Subgroups — C₇₃×#24807 #32934211

Order 18688.

844 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#473×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3056	C₂	1	2	yes	maximal
3	C₂×#470×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2930	C₂	1	1	yes	maximal, characteristic
5	C₂×#430×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2064	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2052	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1979	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1951	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1901	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1815	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₇₃	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×#131×C₇₃	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₇₃	C₂²	1	2	yes	—
16	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
17	#525×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
19	#473×C₇₃	—	2	4	no	—
20	#470×C₇₃	—	2	2	no	—
21	#470×C₇₃	—	2	2	no	—
22	#470×C₇₃	—	2	2	no	—
23	#468×C₇₃	—	2	2	no	—
24	#467×C₇₃	—	2	2	no	—
25	#465×C₇₃	—	2	2	no	—
26	#436×C₇₃	—	2	2	no	—
27	#435×C₇₃	—	2	2	no	—
28	#430×C₇₃	—	2	4	no	—
29	C₂×#108×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×#108×C₇₃	C₂²	1	2	yes	—
31	C₂×#108×C₇₃	C₂²	1	1	yes	characteristic
32	#428×C₇₃	C₂²	1	2	yes	—
33	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic
34	#424×C₇₃	C₂²	1	1	yes	characteristic
35	#419×C₇₃	C₂²	1	2	yes	—
36	#417×C₇₃	C₂²	1	2	yes	—
37	C₂×#103×C₇₃	C₂²	1	2	yes	—
38	C₂×#101×C₇₃	C₂²	1	2	yes	—
39	C₂×#101×C₇₃	C₂²	1	2	yes	—
40	#408×C₇₃	C₂²	1	1	yes	characteristic
41	#407×C₇₃	C₂²	1	1	yes	characteristic
42	#405×C₇₃	C₂²	1	1	yes	characteristic
43	#343×C₇₃	C₂²	1	2	yes	—
44	#343×C₇₃	C₂²	1	2	yes	—
45	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
48	#137×C₇₃	—	2	4	no	—
49	#137×C₇₃	—	4	2	no	—
50	C₂×Q₁₆×C₇₃	—	2	2	no	—
51	C₂×Q₁₆×C₇₃	—	2	1	no	—
52	C₂×Q₁₆×C₇₃	—	2	1	no	—
53	C₂×Q₁₆×C₇₃	—	2	2	no	—
54	C₂×Q₁₆×C₇₃	—	2	2	no	—
55	C₂×SD₁₆×C₇₃	—	2	2	no	—
56	#131×C₇₃	—	2	2	no	—
57	#131×C₇₃	—	2	2	no	—
58	C₂×M₁₆×C₇₃	—	2	2	no	—
59	C₂×M₁₆×C₇₃	—	2	2	no	—
60	C₂×M₁₆×C₇₃	—	2	1	no	—
61	C₂×M₁₆×C₇₃	—	2	2	no	—
62	C₂×M₁₆×C₇₃	—	2	4	no	—
63	C₂×M₁₆×C₇₃	—	4	2	no	—
64	C₂×M₁₆×C₇₃	D₄	1	2	yes	—
65	C₂×M₁₆×C₇₃	D₄	1	2	yes	—
66	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
68	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
69	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
70	C₂²×C₈×C₇₃	—	2	2	no	—
71	C₂²×C₈×C₇₃	—	2	1	no	—
72	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
74	#123×C₇₃	—	2	1	no	—
75	C₂²⋊Q₈×C₇₃	—	2	2	no	—
76	C₂²⋊Q₈×C₇₃	—	2	2	no	—
77	C₂²⋊Q₈×C₇₃	—	2	2	no	—
78	C₂²⋊Q₈×C₇₃	—	2	2	no	—
79	C₂²⋊Q₈×C₇₃	D₄	1	2	yes	—
80	#121×C₇₃	D₄	1	2	yes	—
81	#120×C₇₃	—	2	1	no	—
82	C₄×D₄×C₇₃	—	2	2	no	—
83	#117×C₇₃	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
85	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
86	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
87	#108×C₇₃	—	2	4	no	—
88	#108×C₇₃	—	2	2	no	—
89	#108×C₇₃	D₄	1	4	yes	complemented
90	#107×C₇₃	—	2	2	no	—
91	#106×C₇₃	—	2	1	no	—
92	#106×C₇₃	—	2	1	no	—
93	#106×C₇₃	—	2	2	no	—
94	C₄⋊C₈×C₇₃	—	2	2	no	—
95	#103×C₇₃	—	2	2	no	—
96	#103×C₇₃	—	2	4	no	—
97	#103×C₇₃	—	2	2	no	—
98	#103×C₇₃	—	2	2	no	—
99	#102×C₇₃	—	2	2	no	—
100	#101×C₇₃	—	2	4	no	—
101	#101×C₇₃	—	4	2	no	—
102	C₂²⋊C₈×C₇₃	—	2	2	no	—
103	C₂²⋊C₈×C₇₃	—	2	2	no	—
104	#97×C₇₃	—	2	1	no	—
105	C₄×C₈×C₇₃	—	2	1	no	—
106	C₂⁴×C₇₃	#41	1	1	yes	characteristic
107	#41×C₇₃	—	2	1	no	—
108	#41×C₇₃	—	2	1	no	—
109	#41×C₇₃	—	2	1	no	—
110	#41×C₇₃	—	2	1	no	—
111	C₂×Q₈×C₇₃	—	2	2	no	—
112	C₂×Q₈×C₇₃	—	2	2	no	—
113	C₂×Q₈×C₇₃	—	2	2	no	—
114	C₂×Q₈×C₇₃	—	2	2	no	—
115	C₂×Q₈×C₇₃	—	2	2	no	—
116	C₂×Q₈×C₇₃	—	2	2	no	—
117	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
118	C₂×D₄×C₇₃	—	2	1	no	—
119	C₂×D₄×C₇₃	—	2	2	no	—
120	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₃	—	2	1	no	—
122	C₂²×C₄×C₇₃	—	2	1	no	—
123	C₂²×C₄×C₇₃	—	2	1	no	—
124	C₂²×C₄×C₇₃	—	2	1	no	—
125	C₂²×C₄×C₇₃	—	2	1	no	—
126	C₂²×C₄×C₇₃	—	2	2	no	—
127	C₂²×C₄×C₇₃	—	2	2	no	—
128	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
131	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
132	Q₁₆×C₇₃	—	4	4	no	—
133	Q₁₆×C₇₃	—	4	2	no	—
134	Q₁₆×C₇₃	—	4	2	no	—
135	SD₁₆×C₇₃	—	4	4	no	—
136	M₁₆×C₇₃	—	2	2	no	—
137	M₁₆×C₇₃	—	2	4	no	—
138	M₁₆×C₇₃	—	2	4	no	—
139	M₁₆×C₇₃	—	2	1	no	—
140	M₁₆×C₇₃	—	2	2	no	—
141	M₁₆×C₇₃	—	2	1	no	—
142	M₁₆×C₇₃	—	2	1	no	—
143	M₁₆×C₇₃	—	2	2	no	—
144	M₁₆×C₇₃	—	2	1	no	—
145	M₁₆×C₇₃	—	4	4	no	—
146	M₁₆×C₇₃	—	4	2	no	—
147	M₁₆×C₇₃	C₂×D₄	1	4	yes	—
148	C₂×C₈×C₇₃	—	2	2	no	—
149	C₂×C₈×C₇₃	—	2	1	no	—
150	C₂×C₈×C₇₃	—	2	1	no	—
151	C₂×C₈×C₇₃	—	2	1	no	—
152	C₂×C₈×C₇₃	—	2	1	no	—
153	C₂×C₈×C₇₃	—	2	2	no	—
154	C₂×C₈×C₇₃	—	4	4	no	—
155	C₂×C₈×C₇₃	—	4	2	no	—
156	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
157	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
160	C₂×C₈×C₇₃	#41	1	2	yes	—
161	C₄⋊C₄×C₇₃	—	2	2	no	—
162	C₄⋊C₄×C₇₃	—	2	2	no	—
163	C₄⋊C₄×C₇₃	—	2	2	no	—
164	C₄⋊C₄×C₇₃	—	4	2	no	—
165	C₄⋊C₄×C₇₃	—	4	2	no	—
166	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
167	C₂²⋊C₄×C₇₃	—	2	2	no	—
168	C₂²⋊C₄×C₇₃	—	2	1	no	—
169	C₂²⋊C₄×C₇₃	—	2	2	no	—
170	C₂²⋊C₄×C₇₃	—	4	2	no	—
171	C₂²⋊C₄×C₇₃	—	4	2	no	—
172	C₄²×C₇₃	—	2	1	no	—
173	C₂³×C₇₃	—	2	1	no	—
174	C₂³×C₇₃	—	2	1	no	—
175	C₂³×C₇₃	—	2	1	no	—
176	C₂³×C₇₃	—	4	2	no	—
177	C₂³×C₇₃	#121	1	2	yes	—
178	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
179	Q₈×C₇₃	—	2	1	no	—
180	Q₈×C₇₃	—	2	1	no	—
181	Q₈×C₇₃	—	4	2	no	—
182	Q₈×C₇₃	—	4	2	no	—
183	Q₈×C₇₃	—	4	2	no	—
184	Q₈×C₇₃	—	4	2	no	—
185	D₄×C₇₃	—	2	1	no	—
186	D₄×C₇₃	—	2	1	no	—
187	D₄×C₇₃	—	4	1	no	—
188	D₄×C₇₃	—	4	1	no	—
189	D₄×C₇₃	—	8	2	no	—
190	C₂×C₄×C₇₃	—	2	1	no	—
191	C₂×C₄×C₇₃	—	2	1	no	—
192	C₂×C₄×C₇₃	—	2	2	no	—
193	C₂×C₄×C₇₃	—	2	2	no	—
194	C₂×C₄×C₇₃	—	2	2	no	—
195	C₂×C₄×C₇₃	—	2	2	no	—
196	C₂×C₄×C₇₃	—	2	2	no	—
197	C₂×C₄×C₇₃	—	2	1	no	—
198	C₂×C₄×C₇₃	—	4	1	no	—
199	C₂×C₄×C₇₃	—	4	1	no	—
200	C₂×C₄×C₇₃	—	4	2	no	—
201	C₂×C₄×C₇₃	—	4	2	no	—
202	C₂×C₄×C₇₃	—	4	2	no	—
203	C₂×C₄×C₇₃	—	4	2	no	—
204	C₂×C₄×C₇₃	—	8	2	no	—
205	C₂×C₄×C₇₃	#121	1	2	yes	—
206	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
212	C₈×C₇₃	—	2	2	no	—
213	C₈×C₇₃	—	2	4	no	—
214	C₈×C₇₃	—	4	1	no	—
215	C₈×C₇₃	—	4	1	no	—
216	C₈×C₇₃	—	4	2	no	—
217	C₈×C₇₃	#121	1	2	yes	—
218	C₈×C₇₃	#121	1	2	yes	—
219	C₂²×C₇₃	—	2	2	no	—
220	C₂²×C₇₃	—	2	2	no	—
221	C₂²×C₇₃	—	2	2	no	—
222	C₂²×C₇₃	—	2	2	no	—
223	C₂²×C₇₃	—	4	1	no	—
224	C₂²×C₇₃	—	4	2	no	—
225	C₂²×C₇₃	—	8	1	no	—
226	C₂²×C₇₃	—	8	1	no	—
227	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
228	C₂²×C₇₃	#548	1	1	yes	characteristic
229	C₂²×C₇₃	#553	1	1	yes	characteristic
230	C₄×C₇₃	—	2	2	no	—
231	C₄×C₇₃	—	4	1	no	—
232	C₄×C₇₃	—	4	2	no	—
233	C₄×C₇₃	—	8	2	no	—
234	C₄×C₇₃	—	8	2	no	—
235	C₄×C₇₃	C₂×#121	1	1	yes	characteristic
236	C₄×C₇₃	#537	1	1	yes	characteristic
237	C₄×C₇₃	D₄²	1	1	yes	characteristic
238	C₄×C₇₃	#547	1	1	yes	characteristic
239	#24807	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂×C₇₃	—	2	1	no	—
241	C₂×C₇₃	—	2	1	no	—
242	C₂×C₇₃	—	4	2	no	—
243	C₂×C₇₃	—	8	1	no	—
244	C₂×C₇₃	#2416	1	1	yes	characteristic
245	C₂×C₇₃	#3069	1	2	yes	—
246	C₂×#473	C₂×C₇₃	1	1	yes	characteristic, complemented
247	#3056	C₂×C₇₃	1	2	yes	—
248	C₂×#470	C₂×C₇₃	1	1	yes	characteristic, complemented
249	#2930	C₂×C₇₃	1	1	yes	characteristic
250	C₂×#430	C₂×C₇₃	1	1	yes	characteristic, complemented
251	#2064	C₂×C₇₃	1	2	yes	complemented
252	#2052	C₂×C₇₃	1	2	yes	complemented
253	#1979	C₂×C₇₃	1	1	yes	characteristic, complemented
254	#1951	C₂×C₇₃	1	1	yes	characteristic, complemented
255	#1901	C₂×C₇₃	1	2	yes	complemented
256	#1815	C₂×C₇₃	1	1	yes	characteristic, complemented
257	C₇₃	#24807	1	1	yes	characteristic, direct product factor, Sylow
258	C₂×#137	C₂²×C₇₃	1	2	yes	—
259	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
260	C₂×#131	C₂²×C₇₃	1	1	yes	characteristic
261	C₂²×M₁₆	C₂²×C₇₃	1	2	yes	—
262	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
263	#525	C₂²×C₇₃	1	1	yes	characteristic
264	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
265	#473	—	2	4	no	—
266	#470	—	2	2	no	—
267	#470	—	2	2	no	—
268	#470	—	2	2	no	—
269	#468	—	2	2	no	—
270	#467	—	2	2	no	—
271	#465	—	2	2	no	—
272	#436	—	2	2	no	—
273	#435	—	2	2	no	—
274	#430	—	2	4	no	—
275	C₂×#108	C₂²×C₇₃	1	2	yes	—
276	C₂×#108	C₂²×C₇₃	1	1	yes	characteristic
277	C₂×#108	C₂²×C₇₃	1	1	yes	characteristic
278	#428	C₂²×C₇₃	1	2	yes	—
279	C₂×#106	C₂²×C₇₃	1	1	yes	characteristic
280	#424	C₂²×C₇₃	1	1	yes	characteristic
281	#419	C₂²×C₇₃	1	2	yes	—
282	#417	C₂²×C₇₃	1	2	yes	—
283	C₂×#103	C₂²×C₇₃	1	2	yes	—
284	C₂×#101	C₂²×C₇₃	1	2	yes	—
285	C₂×#101	C₂²×C₇₃	1	2	yes	—
286	#408	C₂²×C₇₃	1	1	yes	characteristic
287	#407	C₂²×C₇₃	1	1	yes	characteristic
288	#405	C₂²×C₇₃	1	1	yes	characteristic
289	#343	C₂²×C₇₃	1	2	yes	—
290	#343	C₂²×C₇₃	1	2	yes	—
291	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
292	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
293	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
294	#137	—	2	4	no	—
295	#137	—	4	2	no	—
296	C₂×Q₁₆	—	2	2	no	—
297	C₂×Q₁₆	—	2	1	no	—
298	C₂×Q₁₆	—	2	1	no	—
299	C₂×Q₁₆	—	2	2	no	—
300	C₂×Q₁₆	—	2	2	no	—
301	C₂×SD₁₆	—	2	2	no	—
302	#131	—	2	2	no	—
303	#131	—	2	2	no	—
304	C₂×M₁₆	—	2	2	no	—
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	—	2	1	no	—
307	C₂×M₁₆	—	2	2	no	—
308	C₂×M₁₆	—	2	4	no	—
309	C₂×M₁₆	—	4	2	no	—
310	C₂×M₁₆	D₄×C₇₃	1	2	yes	—
311	C₂×M₁₆	D₄×C₇₃	1	2	yes	—
312	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
313	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
314	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
315	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
316	C₂²×C₈	—	2	2	no	—
317	C₂²×C₈	—	2	1	no	—
318	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
320	#123	—	2	1	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	—	2	2	no	—
323	C₂²⋊Q₈	—	2	2	no	—
324	C₂²⋊Q₈	—	2	2	no	—
325	C₂²⋊Q₈	D₄×C₇₃	1	2	yes	—
326	#121	D₄×C₇₃	1	2	yes	—
327	#120	—	2	1	no	—
328	C₄×D₄	—	2	2	no	—
329	#117	C₂³×C₇₃	1	1	yes	characteristic
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	#108	—	2	4	no	—
334	#108	—	2	2	no	—
335	#108	D₄×C₇₃	1	4	yes	complemented
336	#107	—	2	2	no	—
337	#106	—	2	1	no	—
338	#106	—	2	1	no	—
339	#106	—	2	2	no	—
340	C₄⋊C₈	—	2	2	no	—
341	#103	—	2	2	no	—
342	#103	—	2	4	no	—
343	#103	—	2	2	no	—
344	#103	—	2	2	no	—
345	#102	—	2	2	no	—
346	#101	—	2	4	no	—
347	#101	—	4	2	no	—
348	C₂²⋊C₈	—	2	2	no	—
349	C₂²⋊C₈	—	2	2	no	—
350	#97	—	2	1	no	—
351	C₄×C₈	—	2	1	no	—
352	C₂⁴	#41×C₇₃	1	1	yes	characteristic
353	#41	—	2	1	no	—
354	#41	—	2	1	no	—
355	#41	—	2	1	no	—
356	#41	—	2	1	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
375	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
376	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
377	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
378	Q₁₆	—	4	4	no	—
379	Q₁₆	—	4	2	no	—
380	Q₁₆	—	4	2	no	—
381	SD₁₆	—	4	4	no	—
382	M₁₆	—	2	2	no	—
383	M₁₆	—	2	4	no	—
384	M₁₆	—	2	4	no	—
385	M₁₆	—	2	1	no	—
386	M₁₆	—	2	2	no	—
387	M₁₆	—	2	1	no	—
388	M₁₆	—	2	1	no	—
389	M₁₆	—	2	2	no	—
390	M₁₆	—	2	1	no	—
391	M₁₆	—	4	4	no	—
392	M₁₆	—	4	2	no	—
393	M₁₆	C₂×D₄×C₇₃	1	4	yes	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	4	4	no	—
401	C₂×C₈	—	4	2	no	—
402	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
403	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
404	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
405	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
406	C₂×C₈	#41×C₇₃	1	2	yes	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₂²⋊C₄	—	4	2	no	—
418	C₄²	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	4	2	no	—
423	C₂³	#121×C₇₃	1	2	yes	—
424	C₂³	C₂×#41×C₇₃	1	1	yes	characteristic
425	Q₈	—	2	1	no	—
426	Q₈	—	2	1	no	—
427	Q₈	—	4	2	no	—
428	Q₈	—	4	2	no	—
429	Q₈	—	4	2	no	—
430	Q₈	—	4	2	no	—
431	D₄	—	2	1	no	—
432	D₄	—	2	1	no	—
433	D₄	—	4	1	no	—
434	D₄	—	4	1	no	—
435	D₄	—	8	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	8	2	no	—
451	C₂×C₄	#121×C₇₃	1	2	yes	—
452	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
454	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
455	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
456	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
457	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
458	C₈	—	2	2	no	—
459	C₈	—	2	4	no	—
460	C₈	—	4	1	no	—
461	C₈	—	4	1	no	—
462	C₈	—	4	2	no	—
463	C₈	#121×C₇₃	1	2	yes	—
464	C₈	#121×C₇₃	1	2	yes	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
474	C₂²	#548×C₇₃	1	1	yes	characteristic
475	C₂²	#553×C₇₃	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	1	no	—
479	C₄	—	8	2	no	—
480	C₄	—	8	2	no	—
481	C₄	C₂×#121×C₇₃	1	1	yes	characteristic
482	C₄	#537×C₇₃	1	1	yes	characteristic
483	C₄	D₄²×C₇₃	1	1	yes	characteristic
484	C₄	#547×C₇₃	1	1	yes	characteristic
485	C₂	—	2	1	no	—
486	C₂	—	2	1	no	—
487	C₂	—	4	2	no	—
488	C₂	—	8	1	no	—
489	C₂	C₇₃×#2416	1	1	yes	characteristic
490	C₂	C₇₃×#3069	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	#525×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂³×C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#473×C₇₃	C₂	semidirect
3. C₂×#470×C₇₃	C₂	semidirect
5. C₂×#430×C₇₃	C₂	semidirect
6. C₇₃×#2064	C₂	semidirect
7. C₇₃×#2052	C₂	semidirect
8. C₇₃×#1979	C₂	semidirect
9. C₇₃×#1951	C₂	semidirect
10. C₇₃×#1901	C₂	semidirect
11. C₇₃×#1815	C₂	semidirect
89. #108×C₇₃	D₄	semidirect
239. #24807	C₇₃	direct (N × H)
246. C₂×#473	C₂×C₇₃	semidirect
248. C₂×#470	C₂×C₇₃	semidirect
250. C₂×#430	C₂×C₇₃	semidirect
251. #2064	C₂×C₇₃	semidirect
252. #2052	C₂×C₇₃	semidirect
253. #1979	C₂×C₇₃	semidirect
254. #1951	C₂×C₇₃	semidirect
255. #1901	C₂×C₇₃	semidirect
256. #1815	C₂×C₇₃	semidirect
257. C₇₃	#24807	direct (N × H)
335. #108	D₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#473×C₇₃	2
C₇₃×#3056	2
C₂×#470×C₇₃	2
C₇₃×#2930	2
C₂×#430×C₇₃	2
C₇₃×#2064	2
C₇₃×#2052	2
C₇₃×#1979	2
C₇₃×#1951	2
C₇₃×#1901	2
C₇₃×#1815	2
#24807	73

Subgroups — C73×#24807 #32934211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#24807 #32934211