Subgroups — #23777724

Order 10112.

1260 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19099301	C₂	1	4	yes	maximal, complemented
2	#19099298	C₂	1	1	yes	maximal, characteristic, complemented
3	#19099233	C₂	1	1	yes	maximal, characteristic, complemented
4	#19099208	C₂	1	2	yes	maximal, complemented
5	#19099201	C₂	1	2	yes	maximal, complemented
6	D₄×D₃₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	#19099198	C₂	1	2	yes	maximal, complemented
8	#19099197	C₂	1	2	yes	maximal, complemented
9	#19099166	C₂	1	2	yes	maximal, complemented
10	#19099164	C₂	1	2	yes	maximal, complemented
11	#19099127	C₂	1	2	yes	maximal, complemented
12	#19099126	C₂	1	2	yes	maximal, complemented
13	#19099121	C₂	1	4	yes	maximal, complemented
14	#127×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#19099100	C₂	1	1	yes	maximal, characteristic, complemented
16	#19099095	C₂	1	1	yes	maximal, characteristic, complemented
17	#550×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11929623	C₂²	1	2	yes	complemented
19	C₂²×D₃₁₆	C₂²	1	2	yes	complemented
20	C₂×D₄×D₇₉	C₂²	1	4	yes	complemented
21	C₂×D₄×D₇₉	C₂²	1	2	yes	complemented
22	C₂×D₄×D₇₉	C₂²	1	2	yes	complemented
23	C₂×D₄×D₇₉	C₂²	1	2	yes	complemented
24	C₂×D₄×D₇₉	C₂²	1	2	yes	complemented
25	#14579158	C₂²	1	1	yes	characteristic
26	#14579157	C₂²	1	2	yes	complemented
27	#14579157	C₂²	1	2	yes	complemented
28	#14579157	C₂²	1	2	yes	complemented
29	#14579157	C₂²	1	2	yes	complemented
30	#14579156	C₂²	1	2	yes	complemented
31	#14579154	C₂²	1	2	yes	complemented
32	#14579152	C₂²	1	1	yes	characteristic, complemented
33	#14579152	C₂²	1	1	yes	characteristic, complemented
34	#14579150	C₂²	1	2	yes	complemented
35	#14579150	C₂²	1	1	yes	characteristic, complemented
36	#14579149	C₂²	1	2	yes	complemented
37	#14579148	C₂²	1	1	yes	characteristic, complemented
38	#14579146	C₂²	1	4	yes	complemented
39	#14579146	C₂²	1	2	yes	complemented
40	#14579145	C₂²	1	4	yes	complemented
41	#14579144	C₂²	1	4	yes	complemented
42	#14579143	C₂²	1	4	yes	complemented
43	#14579143	C₂²	1	2	yes	complemented
44	#14579141	C₂²	1	1	yes	characteristic, complemented
45	#14579137	C₂²	1	1	yes	characteristic, complemented
46	#14579136	C₂²	1	1	yes	characteristic
47	#14579136	C₂²	1	2	yes	complemented
48	#14579135	C₂²	1	4	yes	complemented
49	#14579135	C₂²	1	2	yes	complemented
50	#14579135	C₂²	1	4	yes	complemented
51	#14579134	C₂²	1	4	yes	complemented
52	#14579133	C₂²	1	4	yes	complemented
53	#14579133	C₂²	1	4	yes	complemented
54	#14579133	C₂²	1	4	yes	complemented
55	#14579132	C₂²	1	1	yes	characteristic
56	#14579132	C₂²	1	2	yes	complemented
57	#14579132	C₂²	1	4	yes	complemented
58	#14579131	C₂²	1	4	yes	complemented
59	#14579131	C₂²	1	4	yes	complemented
60	#14579129	C₂²	1	4	yes	complemented
61	#14579129	C₂²	1	4	yes	complemented
62	#14579129	C₂²	1	4	yes	complemented
63	#14579129	C₂²	1	4	yes	complemented
64	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
65	C₄×D₃₁₆	C₂²	1	2	yes	complemented
66	C₄×D₃₁₆	C₂²	1	2	yes	complemented
67	C₄×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
68	D₄×Dic₇₉	C₂²	1	2	yes	complemented
69	#14579123	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
71	#14579120	C₂²	1	2	yes	complemented
72	#14579118	C₂²	1	2	yes	complemented
73	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	4	yes	complemented
74	C₄²×D₇₉	C₂²	1	1	yes	characteristic, complemented
75	C₂×#41×C₇₉	C₂²	1	2	yes	complemented
76	#127×C₇₉	C₂²	1	2	yes	complemented
77	#127×C₇₉	C₂²	1	1	yes	characteristic, complemented
78	#121×C₇₉	C₂²	1	2	yes	complemented
79	#121×C₇₉	C₂²	1	4	yes	complemented
80	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₄×C₇₉	C₂²	1	2	yes	complemented
82	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₇₉	C₂³	1	4	yes	—
84	C₂³×D₇₉	C₂³	1	4	yes	—
85	#11929623	—	4	4	no	—
86	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
87	C₂×D₃₁₆	—	4	4	no	—
88	C₂×D₃₁₆	C₂³	1	2	yes	—
89	C₂×D₃₁₆	C₂³	1	2	yes	—
90	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
91	C₂×D₃₁₆	C₂³	1	2	yes	—
92	C₂×D₃₁₆	C₂³	1	4	yes	—
93	C₂×D₃₁₆	C₂³	1	2	yes	—
94	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
95	C₂×C₂²⋊D₇₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₇₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₇₉	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₇₉	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₇₉	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₇₉	C₂³	1	4	yes	—
101	D₄×D₇₉	—	4	8	no	—
102	D₄×D₇₉	—	4	4	no	—
103	D₄×D₇₉	—	4	4	no	—
104	D₄×D₇₉	—	4	4	no	—
105	D₄×D₇₉	—	4	4	no	—
106	C₂²×Dic₇₉	C₂³	1	4	yes	—
107	C₂×C₄×D₇₉	C₂³	1	2	yes	—
108	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
110	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₇₉	C₂³	1	4	yes	—
112	C₄⋊Dic₇₉	C₂³	1	2	yes	—
113	C₄⋊Dic₇₉	C₂³	1	2	yes	—
114	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
115	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
116	C₄⋊Dic₇₉	C₂³	1	2	yes	—
117	Dic₇₉⋊C₄	C₂³	1	2	yes	—
118	Dic₇₉⋊C₄	C₂³	1	2	yes	—
119	Dic₇₉⋊C₄	C₂³	1	2	yes	—
120	Dic₇₉⋊C₄	C₂³	1	2	yes	—
121	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
122	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
123	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
124	C₂²⋊Dic₇₉	C₂³	1	4	yes	—
125	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
127	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
130	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
131	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
132	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
133	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
134	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
135	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
136	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
137	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
138	C₄×Dic₇₉	C₂³	1	2	yes	—
139	#41×C₇₉	—	4	4	no	—
140	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
141	C₂×D₄×C₇₉	C₂³	1	2	yes	—
142	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
143	C₂×D₄×C₇₉	C₂³	1	2	yes	—
144	C₂×D₄×C₇₉	C₂³	1	4	yes	—
145	C₂×D₄×C₇₉	C₂³	1	2	yes	—
146	C₂×D₄×C₇₉	C₂³	1	4	yes	—
147	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
148	C₂²×C₄×C₇₉	C₂³	1	4	yes	—
149	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
150	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
151	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
152	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
153	C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
154	C₄²×C₇₉	C₂³	1	1	yes	characteristic
155	C₄²×C₇₉	C₂³	1	2	yes	—
156	C₂³×C₇₉	C₂⁴	1	2	yes	—
157	C₂³×C₇₉	C₂⁴	1	4	yes	—
158	C₂²×D₇₉	—	2	8	no	—
159	C₂²×D₇₉	—	4	4	no	—
160	C₂²×D₇₉	—	4	4	no	—
161	C₂²×D₇₉	—	4	4	no	—
162	C₂²×D₇₉	—	4	4	no	—
163	C₂²×D₇₉	—	4	4	no	—
164	C₂²×D₇₉	C₂⁴	1	2	yes	—
165	C₂²×D₇₉	C₂⁴	1	4	yes	—
166	C₂²×D₇₉	C₂⁴	1	1	yes	characteristic
167	Q₈×C₇₉	—	2	2	no	—
168	D₄×C₇₉	—	2	2	no	—
169	D₄×C₇₉	—	2	4	no	—
170	D₄×C₇₉	—	2	4	no	—
171	D₄×C₇₉	—	4	2	no	—
172	D₄×C₇₉	—	4	4	no	—
173	D₄×C₇₉	—	4	4	no	—
174	C₂×C₄×C₇₉	—	2	4	no	—
175	C₂×C₄×C₇₉	—	4	4	no	—
176	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
178	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
179	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
180	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
181	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
182	C₂²⋊D₇₉	—	2	4	no	—
183	C₂²⋊D₇₉	—	4	4	no	—
184	C₂²⋊D₇₉	—	4	4	no	—
185	C₂²⋊D₇₉	—	4	4	no	—
186	C₂²⋊D₇₉	—	4	4	no	—
187	C₂²⋊D₇₉	—	4	4	no	—
188	C₂²⋊D₇₉	—	4	4	no	—
189	C₂×Dic₇₉	—	4	4	no	—
190	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
191	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
192	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
193	C₂×Dic₇₉	C₂⁴	1	2	yes	—
194	C₂×Dic₇₉	C₂⁴	1	2	yes	—
195	C₂×Dic₇₉	C₂⁴	1	2	yes	—
196	D₃₁₆	—	2	4	no	—
197	D₃₁₆	—	2	4	no	—
198	D₃₁₆	—	2	4	no	—
199	D₃₁₆	—	2	2	no	—
200	D₃₁₆	—	4	2	no	—
201	D₃₁₆	—	4	4	no	—
202	C₄×D₇₉	—	2	2	no	—
203	C₄×D₇₉	—	2	2	no	—
204	C₄×D₇₉	—	2	2	no	—
205	C₄×D₇₉	—	2	4	no	—
206	C₄×D₇₉	—	4	4	no	—
207	Dic₁₅₈	—	2	2	no	—
208	C₂²×C₇₉	—	2	2	no	—
209	C₂²×C₇₉	—	2	2	no	—
210	C₂²×C₇₉	—	2	4	no	—
211	C₂²×C₇₉	—	2	4	no	—
212	C₂²×C₇₉	—	2	4	no	—
213	C₂²×C₇₉	—	2	2	no	—
214	C₂²×C₇₉	C₂⁵	1	1	yes	characteristic
215	C₂×D₇₉	—	2	1	no	—
216	C₂×D₇₉	—	2	1	no	—
217	C₂×D₇₉	—	2	2	no	—
218	C₂×D₇₉	—	2	2	no	—
219	C₂×D₇₉	—	2	4	no	—
220	C₂×D₇₉	—	2	4	no	—
221	C₂×D₇₉	—	2	4	no	—
222	C₂×D₇₉	—	2	2	no	—
223	C₂×D₇₉	—	8	8	no	—
224	C₂×D₇₉	—	8	8	no	—
225	C₂×D₇₉	H(5,𝔽₂)	1	2	yes	—
226	C₄×C₇₉	—	2	2	no	—
227	C₄×C₇₉	—	2	2	no	—
228	C₄×C₇₉	—	2	1	no	—
229	C₄×C₇₉	—	2	2	no	—
230	C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
231	C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
232	Dic₇₉	—	2	2	no	—
233	Dic₇₉	—	2	1	no	—
234	Dic₇₉	—	2	1	no	—
235	Dic₇₉	—	2	1	no	—
236	Dic₇₉	—	2	2	no	—
237	Dic₇₉	—	2	2	no	—
238	C₂×C₇₉	—	4	2	no	—
239	C₂×C₇₉	—	4	4	no	—
240	C₂×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
243	D₇₉	—	2	2	no	—
244	D₇₉	—	4	2	no	—
245	D₇₉	—	4	4	no	—
246	#3543	—	79	1	no	maximal, Sylow
247	C₇₉	#3543	1	1	yes	characteristic, complemented, Sylow
248	#560	—	79	4	no	—
249	#559	—	79	1	no	—
250	#550	—	79	1	no	—
251	#550	D₇₉	1	1	yes	characteristic, complemented
252	#546	—	79	2	no	—
253	#546	—	79	2	no	—
254	D₄²	—	79	2	no	—
255	D₄²	—	79	2	no	—
256	D₄²	—	79	1	no	—
257	#540	—	79	2	no	—
258	#540	—	79	2	no	—
259	#535	—	79	2	no	—
260	#535	—	79	2	no	—
261	#534	—	79	4	no	—
262	C₂×#127	—	79	1	no	—
263	#529	—	79	1	no	—
264	#529	—	79	1	no	—
265	C₂×#41	—	79	2	no	—
266	C₂×#41	C₂×D₇₉	1	2	yes	complemented
267	C₂²×D₄	—	79	2	no	—
268	C₂²×D₄	—	79	2	no	—
269	C₂²×D₄	—	79	2	no	—
270	C₂²×D₄	—	79	4	no	—
271	C₂²×D₄	—	79	2	no	—
272	C₂²×D₄	—	79	2	no	—
273	#127	—	79	2	no	—
274	#127	—	79	2	no	—
275	#127	—	79	2	no	—
276	#127	—	79	2	no	—
277	#127	—	79	1	no	—
278	#127	C₂×D₇₉	1	1	yes	characteristic, complemented
279	#127	C₂×D₇₉	1	2	yes	complemented
280	#126	—	79	2	no	—
281	#126	—	79	2	no	—
282	#125	—	79	1	no	—
283	#125	—	79	1	no	—
284	#124	—	79	1	no	—
285	#124	—	79	2	no	—
286	#124	—	79	1	no	—
287	#124	—	79	2	no	—
288	#123	—	79	4	no	—
289	#123	—	79	2	no	—
290	#123	—	79	4	no	—
291	#123	—	79	2	no	—
292	#123	—	79	4	no	—
293	#123	—	79	4	no	—
294	C₂²⋊Q₈	—	79	1	no	—
295	C₂²⋊Q₈	—	79	1	no	—
296	#121	—	79	1	no	—
297	#121	—	79	4	no	—
298	#121	—	79	4	no	—
299	#121	—	79	4	no	—
300	#121	—	79	2	no	—
301	#121	—	79	4	no	—
302	#121	—	79	4	no	—
303	#121	—	79	4	no	—
304	#121	—	79	2	no	—
305	#121	—	79	1	no	—
306	#121	—	79	2	no	—
307	#121	—	79	4	no	—
308	#121	C₂×D₇₉	1	4	yes	complemented
309	#121	C₂×D₇₉	1	2	yes	complemented
310	#120	—	79	4	no	—
311	#120	—	79	4	no	—
312	#120	—	79	4	no	—
313	#120	—	79	4	no	—
314	#120	—	79	4	no	—
315	#120	—	79	4	no	—
316	C₄×Q₈	—	79	1	no	—
317	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
318	C₄×D₄	—	79	2	no	—
319	C₄×D₄	—	79	2	no	—
320	C₄×D₄	—	79	2	no	—
321	C₄×D₄	—	79	2	no	—
322	C₄×D₄	—	79	1	no	—
323	C₄×D₄	—	79	2	no	—
324	C₄×D₄	C₂×D₇₉	1	1	yes	characteristic, complemented
325	C₄×D₄	C₂×D₇₉	1	2	yes	complemented
326	#117	—	79	2	no	—
327	#117	—	79	2	no	—
328	C₂×C₂²⋊C₄	—	79	4	no	—
329	C₂×C₄²	—	79	1	no	—
330	C₂⁴	—	79	4	no	—
331	C₂⁴	—	79	4	no	—
332	#41	—	4	4	no	—
333	#41	—	316	4	no	—
334	C₂×Q₈	—	79	1	no	—
335	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
336	C₂×D₄	—	316	4	no	—
337	C₂×D₄	—	316	8	no	—
338	C₂×D₄	—	316	4	no	—
339	C₂×D₄	—	316	4	no	—
340	C₂×D₄	—	316	4	no	—
341	C₂×D₄	—	316	4	no	—
342	C₂×D₄	—	79	4	no	—
343	C₂×D₄	—	79	4	no	—
344	C₂×D₄	—	79	4	no	—
345	C₂×D₄	—	79	4	no	—
346	C₂×D₄	—	79	4	no	—
347	C₂×D₄	—	79	4	no	—
348	C₂×D₄	—	79	2	no	—
349	C₂×D₄	—	79	4	no	—
350	C₂×D₄	—	79	2	no	—
351	C₂×D₄	—	79	2	no	—
352	C₂×D₄	—	79	2	no	—
353	C₂×D₄	—	79	1	no	—
354	C₂×D₄	—	79	2	no	—
355	C₂×D₄	C₂²×D₇₉	1	2	yes	—
356	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
357	C₂×D₄	C₂²×D₇₉	1	2	yes	—
358	C₂×D₄	C₂²×D₇₉	1	4	yes	—
359	C₂×D₄	C₂²×D₇₉	1	4	yes	—
360	C₂×D₄	C₂²×D₇₉	1	2	yes	—
361	C₂²×C₄	—	79	4	no	—
362	C₂²×C₄	—	79	4	no	—
363	C₂²×C₄	—	79	1	no	—
364	C₂²×C₄	—	79	1	no	—
365	C₂²×C₄	—	79	1	no	—
366	C₂²×C₄	—	79	2	no	—
367	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
368	C₂²×C₄	C₂²×D₇₉	1	4	yes	—
369	C₄⋊C₄	—	79	2	no	—
370	C₄⋊C₄	—	79	2	no	—
371	C₄⋊C₄	—	79	2	no	—
372	C₄⋊C₄	—	79	2	no	—
373	C₄⋊C₄	—	79	2	no	—
374	C₄⋊C₄	—	79	2	no	—
375	C₄⋊C₄	—	79	1	no	—
376	C₄⋊C₄	—	79	1	no	—
377	C₄⋊C₄	—	79	2	no	—
378	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
379	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
380	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
381	C₂²⋊C₄	—	79	2	no	—
382	C₂²⋊C₄	—	79	2	no	—
383	C₂²⋊C₄	—	79	2	no	—
384	C₂²⋊C₄	—	79	4	no	—
385	C₂²⋊C₄	—	79	2	no	—
386	C₂²⋊C₄	—	79	2	no	—
387	C₂²⋊C₄	—	79	4	no	—
388	C₂²⋊C₄	—	79	4	no	—
389	C₂²⋊C₄	—	79	2	no	—
390	C₂²⋊C₄	—	79	2	no	—
391	C₂²⋊C₄	—	79	2	no	—
392	C₂²⋊C₄	—	79	2	no	—
393	C₂²⋊C₄	—	79	4	no	—
394	C₂²⋊C₄	—	79	4	no	—
395	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
396	C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
397	C₄²	—	79	1	no	—
398	C₄²	—	79	1	no	—
399	C₄²	—	79	1	no	—
400	C₄²	—	79	2	no	—
401	C₄²	C₂²×D₇₉	1	1	yes	characteristic
402	C₄²	C₂²×D₇₉	1	2	yes	—
403	C₂³	—	316	4	no	—
404	C₂³	—	316	4	no	—
405	C₂³	—	316	4	no	—
406	C₂³	—	316	4	no	—
407	C₂³	—	316	4	no	—
408	C₂³	—	79	1	no	—
409	C₂³	—	79	4	no	—
410	C₂³	—	79	2	no	—
411	C₂³	—	158	8	no	—
412	C₂³	C₂³×D₇₉	1	2	yes	—
413	C₂³	C₂³×D₇₉	1	4	yes	—
414	Q₈	—	2	2	no	—
415	Q₈	—	158	2	no	—
416	D₄	—	2	4	no	—
417	D₄	—	2	2	no	—
418	D₄	—	2	4	no	—
419	D₄	—	4	4	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	4	no	—
422	D₄	—	316	2	no	—
423	D₄	—	316	4	no	—
424	D₄	—	316	4	no	—
425	D₄	—	316	4	no	—
426	D₄	—	316	4	no	—
427	D₄	—	316	4	no	—
428	D₄	—	316	4	no	—
429	D₄	—	316	4	no	—
430	D₄	—	158	4	no	—
431	D₄	—	158	4	no	—
432	D₄	—	158	2	no	—
433	D₄	—	158	4	no	—
434	D₄	—	158	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	316	4	no	—
438	C₂×C₄	—	316	4	no	—
439	C₂×C₄	—	79	1	no	—
440	C₂×C₄	—	79	1	no	—
441	C₂×C₄	—	79	1	no	—
442	C₂×C₄	—	79	2	no	—
443	C₂×C₄	—	79	2	no	—
444	C₂×C₄	—	79	2	no	—
445	C₂×C₄	—	158	2	no	—
446	C₂×C₄	—	158	2	no	—
447	C₂×C₄	—	158	2	no	—
448	C₂×C₄	—	158	4	no	—
449	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₇₉	1	2	yes	—
451	C₂×C₄	C₂³×D₇₉	1	2	yes	—
452	C₂×C₄	C₂³×D₇₉	1	2	yes	—
453	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
454	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
455	C₂²	—	2	4	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	79	2	no	—
462	C₂²	—	632	8	no	—
463	C₂²	—	632	8	no	—
464	C₂²	—	158	4	no	—
465	C₂²	—	158	2	no	—
466	C₂²	—	158	2	no	—
467	C₂²	—	158	4	no	—
468	C₂²	—	158	2	no	—
469	C₂²	—	158	4	no	—
470	C₂²	—	158	1	no	—
471	C₂²	—	158	1	no	—
472	C₂²	C₂⁴×D₇₉	1	1	yes	characteristic
473	C₄	—	2	2	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	158	2	no	—
478	C₄	—	158	1	no	—
479	C₄	—	158	1	no	—
480	C₄	—	158	2	no	—
481	C₄	—	158	2	no	—
482	C₄	—	158	1	no	—
483	C₄	#14579206	1	2	yes	—
484	C₄	#14579207	1	2	yes	—
485	C₂	—	4	2	no	—
486	C₂	—	4	4	no	—
487	C₂	—	316	2	no	—
488	C₂	—	316	4	no	—
489	C₂	—	158	2	no	—
490	C₂	H(5,𝔽₂)×D₇₉	1	1	yes	characteristic
491	C₂	C₂×#14579206	1	1	yes	characteristic
492	C₂	C₂×#14579207	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁵
Fitting	#550×C₇₉	C₂
hypercenter	#550	D₇₉
hypocenter	C₇₉	#3543
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #550

Complements

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

N	H ≅ G/N	type
1. #19099301	C₂	semidirect
2. #19099298	C₂	semidirect
3. #19099233	C₂	semidirect
4. #19099208	C₂	semidirect
5. #19099201	C₂	semidirect
6. D₄×D₃₁₆	C₂	semidirect
7. #19099198	C₂	semidirect
8. #19099197	C₂	semidirect
9. #19099166	C₂	semidirect
10. #19099164	C₂	semidirect
11. #19099127	C₂	semidirect
12. #19099126	C₂	semidirect
13. #19099121	C₂	semidirect
14. #127×D₇₉	C₂	semidirect
15. #19099100	C₂	semidirect
16. #19099095	C₂	semidirect
17. #550×C₇₉	C₂	semidirect
18. C₂×#11929623	C₂²	semidirect
19. C₂²×D₃₁₆	C₂²	semidirect
20. C₂×D₄×D₇₉	C₂²	semidirect
21. C₂×D₄×D₇₉	C₂²	semidirect
22. C₂×D₄×D₇₉	C₂²	semidirect
23. C₂×D₄×D₇₉	C₂²	semidirect
24. C₂×D₄×D₇₉	C₂²	semidirect
26. #14579157	C₂²	semidirect
27. #14579157	C₂²	semidirect
28. #14579157	C₂²	semidirect
29. #14579157	C₂²	semidirect
30. #14579156	C₂²	semidirect
31. #14579154	C₂²	semidirect
32. #14579152	C₂²	semidirect
33. #14579152	C₂²	semidirect
34. #14579150	C₂²	semidirect
35. #14579150	C₂²	semidirect
36. #14579149	C₂²	semidirect
37. #14579148	C₂²	semidirect
38. #14579146	C₂²	semidirect
39. #14579146	C₂²	semidirect
40. #14579145	C₂²	semidirect
41. #14579144	C₂²	semidirect
42. #14579143	C₂²	semidirect
43. #14579143	C₂²	semidirect
44. #14579141	C₂²	semidirect
45. #14579137	C₂²	semidirect
47. #14579136	C₂²	semidirect
48. #14579135	C₂²	semidirect
49. #14579135	C₂²	semidirect
50. #14579135	C₂²	semidirect
51. #14579134	C₂²	semidirect
52. #14579133	C₂²	semidirect
53. #14579133	C₂²	semidirect
54. #14579133	C₂²	semidirect
56. #14579132	C₂²	semidirect
57. #14579132	C₂²	semidirect
58. #14579131	C₂²	semidirect
59. #14579131	C₂²	semidirect
60. #14579129	C₂²	semidirect
61. #14579129	C₂²	semidirect
62. #14579129	C₂²	semidirect
63. #14579129	C₂²	semidirect
64. C₄×Dic₁₅₈	C₂²	semidirect
65. C₄×D₃₁₆	C₂²	semidirect
66. C₄×D₃₁₆	C₂²	semidirect
67. C₄×D₃₁₆	C₂²	semidirect
68. D₄×Dic₇₉	C₂²	semidirect
69. #14579123	C₂²	semidirect
70. C₄×C₂²⋊D₇₉	C₂²	semidirect
71. #14579120	C₂²	semidirect
72. #14579118	C₂²	semidirect
73. C₂×(C₂×D₇₉)⋊C₄	C₂²	semidirect
74. C₄²×D₇₉	C₂²	semidirect
75. C₂×#41×C₇₉	C₂²	semidirect
76. #127×C₇₉	C₂²	semidirect
77. #127×C₇₉	C₂²	semidirect
78. #121×C₇₉	C₂²	semidirect
79. #121×C₇₉	C₂²	semidirect
80. C₄×Q₈×C₇₉	C₂²	semidirect
81. C₄×D₄×C₇₉	C₂²	semidirect
82. C₄×D₄×C₇₉	C₂²	semidirect
247. C₇₉	#3543	semidirect
251. #550	D₇₉	semidirect
266. C₂×#41	C₂×D₇₉	semidirect
278. #127	C₂×D₇₉	semidirect
279. #127	C₂×D₇₉	semidirect
308. #121	C₂×D₇₉	semidirect
309. #121	C₂×D₇₉	semidirect
317. C₄×Q₈	C₂×D₇₉	semidirect
324. C₄×D₄	C₂×D₇₉	semidirect
325. C₄×D₄	C₂×D₇₉	semidirect