Subgroups — C₇₃×#24858 #32934262

Order 18688.

720 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3079	C₂	1	1	yes	maximal, characteristic
2	C₂×#475×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#137×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#2906	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#2090	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2064	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1908	C₂	1	2	yes	maximal
10	C₇₃×#1815	C₂	1	2	yes	maximal
11	C₇₃×#1801	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×#131×C₇₃	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
17	#477×C₇₃	—	2	1	no	—
18	#476×C₇₃	—	2	1	no	—
19	#475×C₇₃	—	2	1	no	—
20	#475×C₇₃	—	2	1	no	—
21	#475×C₇₃	—	2	1	no	—
22	#475×C₇₃	—	2	2	no	—
23	#474×C₇₃	—	2	1	no	—
24	#441×C₇₃	—	2	1	no	—
25	#440×C₇₃	—	2	1	no	—
26	C₄×Q₁₆×C₇₃	—	2	1	no	—
27	C₄×SD₁₆×C₇₃	—	2	1	no	—
28	C₂×#108×C₇₃	C₂²	1	2	yes	—
29	#428×C₇₃	C₂²	1	2	yes	—
30	#428×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#106×C₇₃	C₂²	1	2	yes	—
32	#424×C₇₃	—	2	2	no	—
33	#424×C₇₃	C₂²	1	2	yes	—
34	#423×C₇₃	—	2	1	no	—
35	#423×C₇₃	C₂²	1	1	yes	characteristic
36	#423×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₇₃	—	2	1	no	—
38	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
39	#419×C₇₃	C₂²	1	1	yes	characteristic
40	#417×C₇₃	C₂²	1	2	yes	—
41	#417×C₇₃	C₂²	1	1	yes	characteristic
42	C₂×#103×C₇₃	C₂²	1	2	yes	—
43	C₂×#101×C₇₃	C₂²	1	2	yes	—
44	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
45	#343×C₇₃	C₂²	1	2	yes	—
46	#343×C₇₃	C₂²	1	2	yes	—
47	#343×C₇₃	C₂²	1	2	yes	—
48	#341×C₇₃	C₂²	1	2	yes	—
49	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₇₃	—	2	1	no	—
51	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
52	#137×C₇₃	—	2	2	no	—
53	#137×C₇₃	Q₈	1	4	yes	complemented
54	C₂×Q₁₆×C₇₃	—	2	1	no	—
55	C₂×SD₁₆×C₇₃	—	2	1	no	—
56	#131×C₇₃	—	2	4	no	—
57	#131×C₇₃	—	4	2	no	—
58	C₂×M₁₆×C₇₃	—	2	2	no	—
59	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
61	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
62	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₇₃	—	2	2	no	—
64	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
65	C₄⋊Q₈×C₇₃	—	2	1	no	—
66	C₄⋊Q₈×C₇₃	—	2	1	no	—
67	C₄⋊Q₈×C₇₃	—	2	1	no	—
68	C₄⋊Q₈×C₇₃	—	2	1	no	—
69	C₄×Q₈×C₇₃	—	2	1	no	—
70	C₄×Q₈×C₇₃	—	2	1	no	—
71	C₄×Q₈×C₇₃	—	2	1	no	—
72	C₄×Q₈×C₇₃	—	2	1	no	—
73	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
74	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
75	C₄×D₄×C₇₃	—	2	1	no	—
76	C₄×D₄×C₇₃	—	2	1	no	—
77	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
78	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
79	#117×C₇₃	—	2	1	no	—
80	#117×C₇₃	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₇₃	—	2	1	no	—
86	C₂×C₄²×C₇₃	—	2	1	no	—
87	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
88	#108×C₇₃	—	4	2	no	—
89	#107×C₇₃	—	2	1	no	—
90	#107×C₇₃	—	2	2	no	—
91	#106×C₇₃	—	2	2	no	—
92	#106×C₇₃	—	2	2	no	—
93	#106×C₇₃	—	2	1	no	—
94	#106×C₇₃	—	2	2	no	—
95	C₄⋊C₈×C₇₃	—	2	2	no	—
96	C₄⋊C₈×C₇₃	—	2	2	no	—
97	C₄⋊C₈×C₇₃	—	2	1	no	—
98	C₄⋊C₈×C₇₃	—	2	1	no	—
99	C₄⋊C₈×C₇₃	—	2	1	no	—
100	C₄⋊C₈×C₇₃	—	2	1	no	—
101	C₄⋊C₈×C₇₃	D₄	1	1	yes	characteristic
102	C₄⋊C₈×C₇₃	D₄	1	1	yes	characteristic
103	C₄⋊C₈×C₇₃	D₄	1	2	yes	—
104	#103×C₇₃	—	2	1	no	—
105	#103×C₇₃	—	2	2	no	—
106	#103×C₇₃	—	2	2	no	—
107	#103×C₇₃	—	2	2	no	—
108	#103×C₇₃	—	2	1	no	—
109	#103×C₇₃	—	2	1	no	—
110	#102×C₇₃	—	2	1	no	—
111	#102×C₇₃	—	2	2	no	—
112	#101×C₇₃	—	4	2	no	—
113	#97×C₇₃	—	2	1	no	—
114	C₄×C₈×C₇₃	—	2	1	no	—
115	#41×C₇₃	—	2	1	no	—
116	#41×C₇₃	—	2	1	no	—
117	#41×C₇₃	C₂×Q₈	1	2	yes	—
118	#41×C₇₃	#41	1	2	yes	—
119	C₂×Q₈×C₇₃	—	2	1	no	—
120	C₂×Q₈×C₇₃	—	2	1	no	—
121	C₂×Q₈×C₇₃	—	2	1	no	—
122	C₂×Q₈×C₇₃	—	2	1	no	—
123	C₂×Q₈×C₇₃	—	2	1	no	—
124	C₂×Q₈×C₇₃	—	4	1	no	—
125	C₂×Q₈×C₇₃	—	4	1	no	—
126	C₂×Q₈×C₇₃	—	8	2	no	—
127	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
128	C₂×Q₈×C₇₃	C₂×Q₈	1	2	yes	—
129	C₂×D₄×C₇₃	—	2	1	no	—
130	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₃	—	2	1	no	—
132	C₂²×C₄×C₇₃	—	2	1	no	—
133	C₂²×C₄×C₇₃	—	2	1	no	—
134	C₂²×C₄×C₇₃	—	2	1	no	—
135	C₂²×C₄×C₇₃	—	2	1	no	—
136	C₂²×C₄×C₇₃	—	2	2	no	—
137	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
138	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
139	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
140	Q₁₆×C₇₃	—	2	4	no	—
141	SD₁₆×C₇₃	—	2	4	no	—
142	M₁₆×C₇₃	—	2	1	no	—
143	M₁₆×C₇₃	—	2	2	no	—
144	M₁₆×C₇₃	—	2	2	no	—
145	M₁₆×C₇₃	—	2	2	no	—
146	M₁₆×C₇₃	—	2	1	no	—
147	M₁₆×C₇₃	—	2	1	no	—
148	M₁₆×C₇₃	—	2	2	no	—
149	M₁₆×C₇₃	—	4	4	no	—
150	M₁₆×C₇₃	C₂×Q₈	1	2	yes	—
151	C₂×C₈×C₇₃	—	2	1	no	—
152	C₂×C₈×C₇₃	—	2	2	no	—
153	C₂×C₈×C₇₃	—	2	2	no	—
154	C₂×C₈×C₇₃	—	2	1	no	—
155	C₂×C₈×C₇₃	—	2	2	no	—
156	C₂×C₈×C₇₃	—	2	2	no	—
157	C₂×C₈×C₇₃	—	4	4	no	—
158	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
159	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
160	C₄⋊C₄×C₇₃	—	2	1	no	—
161	C₄⋊C₄×C₇₃	—	2	1	no	—
162	C₄⋊C₄×C₇₃	—	2	1	no	—
163	C₄⋊C₄×C₇₃	—	2	2	no	—
164	C₄⋊C₄×C₇₃	—	2	2	no	—
165	C₄⋊C₄×C₇₃	—	2	1	no	—
166	C₄⋊C₄×C₇₃	—	4	1	no	—
167	C₄⋊C₄×C₇₃	—	4	1	no	—
168	C₄⋊C₄×C₇₃	—	4	1	no	—
169	C₄⋊C₄×C₇₃	—	4	1	no	—
170	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
171	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
172	C₂²⋊C₄×C₇₃	—	2	1	no	—
173	C₂²⋊C₄×C₇₃	—	2	1	no	—
174	C₂²⋊C₄×C₇₃	—	2	1	no	—
175	C₄²×C₇₃	—	2	1	no	—
176	C₄²×C₇₃	—	2	1	no	—
177	C₄²×C₇₃	—	2	1	no	—
178	C₄²×C₇₃	—	4	1	no	—
179	C₄²×C₇₃	—	4	1	no	—
180	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
184	C₂³×C₇₃	—	2	1	no	—
185	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
186	Q₈×C₇₃	—	2	1	no	—
187	Q₈×C₇₃	—	2	2	no	—
188	Q₈×C₇₃	—	2	2	no	—
189	Q₈×C₇₃	—	4	1	no	—
190	Q₈×C₇₃	—	4	1	no	—
191	Q₈×C₇₃	—	8	2	no	—
192	Q₈×C₇₃	—	8	2	no	—
193	Q₈×C₇₃	C₂²⋊Q₈	1	2	yes	—
194	D₄×C₇₃	—	2	2	no	—
195	D₄×C₇₃	—	2	2	no	—
196	D₄×C₇₃	—	2	1	no	—
197	D₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
198	C₂×C₄×C₇₃	—	2	1	no	—
199	C₂×C₄×C₇₃	—	2	2	no	—
200	C₂×C₄×C₇₃	—	2	2	no	—
201	C₂×C₄×C₇₃	—	2	2	no	—
202	C₂×C₄×C₇₃	—	2	1	no	—
203	C₂×C₄×C₇₃	—	2	1	no	—
204	C₂×C₄×C₇₃	—	2	2	no	—
205	C₂×C₄×C₇₃	—	4	1	no	—
206	C₂×C₄×C₇₃	—	4	1	no	—
207	C₂×C₄×C₇₃	—	4	1	no	—
208	C₂×C₄×C₇₃	—	4	2	no	—
209	C₂×C₄×C₇₃	—	4	1	no	—
210	C₂×C₄×C₇₃	—	4	2	no	—
211	C₂×C₄×C₇₃	—	8	1	no	—
212	C₂×C₄×C₇₃	—	8	1	no	—
213	C₂×C₄×C₇₃	—	8	2	no	—
214	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
215	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
216	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
217	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
218	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
221	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
224	C₈×C₇₃	—	2	2	no	—
225	C₈×C₇₃	—	2	2	no	—
226	C₈×C₇₃	—	2	2	no	—
227	C₈×C₇₃	—	4	1	no	—
228	C₈×C₇₃	—	4	2	no	—
229	C₈×C₇₃	—	4	2	no	—
230	C₂²×C₇₃	—	2	1	no	—
231	C₂²×C₇₃	—	2	1	no	—
232	C₂²×C₇₃	—	2	2	no	—
233	C₂²×C₇₃	—	4	1	no	—
234	C₂²×C₇₃	—	4	1	no	—
235	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
236	C₂²×C₇₃	#552	1	1	yes	characteristic
237	C₂²×C₇₃	#554	1	1	yes	characteristic
238	C₄×C₇₃	—	2	2	no	—
239	C₄×C₇₃	—	2	1	no	—
240	C₄×C₇₃	—	2	1	no	—
241	C₄×C₇₃	—	2	1	no	—
242	C₄×C₇₃	—	4	2	no	—
243	C₄×C₇₃	—	4	1	no	—
244	C₄×C₇₃	—	4	1	no	—
245	C₄×C₇₃	—	8	2	no	—
246	C₄×C₇₃	—	8	1	no	—
247	C₄×C₇₃	#471	1	2	yes	—
248	C₄×C₇₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
249	C₄×C₇₃	#537	1	1	yes	characteristic
250	C₄×C₇₃	#546	1	1	yes	characteristic
251	C₄×C₇₃	D₄×Q₈	1	1	yes	characteristic
252	#24858	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₂×C₇₃	—	2	1	no	—
254	C₂×C₇₃	—	2	1	no	—
255	C₂×C₇₃	—	4	2	no	—
256	C₂×C₇₃	#2417	1	1	yes	characteristic
257	C₂×C₇₃	C₂×#471	1	1	yes	characteristic
258	C₂×C₇₃	#3069	1	1	yes	characteristic
259	#3079	C₂×C₇₃	1	1	yes	characteristic
260	C₂×#475	C₂×C₇₃	1	1	yes	characteristic, complemented
261	C₄×#137	C₂×C₇₃	1	1	yes	characteristic
262	#2906	C₂×C₇₃	1	1	yes	characteristic
263	#2090	C₂×C₇₃	1	2	yes	complemented
264	#2064	C₂×C₇₃	1	2	yes	complemented
265	#1997	C₂×C₇₃	1	1	yes	characteristic, complemented
266	#1950	C₂×C₇₃	1	1	yes	characteristic, complemented
267	#1908	C₂×C₇₃	1	2	yes	—
268	#1815	C₂×C₇₃	1	2	yes	—
269	#1801	C₂×C₇₃	1	1	yes	characteristic, complemented
270	C₇₃	#24858	1	1	yes	characteristic, direct product factor, Sylow
271	C₂×#137	C₂²×C₇₃	1	1	yes	characteristic
272	C₂×#131	C₂²×C₇₃	1	2	yes	—
273	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
274	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
275	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
276	#477	—	2	1	no	—
277	#476	—	2	1	no	—
278	#475	—	2	1	no	—
279	#475	—	2	1	no	—
280	#475	—	2	1	no	—
281	#475	—	2	2	no	—
282	#474	—	2	1	no	—
283	#441	—	2	1	no	—
284	#440	—	2	1	no	—
285	C₄×Q₁₆	—	2	1	no	—
286	C₄×SD₁₆	—	2	1	no	—
287	C₂×#108	C₂²×C₇₃	1	2	yes	—
288	#428	C₂²×C₇₃	1	2	yes	—
289	#428	C₂²×C₇₃	1	1	yes	characteristic
290	C₂×#106	C₂²×C₇₃	1	2	yes	—
291	#424	—	2	2	no	—
292	#424	C₂²×C₇₃	1	2	yes	—
293	#423	—	2	1	no	—
294	#423	C₂²×C₇₃	1	1	yes	characteristic
295	#423	C₂²×C₇₃	1	1	yes	characteristic
296	C₂×C₄⋊C₈	—	2	1	no	—
297	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
298	#419	C₂²×C₇₃	1	1	yes	characteristic
299	#417	C₂²×C₇₃	1	2	yes	—
300	#417	C₂²×C₇₃	1	1	yes	characteristic
301	C₂×#103	C₂²×C₇₃	1	2	yes	—
302	C₂×#101	C₂²×C₇₃	1	2	yes	—
303	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
304	#343	C₂²×C₇₃	1	2	yes	—
305	#343	C₂²×C₇₃	1	2	yes	—
306	#343	C₂²×C₇₃	1	2	yes	—
307	#341	C₂²×C₇₃	1	2	yes	—
308	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
309	C₂²×Q₈	—	2	1	no	—
310	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
311	#137	—	2	2	no	—
312	#137	Q₈×C₇₃	1	4	yes	complemented
313	C₂×Q₁₆	—	2	1	no	—
314	C₂×SD₁₆	—	2	1	no	—
315	#131	—	2	4	no	—
316	#131	—	4	2	no	—
317	C₂×M₁₆	—	2	2	no	—
318	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
319	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
320	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
321	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
322	C₂²×C₈	—	2	2	no	—
323	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
324	C₄⋊Q₈	—	2	1	no	—
325	C₄⋊Q₈	—	2	1	no	—
326	C₄⋊Q₈	—	2	1	no	—
327	C₄⋊Q₈	—	2	1	no	—
328	C₄×Q₈	—	2	1	no	—
329	C₄×Q₈	—	2	1	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	—	2	1	no	—
332	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
333	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
334	C₄×D₄	—	2	1	no	—
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
337	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
338	#117	—	2	1	no	—
339	#117	C₂³×C₇₃	1	1	yes	characteristic
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
344	C₂×C₄²	—	2	1	no	—
345	C₂×C₄²	—	2	1	no	—
346	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
347	#108	—	4	2	no	—
348	#107	—	2	1	no	—
349	#107	—	2	2	no	—
350	#106	—	2	2	no	—
351	#106	—	2	2	no	—
352	#106	—	2	1	no	—
353	#106	—	2	2	no	—
354	C₄⋊C₈	—	2	2	no	—
355	C₄⋊C₈	—	2	2	no	—
356	C₄⋊C₈	—	2	1	no	—
357	C₄⋊C₈	—	2	1	no	—
358	C₄⋊C₈	—	2	1	no	—
359	C₄⋊C₈	—	2	1	no	—
360	C₄⋊C₈	D₄×C₇₃	1	1	yes	characteristic
361	C₄⋊C₈	D₄×C₇₃	1	1	yes	characteristic
362	C₄⋊C₈	D₄×C₇₃	1	2	yes	—
363	#103	—	2	1	no	—
364	#103	—	2	2	no	—
365	#103	—	2	2	no	—
366	#103	—	2	2	no	—
367	#103	—	2	1	no	—
368	#103	—	2	1	no	—
369	#102	—	2	1	no	—
370	#102	—	2	2	no	—
371	#101	—	4	2	no	—
372	#97	—	2	1	no	—
373	C₄×C₈	—	2	1	no	—
374	#41	—	2	1	no	—
375	#41	—	2	1	no	—
376	#41	C₂×Q₈×C₇₃	1	2	yes	—
377	#41	#41×C₇₃	1	2	yes	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	4	1	no	—
384	C₂×Q₈	—	4	1	no	—
385	C₂×Q₈	—	8	2	no	—
386	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
387	C₂×Q₈	C₂×Q₈×C₇₃	1	2	yes	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
397	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
398	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
399	Q₁₆	—	2	4	no	—
400	SD₁₆	—	2	4	no	—
401	M₁₆	—	2	1	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	2	no	—
404	M₁₆	—	2	2	no	—
405	M₁₆	—	2	1	no	—
406	M₁₆	—	2	2	no	—
407	M₁₆	—	2	1	no	—
408	M₁₆	—	4	4	no	—
409	M₁₆	C₂×Q₈×C₇₃	1	2	yes	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	4	4	no	—
417	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
418	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	4	1	no	—
426	C₄⋊C₄	—	4	1	no	—
427	C₄⋊C₄	—	4	1	no	—
428	C₄⋊C₄	—	4	1	no	—
429	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
430	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	1	no	—
434	C₄²	—	2	1	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	1	no	—
437	C₄²	—	4	1	no	—
438	C₄²	—	4	1	no	—
439	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
440	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
441	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
442	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
443	C₂³	—	2	1	no	—
444	C₂³	C₂×#41×C₇₃	1	1	yes	characteristic
445	Q₈	—	2	1	no	—
446	Q₈	—	2	2	no	—
447	Q₈	—	2	2	no	—
448	Q₈	—	4	1	no	—
449	Q₈	—	4	1	no	—
450	Q₈	—	8	2	no	—
451	Q₈	—	8	2	no	—
452	Q₈	C₂²⋊Q₈×C₇₃	1	2	yes	—
453	D₄	—	2	2	no	—
454	D₄	—	2	2	no	—
455	D₄	—	2	1	no	—
456	D₄	C₂²⋊Q₈×C₇₃	1	2	yes	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	8	1	no	—
471	C₂×C₄	—	8	2	no	—
472	C₂×C₄	—	8	1	no	—
473	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
474	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
475	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
476	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
477	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
479	C₂×C₄	C₂²×Q₈×C₇₃	1	1	yes	characteristic
480	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
481	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
482	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
483	C₈	—	2	2	no	—
484	C₈	—	2	2	no	—
485	C₈	—	2	2	no	—
486	C₈	—	4	1	no	—
487	C₈	—	4	2	no	—
488	C₈	—	4	2	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	1	no	—
494	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
495	C₂²	#552×C₇₃	1	1	yes	characteristic
496	C₂²	#554×C₇₃	1	1	yes	characteristic
497	C₄	—	2	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	—	2	2	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	1	no	—
503	C₄	—	4	2	no	—
504	C₄	—	8	2	no	—
505	C₄	—	8	1	no	—
506	C₄	#471×C₇₃	1	2	yes	—
507	C₄	C₂×C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
508	C₄	#537×C₇₃	1	1	yes	characteristic
509	C₄	#546×C₇₃	1	1	yes	characteristic
510	C₄	D₄×Q₈×C₇₃	1	1	yes	characteristic
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	4	2	no	—
514	C₂	C₇₃×#2417	1	1	yes	characteristic
515	C₂	C₂×#471×C₇₃	1	1	yes	characteristic
516	C₂	C₇₃×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#121
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. C₂×#475×C₇₃	C₂	semidirect
5. C₇₃×#2090	C₂	semidirect
6. C₇₃×#2064	C₂	semidirect
7. C₇₃×#1997	C₂	semidirect
8. C₇₃×#1950	C₂	semidirect
11. C₇₃×#1801	C₂	semidirect
53. #137×C₇₃	Q₈	semidirect
252. #24858	C₇₃	direct (N × H)
260. C₂×#475	C₂×C₇₃	semidirect
263. #2090	C₂×C₇₃	semidirect
264. #2064	C₂×C₇₃	semidirect
265. #1997	C₂×C₇₃	semidirect
266. #1950	C₂×C₇₃	semidirect
269. #1801	C₂×C₇₃	semidirect
270. C₇₃	#24858	direct (N × H)
312. #137	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×#3079	2
C₂×#475×C₇₃	2
C₄×#137×C₇₃	2
C₇₃×#2906	2
C₇₃×#2090	2
C₇₃×#2064	2
C₇₃×#1997	2
C₇₃×#1950	2
C₇₃×#1908	2
C₇₃×#1815	2
C₇₃×#1801	2
#24858	73

Subgroups — C73×#24858 #32934262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#24858 #32934262