Subgroups — C₇₃×#25831 #32935235

Order 18688.

946 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3504	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#3166	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3080	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2061	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2060	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1998	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1994	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1860	C₂	1	2	yes	maximal
10	C₇₃×#1859	C₂	1	2	yes	maximal
11	C₄×#104×C₇₃	C₂	1	1	yes	maximal, characteristic
12	#557×C₇₃	—	2	2	no	—
13	#554×C₇₃	—	2	2	no	—
14	#554×C₇₃	—	2	4	no	—
15	#544×C₇₃	—	2	2	no	—
16	#544×C₇₃	C₂²	1	2	yes	—
17	#533×C₇₃	—	2	1	no	—
18	#533×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×#125×C₇₃	—	2	1	no	—
20	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
22	#520×C₇₃	C₂²	1	2	yes	—
23	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
24	#501×C₇₃	—	2	2	no	—
25	#499×C₇₃	—	2	1	no	—
26	#499×C₇₃	—	2	1	no	—
27	#479×C₇₃	—	2	2	no	—
28	#478×C₇₃	—	2	2	no	—
29	#428×C₇₃	C₂²	1	2	yes	—
30	#428×C₇₃	C₂²	1	2	yes	—
31	#428×C₇₃	C₂²	1	2	yes	—
32	#423×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×#104×C₇₃	C₂²	1	1	yes	characteristic
34	C₂×#104×C₇₃	C₂²	1	1	yes	characteristic
35	#417×C₇₃	C₂²	1	2	yes	—
36	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
37	#389×C₇₃	—	2	4	no	—
38	#384×C₇₃	C₂²	1	2	yes	—
39	#382×C₇₃	C₂²	1	2	yes	—
40	C₄³×C₇₃	C₂²	1	1	yes	characteristic
41	#343×C₇₃	C₂²	1	2	yes	—
42	#343×C₇₃	C₂²	1	2	yes	—
43	#339×C₇₃	C₂²	1	2	yes	—
44	#339×C₇₃	C₂²	1	2	yes	—
45	#339×C₇₃	C₂²	1	1	yes	characteristic
46	#339×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
49	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
51	C₄⋊Q₈×C₇₃	—	2	4	no	—
52	C₄⋊Q₈×C₇₃	—	2	2	no	—
53	C₄⋊Q₈×C₇₃	—	2	2	no	—
54	C₄⋊Q₈×C₇₃	D₄	1	2	yes	—
55	#125×C₇₃	—	2	4	no	—
56	#125×C₇₃	—	2	4	no	—
57	#125×C₇₃	—	2	2	no	—
58	#125×C₇₃	—	2	2	no	—
59	#125×C₇₃	—	2	1	no	—
60	#125×C₇₃	—	2	1	no	—
61	#125×C₇₃	—	2	2	no	—
62	#125×C₇₃	—	2	2	no	—
63	#125×C₇₃	—	2	1	no	—
64	#125×C₇₃	—	2	1	no	—
65	#125×C₇₃	D₄	1	1	yes	characteristic
66	#125×C₇₃	D₄	1	1	yes	characteristic
67	C₂²⋊Q₈×C₇₃	—	2	4	no	—
68	C₂²⋊Q₈×C₇₃	—	2	4	no	—
69	C₂²⋊Q₈×C₇₃	—	2	4	no	—
70	C₂²⋊Q₈×C₇₃	—	2	2	no	—
71	C₂²⋊Q₈×C₇₃	—	2	4	no	—
72	C₄×Q₈×C₇₃	—	2	4	no	—
73	C₄×Q₈×C₇₃	—	2	2	no	—
74	C₄×Q₈×C₇₃	—	2	2	no	—
75	C₄×Q₈×C₇₃	D₄	1	2	yes	—
76	C₄×D₄×C₇₃	—	2	2	no	—
77	C₄×D₄×C₇₃	—	2	2	no	—
78	C₄×D₄×C₇₃	—	2	4	no	—
79	C₄×D₄×C₇₃	D₄	1	2	yes	—
80	#117×C₇₃	—	2	2	no	—
81	#117×C₇₃	—	2	1	no	—
82	#117×C₇₃	C₂³	1	1	yes	characteristic
83	#117×C₇₃	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
85	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
86	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
87	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
88	C₂×C₄⋊C₄×C₇₃	D₄	1	4	yes	—
89	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
91	C₂×C₄²×C₇₃	—	2	1	no	—
92	C₂×C₄²×C₇₃	—	2	2	no	—
93	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
96	#107×C₇₃	—	2	2	no	—
97	#107×C₇₃	—	2	2	no	—
98	#107×C₇₃	—	2	2	no	—
99	#106×C₇₃	—	2	2	no	—
100	#106×C₇₃	—	2	2	no	—
101	#106×C₇₃	—	2	2	no	—
102	C₄⋊C₈×C₇₃	—	2	2	no	—
103	#104×C₇₃	Q₈	1	4	yes	complemented
104	#104×C₇₃	Q₈	1	4	yes	complemented
105	#103×C₇₃	—	2	2	no	—
106	#102×C₇₃	—	2	2	no	—
107	#97×C₇₃	—	2	1	no	—
108	C₄×C₈×C₇₃	—	2	1	no	—
109	#95×C₇₃	—	2	4	no	—
110	#41×C₇₃	—	2	1	no	—
111	#41×C₇₃	—	2	1	no	—
112	#41×C₇₃	C₂×Q₈	1	2	yes	—
113	#41×C₇₃	C₂×Q₈	1	2	yes	—
114	C₂×Q₈×C₇₃	—	2	4	no	—
115	C₂×Q₈×C₇₃	—	2	2	no	—
116	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
117	C₂×D₄×C₇₃	—	2	1	no	—
118	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₃	—	2	1	no	—
120	C₂²×C₄×C₇₃	—	2	1	no	—
121	C₂²×C₄×C₇₃	—	2	1	no	—
122	C₂²×C₄×C₇₃	—	2	4	no	—
123	C₂²×C₄×C₇₃	—	2	2	no	—
124	C₂²×C₄×C₇₃	—	2	2	no	—
125	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
128	M₁₆×C₇₃	—	2	1	no	—
129	M₁₆×C₇₃	—	2	1	no	—
130	M₁₆×C₇₃	—	2	2	no	—
131	M₁₆×C₇₃	—	2	2	no	—
132	M₁₆×C₇₃	C₂×Q₈	1	2	yes	—
133	M₁₆×C₇₃	C₂×Q₈	1	2	yes	—
134	C₂×C₈×C₇₃	—	2	1	no	—
135	C₂×C₈×C₇₃	—	2	1	no	—
136	C₂×C₈×C₇₃	—	2	2	no	—
137	C₄⋊C₄×C₇₃	—	2	4	no	—
138	C₄⋊C₄×C₇₃	—	2	4	no	—
139	C₄⋊C₄×C₇₃	—	2	4	no	—
140	C₄⋊C₄×C₇₃	—	2	4	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	2	no	—
145	C₄⋊C₄×C₇₃	—	2	2	no	—
146	C₄⋊C₄×C₇₃	—	2	2	no	—
147	C₄⋊C₄×C₇₃	—	2	2	no	—
148	C₄⋊C₄×C₇₃	—	2	2	no	—
149	C₄⋊C₄×C₇₃	—	2	2	no	—
150	C₄⋊C₄×C₇₃	—	2	2	no	—
151	C₄⋊C₄×C₇₃	—	4	8	no	—
152	C₄⋊C₄×C₇₃	—	4	2	no	—
153	C₄⋊C₄×C₇₃	—	4	2	no	—
154	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
155	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
156	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
157	C₂²⋊C₄×C₇₃	—	2	4	no	—
158	C₂²⋊C₄×C₇₃	—	2	2	no	—
159	C₂²⋊C₄×C₇₃	—	2	1	no	—
160	C₂²⋊C₄×C₇₃	—	2	2	no	—
161	C₄²×C₇₃	—	2	4	no	—
162	C₄²×C₇₃	—	2	2	no	—
163	C₄²×C₇₃	—	2	1	no	—
164	C₄²×C₇₃	—	2	2	no	—
165	C₄²×C₇₃	—	2	1	no	—
166	C₄²×C₇₃	—	2	1	no	—
167	C₄²×C₇₃	—	4	4	no	—
168	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₇₃	C₂×D₄	1	2	yes	—
171	C₄²×C₇₃	C₂×Q₈	1	2	yes	—
172	C₄²×C₇₃	C₂×Q₈	1	2	yes	—
173	C₂³×C₇₃	—	2	1	no	—
174	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₇₃	—	2	1	no	—
176	Q₈×C₇₃	—	8	2	no	—
177	Q₈×C₇₃	—	8	4	no	—
178	Q₈×C₇₃	C₄⋊Q₈	1	2	yes	—
179	D₄×C₇₃	—	2	2	no	—
180	D₄×C₇₃	—	2	2	no	—
181	D₄×C₇₃	—	2	1	no	—
182	D₄×C₇₃	C₄⋊Q₈	1	2	yes	—
183	C₂×C₄×C₇₃	—	2	4	no	—
184	C₂×C₄×C₇₃	—	2	1	no	—
185	C₂×C₄×C₇₃	—	2	2	no	—
186	C₂×C₄×C₇₃	—	2	2	no	—
187	C₂×C₄×C₇₃	—	2	2	no	—
188	C₂×C₄×C₇₃	—	2	2	no	—
189	C₂×C₄×C₇₃	—	2	2	no	—
190	C₂×C₄×C₇₃	—	2	4	no	—
191	C₂×C₄×C₇₃	—	2	2	no	—
192	C₂×C₄×C₇₃	—	2	2	no	—
193	C₂×C₄×C₇₃	—	4	2	no	—
194	C₂×C₄×C₇₃	—	4	2	no	—
195	C₂×C₄×C₇₃	—	4	4	no	—
196	C₂×C₄×C₇₃	—	4	4	no	—
197	C₂×C₄×C₇₃	—	4	2	no	—
198	C₂×C₄×C₇₃	—	8	2	no	—
199	C₂×C₄×C₇₃	—	8	4	no	—
200	C₂×C₄×C₇₃	#120	1	2	yes	—
201	C₂×C₄×C₇₃	#120	1	2	yes	—
202	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
205	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
206	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
207	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
208	C₈×C₇₃	—	2	2	no	—
209	C₈×C₇₃	—	2	2	no	—
210	C₈×C₇₃	—	4	2	no	—
211	C₂²×C₇₃	—	2	2	no	—
212	C₂²×C₇₃	—	2	2	no	—
213	C₂²×C₇₃	—	4	2	no	—
214	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
215	C₂²×C₇₃	D₄×Q₈	1	1	yes	characteristic
216	C₂²×C₇₃	D₄×Q₈	1	1	yes	characteristic
217	C₄×C₇₃	—	2	4	no	—
218	C₄×C₇₃	—	2	2	no	—
219	C₄×C₇₃	—	2	2	no	—
220	C₄×C₇₃	—	2	2	no	—
221	C₄×C₇₃	—	4	2	no	—
222	C₄×C₇₃	—	4	4	no	—
223	C₄×C₇₃	—	4	2	no	—
224	C₄×C₇₃	—	4	2	no	—
225	C₄×C₇₃	—	4	2	no	—
226	C₄×C₇₃	—	8	2	no	—
227	C₄×C₇₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
228	C₄×C₇₃	#536	1	1	yes	characteristic
229	C₄×C₇₃	D₄×Q₈	1	1	yes	characteristic
230	C₄×C₇₃	D₄×Q₈	1	1	yes	characteristic
231	#25831	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂×C₇₃	—	2	1	no	—
233	C₂×C₇₃	—	2	1	no	—
234	C₂×C₇₃	—	4	2	no	—
235	C₂×C₇₃	#2434	1	1	yes	characteristic
236	C₂×C₇₃	#3018	1	2	yes	—
237	#3504	C₂×C₇₃	1	1	yes	characteristic
238	#3166	C₂×C₇₃	1	1	yes	characteristic, complemented
239	#3080	C₂×C₇₃	1	1	yes	characteristic
240	#2859	C₂×C₇₃	1	1	yes	characteristic, complemented
241	#2061	C₂×C₇₃	1	2	yes	complemented
242	#2060	C₂×C₇₃	1	2	yes	complemented
243	#1998	C₂×C₇₃	1	1	yes	characteristic, complemented
244	#1994	C₂×C₇₃	1	1	yes	characteristic, complemented
245	#1860	C₂×C₇₃	1	2	yes	—
246	#1859	C₂×C₇₃	1	2	yes	—
247	C₄×#104	C₂×C₇₃	1	1	yes	characteristic
248	C₇₃	#25831	1	1	yes	characteristic, direct product factor, Sylow
249	#557	—	2	2	no	—
250	#554	—	2	2	no	—
251	#554	—	2	4	no	—
252	#544	—	2	2	no	—
253	#544	C₂²×C₇₃	1	2	yes	—
254	#533	—	2	1	no	—
255	#533	C₂²×C₇₃	1	1	yes	characteristic
256	C₂×#125	—	2	1	no	—
257	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
258	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
259	#520	C₂²×C₇₃	1	2	yes	—
260	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
261	#501	—	2	2	no	—
262	#499	—	2	1	no	—
263	#499	—	2	1	no	—
264	#479	—	2	2	no	—
265	#478	—	2	2	no	—
266	#428	C₂²×C₇₃	1	2	yes	—
267	#428	C₂²×C₇₃	1	2	yes	—
268	#428	C₂²×C₇₃	1	2	yes	—
269	#423	C₂²×C₇₃	1	1	yes	characteristic
270	C₂×#104	C₂²×C₇₃	1	1	yes	characteristic
271	C₂×#104	C₂²×C₇₃	1	1	yes	characteristic
272	#417	C₂²×C₇₃	1	2	yes	—
273	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
274	#389	—	2	4	no	—
275	#384	C₂²×C₇₃	1	2	yes	—
276	#382	C₂²×C₇₃	1	2	yes	—
277	C₄³	C₂²×C₇₃	1	1	yes	characteristic
278	#343	C₂²×C₇₃	1	2	yes	—
279	#343	C₂²×C₇₃	1	2	yes	—
280	#339	C₂²×C₇₃	1	1	yes	characteristic
281	#339	C₂²×C₇₃	1	2	yes	—
282	#339	C₂²×C₇₃	1	1	yes	characteristic
283	#339	C₂²×C₇₃	1	2	yes	—
284	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
285	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
286	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
287	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
288	C₄⋊Q₈	—	2	4	no	—
289	C₄⋊Q₈	—	2	2	no	—
290	C₄⋊Q₈	—	2	2	no	—
291	C₄⋊Q₈	D₄×C₇₃	1	2	yes	—
292	#125	—	2	4	no	—
293	#125	—	2	4	no	—
294	#125	—	2	2	no	—
295	#125	—	2	2	no	—
296	#125	—	2	1	no	—
297	#125	—	2	1	no	—
298	#125	—	2	2	no	—
299	#125	—	2	2	no	—
300	#125	—	2	1	no	—
301	#125	—	2	1	no	—
302	#125	D₄×C₇₃	1	1	yes	characteristic
303	#125	D₄×C₇₃	1	1	yes	characteristic
304	C₂²⋊Q₈	—	2	4	no	—
305	C₂²⋊Q₈	—	2	4	no	—
306	C₂²⋊Q₈	—	2	4	no	—
307	C₂²⋊Q₈	—	2	2	no	—
308	C₂²⋊Q₈	—	2	4	no	—
309	C₄×Q₈	—	2	4	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×Q₈	—	2	2	no	—
312	C₄×Q₈	D₄×C₇₃	1	2	yes	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	—	2	2	no	—
315	C₄×D₄	—	2	4	no	—
316	C₄×D₄	D₄×C₇₃	1	2	yes	—
317	#117	—	2	2	no	—
318	#117	—	2	1	no	—
319	#117	C₂³×C₇₃	1	1	yes	characteristic
320	#117	C₂³×C₇₃	1	2	yes	—
321	C₂×C₄⋊C₄	—	2	4	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	4	no	—
325	C₂×C₄⋊C₄	D₄×C₇₃	1	4	yes	—
326	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
333	#107	—	2	2	no	—
334	#107	—	2	2	no	—
335	#107	—	2	2	no	—
336	#106	—	2	2	no	—
337	#106	—	2	2	no	—
338	#106	—	2	2	no	—
339	C₄⋊C₈	—	2	2	no	—
340	#104	Q₈×C₇₃	1	4	yes	complemented
341	#104	Q₈×C₇₃	1	4	yes	complemented
342	#103	—	2	2	no	—
343	#102	—	2	2	no	—
344	#97	—	2	1	no	—
345	C₄×C₈	—	2	1	no	—
346	#95	—	2	4	no	—
347	#41	—	2	1	no	—
348	#41	—	2	1	no	—
349	#41	C₂×Q₈×C₇₃	1	2	yes	—
350	#41	C₂×Q₈×C₇₃	1	2	yes	—
351	C₂×Q₈	—	2	4	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
363	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
364	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
365	M₁₆	—	2	1	no	—
366	M₁₆	—	2	1	no	—
367	M₁₆	—	2	2	no	—
368	M₁₆	—	2	2	no	—
369	M₁₆	C₂×Q₈×C₇₃	1	2	yes	—
370	M₁₆	C₂×Q₈×C₇₃	1	2	yes	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	2	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	4	8	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
392	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
393	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	2	1	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₄²	—	2	4	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	4	4	no	—
405	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
406	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
407	C₄²	C₂×D₄×C₇₃	1	2	yes	—
408	C₄²	C₂×Q₈×C₇₃	1	2	yes	—
409	C₄²	C₂×Q₈×C₇₃	1	2	yes	—
410	C₂³	—	2	1	no	—
411	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
412	Q₈	—	2	1	no	—
413	Q₈	—	8	2	no	—
414	Q₈	—	8	4	no	—
415	Q₈	C₄⋊Q₈×C₇₃	1	2	yes	—
416	D₄	—	2	2	no	—
417	D₄	—	2	2	no	—
418	D₄	—	2	1	no	—
419	D₄	C₄⋊Q₈×C₇₃	1	2	yes	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	8	2	no	—
436	C₂×C₄	—	8	4	no	—
437	C₂×C₄	#120×C₇₃	1	2	yes	—
438	C₂×C₄	#120×C₇₃	1	2	yes	—
439	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
440	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
441	C₂×C₄	C₂²×Q₈×C₇₃	1	1	yes	characteristic
442	C₂×C₄	C₂²×Q₈×C₇₃	1	1	yes	characteristic
443	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
444	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
445	C₈	—	2	2	no	—
446	C₈	—	2	2	no	—
447	C₈	—	4	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
452	C₂²	D₄×Q₈×C₇₃	1	1	yes	characteristic
453	C₂²	D₄×Q₈×C₇₃	1	1	yes	characteristic
454	C₄	—	2	4	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	4	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	8	2	no	—
464	C₄	C₂×C₄⋊Q₈×C₇₃	1	1	yes	characteristic
465	C₄	#536×C₇₃	1	1	yes	characteristic
466	C₄	D₄×Q₈×C₇₃	1	1	yes	characteristic
467	C₄	D₄×Q₈×C₇₃	1	1	yes	characteristic
468	C₂	—	2	1	no	—
469	C₂	—	2	1	no	—
470	C₂	—	4	2	no	—
471	C₂	C₇₃×#2434	1	1	yes	characteristic
472	C₂	C₇₃×#3018	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#41×C₇₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₃×#3166	C₂	semidirect
4. C₇₃×#2859	C₂	semidirect
5. C₇₃×#2061	C₂	semidirect
6. C₇₃×#2060	C₂	semidirect
7. C₇₃×#1998	C₂	semidirect
8. C₇₃×#1994	C₂	semidirect
103. #104×C₇₃	Q₈	semidirect
104. #104×C₇₃	Q₈	semidirect
231. #25831	C₇₃	direct (N × H)
238. #3166	C₂×C₇₃	semidirect
240. #2859	C₂×C₇₃	semidirect
241. #2061	C₂×C₇₃	semidirect
242. #2060	C₂×C₇₃	semidirect
243. #1998	C₂×C₇₃	semidirect
244. #1994	C₂×C₇₃	semidirect
248. C₇₃	#25831	direct (N × H)
340. #104	Q₈×C₇₃	semidirect
341. #104	Q₈×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3504	2
C₇₃×#3166	2
C₇₃×#3080	2
C₇₃×#2859	2
C₇₃×#2061	2
C₇₃×#2060	2
C₇₃×#1998	2
C₇₃×#1994	2
C₇₃×#1860	2
C₇₃×#1859	2
C₄×#104×C₇₃	2
#25831	73

Subgroups — C73×#25831 #32935235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25831 #32935235