Subgroups — C₂×#23777801 #35196071

Order 20224.

8802 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777801	C₂	1	32	yes	maximal, direct product factor
2	C₂×#19099305	C₂	1	4	yes	maximal, complemented
3	C₂×#19099279	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19099276	C₂	1	4	yes	maximal, complemented
5	C₂×D₄×D₃₁₆	C₂	1	2	yes	maximal, complemented
6	C₂×#19099197	C₂	1	4	yes	maximal, complemented
7	C₂×#19099132	C₂	1	4	yes	maximal, complemented
8	C₂×#19099131	C₂	1	4	yes	maximal, complemented
9	C₂×#19099129	C₂	1	4	yes	maximal, complemented
10	C₂×#19099114	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#19099110	C₂	1	2	yes	maximal, complemented
12	C₂×#555×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#11929625	C₂²	1	2	yes	complemented
14	C₂²×#11929624	C₂²	1	4	yes	complemented
15	C₂³×D₃₁₆	C₂²	1	4	yes	complemented
16	C₂²×D₄×D₇₉	C₂²	1	4	yes	complemented
17	C₂²×D₄×D₇₉	C₂²	1	4	yes	complemented
18	#19099305	C₂²	1	64	yes	complemented
19	#19099279	C₂²	1	16	yes	complemented
20	#19099276	C₂²	1	64	yes	complemented
21	D₄×D₃₁₆	C₂²	1	32	yes	complemented
22	#19099197	C₂²	1	64	yes	complemented
23	#19099132	C₂²	1	64	yes	complemented
24	#19099131	C₂²	1	64	yes	complemented
25	#19099129	C₂²	1	64	yes	complemented
26	#19099114	C₂²	1	16	yes	complemented
27	#19099110	C₂²	1	32	yes	complemented
28	C₂×#14579160	C₂²	1	2	yes	complemented
29	C₂×#14579158	C₂²	1	1	yes	characteristic
30	C₂×#14579158	C₂²	1	4	yes	complemented
31	C₂×#14579157	C₂²	1	2	yes	—
32	C₂×#14579157	C₂²	1	4	yes	complemented
33	C₂×#14579150	C₂²	1	2	yes	complemented
34	C₂×#14579150	C₂²	1	4	yes	complemented
35	C₂×#14579149	C₂²	1	8	yes	complemented
36	C₂×#14579147	C₂²	1	4	yes	complemented
37	C₂×#14579147	C₂²	1	8	yes	complemented
38	C₂×#14579136	C₂²	1	4	yes	complemented
39	C₂×#14579136	C₂²	1	4	yes	complemented
40	C₂×#14579136	C₂²	1	2	yes	complemented
41	C₂×#14579136	C₂²	1	4	yes	complemented
42	C₂×#14579135	C₂²	1	4	yes	complemented
43	C₂×#14579134	C₂²	1	8	yes	complemented
44	C₂×#14579134	C₂²	1	4	yes	complemented
45	C₂×#14579132	C₂²	1	2	yes	complemented
46	C₂×#14579131	C₂²	1	8	yes	complemented
47	C₂×#14579131	C₂²	1	8	yes	complemented
48	C₂×#14579131	C₂²	1	8	yes	complemented
49	C₂×#14579129	C₂²	1	8	yes	complemented
50	C₂×C₄×D₃₁₆	C₂²	1	2	yes	complemented
51	C₂×#14579123	C₂²	1	4	yes	complemented
52	C₂×C₄×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
53	C₂×#14579119	C₂²	1	4	yes	complemented
54	C₂×#14579118	C₂²	1	4	yes	complemented
55	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic, complemented
56	#555×C₇₉	C₂²	1	16	yes	complemented
57	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
58	C₂×#124×C₇₉	C₂²	1	4	yes	complemented
59	C₂×#121×C₇₉	C₂²	1	4	yes	complemented
60	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	complemented
61	C₂×#117×C₇₉	C₂²	1	4	yes	complemented
62	C₂⁴×D₇₉	C₂³	1	8	yes	—
63	C₂×#11929625	—	4	8	no	—
64	C₂×#11929625	C₂³	1	16	yes	complemented
65	C₂×#11929624	—	4	16	no	—
66	C₂×#11929624	C₂³	1	32	yes	complemented
67	C₂²×Dic₁₅₈	C₂³	1	4	yes	—
68	C₂²×D₃₁₆	—	4	16	no	—
69	C₂²×D₃₁₆	C₂³	1	4	yes	—
70	C₂²×D₃₁₆	C₂³	1	2	yes	—
71	C₂²×D₃₁₆	C₂³	1	2	yes	—
72	C₂²×D₃₁₆	C₂³	1	8	yes	—
73	C₂²×D₃₁₆	C₂³	1	4	yes	—
74	C₂²×D₃₁₆	C₂³	1	4	yes	—
75	C₂²×D₃₁₆	C₂³	1	4	yes	—
76	C₂²×D₃₁₆	C₂³	1	32	yes	complemented
77	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
78	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
79	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
80	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
81	C₂×D₄×D₇₉	—	4	16	no	—
82	C₂×D₄×D₇₉	—	4	16	no	—
83	C₂×D₄×D₇₉	C₂³	1	32	yes	complemented
84	C₂×D₄×D₇₉	C₂³	1	32	yes	complemented
85	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
86	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
87	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
88	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
89	#14579160	C₂³	1	16	yes	complemented
90	#14579158	C₂³	1	8	yes	—
91	#14579158	C₂³	1	32	yes	complemented
92	#14579157	C₂³	1	16	yes	—
93	#14579157	C₂³	1	32	yes	complemented
94	#14579150	C₂³	1	32	yes	complemented
95	#14579150	C₂³	1	16	yes	complemented
96	#14579149	C₂³	1	64	yes	complemented
97	#14579147	C₂³	1	64	yes	complemented
98	#14579147	C₂³	1	32	yes	complemented
99	#14579136	C₂³	1	32	yes	complemented
100	#14579136	C₂³	1	32	yes	complemented
101	#14579136	C₂³	1	16	yes	complemented
102	#14579136	C₂³	1	32	yes	complemented
103	#14579135	C₂³	1	32	yes	complemented
104	#14579134	C₂³	1	64	yes	complemented
105	#14579134	C₂³	1	32	yes	complemented
106	#14579132	C₂³	1	16	yes	complemented
107	#14579131	C₂³	1	64	yes	complemented
108	#14579131	C₂³	1	64	yes	complemented
109	#14579131	C₂³	1	64	yes	complemented
110	#14579129	C₂³	1	64	yes	complemented
111	C₄×D₃₁₆	C₂³	1	16	yes	complemented
112	#14579123	C₂³	1	32	yes	complemented
113	C₄×C₂²⋊D₇₉	C₂³	1	32	yes	complemented
114	#14579119	C₂³	1	32	yes	complemented
115	#14579118	C₂³	1	32	yes	complemented
116	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
117	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
118	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
119	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
120	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
121	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
122	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
123	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
124	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
125	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
126	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
127	C₄²×D₇₉	C₂³	1	8	yes	complemented
128	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
129	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
130	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
131	C₂³×C₄×C₇₉	C₂³	1	4	yes	—
132	C₄⋊Q₈×C₇₉	C₂³	1	8	yes	complemented
133	#124×C₇₉	C₂³	1	32	yes	complemented
134	#121×C₇₉	C₂³	1	32	yes	complemented
135	C₄×D₄×C₇₉	C₂³	1	16	yes	complemented
136	#117×C₇₉	C₂³	1	32	yes	complemented
137	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
140	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
141	C₂×C₄²×C₇₉	C₂³	1	4	yes	—
142	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
143	C₂³×D₇₉	—	4	16	no	—
144	C₂³×D₇₉	—	4	16	no	—
145	C₂³×D₇₉	—	4	16	no	—
146	C₂³×D₇₉	C₂⁴	1	4	yes	—
147	C₂³×D₇₉	C₂⁴	1	4	yes	—
148	C₂³×D₇₉	C₂⁴	1	1	yes	characteristic
149	C₂³×D₇₉	C₂⁴	1	32	yes	—
150	#11929625	—	4	32	no	—
151	#11929624	—	4	64	no	—
152	C₂×Dic₁₅₈	—	4	8	no	—
153	C₂×Dic₁₅₈	C₂⁴	1	16	yes	—
154	C₂×D₃₁₆	—	2	16	no	—
155	C₂×D₃₁₆	—	2	8	no	—
156	C₂×D₃₁₆	—	4	8	no	—
157	C₂×D₃₁₆	—	4	8	no	—
158	C₂×D₃₁₆	—	4	4	no	—
159	C₂×D₃₁₆	—	4	8	no	—
160	C₂×D₃₁₆	—	4	16	no	—
161	C₂×D₃₁₆	—	4	64	no	—
162	C₂×D₃₁₆	C₂⁴	1	16	yes	—
163	C₂×D₃₁₆	C₂⁴	1	8	yes	—
164	C₂×D₃₁₆	C₂⁴	1	16	yes	—
165	C₂×D₃₁₆	C₂⁴	1	8	yes	—
166	C₂×D₃₁₆	C₂⁴	1	16	yes	—
167	C₂×D₃₁₆	C₂⁴	1	32	yes	—
168	C₂×D₃₁₆	C₂⁴	1	16	yes	—
169	C₂×C₂²⋊D₇₉	—	2	16	no	—
170	C₂×C₂²⋊D₇₉	—	4	8	no	—
171	C₂×C₂²⋊D₇₉	—	4	8	no	—
172	C₂×C₂²⋊D₇₉	—	4	16	no	—
173	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
174	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
175	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
176	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	—
177	D₄×D₇₉	—	4	64	no	—
178	D₄×D₇₉	—	4	64	no	—
179	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
180	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
181	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×D₇₉	—	2	4	no	—
183	C₂×C₄×D₇₉	—	2	16	no	—
184	C₂×C₄×D₇₉	—	2	8	no	—
185	C₂×C₄×D₇₉	—	2	16	no	—
186	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
187	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
188	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
189	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
190	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
191	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
192	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
193	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
194	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
195	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
196	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
197	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
198	C₄×Dic₇₉	C₂⁴	1	8	yes	—
199	C₄×Dic₇₉	C₂⁴	1	4	yes	—
200	C₄×Dic₇₉	C₂⁴	1	16	yes	—
201	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
202	C₂×Q₈×C₇₉	—	4	4	no	—
203	C₂×Q₈×C₇₉	C₂⁴	1	8	yes	—
204	C₂×D₄×C₇₉	—	2	8	no	—
205	C₂×D₄×C₇₉	—	4	8	no	—
206	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
207	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
208	C₂²×C₄×C₇₉	—	2	16	no	—
209	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₇₉	C₂⁴	1	16	yes	—
211	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
213	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
214	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
215	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
216	C₂²⋊C₄×C₇₉	C₂⁴	1	32	yes	—
217	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
218	C₄²×C₇₉	C₂⁴	1	16	yes	—
219	C₄²×C₇₉	C₂⁴	1	4	yes	—
220	C₂³×C₇₉	—	2	8	no	—
221	C₂³×C₇₉	—	2	8	no	—
222	C₂³×C₇₉	—	2	8	no	—
223	C₂³×C₇₉	C₂⁵	1	8	yes	—
224	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
225	C₂²×D₇₉	—	2	4	no	—
226	C₂²×D₇₉	—	2	8	no	—
227	C₂²×D₇₉	—	2	2	no	—
228	C₂²×D₇₉	—	2	8	no	—
229	C₂²×D₇₉	—	2	8	no	—
230	C₂²×D₇₉	—	2	16	no	—
231	C₂²×D₇₉	—	2	8	no	—
232	C₂²×D₇₉	—	4	32	no	—
233	C₂²×D₇₉	—	4	32	no	—
234	C₂²×D₇₉	—	4	32	no	—
235	C₂²×D₇₉	—	8	64	no	—
236	C₂²×D₇₉	C₂⁵	1	8	yes	—
237	C₂²×D₇₉	C₂⁵	1	8	yes	—
238	C₂²×D₇₉	C₂⁵	1	2	yes	—
239	Q₈×C₇₉	—	4	8	no	—
240	D₄×C₇₉	—	2	16	no	—
241	D₄×C₇₉	—	4	16	no	—
242	C₂×C₄×C₇₉	—	2	8	no	—
243	C₂×C₄×C₇₉	—	2	2	no	—
244	C₂×C₄×C₇₉	—	2	8	no	—
245	C₂×C₄×C₇₉	—	2	32	no	—
246	C₂×C₄×C₇₉	H(5,𝔽₂)	1	8	yes	—
247	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
248	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
249	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
250	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
251	C₂²⋊D₇₉	—	2	32	no	—
252	C₂²⋊D₇₉	—	4	32	no	—
253	C₂²⋊D₇₉	—	4	16	no	—
254	C₂²⋊D₇₉	—	4	16	no	—
255	C₂×Dic₇₉	—	2	8	no	—
256	C₂×Dic₇₉	—	2	4	no	—
257	C₂×Dic₇₉	H(5,𝔽₂)	1	4	yes	—
258	C₂×Dic₇₉	C₂⁵	1	4	yes	—
259	C₂×Dic₇₉	C₂⁵	1	8	yes	—
260	C₂×Dic₇₉	C₂⁵	1	2	yes	—
261	D₃₁₆	—	2	32	no	—
262	D₃₁₆	—	2	16	no	—
263	D₃₁₆	—	4	16	no	—
264	D₃₁₆	—	4	32	no	—
265	D₃₁₆	—	4	16	no	—
266	D₃₁₆	—	4	16	no	—
267	D₃₁₆	—	4	8	no	—
268	C₄×D₇₉	—	2	32	no	—
269	C₄×D₇₉	—	2	16	no	—
270	C₄×D₇₉	—	2	32	no	—
271	C₄×D₇₉	—	2	8	no	—
272	Dic₁₅₈	—	4	16	no	—
273	C₂²×C₇₉	—	2	8	no	—
274	C₂²×C₇₉	—	2	8	no	—
275	C₂²×C₇₉	—	2	8	no	—
276	C₂²×C₇₉	—	4	16	no	—
277	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
278	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
279	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
280	C₂×D₇₉	—	2	8	no	—
281	C₂×D₇₉	—	2	4	no	—
282	C₂×D₇₉	—	2	8	no	—
283	C₂×D₇₉	—	2	16	no	—
284	C₂×D₇₉	—	2	8	no	—
285	C₂×D₇₉	—	2	8	no	—
286	C₂×D₇₉	—	2	2	no	—
287	C₂×D₇₉	—	4	4	no	—
288	C₂×D₇₉	—	4	16	no	—
289	C₂×D₇₉	—	4	16	no	—
290	C₂×D₇₉	—	8	64	no	—
291	C₄×C₇₉	—	2	8	no	—
292	C₄×C₇₉	—	2	8	no	—
293	C₄×C₇₉	—	2	2	no	—
294	C₄×C₇₉	C₂×H(5,𝔽₂)	1	8	yes	—
295	Dic₇₉	—	2	8	no	—
296	Dic₇₉	—	2	4	no	—
297	Dic₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
298	C₂×#3549	—	79	1	no	maximal, Sylow
299	C₂×C₇₉	—	4	8	no	—
300	C₂×C₇₉	#3549	1	4	yes	complemented
301	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
302	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	2	yes	—
303	D₇₉	—	4	2	no	—
304	D₇₉	—	4	8	no	—
305	D₇₉	—	4	8	no	—
306	#3549	—	79	32	no	—
307	C₂×H(3,𝔽₄)	—	79	4	no	—
308	C₂×#555	—	79	1	no	—
309	C₂×#555	—	79	4	no	—
310	C₂×#555	D₇₉	1	1	yes	characteristic, complemented
311	C₂×D₄²	—	79	4	no	—
312	C₂×D₄²	—	79	2	no	—
313	C₂×#535	—	79	4	no	—
314	C₂×#535	—	79	4	no	—
315	C₂×#535	—	79	4	no	—
316	C₂×#532	—	79	1	no	—
317	C₂×#532	—	79	2	no	—
318	C₇₉	C₂×#3549	1	1	yes	characteristic, complemented, Sylow
319	C₂²×#41	—	79	2	no	—
320	C₂²×#41	—	79	4	no	—
321	C₂³×D₄	—	79	4	no	—
322	C₂³×D₄	—	79	4	no	—
323	C₂³×D₄	—	79	4	no	—
324	H(3,𝔽₄)	—	79	64	no	—
325	#555	—	79	16	no	—
326	#555	—	79	64	no	—
327	#555	C₂×D₇₉	1	16	yes	complemented
328	D₄²	—	79	64	no	—
329	D₄²	—	79	32	no	—
330	#535	—	79	64	no	—
331	#535	—	79	64	no	—
332	#535	—	79	64	no	—
333	#532	—	79	16	no	—
334	#532	—	79	32	no	—
335	C₂×C₄⋊Q₈	—	79	2	no	—
336	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
337	C₂×#127	—	79	2	no	—
338	C₂×#127	—	79	4	no	—
339	C₂×#127	—	79	1	no	—
340	C₂×#127	—	79	4	no	—
341	C₂×#124	—	79	2	no	—
342	C₂×#124	—	79	4	no	—
343	C₂×#124	—	79	4	no	—
344	C₂×#124	—	79	8	no	—
345	C₂×#124	—	79	8	no	—
346	C₂×#124	C₂×D₇₉	1	4	yes	complemented
347	C₂×#121	—	79	2	no	—
348	C₂×#121	—	79	4	no	—
349	C₂×#121	—	79	4	no	—
350	C₂×#121	—	79	2	no	—
351	C₂×#121	—	79	4	no	—
352	C₂×#121	—	79	4	no	—
353	C₂×#121	—	79	4	no	—
354	C₂×#121	—	79	8	no	—
355	C₂×#121	C₂×D₇₉	1	4	yes	complemented
356	C₂×#120	—	79	8	no	—
357	C₂×#120	—	79	8	no	—
358	C₂×#120	—	79	8	no	—
359	C₂×#120	—	79	8	no	—
360	C₂×C₄×D₄	—	79	4	no	—
361	C₂×C₄×D₄	—	79	4	no	—
362	C₂×C₄×D₄	—	79	2	no	—
363	C₂×C₄×D₄	C₂×D₇₉	1	2	yes	complemented
364	C₂×#117	—	79	4	no	—
365	C₂×#117	—	79	4	no	—
366	C₂×#117	C₂×D₇₉	1	4	yes	complemented
367	C₂²×C₄²	—	79	1	no	—
368	C₂⁵	—	79	8	no	—
369	C₂×#41	—	316	16	no	—
370	C₂×#41	—	316	8	no	—
371	C₂×#41	—	79	16	no	—
372	C₂×#41	—	79	32	no	—
373	C₂²×Q₈	—	79	4	no	—
374	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
375	C₂²×D₄	—	316	16	no	—
376	C₂²×D₄	—	316	16	no	—
377	C₂²×D₄	—	316	16	no	—
378	C₂²×D₄	—	79	4	no	—
379	C₂²×D₄	—	79	8	no	—
380	C₂²×D₄	—	79	4	no	—
381	C₂²×D₄	—	79	32	no	—
382	C₂²×D₄	—	79	32	no	—
383	C₂²×D₄	—	79	4	no	—
384	C₂²×D₄	—	79	2	no	—
385	C₂²×D₄	—	79	4	no	—
386	C₂²×D₄	—	79	8	no	—
387	C₂²×D₄	—	79	4	no	—
388	C₂²×D₄	—	79	4	no	—
389	C₂²×D₄	—	79	32	no	—
390	C₂²×D₄	—	79	4	no	—
391	C₂²×D₄	—	79	2	no	—
392	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
393	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
394	C₂³×C₄	—	79	4	no	—
395	C₂³×C₄	—	79	4	no	—
396	C₂³×C₄	—	79	1	no	—
397	C₂³×C₄	—	79	2	no	—
398	C₂³×C₄	C₂²×D₇₉	1	4	yes	—
399	C₄⋊Q₈	—	79	16	no	—
400	C₄⋊Q₈	C₂²×D₇₉	1	8	yes	complemented
401	#127	—	79	16	no	—
402	#127	—	79	32	no	—
403	#127	—	79	8	no	—
404	#127	—	79	32	no	—
405	#124	—	79	16	no	—
406	#124	—	79	32	no	—
407	#124	—	79	32	no	—
408	#124	—	79	64	no	—
409	#124	—	79	64	no	—
410	#124	C₂²×D₇₉	1	32	yes	complemented
411	#121	—	79	16	no	—
412	#121	—	79	32	no	—
413	#121	—	79	32	no	—
414	#121	—	79	16	no	—
415	#121	—	79	32	no	—
416	#121	—	79	32	no	—
417	#121	—	79	32	no	—
418	#121	—	79	64	no	—
419	#121	C₂²×D₇₉	1	32	yes	complemented
420	#120	—	79	64	no	—
421	#120	—	79	64	no	—
422	#120	—	79	64	no	—
423	#120	—	79	64	no	—
424	C₄×D₄	—	79	32	no	—
425	C₄×D₄	—	79	32	no	—
426	C₄×D₄	—	79	16	no	—
427	C₄×D₄	C₂²×D₇₉	1	16	yes	complemented
428	#117	—	79	32	no	—
429	#117	—	79	32	no	—
430	#117	C₂²×D₇₉	1	32	yes	complemented
431	C₂×C₄⋊C₄	—	79	4	no	—
432	C₂×C₄⋊C₄	—	79	2	no	—
433	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
434	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
435	C₂×C₂²⋊C₄	—	79	4	no	—
436	C₂×C₂²⋊C₄	—	79	8	no	—
437	C₂×C₂²⋊C₄	—	79	8	no	—
438	C₂×C₂²⋊C₄	—	79	8	no	—
439	C₂×C₂²⋊C₄	—	79	4	no	—
440	C₂×C₂²⋊C₄	—	79	4	no	—
441	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	—
442	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
443	C₂×C₄²	—	79	4	no	—
444	C₂×C₄²	—	79	2	no	—
445	C₂×C₄²	—	79	1	no	—
446	C₂×C₄²	—	79	8	no	—
447	C₂×C₄²	C₂²×D₇₉	1	4	yes	—
448	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
449	C₂⁴	—	316	16	no	—
450	C₂⁴	—	316	16	no	—
451	C₂⁴	—	316	16	no	—
452	C₂⁴	—	79	32	no	—
453	C₂⁴	—	79	4	no	—
454	C₂⁴	—	79	4	no	—
455	C₂⁴	—	79	1	no	—
456	C₂⁴	C₂³×D₇₉	1	4	yes	—
457	#41	—	316	64	no	—
458	#41	—	316	32	no	—
459	C₂×Q₈	—	4	4	no	—
460	C₂×Q₈	—	316	8	no	—
461	C₂×Q₈	—	79	16	no	—
462	C₂×Q₈	C₂³×D₇₉	1	8	yes	—
463	C₂×D₄	—	2	8	no	—
464	C₂×D₄	—	4	8	no	—
465	C₂×D₄	—	316	8	no	—
466	C₂×D₄	—	316	16	no	—
467	C₂×D₄	—	316	8	no	—
468	C₂×D₄	—	316	4	no	—
469	C₂×D₄	—	316	8	no	—
470	C₂×D₄	—	316	64	no	—
471	C₂×D₄	—	316	64	no	—
472	C₂×D₄	—	316	64	no	—
473	C₂×D₄	—	316	16	no	—
474	C₂×D₄	—	316	8	no	—
475	C₂×D₄	—	316	8	no	—
476	C₂×D₄	—	79	16	no	—
477	C₂×D₄	—	79	32	no	—
478	C₂×D₄	—	79	16	no	—
479	C₂×D₄	—	79	16	no	—
480	C₂×D₄	—	79	8	no	—
481	C₂×D₄	—	79	16	no	—
482	C₂×D₄	—	79	32	no	—
483	C₂×D₄	—	79	16	no	—
484	C₂×D₄	—	79	16	no	—
485	C₂×D₄	—	79	16	no	—
486	C₂×D₄	—	79	8	no	—
487	C₂×D₄	—	158	16	no	—
488	C₂×D₄	—	158	16	no	—
489	C₂×D₄	—	158	8	no	—
490	C₂×D₄	C₂³×D₇₉	1	8	yes	—
491	C₂×D₄	C₂³×D₇₉	1	16	yes	—
492	C₂²×C₄	—	2	16	no	—
493	C₂²×C₄	—	79	1	no	—
494	C₂²×C₄	—	79	2	no	—
495	C₂²×C₄	—	79	4	no	—
496	C₂²×C₄	—	79	4	no	—
497	C₂²×C₄	—	79	8	no	—
498	C₂²×C₄	—	79	16	no	—
499	C₂²×C₄	—	79	16	no	—
500	C₂²×C₄	—	158	16	no	—
501	C₂²×C₄	—	158	4	no	—
502	C₂²×C₄	—	158	16	no	—
503	C₂²×C₄	—	158	8	no	—
504	C₂²×C₄	C₂³×D₇₉	1	16	yes	—
505	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
506	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
507	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
508	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
509	C₄⋊C₄	—	79	16	no	—
510	C₄⋊C₄	—	79	8	no	—
511	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
512	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
513	C₂²⋊C₄	—	79	16	no	—
514	C₂²⋊C₄	—	79	32	no	—
515	C₂²⋊C₄	—	79	32	no	—
516	C₂²⋊C₄	—	79	32	no	—
517	C₂²⋊C₄	—	79	16	no	—
518	C₂²⋊C₄	—	79	16	no	—
519	C₂²⋊C₄	C₂³×D₇₉	1	32	yes	—
520	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
521	C₄²	—	79	8	no	—
522	C₄²	—	79	4	no	—
523	C₄²	—	79	16	no	—
524	C₄²	C₂³×D₇₉	1	4	yes	—
525	C₄²	C₂³×D₇₉	1	16	yes	—
526	C₂³	—	2	8	no	—
527	C₂³	—	2	8	no	—
528	C₂³	—	2	8	no	—
529	C₂³	—	316	32	no	—
530	C₂³	—	316	32	no	—
531	C₂³	—	316	32	no	—
532	C₂³	—	79	8	no	—
533	C₂³	—	79	8	no	—
534	C₂³	—	79	2	no	—
535	C₂³	—	632	64	no	—
536	C₂³	—	158	2	no	—
537	C₂³	—	158	8	no	—
538	C₂³	—	158	8	no	—
539	C₂³	—	158	4	no	—
540	C₂³	—	158	8	no	—
541	C₂³	—	158	16	no	—
542	C₂³	—	158	8	no	—
543	C₂³	C₂⁴×D₇₉	1	8	yes	—
544	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
545	Q₈	—	4	8	no	—
546	Q₈	—	316	16	no	—
547	D₄	—	2	16	no	—
548	D₄	—	4	16	no	—
549	D₄	—	316	16	no	—
550	D₄	—	316	32	no	—
551	D₄	—	316	16	no	—
552	D₄	—	316	8	no	—
553	D₄	—	316	16	no	—
554	D₄	—	316	32	no	—
555	D₄	—	316	16	no	—
556	D₄	—	316	16	no	—
557	D₄	—	158	32	no	—
558	D₄	—	158	16	no	—
559	D₄	—	158	32	no	—
560	C₂×C₄	—	2	8	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	8	no	—
563	C₂×C₄	—	2	32	no	—
564	C₂×C₄	—	79	4	no	—
565	C₂×C₄	—	79	2	no	—
566	C₂×C₄	—	79	4	no	—
567	C₂×C₄	—	79	8	no	—
568	C₂×C₄	—	158	32	no	—
569	C₂×C₄	—	158	8	no	—
570	C₂×C₄	—	158	8	no	—
571	C₂×C₄	—	158	4	no	—
572	C₂×C₄	—	158	32	no	—
573	C₂×C₄	—	158	16	no	—
574	C₂×C₄	#14579207	1	8	yes	—
575	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
576	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
577	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
578	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
579	C₂²	—	2	8	no	—
580	C₂²	—	2	8	no	—
581	C₂²	—	2	8	no	—
582	C₂²	—	4	16	no	—
583	C₂²	—	316	16	no	—
584	C₂²	—	316	16	no	—
585	C₂²	—	316	4	no	—
586	C₂²	—	632	64	no	—
587	C₂²	—	158	2	no	—
588	C₂²	—	158	8	no	—
589	C₂²	—	158	8	no	—
590	C₂²	—	158	4	no	—
591	C₂²	—	158	8	no	—
592	C₂²	—	158	8	no	—
593	C₂²	—	158	16	no	—
594	C₂²	H(5,𝔽₂)×D₇₉	1	2	yes	—
595	C₂²	C₂×#14579207	1	4	yes	—
596	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
597	C₄	—	2	8	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	8	no	—
600	C₄	—	79	4	no	—
601	C₄	—	158	8	no	—
602	C₄	—	158	4	no	—
603	C₄	C₂×#14579207	1	8	yes	—
604	C₂	—	4	8	no	—
605	C₂	—	316	8	no	—
606	C₂	—	316	8	no	—
607	C₂	—	316	2	no	—
608	C₂	#23777801	1	4	yes	direct product factor
609	C₂	C₂×H(5,𝔽₂)×D₇₉	1	1	yes	characteristic
610	C₂	C₂²×#14579207	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#555×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂×#555	D₇₉
hypocenter	C₇₉	C₂×#3549
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#555

Complements

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

N	H ≅ G/N	type
1. #23777801	C₂	direct (N × H)
2. C₂×#19099305	C₂	semidirect
3. C₂×#19099279	C₂	semidirect
4. C₂×#19099276	C₂	semidirect
5. C₂×D₄×D₃₁₆	C₂	semidirect
6. C₂×#19099197	C₂	semidirect
7. C₂×#19099132	C₂	semidirect
8. C₂×#19099131	C₂	semidirect
9. C₂×#19099129	C₂	semidirect
10. C₂×#19099114	C₂	semidirect
11. C₂×#19099110	C₂	semidirect
12. C₂×#555×C₇₉	C₂	semidirect
13. C₂²×#11929625	C₂²	semidirect
14. C₂²×#11929624	C₂²	semidirect
15. C₂³×D₃₁₆	C₂²	semidirect
16. C₂²×D₄×D₇₉	C₂²	semidirect
17. C₂²×D₄×D₇₉	C₂²	semidirect
18. #19099305	C₂²	semidirect
19. #19099279	C₂²	semidirect
20. #19099276	C₂²	semidirect
21. D₄×D₃₁₆	C₂²	semidirect
22. #19099197	C₂²	semidirect
23. #19099132	C₂²	semidirect
24. #19099131	C₂²	semidirect
25. #19099129	C₂²	semidirect
26. #19099114	C₂²	semidirect
27. #19099110	C₂²	semidirect
28. C₂×#14579160	C₂²	semidirect
30. C₂×#14579158	C₂²	semidirect
32. C₂×#14579157	C₂²	semidirect
33. C₂×#14579150	C₂²	semidirect
34. C₂×#14579150	C₂²	semidirect
35. C₂×#14579149	C₂²	semidirect
36. C₂×#14579147	C₂²	semidirect
37. C₂×#14579147	C₂²	semidirect
38. C₂×#14579136	C₂²	semidirect
39. C₂×#14579136	C₂²	semidirect
40. C₂×#14579136	C₂²	semidirect
41. C₂×#14579136	C₂²	semidirect
42. C₂×#14579135	C₂²	semidirect
43. C₂×#14579134	C₂²	semidirect
44. C₂×#14579134	C₂²	semidirect
45. C₂×#14579132	C₂²	semidirect
46. C₂×#14579131	C₂²	semidirect
47. C₂×#14579131	C₂²	semidirect
48. C₂×#14579131	C₂²	semidirect
49. C₂×#14579129	C₂²	semidirect
50. C₂×C₄×D₃₁₆	C₂²	semidirect
51. C₂×#14579123	C₂²	semidirect
52. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
53. C₂×#14579119	C₂²	semidirect
54. C₂×#14579118	C₂²	semidirect
55. C₂×C₄²×D₇₉	C₂²	semidirect
56. #555×C₇₉	C₂²	semidirect
57. C₂×C₄⋊Q₈×C₇₉	C₂²	semidirect
58. C₂×#124×C₇₉	C₂²	semidirect
59. C₂×#121×C₇₉	C₂²	semidirect
60. C₂×C₄×D₄×C₇₉	C₂²	semidirect
61. C₂×#117×C₇₉	C₂²	semidirect
64. C₂×#11929625	C₂³	semidirect
66. C₂×#11929624	C₂³	semidirect
76. C₂²×D₃₁₆	C₂³	semidirect
83. C₂×D₄×D₇₉	C₂³	semidirect
84. C₂×D₄×D₇₉	C₂³	semidirect
89. #14579160	C₂³	semidirect
91. #14579158	C₂³	semidirect
93. #14579157	C₂³	semidirect
94. #14579150	C₂³	semidirect
95. #14579150	C₂³	semidirect
96. #14579149	C₂³	semidirect
97. #14579147	C₂³	semidirect
98. #14579147	C₂³	semidirect
99. #14579136	C₂³	semidirect
100. #14579136	C₂³	semidirect
101. #14579136	C₂³	semidirect
102. #14579136	C₂³	semidirect
103. #14579135	C₂³	semidirect
104. #14579134	C₂³	semidirect
105. #14579134	C₂³	semidirect
106. #14579132	C₂³	semidirect
107. #14579131	C₂³	semidirect
108. #14579131	C₂³	semidirect
109. #14579131	C₂³	semidirect
110. #14579129	C₂³	semidirect
111. C₄×D₃₁₆	C₂³	semidirect
112. #14579123	C₂³	semidirect
113. C₄×C₂²⋊D₇₉	C₂³	semidirect
114. #14579119	C₂³	semidirect
115. #14579118	C₂³	semidirect
127. C₄²×D₇₉	C₂³	semidirect
132. C₄⋊Q₈×C₇₉	C₂³	semidirect
133. #124×C₇₉	C₂³	semidirect
134. #121×C₇₉	C₂³	semidirect
135. C₄×D₄×C₇₉	C₂³	semidirect
136. #117×C₇₉	C₂³	semidirect
300. C₂×C₇₉	#3549	semidirect
310. C₂×#555	D₇₉	semidirect
318. C₇₉	C₂×#3549	semidirect
327. #555	C₂×D₇₉	semidirect
336. C₂×C₄⋊Q₈	C₂×D₇₉	semidirect
346. C₂×#124	C₂×D₇₉	semidirect
355. C₂×#121	C₂×D₇₉	semidirect
363. C₂×C₄×D₄	C₂×D₇₉	semidirect
366. C₂×#117	C₂×D₇₉	semidirect
400. C₄⋊Q₈	C₂²×D₇₉	semidirect
410. #124	C₂²×D₇₉	semidirect
419. #121	C₂²×D₇₉	semidirect
427. C₄×D₄	C₂²×D₇₉	semidirect
430. #117	C₂²×D₇₉	semidirect
608. C₂	#23777801	direct (N × H)

Maximal subgroups

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

subgroup	index
#23777801	2
C₂×#19099305	2
C₂×#19099279	2
C₂×#19099276	2
C₂×D₄×D₃₁₆	2
C₂×#19099197	2
C₂×#19099132	2
C₂×#19099131	2
C₂×#19099129	2
C₂×#19099114	2
C₂×#19099110	2
C₂×#555×C₇₉	2
C₂×#3549	79

Subgroups — C2×#23777801 #35196071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777801 #35196071