Subgroups — C₂×#23776789 #35195122

Order 20224.

7302 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23776789	C₂	1	32	yes	maximal, direct product factor
2	C₂×#19099182	C₂	1	4	yes	maximal, complemented
3	C₂×#19099174	C₂	1	2	yes	maximal, complemented
4	C₂×#19099167	C₂	1	2	yes	maximal, complemented
5	C₂×#19099158	C₂	1	4	yes	maximal, complemented
6	C₂×#19099150	C₂	1	4	yes	maximal, complemented
7	C₂×#19099120	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#19099093	C₂	1	8	yes	maximal, complemented
9	C₂×#19099070	C₂	1	2	yes	maximal, complemented
10	C₂×#41×Dic₇₉	C₂	1	2	yes	maximal, complemented
11	C₂²×#14579118	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#532×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×C₄×D₇₉	C₂²	1	1	yes	characteristic
14	#19099182	C₂²	1	64	yes	complemented
15	#19099174	C₂²	1	32	yes	complemented
16	#19099167	C₂²	1	32	yes	complemented
17	#19099158	C₂²	1	64	yes	complemented
18	#19099150	C₂²	1	64	yes	complemented
19	#19099120	C₂²	1	16	yes	complemented
20	C₂×#14579161	C₂²	1	2	yes	complemented
21	#19099093	C₂²	1	128	yes	complemented
22	C₂×#14579156	C₂²	1	8	yes	—
23	C₂×#14579154	C₂²	1	8	yes	complemented
24	C₂×#14579153	C₂²	1	2	yes	complemented
25	C₂×#14579151	C₂²	1	8	yes	complemented
26	C₂×#14579147	C₂²	1	8	yes	—
27	#19099070	C₂²	1	32	yes	complemented
28	C₂×#14579145	C₂²	1	8	yes	—
29	C₂×#14579142	C₂²	1	4	yes	—
30	C₂×#14579142	C₂²	1	8	yes	complemented
31	C₂×#14579140	C₂²	1	4	yes	—
32	C₂×#14579138	C₂²	1	8	yes	complemented
33	C₂×#14579137	C₂²	1	4	yes	—
34	C₂×#14579133	C₂²	1	8	yes	—
35	C₂×#14579132	C₂²	1	4	yes	—
36	C₂×#14579129	C₂²	1	4	yes	—
37	#41×Dic₇₉	C₂²	1	32	yes	complemented
38	C₂×Q₈×Dic₇₉	C₂²	1	4	yes	complemented
39	C₂×C₄×Dic₁₅₈	C₂²	1	4	yes	complemented
40	C₂×D₄×Dic₇₉	C₂²	1	8	yes	—
41	C₂×D₄×Dic₇₉	C₂²	1	4	yes	complemented
42	C₂×C₄×C₂²⋊D₇₉	C₂²	1	8	yes	—
43	C₂×#14579120	C₂²	1	2	yes	—
44	C₂×#14579120	C₂²	1	4	yes	complemented
45	C₂×#14579118	C₂²	1	2	yes	—
46	C₂×#14579118	C₂²	1	4	yes	—
47	C₂×#14579118	C₂²	1	2	yes	—
48	C₂×#14579118	C₂²	1	16	yes	complemented
49	C₂²×Dic₇₉⋊C₄	C₂²	1	2	yes	—
50	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	—
51	C₂²×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
52	C₂²×C₄×Dic₇₉	C₂²	1	4	yes	complemented
53	C₂²×#41×C₇₉	C₂²	1	2	yes	—
54	#532×C₇₉	C₂²	1	16	yes	complemented
55	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
56	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic, complemented
57	C₂×#124×C₇₉	C₂²	1	2	yes	complemented
58	C₂×#121×C₇₉	C₂²	1	4	yes	—
59	C₂×C₄×D₄×C₇₉	C₂²	1	4	yes	complemented
60	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
61	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
62	C₂²×Dic₁₅₈	C₂³	1	4	yes	—
63	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
64	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
65	C₂³×Dic₇₉	C₂³	1	2	yes	—
66	C₂³×Dic₇₉	C₂³	1	8	yes	—
67	C₂²×C₄×D₇₉	—	2	8	no	—
68	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
69	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
70	C₂²×C₄×D₇₉	C₂³	1	8	yes	—
71	#14579161	C₂³	1	16	yes	complemented
72	#14579156	C₂³	1	64	yes	—
73	#14579154	C₂³	1	64	yes	complemented
74	#14579153	C₂³	1	16	yes	complemented
75	#14579151	C₂³	1	64	yes	complemented
76	#14579147	C₂³	1	64	yes	—
77	#14579145	C₂³	1	64	yes	—
78	#14579142	C₂³	1	32	yes	—
79	#14579142	C₂³	1	64	yes	complemented
80	#14579140	C₂³	1	32	yes	—
81	#14579138	C₂³	1	64	yes	complemented
82	#14579137	C₂³	1	32	yes	—
83	#14579133	C₂³	1	64	yes	—
84	#14579132	C₂³	1	32	yes	—
85	#14579129	C₂³	1	32	yes	—
86	Q₈×Dic₇₉	C₂³	1	32	yes	complemented
87	C₄×Dic₁₅₈	C₂³	1	32	yes	complemented
88	D₄×Dic₇₉	C₂³	1	64	yes	—
89	D₄×Dic₇₉	C₂³	1	32	yes	complemented
90	C₄×C₂²⋊D₇₉	C₂³	1	64	yes	—
91	#14579120	C₂³	1	16	yes	—
92	#14579120	C₂³	1	32	yes	complemented
93	#14579118	C₂³	1	16	yes	—
94	#14579118	C₂³	1	16	yes	—
95	#14579118	C₂³	1	32	yes	—
96	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
97	C₂×C₄⋊Dic₇₉	C₂³	1	8	yes	—
98	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
99	C₂×Dic₇₉⋊C₄	C₂³	1	16	yes	—
100	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
101	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
102	C₂×Dic₇₉⋊C₄	C₂³	1	8	yes	—
103	C₂×Dic₇₉⋊C₄	C₂³	1	8	yes	—
104	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
105	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
106	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
107	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	16	yes	—
108	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
109	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
110	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
111	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
112	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
113	C₂×C₄×Dic₇₉	C₂³	1	8	yes	—
114	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
115	C₂×C₄×Dic₇₉	C₂³	1	8	yes	—
116	C₂×C₄×Dic₇₉	C₂³	1	32	yes	complemented
117	C₂×#41×C₇₉	—	2	16	no	—
118	C₂×#41×C₇₉	C₂³	1	16	yes	—
119	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
120	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
121	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
122	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
123	C₂³×C₄×C₇₉	C₂³	1	4	yes	—
124	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
125	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
126	C₄⋊Q₈×C₇₉	C₂³	1	8	yes	complemented
127	#127×C₇₉	C₂³	1	8	yes	complemented
128	#124×C₇₉	C₂³	1	16	yes	complemented
129	#121×C₇₉	C₂³	1	32	yes	—
130	C₄×D₄×C₇₉	C₂³	1	32	yes	complemented
131	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
133	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
134	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₇₉	C₂³	1	8	yes	—
137	C₂³×D₇₉	—	2	4	no	—
138	C₂³×D₇₉	—	4	4	no	—
139	C₂³×D₇₉	C₂⁴	1	2	yes	—
140	C₂³×D₇₉	C₂⁴	1	4	yes	—
141	C₂×Dic₁₅₈	—	4	8	no	—
142	C₂×Dic₁₅₈	C₂⁴	1	16	yes	—
143	C₂×C₂²⋊D₇₉	—	4	16	no	—
144	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	—
145	C₂²×Dic₇₉	—	2	4	no	—
146	C₂²×Dic₇₉	—	4	4	no	—
147	C₂²×Dic₇₉	—	4	16	no	—
148	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
149	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
150	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
151	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
152	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
153	C₂²×Dic₇₉	C₂⁴	1	32	yes	—
154	C₂×C₄×D₇₉	—	2	8	no	—
155	C₂×C₄×D₇₉	—	2	8	no	—
156	C₂×C₄×D₇₉	—	2	32	no	—
157	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
158	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
159	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
160	C₄⋊Dic₇₉	C₂⁴	1	32	yes	—
161	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
162	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
163	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
164	Dic₇₉⋊C₄	C₂⁴	1	32	yes	—
165	Dic₇₉⋊C₄	C₂⁴	1	32	yes	—
166	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
167	C₂²⋊Dic₇₉	C₂⁴	1	32	yes	—
168	C₂²⋊Dic₇₉	C₂⁴	1	32	yes	—
169	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
170	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
171	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
172	C₄×Dic₇₉	C₂⁴	1	8	yes	—
173	C₄×Dic₇₉	C₂⁴	1	8	yes	—
174	C₄×Dic₇₉	C₂⁴	1	16	yes	—
175	C₄×Dic₇₉	C₂⁴	1	32	yes	—
176	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
177	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
178	#41×C₇₉	—	2	64	no	—
179	C₂×Q₈×C₇₉	—	2	8	no	—
180	C₂×Q₈×C₇₉	C₂⁴	1	8	yes	—
181	C₂×D₄×C₇₉	—	2	16	no	—
182	C₂×D₄×C₇₉	—	2	8	no	—
183	C₂×D₄×C₇₉	—	4	8	no	—
184	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
185	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
186	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
187	C₂²×C₄×C₇₉	—	2	16	no	—
188	C₂²×C₄×C₇₉	—	4	4	no	—
189	C₂²×C₄×C₇₉	#41	1	8	yes	—
190	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₇₉	C₂⁴	1	16	yes	—
194	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
195	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
198	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
199	C₂²⋊C₄×C₇₉	C₂⁴	1	32	yes	—
200	C₄²×C₇₉	C₂⁴	1	8	yes	—
201	C₄²×C₇₉	C₂⁴	1	4	yes	—
202	C₄²×C₇₉	C₂⁴	1	4	yes	—
203	C₂³×C₇₉	—	2	4	no	—
204	C₂³×C₇₉	—	2	8	no	—
205	C₂³×C₇₉	—	2	16	no	—
206	C₂³×C₇₉	C₂×#41	1	4	yes	—
207	C₂³×C₇₉	C₂⁵	1	8	yes	—
208	C₂³×C₇₉	C₂⁵	1	2	yes	—
209	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
210	C₂²×D₇₉	—	2	8	no	—
211	C₂²×D₇₉	—	2	4	no	—
212	C₂²×D₇₉	—	2	8	no	—
213	C₂²×D₇₉	—	4	8	no	—
214	C₂²×D₇₉	—	4	16	no	—
215	C₂²×D₇₉	C₂⁵	1	4	yes	—
216	Q₈×C₇₉	—	2	16	no	—
217	D₄×C₇₉	—	2	32	no	—
218	D₄×C₇₉	—	2	16	no	—
219	D₄×C₇₉	—	4	16	no	—
220	C₂×C₄×C₇₉	—	2	8	no	—
221	C₂×C₄×C₇₉	—	2	4	no	—
222	C₂×C₄×C₇₉	—	2	4	no	—
223	C₂×C₄×C₇₉	—	2	32	no	—
224	C₂×C₄×C₇₉	—	4	8	no	—
225	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
226	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
227	C₂×C₄×C₇₉	C₂×#41	1	16	yes	—
228	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
229	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
230	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
231	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
232	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
233	C₂²⋊D₇₉	—	4	32	no	—
234	C₂×Dic₇₉	—	2	8	no	—
235	C₂×Dic₇₉	—	2	4	no	—
236	C₂×Dic₇₉	—	2	8	no	—
237	C₂×Dic₇₉	—	2	16	no	—
238	C₂×Dic₇₉	—	4	32	no	—
239	C₂×Dic₇₉	—	4	8	no	—
240	C₂×Dic₇₉	C₂⁵	1	8	yes	—
241	C₂×Dic₇₉	C₂⁵	1	16	yes	—
242	C₂×Dic₇₉	C₂⁵	1	4	yes	—
243	C₄×D₇₉	—	2	16	no	—
244	C₄×D₇₉	—	2	16	no	—
245	Dic₁₅₈	—	4	16	no	—
246	C₂²×C₇₉	—	2	4	no	—
247	C₂²×C₇₉	—	2	8	no	—
248	C₂²×C₇₉	—	2	8	no	—
249	C₂²×C₇₉	—	2	16	no	—
250	C₂²×C₇₉	—	4	16	no	—
251	C₂²×C₇₉	C₂²×#41	1	4	yes	—
252	C₂²×C₇₉	C₂²×#41	1	2	yes	—
253	C₂²×C₇₉	#585	1	4	yes	—
254	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
255	C₂×D₇₉	—	2	4	no	—
256	C₂×D₇₉	—	2	8	no	—
257	C₂×D₇₉	—	4	16	no	—
258	C₂×D₇₉	—	4	8	no	—
259	C₄×C₇₉	—	2	8	no	—
260	C₄×C₇₉	—	2	4	no	—
261	C₄×C₇₉	—	2	4	no	—
262	C₄×C₇₉	C₂²×#41	1	4	yes	—
263	C₄×C₇₉	C₂²×#41	1	4	yes	—
264	Dic₇₉	—	2	4	no	—
265	Dic₇₉	—	2	16	no	—
266	Dic₇₉	—	2	8	no	—
267	C₂×#3455	—	79	1	no	maximal, Sylow
268	C₂×C₇₉	—	2	4	no	—
269	C₂×C₇₉	—	4	8	no	—
270	C₂×C₇₉	#3455	1	4	yes	complemented
271	C₂×C₇₉	C₂³×#41	1	1	yes	characteristic
272	C₂×C₇₉	C₂×#585	1	2	yes	—
273	D₇₉	—	4	4	no	—
274	#3455	—	79	32	no	—
275	C₂×#542	—	79	4	no	—
276	C₂×#541	—	79	2	no	—
277	C₂×#540	—	79	2	no	—
278	C₂×#539	—	79	4	no	—
279	C₂×#538	—	79	4	no	—
280	C₂×#533	—	79	1	no	—
281	C₂×#532	D₇₉	1	1	yes	characteristic, complemented
282	C₂×#529	—	79	8	no	—
283	C₂×#525	—	79	2	no	—
284	C₂×C₄×#41	—	79	2	no	—
285	C₂²×#117	—	79	1	no	—
286	C₇₉	C₂×#3455	1	1	yes	characteristic, complemented, Sylow
287	C₂²×#41	C₂×D₇₉	1	2	yes	—
288	C₂⁴×C₄	—	79	1	no	—
289	#542	—	79	64	no	—
290	#541	—	79	32	no	—
291	#540	—	79	32	no	—
292	#539	—	79	64	no	—
293	#538	—	79	64	no	—
294	#533	—	79	16	no	—
295	#532	C₂×D₇₉	1	16	yes	complemented
296	C₂×C₄⋊Q₈	—	79	2	no	—
297	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
298	C₂×#127	C₂×D₇₉	1	1	yes	characteristic, complemented
299	#529	—	79	128	no	—
300	C₂×#126	—	79	8	no	—
301	C₂×#126	—	79	8	no	—
302	C₂×#125	—	79	8	no	—
303	C₂×#125	—	79	2	no	—
304	C₂×#124	—	79	8	no	—
305	C₂×#124	C₂×D₇₉	1	2	yes	complemented
306	#525	—	79	32	no	—
307	C₂×#123	—	79	4	no	—
308	C₂×#123	—	79	8	no	—
309	C₂×#123	—	79	8	no	—
310	C₂×C₂²⋊Q₈	—	79	4	no	—
311	C₂×C₂²⋊Q₈	—	79	4	no	—
312	C₂×C₂²⋊Q₈	—	79	8	no	—
313	C₂×#121	—	79	4	no	—
314	C₂×#121	—	79	8	no	—
315	C₂×#121	C₂×D₇₉	1	4	yes	—
316	C₂×#120	—	79	4	no	—
317	C₄×#41	—	79	32	no	—
318	C₂×C₄×Q₈	—	79	4	no	—
319	C₂×C₄×Q₈	—	79	4	no	—
320	C₂×C₄×D₄	—	79	8	no	—
321	C₂×C₄×D₄	—	79	4	no	—
322	C₂×C₄×D₄	—	79	8	no	—
323	C₂×C₄×D₄	C₂×D₇₉	1	4	yes	complemented
324	C₂×#117	—	79	2	no	—
325	C₂×#117	—	79	4	no	—
326	C₂×#117	—	79	4	no	—
327	C₂×#117	—	79	2	no	—
328	C₂×#117	—	79	2	no	—
329	C₂×#117	—	79	16	no	—
330	C₂²×C₄⋊C₄	—	79	2	no	—
331	C₂²×C₂²⋊C₄	—	79	2	no	—
332	C₂²×C₄²	—	79	1	no	—
333	C₂²×C₄²	—	79	4	no	—
334	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
335	C₂⁵	—	79	1	no	—
336	C₂×#41	—	2	16	no	—
337	C₂×#41	C₂²×D₇₉	1	16	yes	—
338	C₂²×Q₈	—	79	4	no	—
339	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
340	C₂²×D₄	—	79	8	no	—
341	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
342	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
343	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
344	C₂³×C₄	—	79	2	no	—
345	C₂³×C₄	—	79	8	no	—
346	C₂³×C₄	—	79	1	no	—
347	C₂³×C₄	—	79	2	no	—
348	C₂³×C₄	—	79	8	no	—
349	C₂³×C₄	—	79	2	no	—
350	C₂³×C₄	—	158	8	no	—
351	C₂³×C₄	C₂²×D₇₉	1	4	yes	—
352	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
353	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
354	C₄⋊Q₈	—	79	16	no	—
355	C₄⋊Q₈	C₂²×D₇₉	1	8	yes	complemented
356	#127	C₂²×D₇₉	1	8	yes	complemented
357	#126	—	79	64	no	—
358	#126	—	79	64	no	—
359	#125	—	79	64	no	—
360	#125	—	79	16	no	—
361	#124	—	79	64	no	—
362	#124	C₂²×D₇₉	1	16	yes	complemented
363	#123	—	79	32	no	—
364	#123	—	79	64	no	—
365	#123	—	79	64	no	—
366	C₂²⋊Q₈	—	79	32	no	—
367	C₂²⋊Q₈	—	79	32	no	—
368	C₂²⋊Q₈	—	79	64	no	—
369	#121	—	79	32	no	—
370	#121	—	79	64	no	—
371	#121	C₂²×D₇₉	1	32	yes	—
372	#120	—	79	32	no	—
373	C₄×Q₈	—	79	32	no	—
374	C₄×Q₈	—	79	32	no	—
375	C₄×D₄	—	79	64	no	—
376	C₄×D₄	—	79	32	no	—
377	C₄×D₄	—	79	64	no	—
378	C₄×D₄	C₂²×D₇₉	1	32	yes	complemented
379	#117	—	79	16	no	—
380	#117	—	79	32	no	—
381	#117	—	79	32	no	—
382	#117	—	79	16	no	—
383	#117	—	79	16	no	—
384	C₂×C₄⋊C₄	—	79	4	no	—
385	C₂×C₄⋊C₄	—	79	4	no	—
386	C₂×C₄⋊C₄	—	79	16	no	—
387	C₂×C₄⋊C₄	—	79	4	no	—
388	C₂×C₄⋊C₄	—	79	8	no	—
389	C₂×C₄⋊C₄	—	79	8	no	—
390	C₂×C₄⋊C₄	—	79	8	no	—
391	C₂×C₄⋊C₄	—	79	4	no	—
392	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
393	C₂×C₂²⋊C₄	—	79	4	no	—
394	C₂×C₂²⋊C₄	—	79	8	no	—
395	C₂×C₂²⋊C₄	—	79	8	no	—
396	C₂×C₂²⋊C₄	—	79	4	no	—
397	C₂×C₂²⋊C₄	—	79	4	no	—
398	C₂×C₂²⋊C₄	—	79	16	no	—
399	C₂×C₂²⋊C₄	—	79	8	no	—
400	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	—
401	C₂×C₄²	—	79	2	no	—
402	C₂×C₄²	—	79	8	no	—
403	C₂×C₄²	—	79	8	no	—
404	C₂×C₄²	—	79	32	no	—
405	C₂×C₄²	—	79	2	no	—
406	C₂×C₄²	—	79	4	no	—
407	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
408	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
409	C₂×C₄²	C₂²×D₇₉	1	8	yes	—
410	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
411	C₂⁴	—	316	4	no	—
412	C₂⁴	—	79	4	no	—
413	C₂⁴	—	79	2	no	—
414	C₂⁴	—	158	4	no	—
415	C₂⁴	C₂³×D₇₉	1	4	yes	—
416	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
417	#41	—	2	64	no	—
418	C₂×Q₈	—	2	8	no	—
419	C₂×Q₈	—	316	8	no	—
420	C₂×Q₈	—	79	16	no	—
421	C₂×Q₈	C₂³×D₇₉	1	8	yes	—
422	C₂×D₄	—	2	16	no	—
423	C₂×D₄	—	2	8	no	—
424	C₂×D₄	—	4	8	no	—
425	C₂×D₄	—	316	16	no	—
426	C₂×D₄	—	79	32	no	—
427	C₂×D₄	C₂³×D₇₉	1	16	yes	—
428	C₂×D₄	C₂³×D₇₉	1	8	yes	—
429	C₂×D₄	C₂³×D₇₉	1	16	yes	—
430	C₂²×C₄	—	2	16	no	—
431	C₂²×C₄	—	4	4	no	—
432	C₂²×C₄	—	316	4	no	—
433	C₂²×C₄	—	316	16	no	—
434	C₂²×C₄	—	79	8	no	—
435	C₂²×C₄	—	79	32	no	—
436	C₂²×C₄	—	79	4	no	—
437	C₂²×C₄	—	79	8	no	—
438	C₂²×C₄	—	79	2	no	—
439	C₂²×C₄	—	79	4	no	—
440	C₂²×C₄	—	79	8	no	—
441	C₂²×C₄	—	79	8	no	—
442	C₂²×C₄	—	158	4	no	—
443	C₂²×C₄	—	158	8	no	—
444	C₂²×C₄	—	158	8	no	—
445	C₂²×C₄	—	158	32	no	—
446	C₂²×C₄	#11929623	1	8	yes	—
447	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
448	C₂²×C₄	C₂³×D₇₉	1	16	yes	—
449	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
450	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
451	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
452	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
453	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
454	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
455	C₄⋊C₄	—	79	16	no	—
456	C₄⋊C₄	—	79	16	no	—
457	C₄⋊C₄	—	79	32	no	—
458	C₄⋊C₄	—	79	32	no	—
459	C₄⋊C₄	—	79	16	no	—
460	C₄⋊C₄	—	79	32	no	—
461	C₄⋊C₄	—	79	16	no	—
462	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
463	C₂²⋊C₄	—	79	16	no	—
464	C₂²⋊C₄	—	79	32	no	—
465	C₂²⋊C₄	—	79	32	no	—
466	C₂²⋊C₄	—	79	16	no	—
467	C₂²⋊C₄	—	79	16	no	—
468	C₂²⋊C₄	—	79	32	no	—
469	C₂²⋊C₄	C₂³×D₇₉	1	32	yes	—
470	C₄²	—	79	8	no	—
471	C₄²	—	79	8	no	—
472	C₄²	—	79	16	no	—
473	C₄²	—	79	32	no	—
474	C₄²	C₂³×D₇₉	1	8	yes	—
475	C₄²	C₂³×D₇₉	1	4	yes	—
476	C₄²	C₂³×D₇₉	1	4	yes	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	16	no	—
479	C₂³	—	2	8	no	—
480	C₂³	—	316	16	no	—
481	C₂³	—	316	8	no	—
482	C₂³	—	79	4	no	—
483	C₂³	—	158	8	no	—
484	C₂³	—	158	8	no	—
485	C₂³	—	158	4	no	—
486	C₂³	C₂×#11929623	1	4	yes	—
487	C₂³	C₂⁴×D₇₉	1	8	yes	—
488	C₂³	C₂⁴×D₇₉	1	2	yes	—
489	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
490	Q₈	—	2	16	no	—
491	Q₈	—	316	16	no	—
492	D₄	—	2	32	no	—
493	D₄	—	2	16	no	—
494	D₄	—	4	16	no	—
495	D₄	—	316	32	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	8	no	—
499	C₂×C₄	—	2	32	no	—
500	C₂×C₄	—	4	8	no	—
501	C₂×C₄	—	316	8	no	—
502	C₂×C₄	—	316	32	no	—
503	C₂×C₄	—	79	8	no	—
504	C₂×C₄	—	79	16	no	—
505	C₂×C₄	—	79	4	no	—
506	C₂×C₄	—	158	8	no	—
507	C₂×C₄	—	158	16	no	—
508	C₂×C₄	—	158	8	no	—
509	C₂×C₄	—	158	4	no	—
510	C₂×C₄	—	158	16	no	—
511	C₂×C₄	—	158	16	no	—
512	C₂×C₄	C₂×#11929623	1	4	yes	—
513	C₂×C₄	C₂×#11929623	1	4	yes	—
514	C₂×C₄	C₂×#11929623	1	16	yes	—
515	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
516	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
517	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
518	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
519	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
520	C₂²	—	2	8	no	—
521	C₂²	—	2	4	no	—
522	C₂²	—	2	8	no	—
523	C₂²	—	2	16	no	—
524	C₂²	—	4	16	no	—
525	C₂²	—	316	16	no	—
526	C₂²	—	316	8	no	—
527	C₂²	—	158	4	no	—
528	C₂²	—	158	8	no	—
529	C₂²	C₂²×#11929623	1	4	yes	—
530	C₂²	C₂²×#11929623	1	2	yes	—
531	C₂²	#19099399	1	4	yes	—
532	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
533	C₄	—	2	8	no	—
534	C₄	—	2	4	no	—
535	C₄	—	2	4	no	—
536	C₄	—	158	4	no	—
537	C₄	—	158	8	no	—
538	C₄	—	158	16	no	—
539	C₄	C₂²×#11929623	1	4	yes	—
540	C₄	C₂²×#11929623	1	4	yes	—
541	C₂	—	2	4	no	—
542	C₂	—	4	8	no	—
543	C₂	—	316	4	no	—
544	C₂	#23776789	1	4	yes	direct product factor
545	C₂	C₂³×#11929623	1	1	yes	characteristic
546	C₂	C₂×#19099399	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#532×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂×#532	D₇₉
hypocenter	C₇₉	C₂×#3455
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #23776789	C₂	direct (N × H)
2. C₂×#19099182	C₂	semidirect
3. C₂×#19099174	C₂	semidirect
4. C₂×#19099167	C₂	semidirect
5. C₂×#19099158	C₂	semidirect
6. C₂×#19099150	C₂	semidirect
7. C₂×#19099120	C₂	semidirect
8. C₂×#19099093	C₂	semidirect
9. C₂×#19099070	C₂	semidirect
10. C₂×#41×Dic₇₉	C₂	semidirect
11. C₂²×#14579118	C₂	semidirect
12. C₂×#532×C₇₉	C₂	semidirect
14. #19099182	C₂²	semidirect
15. #19099174	C₂²	semidirect
16. #19099167	C₂²	semidirect
17. #19099158	C₂²	semidirect
18. #19099150	C₂²	semidirect
19. #19099120	C₂²	semidirect
20. C₂×#14579161	C₂²	semidirect
21. #19099093	C₂²	semidirect
23. C₂×#14579154	C₂²	semidirect
24. C₂×#14579153	C₂²	semidirect
25. C₂×#14579151	C₂²	semidirect
27. #19099070	C₂²	semidirect
30. C₂×#14579142	C₂²	semidirect
32. C₂×#14579138	C₂²	semidirect
37. #41×Dic₇₉	C₂²	semidirect
38. C₂×Q₈×Dic₇₉	C₂²	semidirect
39. C₂×C₄×Dic₁₅₈	C₂²	semidirect
41. C₂×D₄×Dic₇₉	C₂²	semidirect
44. C₂×#14579120	C₂²	semidirect
48. C₂×#14579118	C₂²	semidirect
52. C₂²×C₄×Dic₇₉	C₂²	semidirect
54. #532×C₇₉	C₂²	semidirect
55. C₂×C₄⋊Q₈×C₇₉	C₂²	semidirect
56. C₂×#127×C₇₉	C₂²	semidirect
57. C₂×#124×C₇₉	C₂²	semidirect
59. C₂×C₄×D₄×C₇₉	C₂²	semidirect
71. #14579161	C₂³	semidirect
73. #14579154	C₂³	semidirect
74. #14579153	C₂³	semidirect
75. #14579151	C₂³	semidirect
79. #14579142	C₂³	semidirect
81. #14579138	C₂³	semidirect
86. Q₈×Dic₇₉	C₂³	semidirect
87. C₄×Dic₁₅₈	C₂³	semidirect
89. D₄×Dic₇₉	C₂³	semidirect
92. #14579120	C₂³	semidirect
116. C₂×C₄×Dic₇₉	C₂³	semidirect
126. C₄⋊Q₈×C₇₉	C₂³	semidirect
127. #127×C₇₉	C₂³	semidirect
128. #124×C₇₉	C₂³	semidirect
130. C₄×D₄×C₇₉	C₂³	semidirect
270. C₂×C₇₉	#3455	semidirect
281. C₂×#532	D₇₉	semidirect
286. C₇₉	C₂×#3455	semidirect
295. #532	C₂×D₇₉	semidirect
297. C₂×C₄⋊Q₈	C₂×D₇₉	semidirect
298. C₂×#127	C₂×D₇₉	semidirect
305. C₂×#124	C₂×D₇₉	semidirect
323. C₂×C₄×D₄	C₂×D₇₉	semidirect
355. C₄⋊Q₈	C₂²×D₇₉	semidirect
356. #127	C₂²×D₇₉	semidirect
362. #124	C₂²×D₇₉	semidirect
378. C₄×D₄	C₂²×D₇₉	semidirect
544. C₂	#23776789	direct (N × H)

Maximal subgroups

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

subgroup	index
#23776789	2
C₂×#19099182	2
C₂×#19099174	2
C₂×#19099167	2
C₂×#19099158	2
C₂×#19099150	2
C₂×#19099120	2
C₂×#19099093	2
C₂×#19099070	2
C₂×#41×Dic₇₉	2
C₂²×#14579118	2
C₂×#532×C₇₉	2
C₂×#3455	79

Subgroups — C2×#23776789 #35195122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23776789 #35195122