Subgroups — D₄×#14555785 #31819892

Order 17792.

1648 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14555785	C₂	1	2	yes	maximal, complemented
2	#22581624	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Dic₂₇₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#22581612	C₂	1	2	yes	maximal, complemented
5	#22581608	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581604	C₂	1	2	yes	maximal, complemented
7	#22581599	C₂	1	2	yes	maximal, complemented
8	#22581593	C₂	1	4	yes	maximal, complemented
9	D₄×D₅₅₆	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×C₂²⋊D₁₃₉	C₂	1	2	yes	maximal, complemented
11	#22581503	C₂	1	1	yes	maximal, characteristic, complemented
12	#22581500	C₂	1	2	yes	maximal, complemented
13	#22581464	C₂	1	2	yes	maximal, complemented
14	#22581462	C₂	1	4	yes	maximal, complemented
15	C₄×#14555785	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×D₄×D₁₃₉	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14555785	—	2	16	no	—
19	C₂×#14555785	C₂²	1	1	yes	characteristic
20	C₂×#14555785	C₂²	1	4	yes	complemented
21	C₂×#14555785	C₂²	1	2	yes	complemented
22	C₂×#14555785	C₂²	1	2	yes	complemented
23	C₂×#14555785	C₂²	1	4	yes	complemented
24	C₂×#14555785	C₂²	1	2	yes	complemented
25	C₂²×Dic₂₇₈	C₂²	1	2	yes	complemented
26	C₂²×D₅₅₆	C₂²	1	2	yes	complemented
27	C₂²×C₂²⋊D₁₃₉	C₂²	1	4	yes	complemented
28	C₂×D₄×D₁₃₉	C₂²	1	2	yes	—
29	C₂²×C₄×D₁₃₉	C₂²	1	4	yes	complemented
30	#17984842	C₂²	1	1	yes	characteristic, complemented
31	#17984841	C₂²	1	2	yes	complemented
32	#17984839	C₂²	1	1	yes	characteristic, complemented
33	#17984838	C₂²	1	2	yes	complemented
34	#17984830	C₂²	1	2	yes	complemented
35	#17984828	C₂²	1	4	yes	complemented
36	#17984827	C₂²	1	4	yes	complemented
37	#17984825	C₂²	1	4	yes	complemented
38	#17984824	C₂²	1	4	yes	complemented
39	#17984821	C₂²	1	2	yes	complemented
40	#17984821	C₂²	1	2	yes	complemented
41	#17984820	C₂²	1	4	yes	complemented
42	#17984819	C₂²	1	4	yes	complemented
43	#17984817	C₂²	1	2	yes	complemented
44	#17984816	C₂²	1	2	yes	complemented
45	#17984816	C₂²	1	2	yes	complemented
46	#17984816	C₂²	1	2	yes	complemented
47	#17984816	C₂²	1	2	yes	complemented
48	#17984815	C₂²	1	4	yes	complemented
49	#17984815	C₂²	1	4	yes	complemented
50	#17984814	C₂²	1	4	yes	complemented
51	#17984813	C₂²	1	2	yes	complemented
52	#17984812	C₂²	1	4	yes	complemented
53	#17984811	C₂²	1	4	yes	complemented
54	#17984810	C₂²	1	4	yes	complemented
55	C₄×Dic₂₇₈	C₂²	1	1	yes	characteristic, complemented
56	C₄×Dic₂₇₈	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₅₅₆	C₂²	1	1	yes	characteristic, complemented
58	C₄×D₅₅₆	C₂²	1	1	yes	characteristic, complemented
59	C₄×D₅₅₆	C₂²	1	2	yes	complemented
60	C₄×D₅₅₆	C₂²	1	2	yes	complemented
61	D₄×Dic₁₃₉	C₂²	1	2	yes	—
62	#17984804	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₁₃₉	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₁₃₉	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₁₃₉	C₂²	1	4	yes	complemented
66	C₄×C₂²⋊D₁₃₉	C₂²	1	4	yes	complemented
67	(C₂²⋊D₁₃₉)⋊C₄	C₂²	1	4	yes	complemented
68	#17984801	C₂²	1	1	yes	characteristic, complemented
69	#17984799	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₁₃₉	C₂²	1	2	yes	complemented
71	C₂²⋊C₄×D₁₃₉	C₂²	1	4	yes	complemented
72	C₄²×D₁₃₉	C₂²	1	2	yes	complemented
73	C₂²×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
74	C₂³×C₄×C₁₃₉	C₂²	1	2	yes	complemented
75	C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
76	C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
77	C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
78	C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
80	C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
83	C₂×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
84	C₂³×D₁₃₉	C₂³	1	4	yes	—
85	#14555785	—	2	8	no	—
86	#14555785	—	2	8	no	—
87	#14555785	—	2	16	no	—
88	#14555785	—	2	16	no	—
89	#14555785	—	2	8	no	—
90	#14555785	D₄	1	8	yes	direct product factor
91	C₂×Dic₂₇₈	—	2	8	no	—
92	C₂×Dic₂₇₈	C₂³	1	4	yes	—
93	C₂×Dic₂₇₈	C₂³	1	2	yes	—
94	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
95	C₂×D₅₅₆	—	2	8	no	—
96	C₂×D₅₅₆	C₂³	1	2	yes	—
97	C₂×D₅₅₆	C₂³	1	4	yes	—
98	C₂×D₅₅₆	C₂³	1	2	yes	—
99	C₂×D₅₅₆	C₂³	1	2	yes	—
100	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊D₁₃₉	—	2	16	no	—
102	C₂×C₂²⋊D₁₃₉	C₂³	1	4	yes	—
103	C₂×C₂²⋊D₁₃₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊D₁₃₉	C₂³	1	4	yes	—
105	C₂×C₂²⋊D₁₃₉	C₂³	1	4	yes	—
106	C₂×C₂²⋊D₁₃₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊D₁₃₉	C₂³	1	2	yes	—
108	D₄×D₁₃₉	—	2	8	no	—
109	C₂²×Dic₁₃₉	C₂³	1	4	yes	—
110	C₂×C₄×D₁₃₉	—	2	16	no	—
111	C₂×C₄×D₁₃₉	C₂³	1	2	yes	—
112	C₂×C₄×D₁₃₉	C₂³	1	4	yes	—
113	C₂×C₄×D₁₃₉	C₂³	1	4	yes	—
114	C₂×C₄×D₁₃₉	C₂³	1	4	yes	—
115	C₂×C₄×D₁₃₉	C₂³	1	2	yes	—
116	C₂×C₄×D₁₃₉	C₂³	1	2	yes	—
117	C₄⋊Dic₁₃₉	C₂³	1	2	yes	—
118	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
119	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
120	C₄⋊Dic₁₃₉	C₂³	1	2	yes	—
121	Dic₁₃₉⋊C₄	C₂³	1	4	yes	—
122	Dic₁₃₉⋊C₄	C₂³	1	2	yes	—
123	Dic₁₃₉⋊C₄	C₂³	1	2	yes	—
124	Dic₁₃₉⋊C₄	C₂³	1	4	yes	—
125	C₂²⋊Dic₁₃₉	C₂³	1	4	yes	—
126	C₂²⋊Dic₁₃₉	C₂³	1	2	yes	—
127	C₂²⋊Dic₁₃₉	C₂³	1	4	yes	—
128	(C₂×D₁₃₉)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₁₃₉)⋊C₄	C₂³	1	4	yes	—
130	(C₂×D₁₃₉)⋊C₄	C₂³	1	2	yes	—
131	(C₂×D₁₃₉)⋊C₄	C₂³	1	2	yes	—
132	(C₂×D₁₃₉)⋊C₄	C₂³	1	4	yes	—
133	(C₂×D₁₃₉)⋊C₄	C₂³	1	4	yes	—
134	C₄×Dic₁₃₉	C₂³	1	2	yes	—
135	C₄×Dic₁₃₉	C₂³	1	2	yes	—
136	C₄×Dic₁₃₉	C₂³	1	2	yes	—
137	C₂⁴×C₁₃₉	C₂³	1	2	yes	—
138	C₂×D₄×C₁₃₉	—	2	4	no	—
139	C₂×D₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂²×C₄×C₁₃₉	—	2	8	no	—
143	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂²×C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂²×C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂²×C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂²×C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂²×C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
159	C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
161	C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
162	C₂²×D₁₃₉	—	2	8	no	—
163	C₂²×D₁₃₉	—	2	8	no	—
164	C₂²×D₁₃₉	—	4	4	no	—
165	C₂²×D₁₃₉	C₂⁴	1	4	yes	—
166	C₂²×D₁₃₉	C₂⁴	1	2	yes	—
167	Dic₂₇₈	—	2	4	no	—
168	Dic₂₇₈	—	2	8	no	—
169	Dic₂₇₈	C₂×D₄	1	4	yes	complemented
170	D₅₅₆	—	2	8	no	—
171	D₅₅₆	—	2	4	no	—
172	D₅₅₆	—	2	4	no	—
173	D₅₅₆	—	4	2	no	—
174	D₅₅₆	C₂×D₄	1	4	yes	complemented
175	C₂²⋊D₁₃₉	—	2	8	no	—
176	C₂²⋊D₁₃₉	—	2	8	no	—
177	C₂²⋊D₁₃₉	—	2	8	no	—
178	C₂²⋊D₁₃₉	—	2	8	no	—
179	C₂²⋊D₁₃₉	—	4	4	no	—
180	C₂²⋊D₁₃₉	C₂×D₄	1	8	yes	complemented
181	C₂×Dic₁₃₉	—	2	8	no	—
182	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
183	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
184	C₂×Dic₁₃₉	C₂⁴	1	4	yes	—
185	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
186	C₄×D₁₃₉	—	2	8	no	—
187	C₄×D₁₃₉	—	2	8	no	—
188	C₄×D₁₃₉	—	2	4	no	—
189	C₄×D₁₃₉	—	2	8	no	—
190	C₄×D₁₃₉	—	4	2	no	—
191	C₄×D₁₃₉	C₂×D₄	1	8	yes	complemented
192	C₂³×C₁₃₉	—	2	4	no	—
193	C₂³×C₁₃₉	—	2	4	no	—
194	C₂³×C₁₃₉	—	4	2	no	—
195	C₂³×C₁₃₉	C₂⁴	1	2	yes	—
196	C₂³×C₁₃₉	C₂⁴	1	1	yes	characteristic
197	C₂³×C₁₃₉	C₂⁴	1	2	yes	—
198	D₄×C₁₃₉	—	2	4	no	—
199	D₄×C₁₃₉	—	2	2	no	—
200	D₄×C₁₃₉	#41	1	4	yes	complemented
201	C₂×C₄×C₁₃₉	—	2	4	no	—
202	C₂×C₄×C₁₃₉	—	2	4	no	—
203	C₂×C₄×C₁₃₉	—	2	4	no	—
204	C₂×C₄×C₁₃₉	—	2	4	no	—
205	C₂×C₄×C₁₃₉	—	2	4	no	—
206	C₂×C₄×C₁₃₉	—	2	2	no	—
207	C₂×C₄×C₁₃₉	—	4	1	no	—
208	C₂×C₄×C₁₃₉	C₂×D₄	1	4	yes	complemented
209	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
210	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
211	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
212	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
213	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
214	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
215	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
216	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
217	C₂²×C₁₃₉	—	2	2	no	—
218	C₂²×C₁₃₉	—	2	1	no	—
219	C₂²×C₁₃₉	—	2	1	no	—
220	C₂²×C₁₃₉	—	2	2	no	—
221	C₂²×C₁₃₉	—	2	2	no	—
222	C₂²×C₁₃₉	—	2	2	no	—
223	C₂²×C₁₃₉	—	2	2	no	—
224	C₂²×C₁₃₉	—	4	8	no	—
225	C₂²×C₁₃₉	C₂²×D₄	1	2	yes	—
226	C₂²×C₁₃₉	C₂×#41	1	4	yes	complemented
227	C₂²×C₁₃₉	C₂⁵	1	1	yes	characteristic
228	C₂×D₁₃₉	—	2	2	no	—
229	C₂×D₁₃₉	—	2	2	no	—
230	C₂×D₁₃₉	—	2	4	no	—
231	C₂×D₁₃₉	—	2	4	no	—
232	C₂×D₁₃₉	—	2	4	no	—
233	C₂×D₁₃₉	—	4	16	no	—
234	C₂×D₁₃₉	C₂²×D₄	1	4	yes	—
235	C₄×C₁₃₉	—	2	2	no	—
236	C₄×C₁₃₉	—	2	2	no	—
237	C₄×C₁₃₉	—	2	1	no	—
238	C₄×C₁₃₉	—	2	1	no	—
239	C₄×C₁₃₉	—	2	1	no	—
240	C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
241	C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
242	C₄×C₁₃₉	C₂×#41	1	2	yes	complemented
243	Dic₁₃₉	—	2	4	no	—
244	Dic₁₃₉	—	2	2	no	—
245	Dic₁₃₉	—	2	2	no	—
246	Dic₁₃₉	C₂²×D₄	1	4	yes	—
247	C₂×C₁₃₉	—	2	4	no	—
248	C₂×C₁₃₉	—	2	2	no	—
249	C₂×C₁₃₉	—	4	2	no	—
250	C₂×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
251	C₂×C₁₃₉	C₂²×#41	1	1	yes	characteristic
252	C₂×C₁₃₉	#585	1	1	yes	characteristic
253	D₁₃₉	—	2	4	no	—
254	D₁₃₉	—	4	4	no	—
255	C₁₃₉	D₄×#41	1	1	yes	characteristic, complemented, Sylow
256	D₄×#41	—	139	1	no	maximal, Sylow
257	C₂²×#41	—	139	2	no	—
258	#550	—	139	1	no	—
259	D₄×Q₈	—	139	1	no	—
260	#548	—	139	2	no	—
261	#547	—	139	1	no	—
262	#547	—	139	2	no	—
263	#546	—	139	2	no	—
264	#546	—	139	4	no	—
265	D₄²	—	139	2	no	—
266	D₄²	—	139	1	no	—
267	#532	—	139	2	no	—
268	#532	—	139	1	no	—
269	#525	—	139	2	no	—
270	#525	—	139	4	no	—
271	C₄×#41	—	139	1	no	—
272	C₂×C₄×D₄	—	139	2	no	—
273	C₂×C₄×D₄	D₁₃₉	1	1	yes	characteristic, complemented
274	C₂×#41	—	278	16	no	—
275	C₂×#41	—	139	2	no	—
276	C₂×#41	—	139	4	no	—
277	C₂×#41	—	139	2	no	—
278	C₂×#41	—	139	4	no	—
279	C₂×#41	—	139	2	no	—
280	C₂×#41	—	139	1	no	—
281	C₂²×Q₈	—	139	2	no	—
282	C₂²×D₄	—	139	4	no	—
283	C₂²×D₄	—	139	2	no	—
284	C₂²×D₄	—	139	2	no	—
285	C₂²×D₄	C₂×D₁₃₉	1	1	yes	characteristic
286	C₂³×C₄	—	139	4	no	—
287	C₂³×C₄	C₂×D₁₃₉	1	2	yes	complemented
288	C₄⋊Q₈	—	139	2	no	—
289	C₄⋊Q₈	—	139	1	no	—
290	#127	—	139	2	no	—
291	#127	—	139	1	no	—
292	#124	—	139	4	no	—
293	#124	—	139	2	no	—
294	#123	—	139	4	no	—
295	#123	—	139	4	no	—
296	#123	—	139	4	no	—
297	C₂²⋊Q₈	—	139	2	no	—
298	C₂²⋊Q₈	—	139	2	no	—
299	C₂²⋊Q₈	—	139	4	no	—
300	C₂²⋊Q₈	—	139	4	no	—
301	#121	—	139	4	no	—
302	#121	—	139	2	no	—
303	#121	—	139	2	no	—
304	#121	—	139	2	no	—
305	#121	—	139	2	no	—
306	#121	—	139	2	no	—
307	#121	—	139	2	no	—
308	#121	—	139	4	no	—
309	#121	—	139	4	no	—
310	#120	—	139	4	no	—
311	#120	—	139	4	no	—
312	#120	—	139	4	no	—
313	C₄×Q₈	—	139	1	no	—
314	C₄×Q₈	—	139	1	no	—
315	C₄×D₄	—	139	2	no	—
316	C₄×D₄	—	139	4	no	—
317	C₄×D₄	—	139	2	no	—
318	C₄×D₄	—	139	2	no	—
319	C₄×D₄	—	139	4	no	—
320	C₄×D₄	—	139	2	no	—
321	C₄×D₄	—	139	4	no	—
322	C₄×D₄	—	139	2	no	—
323	C₄×D₄	—	139	1	no	—
324	C₄×D₄	—	139	1	no	—
325	C₄×D₄	—	139	2	no	—
326	C₄×D₄	C₂×D₁₃₉	1	1	yes	characteristic
327	C₄×D₄	C₂×D₁₃₉	1	1	yes	characteristic
328	C₄×D₄	C₂×D₁₃₉	1	2	yes	complemented
329	C₄×D₄	C₂×D₁₃₉	1	1	yes	characteristic, complemented
330	C₄×D₄	C₂×D₁₃₉	1	2	yes	complemented
331	C₄×D₄	C₂×D₁₃₉	1	1	yes	characteristic, complemented
332	#117	—	139	1	no	—
333	#117	—	139	2	no	—
334	C₂×C₄⋊C₄	—	139	2	no	—
335	C₂×C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic, complemented
336	C₂×C₂²⋊C₄	—	139	4	no	—
337	C₂×C₂²⋊C₄	C₂×D₁₃₉	1	2	yes	complemented
338	C₂×C₄²	—	139	2	no	—
339	C₂×C₄²	C₂×D₁₃₉	1	1	yes	characteristic, complemented
340	C₂⁴	—	139	4	no	—
341	C₂⁴	C₂²×D₁₃₉	1	2	yes	—
342	#41	—	278	8	no	—
343	#41	—	278	16	no	—
344	#41	—	278	8	no	—
345	#41	—	278	16	no	—
346	#41	—	278	8	no	—
347	#41	—	139	8	no	—
348	C₂×Q₈	—	278	8	no	—
349	C₂×Q₈	—	139	2	no	—
350	C₂×Q₈	—	139	4	no	—
351	C₂×Q₈	—	139	1	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	278	8	no	—
354	C₂×D₄	—	278	16	no	—
355	C₂×D₄	—	278	8	no	—
356	C₂×D₄	—	139	4	no	—
357	C₂×D₄	—	139	4	no	—
358	C₂×D₄	—	139	4	no	—
359	C₂×D₄	—	139	4	no	—
360	C₂×D₄	—	139	4	no	—
361	C₂×D₄	—	139	2	no	—
362	C₂×D₄	—	139	2	no	—
363	C₂×D₄	—	139	4	no	—
364	C₂×D₄	—	139	2	no	—
365	C₂×D₄	—	139	2	no	—
366	C₂×D₄	—	139	1	no	—
367	C₂×D₄	C₂²×D₁₃₉	1	2	yes	—
368	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
369	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
370	C₂²×C₄	—	2	8	no	—
371	C₂²×C₄	—	278	16	no	—
372	C₂²×C₄	—	139	4	no	—
373	C₂²×C₄	—	139	2	no	—
374	C₂²×C₄	—	139	4	no	—
375	C₂²×C₄	—	139	4	no	—
376	C₂²×C₄	—	139	4	no	—
377	C₂²×C₄	—	139	2	no	—
378	C₂²×C₄	—	139	2	no	—
379	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
380	C₂²×C₄	C₂²×D₁₃₉	1	2	yes	—
381	C₂²×C₄	C₂²×D₁₃₉	1	2	yes	—
382	C₂²×C₄	C₂²×D₁₃₉	1	2	yes	—
383	C₂²×C₄	C₂²×D₁₃₉	1	2	yes	—
384	C₂²×C₄	C₂²×D₁₃₉	1	2	yes	—
385	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
386	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
387	C₄⋊C₄	—	139	4	no	—
388	C₄⋊C₄	—	139	2	no	—
389	C₄⋊C₄	—	139	2	no	—
390	C₄⋊C₄	—	139	2	no	—
391	C₄⋊C₄	—	139	4	no	—
392	C₄⋊C₄	—	139	1	no	—
393	C₄⋊C₄	—	139	1	no	—
394	C₄⋊C₄	—	139	2	no	—
395	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
396	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
397	C₄⋊C₄	C₂²×D₁₃₉	1	2	yes	—
398	C₂²⋊C₄	—	139	4	no	—
399	C₂²⋊C₄	—	139	2	no	—
400	C₂²⋊C₄	—	139	4	no	—
401	C₂²⋊C₄	—	139	4	no	—
402	C₂²⋊C₄	—	139	4	no	—
403	C₂²⋊C₄	—	139	2	no	—
404	C₂²⋊C₄	—	139	2	no	—
405	C₂²⋊C₄	—	139	4	no	—
406	C₂²⋊C₄	—	139	4	no	—
407	C₂²⋊C₄	C₂²×D₁₃₉	1	2	yes	—
408	C₂²⋊C₄	C₂²×D₁₃₉	1	2	yes	—
409	C₂²⋊C₄	C₂²×D₁₃₉	1	2	yes	—
410	C₂²⋊C₄	C₂²×D₁₃₉	1	2	yes	—
411	C₄²	—	139	2	no	—
412	C₄²	—	139	2	no	—
413	C₄²	—	139	2	no	—
414	C₄²	C₂²×D₁₃₉	1	1	yes	characteristic
415	C₄²	C₂²×D₁₃₉	1	1	yes	characteristic
416	C₄²	C₂²×D₁₃₉	1	1	yes	characteristic
417	C₄²	C₂²×D₁₃₉	1	1	yes	characteristic
418	C₂³	—	2	4	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	278	8	no	—
422	C₂³	—	278	8	no	—
423	C₂³	—	556	4	no	—
424	C₂³	—	139	4	no	—
425	C₂³	—	139	2	no	—
426	C₂³	C₂³×D₁₃₉	1	2	yes	—
427	C₂³	C₂³×D₁₃₉	1	1	yes	characteristic
428	C₂³	C₂³×D₁₃₉	1	2	yes	—
429	Q₈	—	278	8	no	—
430	Q₈	—	278	4	no	—
431	Q₈	—	139	4	no	—
432	D₄	—	2	4	no	—
433	D₄	—	2	2	no	—
434	D₄	—	278	8	no	—
435	D₄	—	278	8	no	—
436	D₄	—	278	8	no	—
437	D₄	—	278	8	no	—
438	D₄	—	278	8	no	—
439	D₄	—	278	4	no	—
440	D₄	—	278	4	no	—
441	D₄	—	556	2	no	—
442	D₄	—	556	4	no	—
443	D₄	—	139	8	no	—
444	D₄	—	139	4	no	—
445	D₄	#14555785	1	4	yes	direct product factor
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	278	8	no	—
454	C₂×C₄	—	278	8	no	—
455	C₂×C₄	—	278	8	no	—
456	C₂×C₄	—	278	8	no	—
457	C₂×C₄	—	278	4	no	—
458	C₂×C₄	—	556	2	no	—
459	C₂×C₄	—	139	2	no	—
460	C₂×C₄	—	139	2	no	—
461	C₂×C₄	—	139	4	no	—
462	C₂×C₄	—	139	2	no	—
463	C₂×C₄	—	139	8	no	—
464	C₂×C₄	D₄×D₁₃₉	1	4	yes	complemented
465	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
466	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
467	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
468	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
469	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
470	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
471	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
472	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
473	C₂²	—	2	2	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	8	no	—
481	C₂²	—	278	2	no	—
482	C₂²	—	278	2	no	—
483	C₂²	—	278	4	no	—
484	C₂²	—	278	4	no	—
485	C₂²	—	278	4	no	—
486	C₂²	—	556	16	no	—
487	C₂²	—	139	4	no	—
488	C₂²	C₂×D₄×D₁₃₉	1	2	yes	—
489	C₂²	C₂×#14555785	1	4	yes	complemented
490	C₂²	C₂⁴×D₁₃₉	1	1	yes	characteristic
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	278	4	no	—
497	C₄	—	278	2	no	—
498	C₄	—	278	2	no	—
499	C₄	—	139	4	no	—
500	C₄	C₂×D₄×D₁₃₉	1	2	yes	—
501	C₄	C₂×D₄×D₁₃₉	1	2	yes	—
502	C₄	C₂×#14555785	1	2	yes	complemented
503	C₂	—	2	2	no	—
504	C₂	—	2	4	no	—
505	C₂	—	4	2	no	—
506	C₂	—	278	4	no	—
507	C₂	—	556	4	no	—
508	C₂	C₂²×D₄×D₁₃₉	1	1	yes	characteristic
509	C₂	C₂²×#14555785	1	1	yes	characteristic
510	C₂	#22581789	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₃₉
commutator, socle, cosocle	C₂²×C₁₃₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₃₉
Fitting	C₂×C₄×D₄×C₁₃₉	C₂
hypercenter	C₂×C₄×D₄	D₁₃₉
hypocenter	C₁₃₉	D₄×#41
LCS	G ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#14555785	C₂	semidirect
2. #22581624	C₂	semidirect
3. D₄×Dic₂₇₈	C₂	semidirect
4. #22581612	C₂	semidirect
5. #22581608	C₂	semidirect
6. #22581604	C₂	semidirect
7. #22581599	C₂	semidirect
8. #22581593	C₂	semidirect
9. D₄×D₅₅₆	C₂	semidirect
10. D₄×C₂²⋊D₁₃₉	C₂	semidirect
11. #22581503	C₂	semidirect
12. #22581500	C₂	semidirect
13. #22581464	C₂	semidirect
14. #22581462	C₂	semidirect
15. C₄×#14555785	C₂	semidirect
16. C₄×D₄×D₁₃₉	C₂	semidirect
17. C₂×C₄×D₄×C₁₃₉	C₂	semidirect
20. C₂×#14555785	C₂²	semidirect
21. C₂×#14555785	C₂²	semidirect
22. C₂×#14555785	C₂²	semidirect
23. C₂×#14555785	C₂²	semidirect
24. C₂×#14555785	C₂²	semidirect
25. C₂²×Dic₂₇₈	C₂²	semidirect
26. C₂²×D₅₅₆	C₂²	semidirect
27. C₂²×C₂²⋊D₁₃₉	C₂²	semidirect
29. C₂²×C₄×D₁₃₉	C₂²	semidirect
30. #17984842	C₂²	semidirect
31. #17984841	C₂²	semidirect
32. #17984839	C₂²	semidirect
33. #17984838	C₂²	semidirect
34. #17984830	C₂²	semidirect
35. #17984828	C₂²	semidirect
36. #17984827	C₂²	semidirect
37. #17984825	C₂²	semidirect
38. #17984824	C₂²	semidirect
39. #17984821	C₂²	semidirect
40. #17984821	C₂²	semidirect
41. #17984820	C₂²	semidirect
42. #17984819	C₂²	semidirect
43. #17984817	C₂²	semidirect
44. #17984816	C₂²	semidirect
45. #17984816	C₂²	semidirect
46. #17984816	C₂²	semidirect
47. #17984816	C₂²	semidirect
48. #17984815	C₂²	semidirect
49. #17984815	C₂²	semidirect
50. #17984814	C₂²	semidirect
51. #17984813	C₂²	semidirect
52. #17984812	C₂²	semidirect
53. #17984811	C₂²	semidirect
54. #17984810	C₂²	semidirect
55. C₄×Dic₂₇₈	C₂²	semidirect
56. C₄×Dic₂₇₈	C₂²	semidirect
57. C₄×D₅₅₆	C₂²	semidirect
58. C₄×D₅₅₆	C₂²	semidirect
59. C₄×D₅₅₆	C₂²	semidirect
60. C₄×D₅₅₆	C₂²	semidirect
62. #17984804	C₂²	semidirect
63. C₄×C₂²⋊D₁₃₉	C₂²	semidirect
64. C₄×C₂²⋊D₁₃₉	C₂²	semidirect
65. C₄×C₂²⋊D₁₃₉	C₂²	semidirect
66. C₄×C₂²⋊D₁₃₉	C₂²	semidirect
67. (C₂²⋊D₁₃₉)⋊C₄	C₂²	semidirect
68. #17984801	C₂²	semidirect
69. #17984799	C₂²	semidirect
70. C₄⋊C₄×D₁₃₉	C₂²	semidirect
71. C₂²⋊C₄×D₁₃₉	C₂²	semidirect
72. C₄²×D₁₃₉	C₂²	semidirect
74. C₂³×C₄×C₁₃₉	C₂²	semidirect
77. C₄×D₄×C₁₃₉	C₂²	semidirect
78. C₄×D₄×C₁₃₉	C₂²	semidirect
79. C₄×D₄×C₁₃₉	C₂²	semidirect
80. C₄×D₄×C₁₃₉	C₂²	semidirect
81. C₂×C₄⋊C₄×C₁₃₉	C₂²	semidirect
82. C₂×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
83. C₂×C₄²×C₁₃₉	C₂²	semidirect
90. #14555785	D₄	direct (N × H)
169. Dic₂₇₈	C₂×D₄	semidirect
174. D₅₅₆	C₂×D₄	semidirect
180. C₂²⋊D₁₃₉	C₂×D₄	semidirect
191. C₄×D₁₃₉	C₂×D₄	semidirect
200. D₄×C₁₃₉	#41	semidirect
208. C₂×C₄×C₁₃₉	C₂×D₄	semidirect
226. C₂²×C₁₃₉	C₂×#41	semidirect
242. C₄×C₁₃₉	C₂×#41	semidirect
255. C₁₃₉	D₄×#41	semidirect
273. C₂×C₄×D₄	D₁₃₉	semidirect
287. C₂³×C₄	C₂×D₁₃₉	semidirect
328. C₄×D₄	C₂×D₁₃₉	semidirect
329. C₄×D₄	C₂×D₁₃₉	semidirect
330. C₄×D₄	C₂×D₁₃₉	semidirect
331. C₄×D₄	C₂×D₁₃₉	semidirect
335. C₂×C₄⋊C₄	C₂×D₁₃₉	semidirect
337. C₂×C₂²⋊C₄	C₂×D₁₃₉	semidirect
339. C₂×C₄²	C₂×D₁₃₉	semidirect
445. D₄	#14555785	direct (N × H)
464. C₂×C₄	D₄×D₁₃₉	semidirect
489. C₂²	C₂×#14555785	semidirect
502. C₄	C₂×#14555785	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14555785	2
#22581624	2
D₄×Dic₂₇₈	2
#22581612	2
#22581608	2
#22581604	2
#22581599	2
#22581593	2
D₄×D₅₅₆	2
D₄×C₂²⋊D₁₃₉	2
#22581503	2
#22581500	2
#22581464	2
#22581462	2
C₄×#14555785	2
C₄×D₄×D₁₃₉	2
C₂×C₄×D₄×C₁₃₉	2
D₄×#41	139

Subgroups — D4×#14555785 #31819892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#14555785 #31819892