Subgroups — C₇₃×#25758 #32935162

Order 18688.

1546 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#494×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#461×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#452×C₇₃	C₂	1	4	yes	maximal, complemented
5	C₇₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2001	C₂	1	4	yes	maximal, complemented
7	C₇₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#102×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₇₃	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₇₃	C₂²	1	4	yes	—
12	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
13	#547×C₇₃	—	2	4	no	—
14	#547×C₇₃	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#123×C₇₃	—	2	2	no	—
18	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	4	yes	—
20	C₂×#121×C₇₃	—	2	1	no	—
21	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₇₃	—	2	1	no	—
24	#494×C₇₃	—	2	4	no	—
25	#461×C₇₃	—	2	4	no	—
26	#452×C₇₃	—	2	16	no	—
27	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×#103×C₇₃	C₂²	1	4	yes	—
29	C₂×#103×C₇₃	C₂²	1	2	yes	—
30	C₂×#102×C₇₃	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₈×C₇₃	C₂²	1	4	yes	—
32	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
33	#399×C₇₃	—	2	2	no	—
34	#390×C₇₃	—	2	1	no	—
35	#384×C₇₃	—	2	1	no	—
36	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
37	#340×C₇₃	C₂²	1	2	yes	—
38	C₂×#41×C₇₃	—	2	4	no	—
39	C₂×#41×C₇₃	—	2	4	no	—
40	C₂×#41×C₇₃	—	2	8	no	—
41	C₂×#41×C₇₃	—	4	4	no	—
42	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
43	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
44	C₂²×D₄×C₇₃	—	2	2	no	—
45	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₇₃	—	2	1	no	—
48	C₂³×C₄×C₇₃	—	2	2	no	—
49	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
50	C₂×Q₁₆×C₇₃	—	2	8	no	—
51	C₂×Q₁₆×C₇₃	—	2	8	no	—
52	C₂×Q₁₆×C₇₃	—	4	4	no	—
53	C₂×SD₁₆×C₇₃	—	2	8	no	—
54	C₂×SD₁₆×C₇₃	—	2	4	no	—
55	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₇₃	—	2	2	no	—
58	C₄⋊Q₈×C₇₃	—	2	2	no	—
59	C₄⋊Q₈×C₇₃	—	2	2	no	—
60	C₄⋊Q₈×C₇₃	D₄	1	4	yes	—
61	#123×C₇₃	—	2	16	no	—
62	C₂²⋊Q₈×C₇₃	—	2	4	no	—
63	C₂²⋊Q₈×C₇₃	—	2	4	no	—
64	C₂²⋊Q₈×C₇₃	—	2	8	no	—
65	C₂²⋊Q₈×C₇₃	—	4	4	no	—
66	#121×C₇₃	—	2	8	no	—
67	C₄×D₄×C₇₃	—	2	2	no	—
68	C₄×D₄×C₇₃	—	2	2	no	—
69	C₄×D₄×C₇₃	—	2	2	no	—
70	C₄×D₄×C₇₃	D₄	1	4	yes	—
71	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
72	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
74	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
76	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
77	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
78	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
84	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
85	C₂×C₄²×C₇₃	—	2	1	no	—
86	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₇₃	—	2	2	no	—
88	#103×C₇₃	—	2	8	no	—
89	#103×C₇₃	—	2	4	no	—
90	#102×C₇₃	D₄	1	8	yes	complemented
91	C₂²⋊C₈×C₇₃	—	2	8	no	—
92	C₄×C₈×C₇₃	—	2	2	no	—
93	#95×C₇₃	—	2	1	no	—
94	C₂⁴×C₇₃	—	2	1	no	—
95	C₂⁴×C₇₃	C₂×D₄	1	2	yes	—
96	#41×C₇₃	—	4	16	no	—
97	#41×C₇₃	—	4	8	no	—
98	#41×C₇₃	—	4	8	no	—
99	C₂×Q₈×C₇₃	—	2	2	no	—
100	C₂×Q₈×C₇₃	—	2	4	no	—
101	C₂×Q₈×C₇₃	—	2	2	no	—
102	C₂×Q₈×C₇₃	—	2	4	no	—
103	C₂×Q₈×C₇₃	—	2	2	no	—
104	C₂×Q₈×C₇₃	—	2	4	no	—
105	C₂×Q₈×C₇₃	—	2	4	no	—
106	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
107	C₂×D₄×C₇₃	—	2	8	no	—
108	C₂×D₄×C₇₃	—	2	2	no	—
109	C₂×D₄×C₇₃	—	2	2	no	—
110	C₂×D₄×C₇₃	—	2	2	no	—
111	C₂×D₄×C₇₃	—	2	1	no	—
112	C₂×D₄×C₇₃	—	2	2	no	—
113	C₂×D₄×C₇₃	—	4	8	no	—
114	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
115	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₇₃	—	2	8	no	—
117	C₂²×C₄×C₇₃	—	2	2	no	—
118	C₂²×C₄×C₇₃	—	2	1	no	—
119	C₂²×C₄×C₇₃	—	2	2	no	—
120	C₂²×C₄×C₇₃	—	2	4	no	—
121	C₂²×C₄×C₇₃	—	2	4	no	—
122	C₂²×C₄×C₇₃	—	2	2	no	—
123	C₂²×C₄×C₇₃	—	2	2	no	—
124	C₂²×C₄×C₇₃	—	2	4	no	—
125	C₂²×C₄×C₇₃	—	2	2	no	—
126	C₂²×C₄×C₇₃	—	4	8	no	—
127	C₂²×C₄×C₇₃	—	4	2	no	—
128	C₂²×C₄×C₇₃	—	4	2	no	—
129	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
133	Q₁₆×C₇₃	—	4	16	no	—
134	SD₁₆×C₇₃	—	4	8	no	—
135	C₂×C₈×C₇₃	—	2	2	no	—
136	C₂×C₈×C₇₃	—	2	2	no	—
137	C₂×C₈×C₇₃	—	2	4	no	—
138	C₂×C₈×C₇₃	—	2	2	no	—
139	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
140	C₄⋊C₄×C₇₃	—	2	8	no	—
141	C₄⋊C₄×C₇₃	—	2	2	no	—
142	C₄⋊C₄×C₇₃	—	2	4	no	—
143	C₄⋊C₄×C₇₃	—	2	4	no	—
144	C₄⋊C₄×C₇₃	—	2	1	no	—
145	C₄⋊C₄×C₇₃	—	2	2	no	—
146	C₄⋊C₄×C₇₃	—	4	8	no	—
147	C₄⋊C₄×C₇₃	—	4	2	no	—
148	C₄⋊C₄×C₇₃	—	4	2	no	—
149	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
150	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
151	C₂²⋊C₄×C₇₃	—	2	8	no	—
152	C₂²⋊C₄×C₇₃	—	2	4	no	—
153	C₂²⋊C₄×C₇₃	—	2	4	no	—
154	C₂²⋊C₄×C₇₃	—	4	8	no	—
155	C₄²×C₇₃	—	4	2	no	—
156	C₄²×C₇₃	C₂×D₄	1	2	yes	—
157	C₄²×C₇₃	C₂×D₄	1	2	yes	—
158	C₂³×C₇₃	—	2	2	no	—
159	C₂³×C₇₃	—	2	4	no	—
160	C₂³×C₇₃	—	2	2	no	—
161	C₂³×C₇₃	—	2	4	no	—
162	C₂³×C₇₃	—	2	2	no	—
163	C₂³×C₇₃	—	2	2	no	—
164	C₂³×C₇₃	—	2	4	no	—
165	C₂³×C₇₃	—	4	1	no	—
166	C₂³×C₇₃	—	4	1	no	—
167	C₂³×C₇₃	—	4	2	no	—
168	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₇₃	—	2	8	no	—
170	Q₈×C₇₃	—	4	2	no	—
171	Q₈×C₇₃	—	4	2	no	—
172	Q₈×C₇₃	—	4	2	no	—
173	Q₈×C₇₃	—	4	2	no	—
174	Q₈×C₇₃	—	4	4	no	—
175	D₄×C₇₃	—	2	2	no	—
176	D₄×C₇₃	—	2	4	no	—
177	D₄×C₇₃	—	4	16	no	—
178	D₄×C₇₃	—	4	4	no	—
179	D₄×C₇₃	#127	1	4	yes	—
180	C₂×C₄×C₇₃	—	2	2	no	—
181	C₂×C₄×C₇₃	—	2	2	no	—
182	C₂×C₄×C₇₃	—	2	2	no	—
183	C₂×C₄×C₇₃	—	2	4	no	—
184	C₂×C₄×C₇₃	—	2	4	no	—
185	C₂×C₄×C₇₃	—	2	4	no	—
186	C₂×C₄×C₇₃	—	4	16	no	—
187	C₂×C₄×C₇₃	—	4	4	no	—
188	C₂×C₄×C₇₃	—	4	2	no	—
189	C₂×C₄×C₇₃	—	4	1	no	—
190	C₂×C₄×C₇₃	—	4	1	no	—
191	C₂×C₄×C₇₃	—	4	2	no	—
192	C₂×C₄×C₇₃	—	4	2	no	—
193	C₂×C₄×C₇₃	—	4	2	no	—
194	C₂×C₄×C₇₃	—	4	4	no	—
195	C₂×C₄×C₇₃	—	4	8	no	—
196	C₂×C₄×C₇₃	—	4	2	no	—
197	C₂×C₄×C₇₃	—	4	4	no	—
198	C₂×C₄×C₇₃	#120	1	2	yes	—
199	C₂×C₄×C₇₃	#120	1	2	yes	—
200	C₂×C₄×C₇₃	#135	1	2	yes	—
201	C₂×C₄×C₇₃	#137	1	2	yes	—
202	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
204	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
206	C₈×C₇₃	—	2	4	no	—
207	C₈×C₇₃	—	4	2	no	—
208	C₂²×C₇₃	—	2	4	no	—
209	C₂²×C₇₃	—	4	2	no	—
210	C₂²×C₇₃	—	4	2	no	—
211	C₂²×C₇₃	—	4	4	no	—
212	C₂²×C₇₃	—	4	4	no	—
213	C₂²×C₇₃	—	4	2	no	—
214	C₂²×C₇₃	—	4	2	no	—
215	C₂²×C₇₃	—	4	2	no	—
216	C₂²×C₇₃	—	4	4	no	—
217	C₂²×C₇₃	—	4	4	no	—
218	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
219	C₂²×C₇₃	D₄²	1	2	yes	—
220	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
221	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
222	C₂²×C₇₃	#578	1	2	yes	—
223	C₄×C₇₃	—	2	2	no	—
224	C₄×C₇₃	—	4	2	no	—
225	C₄×C₇₃	—	4	4	no	—
226	C₄×C₇₃	—	4	2	no	—
227	C₄×C₇₃	—	4	4	no	—
228	C₄×C₇₃	—	8	2	no	—
229	C₄×C₇₃	#452	1	4	yes	complemented
230	C₄×C₇₃	C₂×#127	1	1	yes	characteristic
231	C₄×C₇₃	#535	1	1	yes	characteristic
232	C₄×C₇₃	D₄²	1	2	yes	—
233	#25758	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂×C₇₃	—	4	4	no	—
235	C₂×C₇₃	—	8	2	no	—
236	C₂×C₇₃	#2433	1	1	yes	characteristic
237	C₂×C₇₃	C₂×#452	1	1	yes	characteristic
238	C₂×C₇₃	#3011	1	1	yes	characteristic
239	C₂×C₇₃	#3276	1	2	yes	—
240	C₂×C₇₃	#3283	1	2	yes	—
241	C₂×#547	C₂×C₇₃	1	1	yes	characteristic
242	C₂×#494	C₂×C₇₃	1	1	yes	characteristic, complemented
243	C₂×#461	C₂×C₇₃	1	1	yes	characteristic, complemented
244	C₂×#452	C₂×C₇₃	1	4	yes	complemented
245	#2542	C₂×C₇₃	1	1	yes	characteristic, complemented
246	#2001	C₂×C₇₃	1	4	yes	complemented
247	#1981	C₂×C₇₃	1	1	yes	characteristic, complemented
248	#1954	C₂×C₇₃	1	1	yes	characteristic, complemented
249	C₄×#102	C₂×C₇₃	1	1	yes	characteristic, complemented
250	C₇₃	#25758	1	1	yes	characteristic, direct product factor, Sylow
251	C₂²×#41	C₂²×C₇₃	1	2	yes	—
252	C₂²×Q₁₆	C₂²×C₇₃	1	4	yes	—
253	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
254	#547	—	2	4	no	—
255	#547	—	2	4	no	—
256	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
257	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
258	C₂×#123	—	2	2	no	—
259	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
260	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	4	yes	—
261	C₂×#121	—	2	1	no	—
262	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
263	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	—	2	1	no	—
265	#494	—	2	4	no	—
266	#461	—	2	4	no	—
267	#452	—	2	16	no	—
268	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
269	C₂×#103	C₂²×C₇₃	1	4	yes	—
270	C₂×#103	C₂²×C₇₃	1	2	yes	—
271	C₂×#102	C₂²×C₇₃	1	2	yes	—
272	C₂×C₂²⋊C₈	C₂²×C₇₃	1	4	yes	—
273	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
274	#399	—	2	2	no	—
275	#390	—	2	1	no	—
276	#384	—	2	1	no	—
277	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
278	#340	C₂²×C₇₃	1	2	yes	—
279	C₂×#41	—	2	4	no	—
280	C₂×#41	—	2	4	no	—
281	C₂×#41	—	2	8	no	—
282	C₂×#41	—	4	4	no	—
283	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
284	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
285	C₂²×D₄	—	2	2	no	—
286	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
287	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
288	C₂³×C₄	—	2	1	no	—
289	C₂³×C₄	—	2	2	no	—
290	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
291	C₂×Q₁₆	—	2	8	no	—
292	C₂×Q₁₆	—	2	8	no	—
293	C₂×Q₁₆	—	4	4	no	—
294	C₂×SD₁₆	—	2	8	no	—
295	C₂×SD₁₆	—	2	4	no	—
296	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
297	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
298	C₄⋊Q₈	—	2	2	no	—
299	C₄⋊Q₈	—	2	2	no	—
300	C₄⋊Q₈	—	2	2	no	—
301	C₄⋊Q₈	D₄×C₇₃	1	4	yes	—
302	#123	—	2	16	no	—
303	C₂²⋊Q₈	—	2	4	no	—
304	C₂²⋊Q₈	—	2	4	no	—
305	C₂²⋊Q₈	—	2	8	no	—
306	C₂²⋊Q₈	—	4	4	no	—
307	#121	—	2	8	no	—
308	C₄×D₄	—	2	2	no	—
309	C₄×D₄	—	2	2	no	—
310	C₄×D₄	—	2	2	no	—
311	C₄×D₄	D₄×C₇₃	1	4	yes	—
312	C₂×C₄⋊C₄	—	2	8	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	4	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	2	4	no	—
325	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
328	C₄⋊C₈	—	2	2	no	—
329	#103	—	2	8	no	—
330	#103	—	2	4	no	—
331	#102	D₄×C₇₃	1	8	yes	complemented
332	C₂²⋊C₈	—	2	8	no	—
333	C₄×C₈	—	2	2	no	—
334	#95	—	2	1	no	—
335	C₂⁴	—	2	1	no	—
336	C₂⁴	C₂×D₄×C₇₃	1	2	yes	—
337	#41	—	4	16	no	—
338	#41	—	4	8	no	—
339	#41	—	4	8	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	4	no	—
346	C₂×Q₈	—	2	4	no	—
347	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
348	C₂×D₄	—	2	8	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	4	8	no	—
355	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
356	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
357	C₂²×C₄	—	2	8	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	4	8	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
373	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
374	Q₁₆	—	4	16	no	—
375	SD₁₆	—	4	8	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	4	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	4	8	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
391	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
392	C₂²⋊C₄	—	2	8	no	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	4	8	no	—
396	C₄²	—	4	2	no	—
397	C₄²	C₂×D₄×C₇₃	1	2	yes	—
398	C₄²	C₂×D₄×C₇₃	1	2	yes	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	4	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	4	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	2	no	—
409	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
410	Q₈	—	2	8	no	—
411	Q₈	—	4	2	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	4	no	—
416	D₄	—	2	2	no	—
417	D₄	—	2	4	no	—
418	D₄	—	4	16	no	—
419	D₄	—	4	4	no	—
420	D₄	#127×C₇₃	1	4	yes	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	4	16	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	8	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	#120×C₇₃	1	2	yes	—
440	C₂×C₄	#120×C₇₃	1	2	yes	—
441	C₂×C₄	#135×C₇₃	1	2	yes	—
442	C₂×C₄	#137×C₇₃	1	2	yes	—
443	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
444	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
445	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
446	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
447	C₈	—	2	4	no	—
448	C₈	—	4	2	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	4	4	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	2	no	—
459	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
460	C₂²	D₄²×C₇₃	1	2	yes	—
461	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
462	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
463	C₂²	#578×C₇₃	1	2	yes	—
464	C₄	—	2	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	4	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	4	no	—
469	C₄	—	8	2	no	—
470	C₄	#452×C₇₃	1	4	yes	complemented
471	C₄	C₂×#127×C₇₃	1	1	yes	characteristic
472	C₄	#535×C₇₃	1	1	yes	characteristic
473	C₄	D₄²×C₇₃	1	2	yes	—
474	C₂	—	4	4	no	—
475	C₂	—	8	2	no	—
476	C₂	C₇₃×#2433	1	1	yes	characteristic
477	C₂	C₂×#452×C₇₃	1	1	yes	characteristic
478	C₂	C₇₃×#3011	1	1	yes	characteristic
479	C₂	C₇₃×#3276	1	2	yes	—
480	C₂	C₇₃×#3283	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#547×C₇₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×D₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#494×C₇₃	C₂	semidirect
3. C₂×#461×C₇₃	C₂	semidirect
4. C₂×#452×C₇₃	C₂	semidirect
5. C₇₃×#2542	C₂	semidirect
6. C₇₃×#2001	C₂	semidirect
7. C₇₃×#1981	C₂	semidirect
8. C₇₃×#1954	C₂	semidirect
9. C₄×#102×C₇₃	C₂	semidirect
90. #102×C₇₃	D₄	semidirect
229. C₄×C₇₃	#452	semidirect
233. #25758	C₇₃	direct (N × H)
242. C₂×#494	C₂×C₇₃	semidirect
243. C₂×#461	C₂×C₇₃	semidirect
244. C₂×#452	C₂×C₇₃	semidirect
245. #2542	C₂×C₇₃	semidirect
246. #2001	C₂×C₇₃	semidirect
247. #1981	C₂×C₇₃	semidirect
248. #1954	C₂×C₇₃	semidirect
249. C₄×#102	C₂×C₇₃	semidirect
250. C₇₃	#25758	direct (N × H)
331. #102	D₄×C₇₃	semidirect
470. C₄	#452×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#547×C₇₃	2
C₂×#494×C₇₃	2
C₂×#461×C₇₃	2
C₂×#452×C₇₃	2
C₇₃×#2542	2
C₇₃×#2001	2
C₇₃×#1981	2
C₇₃×#1954	2
C₄×#102×C₇₃	2
#25758	73

Subgroups — C73×#25758 #32935162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25758 #32935162