Subgroups — C₇₃×#25806 #32935210

Order 18688.

1402 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#578×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#494×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#473×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#456×C₇₃	C₂	1	2	yes	maximal, complemented
6	C₇₃×#3011	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2020	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2005	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1979	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1974	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₇₃	C₂²	1	2	yes	—
13	#578×C₇₃	—	2	4	no	—
14	#578×C₇₃	—	2	4	no	—
15	C₂×#137×C₇₃	—	2	2	no	—
16	C₂×#137×C₇₃	C₂²	1	2	yes	—
17	C₂×#137×C₇₃	C₂²	1	2	yes	—
18	C₂×#137×C₇₃	C₂²	1	2	yes	—
19	C₂×#135×C₇₃	—	2	1	no	—
20	C₂×#135×C₇₃	C₂²	1	1	yes	characteristic
21	C₂²×Q₁₆×C₇₃	—	2	1	no	—
22	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
23	C₂²×Q₁₆×C₇₃	C₂²	1	2	yes	—
24	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#131×C₇₃	C₂²	1	1	yes	characteristic
26	#536×C₇₃	C₂²	1	2	yes	—
27	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
28	#497×C₇₃	—	2	2	no	—
29	#495×C₇₃	—	2	1	no	—
30	#494×C₇₃	—	2	4	no	—
31	#494×C₇₃	—	2	1	no	—
32	#473×C₇₃	—	2	4	no	—
33	#456×C₇₃	—	2	8	no	—
34	#452×C₇₃	—	2	4	no	—
35	#451×C₇₃	—	2	4	no	—
36	C₂×#108×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×#104×C₇₃	C₂²	1	2	yes	—
38	C₂×#104×C₇₃	C₂²	1	1	yes	characteristic
39	#419×C₇₃	C₂²	1	2	yes	—
40	#416×C₇₃	C₂²	1	1	yes	characteristic
41	C₂×#101×C₇₃	C₂²	1	2	yes	—
42	C₂×#101×C₇₃	C₂²	1	2	yes	—
43	#408×C₇₃	C₂²	1	2	yes	—
44	#405×C₇₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
46	#341×C₇₃	C₂²	1	1	yes	characteristic
47	#339×C₇₃	C₂²	1	1	yes	characteristic
48	2₋¹⁺⁴×C₇₃	—	2	4	no	—
49	2₋¹⁺⁴×C₇₃	—	2	4	no	—
50	2₋¹⁺⁴×C₇₃	—	2	4	no	—
51	2₋¹⁺⁴×C₇₃	—	4	2	no	—
52	C₂×#41×C₇₃	—	2	2	no	—
53	C₂×#41×C₇₃	—	2	2	no	—
54	C₂×#41×C₇₃	—	4	2	no	—
55	C₂×#41×C₇₃	C₂³	1	2	yes	—
56	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₇₃	—	2	2	no	—
58	C₂²×Q₈×C₇₃	—	2	2	no	—
59	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
60	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
61	#137×C₇₃	—	2	16	no	—
62	#137×C₇₃	—	2	4	no	—
63	#137×C₇₃	—	2	4	no	—
64	#137×C₇₃	—	2	4	no	—
65	#137×C₇₃	—	2	4	no	—
66	#137×C₇₃	—	2	4	no	—
67	#137×C₇₃	—	4	2	no	—
68	#135×C₇₃	—	2	8	no	—
69	#135×C₇₃	—	2	2	no	—
70	#135×C₇₃	—	2	2	no	—
71	C₂×Q₁₆×C₇₃	—	2	8	no	—
72	C₂×Q₁₆×C₇₃	—	2	2	no	—
73	C₂×Q₁₆×C₇₃	—	2	2	no	—
74	C₂×Q₁₆×C₇₃	—	2	4	no	—
75	C₂×Q₁₆×C₇₃	—	2	2	no	—
76	C₂×Q₁₆×C₇₃	—	2	1	no	—
77	C₂×Q₁₆×C₇₃	—	2	1	no	—
78	C₂×Q₁₆×C₇₃	—	2	2	no	—
79	C₂×Q₁₆×C₇₃	—	2	4	no	—
80	C₂×Q₁₆×C₇₃	—	2	2	no	—
81	C₂×Q₁₆×C₇₃	—	2	2	no	—
82	C₂×Q₁₆×C₇₃	—	2	1	no	—
83	C₂×Q₁₆×C₇₃	—	2	1	no	—
84	C₂×Q₁₆×C₇₃	—	4	2	no	—
85	C₂×Q₁₆×C₇₃	D₄	1	1	yes	characteristic
86	C₂×Q₁₆×C₇₃	D₄	1	4	yes	—
87	C₂×SD₁₆×C₇₃	—	2	2	no	—
88	C₂×SD₁₆×C₇₃	—	2	2	no	—
89	C₂×SD₁₆×C₇₃	—	2	2	no	—
90	C₂×SD₁₆×C₇₃	D₄	1	2	yes	—
91	C₂×D₈×C₇₃	D₄	1	1	yes	characteristic
92	#131×C₇₃	—	2	2	no	—
93	#131×C₇₃	D₄	1	4	yes	—
94	C₂×M₁₆×C₇₃	—	2	1	no	—
95	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
96	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
97	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₇₃	—	2	1	no	—
99	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₇₃	—	2	4	no	—
102	C₄⋊Q₈×C₇₃	—	2	2	no	—
103	C₄⋊Q₈×C₇₃	—	2	4	no	—
104	#124×C₇₃	—	2	2	no	—
105	#123×C₇₃	—	4	2	no	—
106	C₂²⋊Q₈×C₇₃	—	2	4	no	—
107	#117×C₇₃	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₇₃	—	4	2	no	—
109	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
110	#108×C₇₃	—	2	2	no	—
111	#104×C₇₃	—	2	4	no	—
112	#104×C₇₃	D₄	1	4	yes	—
113	#103×C₇₃	—	2	4	no	—
114	#103×C₇₃	D₄	1	2	yes	—
115	#102×C₇₃	D₄	1	2	yes	—
116	#101×C₇₃	—	2	4	no	—
117	#101×C₇₃	—	2	4	no	—
118	C₂²⋊C₈×C₇₃	—	2	4	no	—
119	#97×C₇₃	—	2	1	no	—
120	C₄×C₈×C₇₃	—	2	2	no	—
121	C₄×C₈×C₇₃	—	2	1	no	—
122	#41×C₇₃	—	2	1	no	—
123	#41×C₇₃	—	2	1	no	—
124	#41×C₇₃	—	2	8	no	—
125	#41×C₇₃	—	2	2	no	—
126	#41×C₇₃	—	2	2	no	—
127	#41×C₇₃	—	2	2	no	—
128	#41×C₇₃	—	2	2	no	—
129	#41×C₇₃	—	4	4	no	—
130	#41×C₇₃	—	4	8	no	—
131	#41×C₇₃	—	4	4	no	—
132	#41×C₇₃	—	4	8	no	—
133	#41×C₇₃	—	4	4	no	—
134	#41×C₇₃	C₂×D₄	1	2	yes	—
135	#41×C₇₃	C₂×D₄	1	2	yes	—
136	C₂×Q₈×C₇₃	—	2	2	no	—
137	C₂×Q₈×C₇₃	—	2	8	no	—
138	C₂×Q₈×C₇₃	—	2	2	no	—
139	C₂×Q₈×C₇₃	—	2	2	no	—
140	C₂×Q₈×C₇₃	—	2	2	no	—
141	C₂×Q₈×C₇₃	—	2	2	no	—
142	C₂×Q₈×C₇₃	—	2	2	no	—
143	C₂×Q₈×C₇₃	—	2	2	no	—
144	C₂×Q₈×C₇₃	—	2	2	no	—
145	C₂×Q₈×C₇₃	—	2	2	no	—
146	C₂×Q₈×C₇₃	—	2	2	no	—
147	C₂×Q₈×C₇₃	—	2	2	no	—
148	C₂×Q₈×C₇₃	—	4	2	no	—
149	C₂×Q₈×C₇₃	—	4	4	no	—
150	C₂×Q₈×C₇₃	—	4	4	no	—
151	C₂×Q₈×C₇₃	—	4	4	no	—
152	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
153	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
154	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
155	C₂×D₄×C₇₃	—	2	1	no	—
156	C₂×D₄×C₇₃	—	2	2	no	—
157	C₂×D₄×C₇₃	—	4	2	no	—
158	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
159	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₇₃	—	2	1	no	—
161	C₂²×C₄×C₇₃	—	2	1	no	—
162	C₂²×C₄×C₇₃	—	2	2	no	—
163	C₂²×C₄×C₇₃	—	2	2	no	—
164	C₂²×C₄×C₇₃	—	2	2	no	—
165	C₂²×C₄×C₇₃	—	4	2	no	—
166	C₂²×C₄×C₇₃	—	4	2	no	—
167	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
168	Q₁₆×C₇₃	—	2	8	no	—
169	Q₁₆×C₇₃	—	2	2	no	—
170	Q₁₆×C₇₃	—	2	4	no	—
171	Q₁₆×C₇₃	—	2	4	no	—
172	Q₁₆×C₇₃	—	4	8	no	—
173	Q₁₆×C₇₃	—	4	4	no	—
174	Q₁₆×C₇₃	—	4	4	no	—
175	Q₁₆×C₇₃	—	4	2	no	—
176	Q₁₆×C₇₃	—	4	2	no	—
177	SD₁₆×C₇₃	—	2	8	no	—
178	SD₁₆×C₇₃	—	2	4	no	—
179	SD₁₆×C₇₃	—	4	4	no	—
180	SD₁₆×C₇₃	—	4	4	no	—
181	D₈×C₇₃	—	2	2	no	—
182	M₁₆×C₇₃	—	2	1	no	—
183	M₁₆×C₇₃	—	2	1	no	—
184	M₁₆×C₇₃	—	2	4	no	—
185	M₁₆×C₇₃	—	2	2	no	—
186	M₁₆×C₇₃	—	2	2	no	—
187	M₁₆×C₇₃	C₂×D₄	1	2	yes	—
188	M₁₆×C₇₃	C₂×D₄	1	2	yes	—
189	C₂×C₈×C₇₃	—	2	1	no	—
190	C₂×C₈×C₇₃	—	2	1	no	—
191	C₂×C₈×C₇₃	—	2	1	no	—
192	C₂×C₈×C₇₃	—	2	1	no	—
193	C₂×C₈×C₇₃	—	2	4	no	—
194	C₂×C₈×C₇₃	—	2	2	no	—
195	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
196	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
197	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
198	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
199	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
200	C₄⋊C₄×C₇₃	—	4	8	no	—
201	C₄⋊C₄×C₇₃	—	4	4	no	—
202	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
203	C₂²⋊C₄×C₇₃	—	2	1	no	—
204	C₂²⋊C₄×C₇₃	—	4	4	no	—
205	C₄²×C₇₃	—	2	1	no	—
206	C₄²×C₇₃	—	2	1	no	—
207	C₄²×C₇₃	C₂×D₄	1	2	yes	—
208	C₂³×C₇₃	—	2	1	no	—
209	C₂³×C₇₃	—	2	2	no	—
210	C₂³×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
211	Q₈×C₇₃	—	2	1	no	—
212	Q₈×C₇₃	—	2	4	no	—
213	Q₈×C₇₃	—	2	2	no	—
214	Q₈×C₇₃	—	2	4	no	—
215	Q₈×C₇₃	—	2	2	no	—
216	Q₈×C₇₃	—	4	8	no	—
217	Q₈×C₇₃	—	4	2	no	—
218	Q₈×C₇₃	—	4	2	no	—
219	Q₈×C₇₃	—	4	2	no	—
220	Q₈×C₇₃	—	4	2	no	—
221	Q₈×C₇₃	—	4	2	no	—
222	Q₈×C₇₃	—	4	2	no	—
223	Q₈×C₇₃	#127	1	2	yes	—
224	D₄×C₇₃	—	2	2	no	—
225	D₄×C₇₃	—	2	2	no	—
226	D₄×C₇₃	—	2	2	no	—
227	D₄×C₇₃	—	2	1	no	—
228	D₄×C₇₃	—	2	2	no	—
229	D₄×C₇₃	—	4	8	no	—
230	D₄×C₇₃	—	4	2	no	—
231	D₄×C₇₃	—	4	2	no	—
232	D₄×C₇₃	#127	1	2	yes	—
233	C₂×C₄×C₇₃	—	2	4	no	—
234	C₂×C₄×C₇₃	—	2	2	no	—
235	C₂×C₄×C₇₃	—	2	1	no	—
236	C₂×C₄×C₇₃	—	2	2	no	—
237	C₂×C₄×C₇₃	—	2	2	no	—
238	C₂×C₄×C₇₃	—	2	4	no	—
239	C₂×C₄×C₇₃	—	2	2	no	—
240	C₂×C₄×C₇₃	—	2	2	no	—
241	C₂×C₄×C₇₃	—	4	8	no	—
242	C₂×C₄×C₇₃	—	4	8	no	—
243	C₂×C₄×C₇₃	—	4	2	no	—
244	C₂×C₄×C₇₃	—	4	2	no	—
245	C₂×C₄×C₇₃	—	4	2	no	—
246	C₂×C₄×C₇₃	—	4	2	no	—
247	C₂×C₄×C₇₃	—	4	2	no	—
248	C₂×C₄×C₇₃	—	4	2	no	—
249	C₂×C₄×C₇₃	—	4	2	no	—
250	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
256	C₈×C₇₃	—	2	2	no	—
257	C₈×C₇₃	—	2	2	no	—
258	C₈×C₇₃	—	2	2	no	—
259	C₈×C₇₃	—	4	2	no	—
260	C₈×C₇₃	#120	1	2	yes	—
261	C₈×C₇₃	#120	1	2	yes	—
262	C₂²×C₇₃	—	2	2	no	—
263	C₂²×C₇₃	—	2	2	no	—
264	C₂²×C₇₃	—	4	2	no	—
265	C₂²×C₇₃	—	4	2	no	—
266	C₂²×C₇₃	—	4	4	no	—
267	C₂²×C₇₃	#535	1	1	yes	characteristic
268	C₂²×C₇₃	D₄²	1	1	yes	characteristic
269	C₂²×C₇₃	D₄²	1	1	yes	characteristic
270	C₄×C₇₃	—	2	4	no	—
271	C₄×C₇₃	—	2	2	no	—
272	C₄×C₇₃	—	4	4	no	—
273	C₄×C₇₃	—	4	2	no	—
274	C₄×C₇₃	—	4	2	no	—
275	C₄×C₇₃	—	8	2	no	—
276	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
277	C₄×C₇₃	C₂×#127	1	1	yes	characteristic
278	C₄×C₇₃	D₄²	1	1	yes	characteristic
279	C₄×C₇₃	D₄²	1	1	yes	characteristic
280	#25806	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂×C₇₃	—	2	1	no	—
282	C₂×C₇₃	—	2	1	no	—
283	C₂×C₇₃	—	4	2	no	—
284	C₂×C₇₃	—	8	2	no	—
285	C₂×C₇₃	#2433	1	1	yes	characteristic
286	C₂×C₇₃	#3293	1	2	yes	—
287	C₂×#578	C₂×C₇₃	1	1	yes	characteristic
288	#3156	C₂×C₇₃	1	1	yes	characteristic, complemented
289	C₂×#494	C₂×C₇₃	1	1	yes	characteristic, complemented
290	C₂×#473	C₂×C₇₃	1	1	yes	characteristic, complemented
291	C₂×#456	C₂×C₇₃	1	2	yes	complemented
292	#3011	C₂×C₇₃	1	2	yes	complemented
293	#2020	C₂×C₇₃	1	2	yes	complemented
294	#2005	C₂×C₇₃	1	2	yes	complemented
295	#1979	C₂×C₇₃	1	1	yes	characteristic, complemented
296	#1974	C₂×C₇₃	1	1	yes	characteristic, complemented
297	#1764	C₂×C₇₃	1	1	yes	characteristic, complemented
298	C₇₃	#25806	1	1	yes	characteristic, direct product factor, Sylow
299	C₂×2₋¹⁺⁴	C₂²×C₇₃	1	2	yes	—
300	#578	—	2	4	no	—
301	#578	—	2	4	no	—
302	C₂×#137	—	2	2	no	—
303	C₂×#137	C₂²×C₇₃	1	2	yes	—
304	C₂×#137	C₂²×C₇₃	1	2	yes	—
305	C₂×#137	C₂²×C₇₃	1	2	yes	—
306	C₂×#135	—	2	1	no	—
307	C₂×#135	C₂²×C₇₃	1	1	yes	characteristic
308	C₂²×Q₁₆	—	2	1	no	—
309	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
310	C₂²×Q₁₆	C₂²×C₇₃	1	2	yes	—
311	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
312	C₂×#131	C₂²×C₇₃	1	1	yes	characteristic
313	#536	C₂²×C₇₃	1	2	yes	—
314	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
315	#497	—	2	2	no	—
316	#495	—	2	1	no	—
317	#494	—	2	4	no	—
318	#494	—	2	1	no	—
319	#473	—	2	4	no	—
320	#456	—	2	8	no	—
321	#452	—	2	4	no	—
322	#451	—	2	4	no	—
323	C₂×#108	C₂²×C₇₃	1	1	yes	characteristic
324	C₂×#104	C₂²×C₇₃	1	2	yes	—
325	C₂×#104	C₂²×C₇₃	1	1	yes	characteristic
326	#419	C₂²×C₇₃	1	2	yes	—
327	#416	C₂²×C₇₃	1	1	yes	characteristic
328	C₂×#101	C₂²×C₇₃	1	2	yes	—
329	C₂×#101	C₂²×C₇₃	1	2	yes	—
330	#408	C₂²×C₇₃	1	2	yes	—
331	#405	C₂²×C₇₃	1	1	yes	characteristic
332	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
333	#341	C₂²×C₇₃	1	1	yes	characteristic
334	#339	C₂²×C₇₃	1	1	yes	characteristic
335	2₋¹⁺⁴	—	2	4	no	—
336	2₋¹⁺⁴	—	2	4	no	—
337	2₋¹⁺⁴	—	2	4	no	—
338	2₋¹⁺⁴	—	4	2	no	—
339	C₂×#41	—	2	2	no	—
340	C₂×#41	—	2	2	no	—
341	C₂×#41	—	4	2	no	—
342	C₂×#41	C₂³×C₇₃	1	2	yes	—
343	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
344	C₂²×Q₈	—	2	2	no	—
345	C₂²×Q₈	—	2	2	no	—
346	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
347	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
348	#137	—	2	16	no	—
349	#137	—	2	4	no	—
350	#137	—	2	4	no	—
351	#137	—	2	4	no	—
352	#137	—	2	4	no	—
353	#137	—	2	4	no	—
354	#137	—	4	2	no	—
355	#135	—	2	8	no	—
356	#135	—	2	2	no	—
357	#135	—	2	2	no	—
358	C₂×Q₁₆	—	2	8	no	—
359	C₂×Q₁₆	—	2	2	no	—
360	C₂×Q₁₆	—	2	4	no	—
361	C₂×Q₁₆	—	2	2	no	—
362	C₂×Q₁₆	—	2	2	no	—
363	C₂×Q₁₆	—	2	1	no	—
364	C₂×Q₁₆	—	2	1	no	—
365	C₂×Q₁₆	—	2	2	no	—
366	C₂×Q₁₆	—	2	4	no	—
367	C₂×Q₁₆	—	2	2	no	—
368	C₂×Q₁₆	—	2	2	no	—
369	C₂×Q₁₆	—	2	1	no	—
370	C₂×Q₁₆	—	2	1	no	—
371	C₂×Q₁₆	—	4	2	no	—
372	C₂×Q₁₆	D₄×C₇₃	1	1	yes	characteristic
373	C₂×Q₁₆	D₄×C₇₃	1	4	yes	—
374	C₂×SD₁₆	—	2	2	no	—
375	C₂×SD₁₆	—	2	2	no	—
376	C₂×SD₁₆	—	2	2	no	—
377	C₂×SD₁₆	D₄×C₇₃	1	2	yes	—
378	C₂×D₈	D₄×C₇₃	1	1	yes	characteristic
379	#131	—	2	2	no	—
380	#131	D₄×C₇₃	1	4	yes	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
383	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
384	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
385	C₂²×C₈	—	2	1	no	—
386	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
387	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
388	C₄⋊Q₈	—	2	4	no	—
389	C₄⋊Q₈	—	2	2	no	—
390	C₄⋊Q₈	—	2	4	no	—
391	#124	—	2	2	no	—
392	#123	—	4	2	no	—
393	C₂²⋊Q₈	—	2	4	no	—
394	#117	C₂³×C₇₃	1	1	yes	characteristic
395	C₂×C₄⋊C₄	—	4	2	no	—
396	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
397	#108	—	2	2	no	—
398	#104	—	2	4	no	—
399	#104	D₄×C₇₃	1	4	yes	—
400	#103	—	2	4	no	—
401	#103	D₄×C₇₃	1	2	yes	—
402	#102	D₄×C₇₃	1	2	yes	—
403	#101	—	2	4	no	—
404	#101	—	2	4	no	—
405	C₂²⋊C₈	—	2	4	no	—
406	#97	—	2	1	no	—
407	C₄×C₈	—	2	2	no	—
408	C₄×C₈	—	2	1	no	—
409	#41	—	2	1	no	—
410	#41	—	2	1	no	—
411	#41	—	2	8	no	—
412	#41	—	2	2	no	—
413	#41	—	2	2	no	—
414	#41	—	2	2	no	—
415	#41	—	2	2	no	—
416	#41	—	4	4	no	—
417	#41	—	4	8	no	—
418	#41	—	4	4	no	—
419	#41	—	4	8	no	—
420	#41	—	4	4	no	—
421	#41	C₂×D₄×C₇₃	1	2	yes	—
422	#41	C₂×D₄×C₇₃	1	2	yes	—
423	C₂×Q₈	—	2	2	no	—
424	C₂×Q₈	—	2	8	no	—
425	C₂×Q₈	—	2	2	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	2	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	2	2	no	—
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	4	2	no	—
436	C₂×Q₈	—	4	4	no	—
437	C₂×Q₈	—	4	4	no	—
438	C₂×Q₈	—	4	4	no	—
439	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
440	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
441	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	4	2	no	—
445	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
446	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	4	2	no	—
453	C₂²×C₄	—	4	2	no	—
454	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
455	Q₁₆	—	2	8	no	—
456	Q₁₆	—	2	2	no	—
457	Q₁₆	—	2	4	no	—
458	Q₁₆	—	2	4	no	—
459	Q₁₆	—	4	8	no	—
460	Q₁₆	—	4	4	no	—
461	Q₁₆	—	4	4	no	—
462	Q₁₆	—	4	2	no	—
463	Q₁₆	—	4	2	no	—
464	SD₁₆	—	2	8	no	—
465	SD₁₆	—	2	4	no	—
466	SD₁₆	—	4	4	no	—
467	SD₁₆	—	4	4	no	—
468	D₈	—	2	2	no	—
469	M₁₆	—	2	1	no	—
470	M₁₆	—	2	1	no	—
471	M₁₆	—	2	4	no	—
472	M₁₆	—	2	2	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	C₂×D₄×C₇₃	1	2	yes	—
475	M₁₆	C₂×D₄×C₇₃	1	2	yes	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	4	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
483	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
484	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
485	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
486	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
487	C₄⋊C₄	—	4	8	no	—
488	C₄⋊C₄	—	4	4	no	—
489	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	4	4	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	C₂×D₄×C₇₃	1	2	yes	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	2	no	—
497	C₂³	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
498	Q₈	—	2	1	no	—
499	Q₈	—	2	4	no	—
500	Q₈	—	2	2	no	—
501	Q₈	—	2	4	no	—
502	Q₈	—	2	2	no	—
503	Q₈	—	4	8	no	—
504	Q₈	—	4	2	no	—
505	Q₈	—	4	2	no	—
506	Q₈	—	4	2	no	—
507	Q₈	—	4	2	no	—
508	Q₈	—	4	2	no	—
509	Q₈	—	4	2	no	—
510	Q₈	#127×C₇₃	1	2	yes	—
511	D₄	—	2	2	no	—
512	D₄	—	2	2	no	—
513	D₄	—	2	2	no	—
514	D₄	—	2	1	no	—
515	D₄	—	2	2	no	—
516	D₄	—	4	8	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	2	no	—
519	D₄	#127×C₇₃	1	2	yes	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	4	8	no	—
529	C₂×C₄	—	4	8	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
538	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
539	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
540	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
542	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
543	C₈	—	2	2	no	—
544	C₈	—	2	2	no	—
545	C₈	—	2	2	no	—
546	C₈	—	4	2	no	—
547	C₈	#120×C₇₃	1	2	yes	—
548	C₈	#120×C₇₃	1	2	yes	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	4	no	—
553	C₂²	—	4	2	no	—
554	C₂²	#535×C₇₃	1	1	yes	characteristic
555	C₂²	D₄²×C₇₃	1	1	yes	characteristic
556	C₂²	D₄²×C₇₃	1	1	yes	characteristic
557	C₄	—	2	4	no	—
558	C₄	—	2	2	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	4	no	—
562	C₄	—	8	2	no	—
563	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
564	C₄	C₂×#127×C₇₃	1	1	yes	characteristic
565	C₄	D₄²×C₇₃	1	1	yes	characteristic
566	C₄	D₄²×C₇₃	1	1	yes	characteristic
567	C₂	—	2	1	no	—
568	C₂	—	2	1	no	—
569	C₂	—	4	2	no	—
570	C₂	—	8	2	no	—
571	C₂	C₇₃×#2433	1	1	yes	characteristic
572	C₂	C₇₃×#3293	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#578×C₇₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂²×C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₃×#3156	C₂	semidirect
3. C₂×#494×C₇₃	C₂	semidirect
4. C₂×#473×C₇₃	C₂	semidirect
5. C₂×#456×C₇₃	C₂	semidirect
6. C₇₃×#3011	C₂	semidirect
7. C₇₃×#2020	C₂	semidirect
8. C₇₃×#2005	C₂	semidirect
9. C₇₃×#1979	C₂	semidirect
10. C₇₃×#1974	C₂	semidirect
11. C₇₃×#1764	C₂	semidirect
280. #25806	C₇₃	direct (N × H)
288. #3156	C₂×C₇₃	semidirect
289. C₂×#494	C₂×C₇₃	semidirect
290. C₂×#473	C₂×C₇₃	semidirect
291. C₂×#456	C₂×C₇₃	semidirect
292. #3011	C₂×C₇₃	semidirect
293. #2020	C₂×C₇₃	semidirect
294. #2005	C₂×C₇₃	semidirect
295. #1979	C₂×C₇₃	semidirect
296. #1974	C₂×C₇₃	semidirect
297. #1764	C₂×C₇₃	semidirect
298. C₇₃	#25806	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#578×C₇₃	2
C₇₃×#3156	2
C₂×#494×C₇₃	2
C₂×#473×C₇₃	2
C₂×#456×C₇₃	2
C₇₃×#3011	2
C₇₃×#2020	2
C₇₃×#2005	2
C₇₃×#1979	2
C₇₃×#1974	2
C₇₃×#1764	2
#25806	73

Subgroups — C73×#25806 #32935210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25806 #32935210