Subgroups — #34204007

Order 20224.

928 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23765149	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19098376	C₂	1	1	yes	maximal, characteristic, complemented
3	#23765136	C₂	1	1	yes	maximal, characteristic, complemented
4	#23765116	C₂	1	1	yes	maximal, characteristic, complemented
5	#23765028	C₂	1	1	yes	maximal, characteristic, complemented
6	#23763454	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#576×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×#14579101	C₂²	1	1	yes	characteristic, complemented
9	C₂×#14579101	C₂²	1	1	yes	characteristic, complemented
10	C₂×#14579097	C₂²	1	1	yes	characteristic, complemented
11	#19098601	C₂²	1	1	yes	characteristic, complemented
12	#19098580	—	2	1	no	—
13	#19098379	—	2	1	no	—
14	#19098376	—	2	2	no	—
15	#19098376	—	2	1	no	—
16	#19098373	—	2	2	no	—
17	#19098364	—	2	2	no	—
18	#19098347	—	2	2	no	—
19	#19098335	—	2	1	no	—
20	C₂×H(5,𝔽₂)×C₇₉	—	2	1	no	—
21	#576×C₇₉	—	2	2	no	—
22	#576×C₇₉	—	2	2	no	—
23	#576×C₇₉	—	2	2	no	—
24	#576×C₇₉	C₄	1	4	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₇₉	—	2	2	no	—
26	C₂×AGL(1,ℤ/8)×C₇₉	—	2	1	no	—
27	C₂×#135×C₇₉	—	2	1	no	—
28	C₂×#135×C₇₉	C₂²	1	1	yes	characteristic
29	C₂²×D₈×C₇₉	—	2	1	no	—
30	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×#131×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×#11929608	—	2	1	no	—
33	#14579120	—	2	1	no	—
34	#14579101	—	2	1	no	—
35	#14579101	—	2	1	no	—
36	#14579101	—	2	1	no	—
37	#14579101	—	2	1	no	—
38	C₂×C₇₉⋊C₁₆	—	2	1	no	—
39	C₂×C₇₉⋊C₁₆	—	2	1	no	—
40	#14579097	—	2	1	no	—
41	#14579097	—	2	1	no	—
42	#14579095	—	2	1	no	—
43	#14579093	—	2	1	no	—
44	#14579088	—	4	2	no	—
45	H(5,𝔽₂)×C₇₉	—	2	4	no	—
46	H(5,𝔽₂)×C₇₉	—	2	4	no	—
47	H(5,𝔽₂)×C₇₉	—	4	2	no	—
48	H(5,𝔽₂)×C₇₉	—	4	2	no	—
49	C₂×#41×C₇₉	—	2	2	no	—
50	C₂×#41×C₇₉	—	2	1	no	—
51	C₂×#41×C₇₉	—	4	1	no	—
52	C₂×#41×C₇₉	D₄	1	1	yes	characteristic
53	C₂²×D₄×C₇₉	—	2	2	no	—
54	C₂²×D₄×C₇₉	—	2	1	no	—
55	C₂²×D₄×C₇₉	—	4	2	no	—
56	C₂²×D₄×C₇₉	—	4	1	no	—
57	AGL(1,ℤ/8)×C₇₉	—	2	8	no	—
58	AGL(1,ℤ/8)×C₇₉	—	2	4	no	—
59	AGL(1,ℤ/8)×C₇₉	—	2	8	no	—
60	AGL(1,ℤ/8)×C₇₉	—	2	4	no	—
61	#135×C₇₉	—	2	4	no	—
62	#135×C₇₉	—	2	4	no	—
63	#135×C₇₉	—	2	1	no	—
64	#135×C₇₉	—	2	1	no	—
65	#135×C₇₉	C₂×C₄	1	2	yes	—
66	#135×C₇₉	D₄	1	2	yes	—
67	C₂×Q₁₆×C₇₉	D₄	1	1	yes	characteristic
68	C₂×SD₁₆×C₇₉	—	2	2	no	—
69	C₂×SD₁₆×C₇₉	—	2	1	no	—
70	C₂×D₈×C₇₉	—	2	2	no	—
71	C₂×D₈×C₇₉	—	2	4	no	—
72	C₂×D₈×C₇₉	—	2	4	no	—
73	C₂×D₈×C₇₉	—	2	1	no	—
74	C₂×D₈×C₇₉	—	2	1	no	—
75	C₂×D₈×C₇₉	—	2	1	no	—
76	C₂×D₈×C₇₉	C₂×C₄	1	2	yes	—
77	C₂×D₈×C₇₉	D₄	1	1	yes	characteristic
78	C₂×D₈×C₇₉	D₄	1	2	yes	—
79	C₂×D₈×C₇₉	D₄	1	2	yes	—
80	#131×C₇₉	—	2	1	no	—
81	#131×C₇₉	—	2	1	no	—
82	#131×C₇₉	C₂×C₄	1	2	yes	—
83	#131×C₇₉	D₄	1	2	yes	—
84	C₂×M₁₆×C₇₉	—	2	1	no	—
85	C₂×M₁₆×C₇₉	D₄	1	1	yes	characteristic
86	C₂²×C₈×C₇₉	—	2	1	no	—
87	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
88	#11929608	—	4	1	no	—
89	#11929608	—	4	1	no	—
90	C₂×C₇₉⋊C₈	—	4	1	no	—
91	C₄⋊Dic₇₉	—	4	1	no	—
92	C₂²⋊Dic₇₉	—	4	1	no	—
93	C₄×Dic₇₉	—	4	1	no	—
94	C₇₉⋊C₁₆	—	4	1	no	—
95	C₇₉⋊C₁₆	—	4	1	no	—
96	C₂⁴×C₇₉	—	4	2	no	—
97	C₂⁴×C₇₉	—	4	1	no	—
98	#41×C₇₉	—	2	1	no	—
99	#41×C₇₉	—	2	1	no	—
100	#41×C₇₉	—	2	8	no	—
101	#41×C₇₉	—	2	2	no	—
102	#41×C₇₉	—	2	2	no	—
103	#41×C₇₉	—	4	4	no	—
104	#41×C₇₉	—	4	4	no	—
105	#41×C₇₉	—	4	4	no	—
106	#41×C₇₉	—	4	1	no	—
107	#41×C₇₉	—	4	1	no	—
108	#41×C₇₉	C₂²⋊C₄	1	2	yes	—
109	#41×C₇₉	D₈	1	2	yes	—
110	C₂×Q₈×C₇₉	—	2	1	no	—
111	C₂×Q₈×C₇₉	SD₁₆	1	1	yes	characteristic
112	C₂×D₄×C₇₉	—	2	1	no	—
113	C₂×D₄×C₇₉	—	2	8	no	—
114	C₂×D₄×C₇₉	—	2	2	no	—
115	C₂×D₄×C₇₉	—	2	1	no	—
116	C₂×D₄×C₇₉	—	2	2	no	—
117	C₂×D₄×C₇₉	—	2	2	no	—
118	C₂×D₄×C₇₉	—	4	2	no	—
119	C₂×D₄×C₇₉	—	4	4	no	—
120	C₂×D₄×C₇₉	—	4	8	no	—
121	C₂×D₄×C₇₉	—	4	8	no	—
122	C₂×D₄×C₇₉	—	4	4	no	—
123	C₂×D₄×C₇₉	—	4	2	no	—
124	C₂×D₄×C₇₉	—	4	1	no	—
125	C₂×D₄×C₇₉	—	4	4	no	—
126	C₂×D₄×C₇₉	—	4	1	no	—
127	C₂×D₄×C₇₉	—	4	1	no	—
128	C₂×D₄×C₇₉	—	4	1	no	—
129	C₂×D₄×C₇₉	SD₁₆	1	1	yes	characteristic
130	C₂²×C₄×C₇₉	—	2	1	no	—
131	C₂²×C₄×C₇₉	—	4	2	no	—
132	C₂²×C₄×C₇₉	—	4	1	no	—
133	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
134	Q₁₆×C₇₉	—	2	1	no	—
135	Q₁₆×C₇₉	C₂²⋊C₄	1	2	yes	—
136	SD₁₆×C₇₉	—	2	8	no	—
137	SD₁₆×C₇₉	—	2	2	no	—
138	SD₁₆×C₇₉	—	2	2	no	—
139	D₈×C₇₉	—	2	8	no	—
140	D₈×C₇₉	—	2	2	no	—
141	D₈×C₇₉	—	2	1	no	—
142	D₈×C₇₉	—	2	2	no	—
143	D₈×C₇₉	—	2	2	no	—
144	D₈×C₇₉	C₂²⋊C₄	1	2	yes	—
145	D₈×C₇₉	C₂²⋊C₄	1	4	yes	—
146	M₁₆×C₇₉	—	2	2	no	—
147	M₁₆×C₇₉	—	2	2	no	—
148	M₁₆×C₇₉	—	2	1	no	—
149	M₁₆×C₇₉	C₂²⋊C₄	1	2	yes	—
150	C₂×C₈×C₇₉	—	2	2	no	—
151	C₂×C₈×C₇₉	—	2	2	no	—
152	C₂×C₈×C₇₉	—	2	1	no	—
153	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
159	C₂³×C₇₉	—	2	1	no	—
160	C₂³×C₇₉	—	4	8	no	—
161	C₂³×C₇₉	—	4	2	no	—
162	C₂³×C₇₉	—	4	1	no	—
163	C₂³×C₇₉	—	4	2	no	—
164	C₂³×C₇₉	—	4	2	no	—
165	C₂³×C₇₉	—	16	2	no	—
166	C₂³×C₇₉	—	16	4	no	—
167	C₂³×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
168	Q₈×C₇₉	—	2	1	no	—
169	Q₈×C₇₉	—	2	2	no	—
170	Q₈×C₇₉	—	4	1	no	—
171	Q₈×C₇₉	#102	1	2	yes	—
172	D₄×C₇₉	—	2	2	no	—
173	D₄×C₇₉	—	2	2	no	—
174	D₄×C₇₉	—	2	2	no	—
175	D₄×C₇₉	—	2	4	no	—
176	D₄×C₇₉	—	2	1	no	—
177	D₄×C₇₉	—	4	8	no	—
178	D₄×C₇₉	—	4	8	no	—
179	D₄×C₇₉	—	4	2	no	—
180	D₄×C₇₉	—	4	2	no	—
181	D₄×C₇₉	—	4	2	no	—
182	D₄×C₇₉	—	4	1	no	—
183	D₄×C₇₉	—	4	2	no	—
184	D₄×C₇₉	—	4	2	no	—
185	D₄×C₇₉	#102	1	2	yes	—
186	C₂×C₄×C₇₉	—	2	1	no	—
187	C₂×C₄×C₇₉	—	2	2	no	—
188	C₂×C₄×C₇₉	—	2	2	no	—
189	C₂×C₄×C₇₉	—	4	8	no	—
190	C₂×C₄×C₇₉	—	4	1	no	—
191	C₂×C₄×C₇₉	—	4	2	no	—
192	C₂×C₄×C₇₉	—	4	2	no	—
193	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
195	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
196	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
197	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
198	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₂×Dic₇₉	—	8	1	no	—
200	C₈×C₇₉	—	2	2	no	—
201	C₈×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₈×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₈×C₇₉	#120	1	1	yes	characteristic
204	C₈×C₇₉	#120	1	1	yes	characteristic
205	C₇₉⋊C₈	—	8	1	no	—
206	C₂²×C₇₉	—	2	2	no	—
207	C₂²×C₇₉	—	4	1	no	—
208	C₂²×C₇₉	—	4	2	no	—
209	C₂²×C₇₉	—	4	4	no	—
210	C₂²×C₇₉	—	4	2	no	—
211	C₂²×C₇₉	—	8	4	no	—
212	C₂²×C₇₉	—	8	2	no	—
213	C₂²×C₇₉	—	16	2	no	—
214	C₂²×C₇₉	—	16	2	no	—
215	C₂²×C₇₉	—	16	8	no	—
216	C₂²×C₇₉	#418	1	1	yes	characteristic
217	C₂²×C₇₉	#447	1	1	yes	characteristic
218	C₂²×C₇₉	#450	1	1	yes	characteristic
219	C₄×C₇₉	—	2	2	no	—
220	C₄×C₇₉	—	4	2	no	—
221	C₄×C₇₉	#379	1	1	yes	characteristic
222	C₄×C₇₉	C₂×#102	1	1	yes	characteristic
223	C₄×C₇₉	#447	1	1	yes	characteristic
224	C₄×C₇₉	#450	1	1	yes	characteristic
225	Dic₇₉	—	16	1	no	—
226	#12750	—	79	1	no	maximal, Sylow
227	C₂×C₇₉	—	2	1	no	—
228	C₂×C₇₉	—	2	1	no	—
229	C₂×C₇₉	—	2	1	no	—
230	C₂×C₇₉	—	4	2	no	—
231	C₂×C₇₉	—	8	4	no	—
232	C₂×C₇₉	—	8	2	no	—
233	C₂×C₇₉	#1786	1	1	yes	characteristic
234	C₂×#576	D₇₉	1	1	yes	characteristic
235	#2148	—	79	1	no	—
236	C₂×#361	—	79	1	no	—
237	#2145	—	79	1	no	—
238	#2140	—	79	1	no	—
239	#2117	—	79	1	no	—
240	#1814	—	79	1	no	—
241	C₇₉	#12750	1	1	yes	characteristic, complemented, Sylow
242	C₂×H(5,𝔽₂)	—	2	1	no	—
243	#576	—	2	2	no	—
244	#576	—	2	2	no	—
245	#576	—	2	2	no	—
246	#576	Dic₇₉	1	4	yes	complemented
247	C₂×AGL(1,ℤ/8)	—	2	2	no	—
248	C₂×AGL(1,ℤ/8)	—	2	1	no	—
249	C₂×#135	—	2	1	no	—
250	C₂×#135	C₂×D₇₉	1	1	yes	characteristic
251	C₂²×D₈	—	2	1	no	—
252	C₂²×D₈	C₂×D₇₉	1	1	yes	characteristic
253	C₂×#131	C₂×D₇₉	1	1	yes	characteristic
254	C₂×M₃₂	—	79	1	no	—
255	C₂×M₃₂	—	79	1	no	—
256	C₂×#108	—	79	1	no	—
257	#427	—	79	1	no	—
258	#421	—	158	1	no	—
259	#362	—	158	1	no	—
260	#361	—	158	2	no	—
261	#361	—	158	1	no	—
262	#360	—	158	2	no	—
263	#357	—	158	2	no	—
264	#350	—	158	2	no	—
265	#344	—	158	1	no	—
266	H(5,𝔽₂)	—	2	4	no	—
267	H(5,𝔽₂)	—	2	4	no	—
268	H(5,𝔽₂)	—	4	2	no	—
269	H(5,𝔽₂)	—	4	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	1	no	—
272	C₂×#41	—	4	1	no	—
273	C₂×#41	C₂²⋊D₇₉	1	1	yes	characteristic
274	C₂²×D₄	—	2	2	no	—
275	C₂²×D₄	—	2	1	no	—
276	C₂²×D₄	—	4	2	no	—
277	C₂²×D₄	—	4	1	no	—
278	AGL(1,ℤ/8)	—	2	4	no	—
279	AGL(1,ℤ/8)	—	2	8	no	—
280	AGL(1,ℤ/8)	—	2	8	no	—
281	AGL(1,ℤ/8)	—	2	4	no	—
282	#135	—	2	4	no	—
283	#135	—	2	4	no	—
284	#135	—	2	1	no	—
285	#135	—	2	1	no	—
286	#135	C₂×Dic₇₉	1	2	yes	—
287	#135	C₂²⋊D₇₉	1	2	yes	—
288	C₂×Q₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
289	C₂×SD₁₆	—	2	2	no	—
290	C₂×SD₁₆	—	2	1	no	—
291	C₂×D₈	—	2	2	no	—
292	C₂×D₈	—	2	4	no	—
293	C₂×D₈	—	2	4	no	—
294	C₂×D₈	—	2	1	no	—
295	C₂×D₈	—	2	1	no	—
296	C₂×D₈	—	2	1	no	—
297	C₂×D₈	C₂×Dic₇₉	1	2	yes	—
298	C₂×D₈	C₂²⋊D₇₉	1	1	yes	characteristic
299	C₂×D₈	C₂²⋊D₇₉	1	2	yes	—
300	C₂×D₈	C₂²⋊D₇₉	1	2	yes	—
301	#131	—	2	1	no	—
302	#131	—	2	1	no	—
303	#131	C₂×Dic₇₉	1	2	yes	—
304	#131	C₂²⋊D₇₉	1	2	yes	—
305	C₂×M₁₆	—	2	1	no	—
306	C₂×M₁₆	—	158	1	no	—
307	C₂×M₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
310	#117	—	158	1	no	—
311	M₃₂	—	158	1	no	—
312	M₃₂	—	158	1	no	—
313	M₃₂	—	158	1	no	—
314	M₃₂	—	158	1	no	—
315	C₂×C₁₆	—	158	1	no	—
316	C₂×C₁₆	—	158	1	no	—
317	#108	—	158	1	no	—
318	#108	—	158	1	no	—
319	#107	—	158	1	no	—
320	#106	—	158	1	no	—
321	#104	—	316	2	no	—
322	C₂⁴	—	4	2	no	—
323	C₂⁴	—	4	1	no	—
324	#41	—	2	1	no	—
325	#41	—	2	1	no	—
326	#41	—	2	8	no	—
327	#41	—	2	2	no	—
328	#41	—	2	2	no	—
329	#41	—	4	4	no	—
330	#41	—	4	4	no	—
331	#41	—	4	4	no	—
332	#41	—	4	1	no	—
333	#41	—	4	1	no	—
334	#41	C₂²⋊Dic₇₉	1	2	yes	—
335	#41	#11929609	1	2	yes	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	#11929612	1	1	yes	characteristic
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	4	4	no	—
346	C₂×D₄	—	4	8	no	—
347	C₂×D₄	—	4	8	no	—
348	C₂×D₄	—	4	4	no	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	—	4	1	no	—
351	C₂×D₄	—	4	4	no	—
352	C₂×D₄	—	4	1	no	—
353	C₂×D₄	—	4	1	no	—
354	C₂×D₄	—	4	1	no	—
355	C₂×D₄	#11929612	1	1	yes	characteristic
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
360	Q₁₆	—	2	1	no	—
361	Q₁₆	C₂²⋊Dic₇₉	1	2	yes	—
362	SD₁₆	—	2	8	no	—
363	SD₁₆	—	2	2	no	—
364	SD₁₆	—	2	2	no	—
365	D₈	—	2	8	no	—
366	D₈	—	2	2	no	—
367	D₈	—	2	1	no	—
368	D₈	—	2	2	no	—
369	D₈	—	2	2	no	—
370	D₈	C₂²⋊Dic₇₉	1	2	yes	—
371	D₈	C₂²⋊Dic₇₉	1	4	yes	—
372	M₁₆	—	2	1	no	—
373	M₁₆	—	2	2	no	—
374	M₁₆	—	2	2	no	—
375	M₁₆	—	316	1	no	—
376	M₁₆	—	316	1	no	—
377	M₁₆	C₂²⋊Dic₇₉	1	2	yes	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	316	1	no	—
382	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
383	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
384	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
385	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
386	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
387	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
388	C₄⋊C₄	—	316	1	no	—
389	C₂²⋊C₄	—	316	1	no	—
390	C₄²	—	316	1	no	—
391	C₁₆	—	316	1	no	—
392	C₁₆	—	316	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	4	8	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	16	2	no	—
400	C₂³	—	16	4	no	—
401	C₂³	#14579187	1	1	yes	characteristic
402	Q₈	—	2	1	no	—
403	Q₈	—	2	2	no	—
404	Q₈	—	4	1	no	—
405	Q₈	#14579082	1	2	yes	—
406	D₄	—	2	2	no	—
407	D₄	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	4	no	—
410	D₄	—	2	1	no	—
411	D₄	—	4	8	no	—
412	D₄	—	4	8	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	1	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	2	no	—
419	D₄	#14579082	1	2	yes	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	632	1	no	—
428	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
429	C₂×C₄	#14579130	1	1	yes	characteristic
430	C₂×C₄	#14579130	1	1	yes	characteristic
431	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
432	C₂×C₄	C₂×#11929612	1	1	yes	characteristic
433	C₂×C₄	#14579187	1	1	yes	characteristic
434	C₈	—	2	2	no	—
435	C₈	—	632	1	no	—
436	C₈	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
437	C₈	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
438	C₈	#14579130	1	1	yes	characteristic
439	C₈	#14579130	1	1	yes	characteristic
440	C₂²	—	2	2	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	8	4	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	16	2	no	—
448	C₂²	—	16	2	no	—
449	C₂²	—	16	8	no	—
450	C₂²	#19098568	1	1	yes	characteristic
451	C₂²	#19098697	1	1	yes	characteristic
452	C₂²	#19098714	1	1	yes	characteristic
453	C₄	—	2	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	1264	1	no	—
456	C₄	#19098419	1	1	yes	characteristic
457	C₄	C₂×#14579082	1	1	yes	characteristic
458	C₄	#19098697	1	1	yes	characteristic
459	C₄	#19098714	1	1	yes	characteristic
460	C₂	—	2	1	no	—
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	4	2	no	—
464	C₂	—	8	4	no	—
465	C₂	—	8	2	no	—
466	C₂	#23763331	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23763331
commutator	C₂×C₈×C₇₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting, prime radical	C₂×#576×C₇₉	C₂
socle	C₂×C₇₉	#1786
cosocle	C₂²×C₈×C₇₉	C₂³
hypercenter	C₂×#576	D₇₉
hypocenter	C₇₉	#12750
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ C₂×#576

Complements

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

N	H ≅ G/N	type
1. #23765149	C₂	semidirect
2. C₂×#19098376	C₂	semidirect
3. #23765136	C₂	semidirect
4. #23765116	C₂	semidirect
5. #23765028	C₂	semidirect
6. #23763454	C₂	semidirect
8. C₂×#14579101	C₂²	semidirect
9. C₂×#14579101	C₂²	semidirect
10. C₂×#14579097	C₂²	semidirect
11. #19098601	C₂²	semidirect
24. #576×C₇₉	C₄	semidirect
241. C₇₉	#12750	semidirect
246. #576	Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23765149	2
C₂×#19098376	2
#23765136	2
#23765116	2
#23765028	2
#23763454	2
C₂×#576×C₇₉	2
#12750	79