22581232	2
#22581190	2
#22581187	2
#22581147	2
#22581089	2
#22581088	2
#22581035	2
(C₂²⋊D₁₃₉)⋊C₈	2
C₂×#17984762	2
#102×D₁₃₉	2
#480×C₁₃₉	2
#3294	139