Subgroups — #23777736

Order 10112.

1004 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19099316	C₂	1	2	yes	maximal, complemented
2	#19099314	C₂	1	2	yes	maximal, complemented
3	#19099293	C₂	1	1	yes	maximal, characteristic, complemented
4	#19099277	C₂	1	1	yes	maximal, characteristic, complemented
5	#19099272	C₂	1	1	yes	maximal, characteristic, complemented
6	#19099268	C₂	1	1	yes	maximal, characteristic, complemented
7	#19099253	C₂	1	1	yes	maximal, characteristic, complemented
8	#19099250	C₂	1	2	yes	maximal, complemented
9	#19099248	C₂	1	1	yes	maximal, characteristic, complemented
10	#19099213	C₂	1	1	yes	maximal, characteristic, complemented
11	#19099212	C₂	1	2	yes	maximal, complemented
12	#19099194	C₂	1	1	yes	maximal, characteristic, complemented
13	#19099192	C₂	1	2	yes	maximal, complemented
14	#19099190	C₂	1	1	yes	maximal, characteristic, complemented
15	#19099181	C₂	1	2	yes	maximal, complemented
16	#19099180	C₂	1	1	yes	maximal, characteristic, complemented
17	#19099178	C₂	1	1	yes	maximal, characteristic, complemented
18	#19099135	C₂	1	2	yes	maximal, complemented
19	#19099134	C₂	1	2	yes	maximal, complemented
20	C₂×#14579160	C₂	1	1	yes	maximal, characteristic, complemented
21	#19099094	C₂	1	1	yes	maximal, characteristic, complemented
22	#19099093	C₂	1	1	yes	maximal, characteristic, complemented
23	#547×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11929623	C₂²	1	2	yes	—
25	C₂²×Dic₁₅₈	C₂²	1	2	yes	—
26	#14579160	C₂²	1	1	yes	characteristic
27	#14579160	C₂²	1	1	yes	characteristic
28	#14579160	C₂²	1	2	yes	—
29	#14579160	C₂²	1	2	yes	—
30	#14579160	C₂²	1	1	yes	characteristic
31	#14579160	C₂²	1	1	yes	characteristic
32	#14579160	C₂²	1	1	yes	characteristic
33	#14579160	C₂²	1	2	yes	—
34	#14579160	C₂²	1	2	yes	—
35	#14579159	C₂²	1	2	yes	—
36	#14579159	C₂²	1	2	yes	—
37	#14579159	C₂²	1	2	yes	—
38	#14579156	C₂²	1	2	yes	—
39	#14579156	C₂²	1	1	yes	characteristic
40	#14579154	C₂²	1	2	yes	—
41	#14579154	C₂²	1	2	yes	—
42	#14579154	C₂²	1	2	yes	—
43	#14579154	C₂²	1	2	yes	—
44	#14579154	C₂²	1	1	yes	characteristic
45	#14579153	C₂²	1	1	yes	characteristic
46	#14579152	C₂²	1	1	yes	characteristic
47	#14579152	C₂²	1	1	yes	characteristic
48	#14579152	C₂²	1	2	yes	—
49	#14579151	C₂²	1	2	yes	—
50	#14579151	C₂²	1	1	yes	characteristic
51	#14579151	C₂²	1	2	yes	—
52	#14579151	C₂²	1	2	yes	—
53	#14579151	C₂²	1	2	yes	—
54	#14579148	C₂²	1	1	yes	characteristic
55	#14579148	C₂²	1	2	yes	—
56	#14579148	C₂²	1	2	yes	—
57	#14579147	C₂²	1	2	yes	—
58	#14579147	C₂²	1	1	yes	characteristic
59	#14579147	C₂²	1	2	yes	—
60	#14579145	C₂²	1	1	yes	characteristic
61	#14579144	C₂²	1	2	yes	—
62	#14579144	C₂²	1	2	yes	—
63	#14579143	C₂²	1	2	yes	—
64	#14579142	C₂²	1	2	yes	—
65	#14579142	C₂²	1	2	yes	—
66	#14579142	C₂²	1	2	yes	—
67	#14579142	C₂²	1	1	yes	characteristic
68	#14579142	C₂²	1	2	yes	—
69	#14579141	C₂²	1	1	yes	characteristic
70	#14579140	C₂²	1	2	yes	—
71	#14579140	C₂²	1	1	yes	characteristic
72	#14579140	C₂²	1	2	yes	—
73	#14579140	C₂²	1	2	yes	—
74	#14579140	C₂²	1	1	yes	characteristic
75	#14579140	C₂²	1	2	yes	—
76	#14579140	C₂²	1	2	yes	—
77	#14579139	C₂²	1	2	yes	—
78	#14579139	C₂²	1	2	yes	—
79	#14579138	C₂²	1	2	yes	—
80	#14579138	C₂²	1	2	yes	—
81	#14579138	C₂²	1	2	yes	—
82	#14579138	C₂²	1	1	yes	characteristic
83	#14579138	C₂²	1	2	yes	—
84	#14579137	C₂²	1	2	yes	—
85	#14579133	C₂²	1	2	yes	—
86	#14579133	C₂²	1	1	yes	characteristic
87	#14579132	C₂²	1	1	yes	characteristic
88	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
89	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
90	#14579126	C₂²	1	1	yes	characteristic
91	#14579126	C₂²	1	2	yes	—
92	#14579126	C₂²	1	1	yes	characteristic
93	D₄×Dic₇₉	C₂²	1	1	yes	characteristic
94	D₄×Dic₇₉	C₂²	1	2	yes	—
95	D₄×Dic₇₉	C₂²	1	1	yes	characteristic
96	C₄×C₂²⋊D₇₉	C₂²	1	2	yes	—
97	C₄×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
98	C₄×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
99	#14579120	C₂²	1	1	yes	characteristic
100	#14579120	C₂²	1	1	yes	characteristic
101	#14579120	C₂²	1	2	yes	—
102	#14579119	C₂²	1	1	yes	characteristic
103	#14579118	C₂²	1	1	yes	characteristic
104	#14579117	C₂²	1	2	yes	—
105	#14579117	C₂²	1	2	yes	—
106	#14579117	C₂²	1	2	yes	—
107	C₂×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
108	C₂×Dic₇₉⋊C₄	C₂²	1	2	yes	—
109	C₂×Dic₇₉⋊C₄	C₂²	1	2	yes	—
110	C₄⋊C₄×D₇₉	C₂²	1	1	yes	characteristic
111	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
112	C₂×#41×C₇₉	C₂²	1	2	yes	—
113	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
114	#123×C₇₉	C₂²	1	2	yes	—
115	#123×C₇₉	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	—
117	#121×C₇₉	C₂²	1	1	yes	characteristic
118	#121×C₇₉	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
123	#11929623	—	4	4	no	—
124	C₂×Dic₁₅₈	—	4	4	no	—
125	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
126	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₅₈	C₂³	1	2	yes	—
128	C₂×Dic₁₅₈	C₂³	1	2	yes	—
129	C₂×Dic₁₅₈	C₂³	1	2	yes	—
130	C₂×Dic₁₅₈	C₂³	1	2	yes	—
131	C₂×Dic₁₅₈	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₇₉	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₇₉	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
135	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
136	C₂²×Dic₇₉	C₂³	1	2	yes	—
137	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
138	C₂²×Dic₇₉	C₂³	1	2	yes	—
139	C₂²×Dic₇₉	C₂³	1	2	yes	—
140	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₇₉	C₂³	1	2	yes	—
142	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
144	C₄⋊Dic₇₉	C₂³	1	2	yes	—
145	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₇₉	C₂³	1	2	yes	—
148	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₇₉	C₂³	1	2	yes	—
150	C₄⋊Dic₇₉	C₂³	1	2	yes	—
151	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
152	Dic₇₉⋊C₄	C₂³	1	2	yes	—
153	Dic₇₉⋊C₄	C₂³	1	2	yes	—
154	Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
155	Dic₇₉⋊C₄	C₂³	1	2	yes	—
156	Dic₇₉⋊C₄	C₂³	1	2	yes	—
157	Dic₇₉⋊C₄	C₂³	1	2	yes	—
158	Dic₇₉⋊C₄	C₂³	1	2	yes	—
159	Dic₇₉⋊C₄	C₂³	1	2	yes	—
160	Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
161	Dic₇₉⋊C₄	C₂³	1	2	yes	—
162	Dic₇₉⋊C₄	C₂³	1	2	yes	—
163	Dic₇₉⋊C₄	C₂³	1	2	yes	—
164	Dic₇₉⋊C₄	C₂³	1	2	yes	—
165	Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
166	Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
167	Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
168	Dic₇₉⋊C₄	C₂³	1	2	yes	—
169	Dic₇₉⋊C₄	C₂³	1	2	yes	—
170	Dic₇₉⋊C₄	C₂³	1	2	yes	—
171	Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₇₉⋊C₄	C₂³	1	2	yes	—
173	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
174	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
175	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
176	C₂²⋊Dic₇₉	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₇₉	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₇₉	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₇₉	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
184	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
185	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
191	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
192	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
193	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
194	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
195	C₄×Dic₇₉	C₂³	1	2	yes	—
196	C₄×Dic₇₉	C₂³	1	2	yes	—
197	C₄×Dic₇₉	C₂³	1	2	yes	—
198	C₄×Dic₇₉	C₂³	1	2	yes	—
199	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
200	C₄×Dic₇₉	C₂³	1	2	yes	—
201	#41×C₇₉	—	4	4	no	—
202	C₂×Q₈×C₇₉	C₂³	1	2	yes	—
203	C₂×D₄×C₇₉	C₂³	1	2	yes	—
204	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₇₉	C₂³	1	2	yes	—
207	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
208	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
211	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
212	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
216	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
217	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
224	C₄²×C₇₉	C₂³	1	1	yes	characteristic
225	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
226	C₂³×C₇₉	C₂⁴	1	2	yes	—
227	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
228	C₂²×D₇₉	C₂⁴	1	1	yes	characteristic
229	Q₈×C₇₉	—	4	2	no	—
230	D₄×C₇₉	—	2	4	no	—
231	D₄×C₇₉	—	2	2	no	—
232	D₄×C₇₉	—	2	2	no	—
233	D₄×C₇₉	—	4	2	no	—
234	C₂×C₄×C₇₉	—	2	4	no	—
235	C₂×C₄×C₇₉	—	2	2	no	—
236	C₂×C₄×C₇₉	—	2	2	no	—
237	C₂×C₄×C₇₉	—	4	2	no	—
238	C₂×C₄×C₇₉	—	4	2	no	—
239	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
243	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
244	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
246	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
247	C₂²⋊D₇₉	—	2	2	no	—
248	C₂²⋊D₇₉	—	2	2	no	—
249	C₂²⋊D₇₉	—	4	2	no	—
250	C₂×Dic₇₉	—	2	2	no	—
251	C₂×Dic₇₉	—	2	4	no	—
252	C₂×Dic₇₉	—	2	2	no	—
253	C₂×Dic₇₉	—	2	4	no	—
254	C₂×Dic₇₉	—	4	2	no	—
255	C₂×Dic₇₉	C₂⁴	1	2	yes	—
256	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₇₉	C₂⁴	1	2	yes	—
259	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₇₉	C₂⁴	1	2	yes	—
263	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₇₉	C₂⁴	1	2	yes	—
265	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
266	C₄×D₇₉	—	2	2	no	—
267	C₄×D₇₉	—	4	2	no	—
268	Dic₁₅₈	—	2	2	no	—
269	Dic₁₅₈	—	2	2	no	—
270	Dic₁₅₈	—	4	2	no	—
271	Dic₁₅₈	—	4	2	no	—
272	Dic₁₅₈	—	4	2	no	—
273	Dic₁₅₈	—	4	2	no	—
274	Dic₁₅₈	—	4	2	no	—
275	C₂²×C₇₉	—	2	1	no	—
276	C₂²×C₇₉	—	2	1	no	—
277	C₂²×C₇₉	—	2	2	no	—
278	C₂²×C₇₉	—	2	1	no	—
279	C₂²×C₇₉	—	2	1	no	—
280	C₂²×C₇₉	—	2	1	no	—
281	C₂²×C₇₉	—	2	2	no	—
282	C₂²×C₇₉	—	2	2	no	—
283	C₂²×C₇₉	H(5,𝔽₂)	1	2	yes	—
284	C₂²×C₇₉	C₂⁵	1	1	yes	characteristic
285	C₂×D₇₉	—	2	1	no	—
286	C₂×D₇₉	—	2	1	no	—
287	C₂×D₇₉	—	2	1	no	—
288	C₄×C₇₉	—	2	2	no	—
289	C₄×C₇₉	—	2	2	no	—
290	C₄×C₇₉	—	2	1	no	—
291	C₄×C₇₉	—	2	2	no	—
292	C₄×C₇₉	—	2	1	no	—
293	C₄×C₇₉	—	2	1	no	—
294	C₄×C₇₉	—	2	1	no	—
295	C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
296	Dic₇₉	—	2	1	no	—
297	Dic₇₉	—	2	2	no	—
298	Dic₇₉	—	2	1	no	—
299	Dic₇₉	—	2	1	no	—
300	Dic₇₉	—	2	2	no	—
301	Dic₇₉	—	2	1	no	—
302	Dic₇₉	—	2	2	no	—
303	Dic₇₉	—	2	1	no	—
304	Dic₇₉	—	2	1	no	—
305	Dic₇₉	—	2	2	no	—
306	Dic₇₉	2₋¹⁺⁴	1	2	yes	—
307	C₂×C₇₉	—	2	2	no	—
308	C₂×C₇₉	—	4	2	no	—
309	C₂×C₇₉	—	4	1	no	—
310	C₂×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
311	C₂×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
312	C₂×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
313	D₇₉	—	4	1	no	—
314	#3544	—	79	1	no	maximal, Sylow
315	C₇₉	#3544	1	1	yes	characteristic, complemented, Sylow
316	#563	—	79	2	no	—
317	#563	—	79	2	no	—
318	Q₈²	—	79	1	no	—
319	#555	—	79	1	no	—
320	#554	—	79	1	no	—
321	#554	—	79	1	no	—
322	#552	—	79	2	no	—
323	#552	—	79	1	no	—
324	#552	—	79	1	no	—
325	#547	—	79	2	no	—
326	#547	—	79	1	no	—
327	#547	D₇₉	1	1	yes	characteristic, complemented
328	#544	—	79	1	no	—
329	#544	—	79	2	no	—
330	#544	—	79	1	no	—
331	#542	—	79	2	no	—
332	#542	—	79	1	no	—
333	#542	—	79	1	no	—
334	#536	—	79	2	no	—
335	#536	—	79	2	no	—
336	C₂×C₄⋊Q₈	—	79	1	no	—
337	#529	—	79	1	no	—
338	#529	—	79	1	no	—
339	C₂×#41	—	79	2	no	—
340	C₂×#41	C₂×D₇₉	1	2	yes	—
341	C₂²×Q₈	—	79	2	no	—
342	C₄⋊Q₈	—	79	2	no	—
343	C₄⋊Q₈	—	79	2	no	—
344	C₄⋊Q₈	—	79	2	no	—
345	C₄⋊Q₈	—	79	2	no	—
346	C₄⋊Q₈	—	79	1	no	—
347	C₄⋊Q₈	—	79	1	no	—
348	C₄⋊Q₈	—	79	1	no	—
349	C₄⋊Q₈	—	79	1	no	—
350	C₄⋊Q₈	—	79	2	no	—
351	C₄⋊Q₈	—	79	2	no	—
352	C₄⋊Q₈	—	79	2	no	—
353	C₄⋊Q₈	—	79	1	no	—
354	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
355	#126	—	79	1	no	—
356	#126	—	79	2	no	—
357	#126	—	79	1	no	—
358	#126	—	79	2	no	—
359	#126	—	79	2	no	—
360	#126	—	79	2	no	—
361	#126	—	79	2	no	—
362	#125	—	79	1	no	—
363	#125	—	79	1	no	—
364	#125	—	79	2	no	—
365	#125	—	79	1	no	—
366	#125	—	79	2	no	—
367	#125	—	79	2	no	—
368	#125	—	79	2	no	—
369	#125	—	79	2	no	—
370	#125	—	79	1	no	—
371	#124	—	79	1	no	—
372	#124	—	79	2	no	—
373	#124	—	79	2	no	—
374	#124	—	79	1	no	—
375	#124	—	79	2	no	—
376	#124	—	79	2	no	—
377	#123	—	79	2	no	—
378	#123	—	79	1	no	—
379	#123	—	79	2	no	—
380	#123	—	79	2	no	—
381	#123	—	79	2	no	—
382	#123	—	79	2	no	—
383	#123	—	79	2	no	—
384	#123	—	79	1	no	—
385	#123	—	79	2	no	—
386	#123	C₂×D₇₉	1	2	yes	—
387	#123	C₂×D₇₉	1	2	yes	—
388	C₂²⋊Q₈	—	79	2	no	—
389	C₂²⋊Q₈	—	79	1	no	—
390	C₂²⋊Q₈	—	79	2	no	—
391	C₂²⋊Q₈	—	79	2	no	—
392	C₂²⋊Q₈	—	79	2	no	—
393	C₂²⋊Q₈	—	79	2	no	—
394	C₂²⋊Q₈	—	79	1	no	—
395	C₂²⋊Q₈	—	79	2	no	—
396	C₂²⋊Q₈	—	79	2	no	—
397	C₂²⋊Q₈	—	79	2	no	—
398	C₂²⋊Q₈	—	79	1	no	—
399	C₂²⋊Q₈	—	79	1	no	—
400	C₂²⋊Q₈	—	79	2	no	—
401	C₂²⋊Q₈	—	79	2	no	—
402	C₂²⋊Q₈	—	79	2	no	—
403	C₂²⋊Q₈	—	79	2	no	—
404	C₂²⋊Q₈	C₂×D₇₉	1	2	yes	—
405	#121	—	79	1	no	—
406	#121	—	79	1	no	—
407	#121	—	79	2	no	—
408	#121	C₂×D₇₉	1	1	yes	characteristic
409	#121	C₂×D₇₉	1	1	yes	characteristic
410	C₄×Q₈	—	79	1	no	—
411	C₄×Q₈	—	79	2	no	—
412	C₄×Q₈	—	79	1	no	—
413	C₄×Q₈	—	79	1	no	—
414	C₄×Q₈	—	79	1	no	—
415	C₄×D₄	—	79	2	no	—
416	C₄×D₄	—	79	1	no	—
417	C₄×D₄	—	79	1	no	—
418	C₄×D₄	—	79	1	no	—
419	C₄×D₄	—	79	1	no	—
420	C₄×D₄	—	79	2	no	—
421	C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
422	C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
423	#117	—	79	1	no	—
424	#117	—	79	2	no	—
425	#117	—	79	1	no	—
426	#117	—	79	1	no	—
427	#117	—	79	2	no	—
428	#117	—	79	2	no	—
429	#117	—	79	2	no	—
430	#117	—	79	1	no	—
431	C₂×C₄⋊C₄	—	79	2	no	—
432	C₂×C₄⋊C₄	—	79	1	no	—
433	C₂×C₄⋊C₄	—	79	2	no	—
434	C₂×C₄⋊C₄	—	79	1	no	—
435	C₂×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
437	C₂×C₄²	—	79	1	no	—
438	#41	—	4	4	no	—
439	#41	—	316	4	no	—
440	C₂×Q₈	—	316	4	no	—
441	C₂×Q₈	—	79	2	no	—
442	C₂×Q₈	—	79	2	no	—
443	C₂×Q₈	—	79	2	no	—
444	C₂×Q₈	—	79	2	no	—
445	C₂×Q₈	—	79	2	no	—
446	C₂×Q₈	—	79	1	no	—
447	C₂×Q₈	—	79	1	no	—
448	C₂×Q₈	C₂²×D₇₉	1	2	yes	—
449	C₂×D₄	—	79	2	no	—
450	C₂×D₄	—	79	1	no	—
451	C₂×D₄	—	79	1	no	—
452	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
453	C₂×D₄	C₂²×D₇₉	1	2	yes	—
454	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
455	C₂×D₄	C₂²×D₇₉	1	2	yes	—
456	C₂²×C₄	—	79	2	no	—
457	C₂²×C₄	—	79	2	no	—
458	C₂²×C₄	—	79	1	no	—
459	C₂²×C₄	—	79	1	no	—
460	C₂²×C₄	—	79	2	no	—
461	C₂²×C₄	—	79	2	no	—
462	C₂²×C₄	—	79	1	no	—
463	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
464	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
465	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
466	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
467	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
468	C₄⋊C₄	—	79	2	no	—
469	C₄⋊C₄	—	79	1	no	—
470	C₄⋊C₄	—	79	2	no	—
471	C₄⋊C₄	—	79	2	no	—
472	C₄⋊C₄	—	79	2	no	—
473	C₄⋊C₄	—	79	2	no	—
474	C₄⋊C₄	—	79	2	no	—
475	C₄⋊C₄	—	79	2	no	—
476	C₄⋊C₄	—	79	1	no	—
477	C₄⋊C₄	—	79	2	no	—
478	C₄⋊C₄	—	79	2	no	—
479	C₄⋊C₄	—	79	2	no	—
480	C₄⋊C₄	—	79	1	no	—
481	C₄⋊C₄	—	79	2	no	—
482	C₄⋊C₄	—	79	1	no	—
483	C₄⋊C₄	—	79	1	no	—
484	C₄⋊C₄	—	79	2	no	—
485	C₄⋊C₄	—	79	1	no	—
486	C₄⋊C₄	—	79	2	no	—
487	C₄⋊C₄	—	79	2	no	—
488	C₄⋊C₄	—	79	2	no	—
489	C₄⋊C₄	—	79	1	no	—
490	C₄⋊C₄	—	79	1	no	—
491	C₄⋊C₄	—	79	2	no	—
492	C₄⋊C₄	—	79	1	no	—
493	C₄⋊C₄	—	79	2	no	—
494	C₄⋊C₄	—	79	2	no	—
495	C₄⋊C₄	—	79	1	no	—
496	C₄⋊C₄	—	79	1	no	—
497	C₄⋊C₄	—	79	2	no	—
498	C₄⋊C₄	—	79	1	no	—
499	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
503	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
504	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
506	C₂²⋊C₄	—	79	2	no	—
507	C₂²⋊C₄	—	79	1	no	—
508	C₂²⋊C₄	—	79	1	no	—
509	C₂²⋊C₄	—	79	2	no	—
510	C₂²⋊C₄	—	79	2	no	—
511	C₂²⋊C₄	—	79	1	no	—
512	C₂²⋊C₄	—	79	2	no	—
513	C₂²⋊C₄	—	79	2	no	—
514	C₂²⋊C₄	—	79	2	no	—
515	C₂²⋊C₄	—	79	1	no	—
516	C₂²⋊C₄	—	79	2	no	—
517	C₂²⋊C₄	—	79	2	no	—
518	C₂²⋊C₄	—	79	1	no	—
519	C₂²⋊C₄	—	79	2	no	—
520	C₂²⋊C₄	—	79	1	no	—
521	C₂²⋊C₄	—	79	2	no	—
522	C₂²⋊C₄	—	79	1	no	—
523	C₂²⋊C₄	—	79	1	no	—
524	C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
525	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
529	C₄²	—	79	1	no	—
530	C₄²	—	79	1	no	—
531	C₄²	—	79	1	no	—
532	C₄²	—	79	1	no	—
533	C₄²	—	79	2	no	—
534	C₄²	—	79	2	no	—
535	C₄²	—	79	2	no	—
536	C₄²	—	79	1	no	—
537	C₄²	—	79	2	no	—
538	C₄²	—	79	2	no	—
539	C₄²	C₂²×D₇₉	1	1	yes	characteristic
540	C₂³	—	79	1	no	—
541	C₂³	C₂³×D₇₉	1	1	yes	characteristic
542	C₂³	C₂³×D₇₉	1	2	yes	—
543	C₂³	C₂³×D₇₉	1	1	yes	characteristic
544	Q₈	—	4	2	no	—
545	Q₈	—	316	2	no	—
546	Q₈	—	316	2	no	—
547	Q₈	—	316	2	no	—
548	Q₈	—	316	2	no	—
549	Q₈	—	316	2	no	—
550	Q₈	—	158	2	no	—
551	Q₈	—	158	2	no	—
552	D₄	—	2	2	no	—
553	D₄	—	2	4	no	—
554	D₄	—	2	2	no	—
555	D₄	—	4	2	no	—
556	D₄	—	316	2	no	—
557	D₄	—	158	2	no	—
558	D₄	—	158	2	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	316	2	no	—
565	C₂×C₄	—	316	2	no	—
566	C₂×C₄	—	79	1	no	—
567	C₂×C₄	—	79	1	no	—
568	C₂×C₄	—	79	2	no	—
569	C₂×C₄	—	79	1	no	—
570	C₂×C₄	—	79	2	no	—
571	C₂×C₄	—	79	1	no	—
572	C₂×C₄	—	79	1	no	—
573	C₂×C₄	—	79	1	no	—
574	C₂×C₄	—	79	2	no	—
575	C₂×C₄	—	79	1	no	—
576	C₂×C₄	—	79	2	no	—
577	C₂×C₄	—	158	2	no	—
578	C₂×C₄	—	158	4	no	—
579	C₂×C₄	—	158	2	no	—
580	C₂×C₄	—	158	4	no	—
581	C₂×C₄	—	158	2	no	—
582	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
583	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₇₉	1	2	yes	—
586	C₂×C₄	C₂³×D₇₉	1	2	yes	—
587	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₇₉	1	2	yes	—
589	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	158	1	no	—
599	C₂²	—	158	1	no	—
600	C₂²	—	158	1	no	—
601	C₂²	#14579206	1	2	yes	—
602	C₂²	C₂⁴×D₇₉	1	1	yes	characteristic
603	C₄	—	2	2	no	—
604	C₄	—	2	2	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	79	2	no	—
611	C₄	—	158	2	no	—
612	C₄	—	158	1	no	—
613	C₄	—	158	2	no	—
614	C₄	—	158	1	no	—
615	C₄	—	158	1	no	—
616	C₄	—	158	1	no	—
617	C₄	—	158	2	no	—
618	C₄	—	158	1	no	—
619	C₄	—	158	1	no	—
620	C₄	—	158	2	no	—
621	C₄	#14579208	1	2	yes	—
622	C₂	—	2	2	no	—
623	C₂	—	4	1	no	—
624	C₂	—	4	2	no	—
625	C₂	—	316	1	no	—
626	C₂	C₂×#14579206	1	1	yes	characteristic
627	C₂	2₋¹⁺⁴×D₇₉	1	1	yes	characteristic
628	C₂	C₂×#14579208	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁵
Fitting	#547×C₇₉	C₂
hypercenter	#547	D₇₉
hypocenter	C₇₉	#3544
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. #19099316	C₂	semidirect
2. #19099314	C₂	semidirect
3. #19099293	C₂	semidirect
4. #19099277	C₂	semidirect
5. #19099272	C₂	semidirect
6. #19099268	C₂	semidirect
7. #19099253	C₂	semidirect
8. #19099250	C₂	semidirect
9. #19099248	C₂	semidirect
10. #19099213	C₂	semidirect
11. #19099212	C₂	semidirect
12. #19099194	C₂	semidirect
13. #19099192	C₂	semidirect
14. #19099190	C₂	semidirect
15. #19099181	C₂	semidirect
16. #19099180	C₂	semidirect
17. #19099178	C₂	semidirect
18. #19099135	C₂	semidirect
19. #19099134	C₂	semidirect
20. C₂×#14579160	C₂	semidirect
21. #19099094	C₂	semidirect
22. #19099093	C₂	semidirect
23. #547×C₇₉	C₂	semidirect
315. C₇₉	#3544	semidirect
327. #547	D₇₉	semidirect