Subgroups — #34021389

Order 18688.

810 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626409	C₂	1	2	yes	maximal
2	#22625868	C₂	1	1	yes	maximal, characteristic, complemented
3	#22625867	C₂	1	1	yes	maximal, characteristic, complemented
4	#22625854	C₂	1	2	yes	maximal, complemented
5	#22625809	C₂	1	2	yes	maximal
6	#22625808	C₂	1	2	yes	maximal
7	#22625745	C₂	1	2	yes	maximal, complemented
8	C₄×#14556660	C₂	1	2	yes	maximal, complemented
9	#405×D₇₃	C₂	1	1	yes	maximal, characteristic
10	C₂×#14556660	C₂²	1	2	yes	—
11	C₂×#14556660	C₂²	1	2	yes	—
12	C₂×#14556660	C₂²	1	2	yes	—
13	C₂×#14556659	C₂²	1	2	yes	—
14	#17989537	—	2	4	no	—
15	#17989536	—	2	4	no	—
16	#17989533	C₂²	1	2	yes	—
17	#17989531	C₂²	1	2	yes	—
18	#17989529	C₂²	1	4	yes	—
19	C₄×C₄⋊#64408	C₂²	1	4	yes	—
20	#17989461	C₂²	1	4	yes	—
21	#17989461	C₂²	1	4	yes	—
22	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
23	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
24	#117×D₇₃	C₂²	1	1	yes	characteristic
25	#17988545	C₄	1	1	yes	characteristic, complemented
26	#17988544	C₄	1	1	yes	characteristic, complemented
27	#17988544	C₄	1	1	yes	characteristic, complemented
28	#17988543	C₄	1	1	yes	characteristic, complemented
29	#17988542	C₄	1	1	yes	characteristic, complemented
30	#17988541	C₄	1	1	yes	characteristic, complemented
31	#17988541	C₄	1	1	yes	characteristic, complemented
32	#97×D₇₃	C₂²	1	1	yes	characteristic
33	#97×D₇₃	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
36	#405×C₇₃	C₄	1	1	yes	characteristic, complemented
37	C₂×C₄⋊#64408	—	2	4	no	—
38	C₂×C₄⋊#64408	C₂³	1	4	yes	—
39	C₂×C₄⋊#64408	C₂³	1	4	yes	—
40	C₂×C₂²⋊#64408	—	2	4	no	—
41	C₂×C₄×#64408	—	2	4	no	—
42	#14556660	—	2	4	no	—
43	#14556660	—	2	4	no	—
44	#14556660	—	2	4	no	—
45	#14556659	—	2	4	no	—
46	(C₂×#64408)⋊C₄	—	2	4	no	—
47	(C₂×#64408)⋊C₄	—	2	4	no	—
48	(C₂×#64408)⋊C₄	—	2	4	no	—
49	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
50	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
51	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
52	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
53	M₁₆×D₇₃	—	2	2	no	—
54	M₁₆×D₇₃	—	2	2	no	—
55	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₇₃	—	2	2	no	—
57	C₂×C₈×D₇₃	—	2	2	no	—
58	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
61	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
63	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
64	#14556550	C₂×C₄	1	1	yes	characteristic
65	#14556549	Q₈	1	2	yes	—
66	#14556548	C₂×C₄	1	1	yes	characteristic
67	#14556548	C₂×C₄	1	1	yes	characteristic
68	#14556547	Q₈	1	2	yes	—
69	C₄⋊C₄×D₇₃	D₄	1	2	yes	—
70	C₂²⋊C₄×D₇₃	D₄	1	2	yes	—
71	C₄²×D₇₃	C₂³	1	1	yes	characteristic
72	C₄²×D₇₃	C₂³	1	1	yes	characteristic
73	#14556502	C₂×C₄	1	1	yes	characteristic
74	#14556502	C₂×C₄	1	1	yes	characteristic
75	#14556501	C₂×C₄	1	1	yes	characteristic
76	#14556501	C₂×C₄	1	1	yes	characteristic
77	#14556501	C₂×C₄	1	1	yes	characteristic
78	#14556501	C₂×C₄	1	1	yes	characteristic
79	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
80	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
85	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
87	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
88	#97×C₇₃	C₂×C₄	1	1	yes	characteristic
89	#97×C₇₃	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
92	C₂²×#64408	—	2	4	no	—
93	C₂²×#64408	—	2	4	no	—
94	C₄⋊#64408	—	2	4	no	—
95	C₄⋊#64408	—	2	4	no	—
96	C₄⋊#64408	—	2	4	no	—
97	C₄⋊#64408	—	2	4	no	—
98	C₄⋊#64408	—	8	4	no	—
99	C₂²⋊#64408	—	8	4	no	—
100	C₄×#64408	—	8	4	no	—
101	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
103	C₂×C₄×D₇₃	—	2	1	no	—
104	C₂×C₄×D₇₃	—	2	1	no	—
105	C₂×C₄×D₇₃	—	2	1	no	—
106	C₂×C₄×D₇₃	—	2	1	no	—
107	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
109	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
110	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
112	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
113	#11924012	—	2	2	no	—
114	#11924011	—	2	2	no	—
115	#11924011	—	2	2	no	—
116	C₂×#10596831	—	2	2	no	—
117	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
118	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
119	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
120	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
121	C₈×D₇₃	—	2	1	no	—
122	C₈×D₇₃	—	2	1	no	—
123	C₈×D₇₃	—	2	1	no	—
124	C₈×D₇₃	—	2	1	no	—
125	C₈×D₇₃	—	2	2	no	—
126	C₈×D₇₃	—	2	2	no	—
127	C₈×D₇₃	#41	1	2	yes	—
128	C₈×D₇₃	#41	1	2	yes	—
129	C₈×D₇₃	#41	1	2	yes	—
130	C₈×D₇₃	#41	1	2	yes	—
131	C₄⋊Dic₇₃	C₄⋊C₄	1	2	yes	—
132	#11924007	C₄⋊C₄	1	2	yes	—
133	#11924007	C₄⋊C₄	1	2	yes	—
134	C₂²⋊Dic₇₃	C₄⋊C₄	1	2	yes	—
135	#11924005	C₄⋊C₄	1	2	yes	—
136	#11924005	C₄⋊C₄	1	2	yes	—
137	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₇₃	C₂×Q₈	1	2	yes	—
140	C₄×Dic₇₃	C₂×Q₈	1	2	yes	—
141	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
142	M₁₆×C₇₃	—	2	2	no	—
143	C₂×C₈×C₇₃	—	2	2	no	—
144	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
148	C₄⋊C₄×C₇₃	C₄⋊C₄	1	2	yes	—
149	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	2	yes	—
150	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
152	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂²×D₇₃	—	2	1	no	—
154	C₂²×D₇₃	—	2	1	no	—
155	C₂²×D₇₃	—	2	2	no	—
156	C₂²×D₇₃	—	2	2	no	—
157	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
159	C₂×#64408	—	4	4	no	—
160	C₂×#64408	—	4	4	no	—
161	C₂×#64408	—	4	4	no	—
162	C₂×#64408	—	4	4	no	—
163	C₂×#64408	—	4	4	no	—
164	C₂×#64408	—	4	4	no	—
165	C₂×C₄×C₇₃	—	2	1	no	—
166	C₂×C₄×C₇₃	—	2	1	no	—
167	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
168	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
169	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
171	C₂×Dic₇₃	—	2	1	no	—
172	C₂×Dic₇₃	—	2	1	no	—
173	C₂×Dic₇₃	C₂×C₄⋊C₄	1	2	yes	—
174	C₂×Dic₇₃	C₂×C₄⋊C₄	1	2	yes	—
175	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×Dic₇₃	C₂²×Q₈	1	1	yes	characteristic
177	C₄×D₇₃	—	2	1	no	—
178	C₄×D₇₃	—	2	1	no	—
179	C₄×D₇₃	—	2	2	no	—
180	C₄×D₇₃	—	2	2	no	—
181	C₄×D₇₃	—	2	2	no	—
182	C₄×D₇₃	—	2	2	no	—
183	C₄×D₇₃	—	2	1	no	—
184	C₄×D₇₃	—	2	1	no	—
185	C₄×D₇₃	—	2	1	no	—
186	C₄×D₇₃	—	2	1	no	—
187	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
188	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
189	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
190	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
191	C₈×C₇₃	—	2	1	no	—
192	C₈×C₇₃	—	2	1	no	—
193	C₈×C₇₃	#117	1	2	yes	—
194	C₈×C₇₃	#117	1	2	yes	—
195	#10596831	—	2	1	no	—
196	#10596831	—	2	1	no	—
197	#10596831	#117	1	2	yes	—
198	#10596831	#117	1	2	yes	—
199	C₂²×C₇₃	—	2	2	no	—
200	C₂²×C₇₃	—	2	1	no	—
201	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
202	C₂×D₇₃	—	2	2	no	—
203	C₂×D₇₃	—	2	1	no	—
204	C₂×D₇₃	—	4	2	no	—
205	C₂×D₇₃	—	4	1	no	—
206	C₂×D₇₃	—	4	1	no	—
207	C₂×D₇₃	#532	1	1	yes	characteristic
208	C₂×D₇₃	#532	1	1	yes	characteristic
209	C₂×D₇₃	#576	1	2	yes	—
210	C₂×D₇₃	#578	1	2	yes	—
211	#64408	—	8	4	no	—
212	#64408	—	8	4	no	—
213	C₄×C₇₃	—	2	2	no	—
214	C₄×C₇₃	—	2	2	no	—
215	C₄×C₇₃	—	2	1	no	—
216	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
217	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
218	Dic₇₃	—	2	2	no	—
219	Dic₇₃	—	2	2	no	—
220	Dic₇₃	—	2	1	no	—
221	Dic₇₃	#533	1	1	yes	characteristic
222	Dic₇₃	#533	1	1	yes	characteristic
223	#20821	—	73	1	no	maximal, Sylow
224	C₂×C₇₃	—	4	1	no	—
225	C₂×C₇₃	#2285	1	1	yes	characteristic
226	C₂×C₇₃	#2913	1	2	yes	—
227	D₇₃	—	4	1	no	—
228	D₇₃	#3175	1	2	yes	—
229	D₇₃	#3176	1	1	yes	characteristic
230	D₇₃	#3177	1	1	yes	characteristic
231	C₂×#405	—	73	1	no	—
232	#2314	—	73	2	no	—
233	#1846	—	73	1	no	—
234	#1845	—	73	1	no	—
235	#1836	—	73	2	no	—
236	#1809	—	73	2	no	—
237	#1808	—	73	2	no	—
238	#1776	—	73	2	no	—
239	C₄×#107	—	73	2	no	—
240	C₇₃	#20821	1	1	yes	characteristic, complemented, Sylow
241	C₂²×M₁₆	—	73	1	no	—
242	C₂³×C₈	—	73	1	no	—
243	C₂×#117	—	73	1	no	—
244	C₂×#107	—	73	2	no	—
245	C₂×#107	—	73	2	no	—
246	C₂×#107	—	73	2	no	—
247	C₂×#106	—	73	2	no	—
248	#405	—	73	1	no	—
249	#405	—	73	1	no	—
250	#405	—	73	1	no	—
251	#405	—	73	1	no	—
252	#405	—	73	1	no	—
253	#405	—	73	1	no	—
254	#405	—	73	1	no	—
255	#405	#64408	1	1	yes	characteristic, complemented
256	C₂×#97	—	73	1	no	—
257	C₂×#97	—	73	1	no	—
258	C₂×C₄×C₈	—	73	1	no	—
259	C₂×C₄×C₈	—	73	1	no	—
260	#388	—	146	4	no	—
261	#387	—	146	4	no	—
262	#384	—	73	2	no	—
263	#382	—	73	2	no	—
264	#380	—	73	4	no	—
265	C₄×C₄⋊C₄	—	73	4	no	—
266	#340	—	73	4	no	—
267	#340	—	73	4	no	—
268	C₂³×C₄	—	73	1	no	—
269	C₂×M₁₆	—	73	1	no	—
270	C₂×M₁₆	—	73	1	no	—
271	C₂×M₁₆	—	73	1	no	—
272	C₂×M₁₆	—	146	2	no	—
273	C₂×M₁₆	—	146	2	no	—
274	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic
275	C₂²×C₈	—	73	1	no	—
276	C₂²×C₈	—	73	1	no	—
277	C₂²×C₈	—	73	1	no	—
278	C₂²×C₈	—	73	1	no	—
279	C₂²×C₈	—	73	1	no	—
280	C₂²×C₈	—	73	1	no	—
281	C₂²×C₈	—	73	1	no	—
282	C₂²×C₈	—	146	2	no	—
283	C₂²×C₈	—	146	2	no	—
284	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
285	#117	—	73	1	no	—
286	#117	—	73	2	no	—
287	#117	—	73	2	no	—
288	#117	—	73	1	no	—
289	#117	—	73	1	no	—
290	#117	C₂×#64408	1	1	yes	characteristic
291	C₂×C₄⋊C₄	—	73	2	no	—
292	C₂×C₄⋊C₄	—	73	4	no	—
293	C₂×C₄⋊C₄	—	73	4	no	—
294	C₂×C₄⋊C₄	—	146	4	no	—
295	C₂×C₂²⋊C₄	—	73	2	no	—
296	C₂×C₂²⋊C₄	—	146	4	no	—
297	C₂×C₄²	—	73	1	no	—
298	C₂×C₄²	—	73	1	no	—
299	C₂×C₄²	—	146	4	no	—
300	#107	—	146	4	no	—
301	#107	—	146	4	no	—
302	#107	—	146	4	no	—
303	#106	—	146	4	no	—
304	#97	—	73	1	no	—
305	#97	—	73	1	no	—
306	#97	—	73	1	no	—
307	#97	—	73	1	no	—
308	#97	—	73	1	no	—
309	#97	—	73	1	no	—
310	#97	C₂×#64408	1	1	yes	characteristic
311	#97	C₂×#64408	1	1	yes	characteristic
312	C₄×C₈	—	73	1	no	—
313	C₄×C₈	—	73	1	no	—
314	C₄×C₈	—	73	1	no	—
315	C₄×C₈	—	73	1	no	—
316	C₄×C₈	—	73	1	no	—
317	C₄×C₈	—	73	1	no	—
318	C₄×C₈	C₂×#64408	1	1	yes	characteristic
319	C₄×C₈	C₂×#64408	1	1	yes	characteristic
320	#95	—	146	4	no	—
321	#95	—	146	4	no	—
322	#95	—	146	4	no	—
323	C₂⁴	—	73	1	no	—
324	C₂²×C₄	—	73	1	no	—
325	C₂²×C₄	—	73	1	no	—
326	C₂²×C₄	—	73	1	no	—
327	C₂²×C₄	—	73	1	no	—
328	C₂²×C₄	—	73	2	no	—
329	C₂²×C₄	—	73	2	no	—
330	C₂²×C₄	—	73	1	no	—
331	C₂²×C₄	—	146	1	no	—
332	C₂²×C₄	—	146	1	no	—
333	C₂²×C₄	—	146	1	no	—
334	C₂²×C₄	—	146	1	no	—
335	C₂²×C₄	—	146	4	no	—
336	C₂²×C₄	—	146	4	no	—
337	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
338	M₁₆	—	2	2	no	—
339	M₁₆	—	146	2	no	—
340	M₁₆	—	146	2	no	—
341	M₁₆	—	146	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	73	1	no	—
344	C₂×C₈	—	73	1	no	—
345	C₂×C₈	—	73	2	no	—
346	C₂×C₈	—	73	2	no	—
347	C₂×C₈	—	73	2	no	—
348	C₂×C₈	—	73	2	no	—
349	C₂×C₈	—	73	1	no	—
350	C₂×C₈	—	73	1	no	—
351	C₂×C₈	—	146	2	no	—
352	C₂×C₈	—	146	1	no	—
353	C₂×C₈	—	146	1	no	—
354	C₂×C₈	—	146	1	no	—
355	C₂×C₈	—	146	1	no	—
356	C₂×C₈	—	146	2	no	—
357	C₂×C₈	—	146	2	no	—
358	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
359	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
360	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
361	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
362	C₄⋊C₄	—	584	4	no	—
363	C₄⋊C₄	—	73	2	no	—
364	C₄⋊C₄	—	73	2	no	—
365	C₄⋊C₄	—	73	2	no	—
366	C₄⋊C₄	—	146	4	no	—
367	C₄⋊C₄	—	146	4	no	—
368	C₄⋊C₄	—	146	4	no	—
369	C₄⋊C₄	—	146	4	no	—
370	C₄⋊C₄	C₄⋊#64408	1	2	yes	—
371	C₂²⋊C₄	—	584	4	no	—
372	C₂²⋊C₄	—	73	2	no	—
373	C₂²⋊C₄	—	73	2	no	—
374	C₂²⋊C₄	—	73	2	no	—
375	C₂²⋊C₄	C₄⋊#64408	1	2	yes	—
376	C₄²	—	584	4	no	—
377	C₄²	—	73	1	no	—
378	C₄²	—	73	1	no	—
379	C₄²	—	73	2	no	—
380	C₄²	—	73	2	no	—
381	C₄²	C₂²×#64408	1	1	yes	characteristic
382	C₄²	C₂²×#64408	1	1	yes	characteristic
383	C₂³	—	73	1	no	—
384	C₂³	—	73	1	no	—
385	C₂³	—	146	2	no	—
386	C₂³	—	146	1	no	—
387	C₂³	—	146	1	no	—
388	C₂³	—	146	2	no	—
389	C₂³	C₂×C₄⋊#64408	1	1	yes	characteristic
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	292	4	no	—
393	C₂×C₄	—	292	4	no	—
394	C₂×C₄	—	292	4	no	—
395	C₂×C₄	—	292	4	no	—
396	C₂×C₄	—	292	4	no	—
397	C₂×C₄	—	292	4	no	—
398	C₂×C₄	—	73	1	no	—
399	C₂×C₄	—	73	1	no	—
400	C₂×C₄	—	73	1	no	—
401	C₂×C₄	—	73	1	no	—
402	C₂×C₄	—	73	1	no	—
403	C₂×C₄	—	73	2	no	—
404	C₂×C₄	—	73	2	no	—
405	C₂×C₄	—	73	1	no	—
406	C₂×C₄	—	146	1	no	—
407	C₂×C₄	—	146	1	no	—
408	C₂×C₄	—	146	2	no	—
409	C₂×C₄	—	146	2	no	—
410	C₂×C₄	—	146	1	no	—
411	C₂×C₄	—	146	1	no	—
412	C₂×C₄	—	146	2	no	—
413	C₂×C₄	—	146	2	no	—
414	C₂×C₄	—	146	1	no	—
415	C₂×C₄	—	146	1	no	—
416	C₂×C₄	—	146	1	no	—
417	C₂×C₄	—	146	1	no	—
418	C₂×C₄	C₂×C₄⋊#64408	1	2	yes	—
419	C₂×C₄	C₂×C₄⋊#64408	1	2	yes	—
420	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
421	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
422	C₈	—	2	1	no	—
423	C₈	—	2	1	no	—
424	C₈	—	73	2	no	—
425	C₈	—	73	2	no	—
426	C₈	—	146	1	no	—
427	C₈	—	146	1	no	—
428	C₈	#14556670	1	2	yes	—
429	C₈	#14556670	1	2	yes	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	292	1	no	—
433	C₂²	—	292	2	no	—
434	C₂²	—	292	1	no	—
435	C₂²	—	73	2	no	—
436	C₂²	—	73	2	no	—
437	C₂²	—	73	1	no	—
438	C₂²	—	73	1	no	—
439	C₂²	—	146	2	no	—
440	C₂²	—	146	1	no	—
441	C₂²	C₂²×C₄⋊#64408	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	1	no	—
445	C₄	—	584	4	no	—
446	C₄	—	584	4	no	—
447	C₄	—	73	1	no	—
448	C₄	—	73	1	no	—
449	C₄	—	146	2	no	—
450	C₄	—	146	2	no	—
451	C₄	—	146	1	no	—
452	C₄	C₂×#14556670	1	1	yes	characteristic
453	C₄	C₂×#14556670	1	1	yes	characteristic
454	C₂	—	4	1	no	—
455	C₂	—	292	1	no	—
456	C₂	—	73	1	no	—
457	C₂	—	73	2	no	—
458	C₂	—	73	1	no	—
459	C₂	#22626380	1	1	yes	characteristic
460	C₂	#22626586	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#64408
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#64408
Fitting	#405×C₇₃	C₄
socle	C₂²×C₇₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₇₃	C₂×D₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	#405	#64408
hypocenter	C₇₃	#20821
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
2. #22625868	C₂	semidirect
3. #22625867	C₂	semidirect
4. #22625854	C₂	semidirect
7. #22625745	C₂	semidirect
8. C₄×#14556660	C₂	semidirect
25. #17988545	C₄	semidirect
26. #17988544	C₄	semidirect
27. #17988544	C₄	semidirect
28. #17988543	C₄	semidirect
29. #17988542	C₄	semidirect
30. #17988541	C₄	semidirect
31. #17988541	C₄	semidirect
36. #405×C₇₃	C₄	semidirect
240. C₇₃	#20821	semidirect
255. #405	#64408	semidirect

Maximal subgroups

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

subgroup	index
#22626409	2
#22625868	2
#22625867	2
#22625854	2
#22625809	2
#22625808	2
#22625745	2
C₄×#14556660	2
#405×D₇₃	2
#20821	73