Subgroups — C₂×C₇₃×#2540 #32944291

Order 18688.

4566 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	C₂²×#124×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊Q₈×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₂²×#121×C₇₃	C₂	1	2	yes	maximal, complemented
4	C₂²×C₄×D₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2540	C₂	1	16	yes	maximal, direct product factor
6	C₂×#399×C₇₃	C₂	1	2	yes	maximal, complemented
7	C₂×#392×C₇₃	C₂	1	2	yes	maximal, complemented
8	C₂×#390×C₇₃	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×C₄⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₇₃	C₂²	1	4	yes	—
14	C₂⁴×C₄×C₇₃	C₂²	1	2	yes	—
15	C₂×#124×C₇₃	—	2	8	no	—
16	C₂×#124×C₇₃	C₂²	1	8	yes	complemented
17	C₂×C₂²⋊Q₈×C₇₃	—	2	16	no	—
18	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	16	yes	complemented
19	C₂×#121×C₇₃	—	2	16	no	—
20	C₂×#121×C₇₃	C₂²	1	16	yes	complemented
21	C₂×C₄×D₄×C₇₃	—	2	8	no	—
22	C₂×C₄×D₄×C₇₃	C₂²	1	8	yes	complemented
23	C₂²×C₄⋊C₄×C₇₃	C₂²	1	4	yes	—
24	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	4	yes	—
29	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	4	yes	—
30	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
31	C₂²×C₄²×C₇₃	C₂²	1	2	yes	—
32	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
33	#399×C₇₃	C₂²	1	16	yes	complemented
34	#392×C₇₃	C₂²	1	16	yes	complemented
35	#390×C₇₃	C₂²	1	32	yes	complemented
36	C₄×C₄⋊C₄×C₇₃	C₂²	1	8	yes	complemented
37	C₂×#95×C₇₃	C₂²	1	2	yes	—
38	C₂⁵×C₇₃	C₂³	1	2	yes	—
39	C₂⁵×C₇₃	C₂³	1	2	yes	—
40	C₂²×Q₈×C₇₃	—	2	8	no	—
41	C₂²×Q₈×C₇₃	—	2	4	no	—
42	C₂²×Q₈×C₇₃	C₂³	1	4	yes	—
43	C₂²×D₄×C₇₃	—	2	8	no	—
44	C₂²×D₄×C₇₃	—	2	16	no	—
45	C₂²×D₄×C₇₃	—	2	4	no	—
46	C₂²×D₄×C₇₃	—	2	16	no	—
47	C₂²×D₄×C₇₃	—	2	8	no	—
48	C₂²×D₄×C₇₃	—	2	4	no	—
49	C₂²×D₄×C₇₃	—	4	8	no	—
50	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
51	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
52	C₂²×D₄×C₇₃	C₂³	1	16	yes	—
53	C₂³×C₄×C₇₃	—	2	8	no	—
54	C₂³×C₄×C₇₃	—	2	8	no	—
55	C₂³×C₄×C₇₃	—	2	8	no	—
56	C₂³×C₄×C₇₃	C₂³	1	8	yes	—
57	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
59	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
61	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
63	#124×C₇₃	—	2	32	no	—
64	C₂²⋊Q₈×C₇₃	—	2	64	no	—
65	#121×C₇₃	—	2	64	no	—
66	C₄×D₄×C₇₃	—	2	32	no	—
67	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
68	C₂×C₄⋊C₄×C₇₃	—	2	16	no	—
69	C₂×C₄⋊C₄×C₇₃	D₄	1	16	yes	complemented
70	C₂×C₄⋊C₄×C₇₃	C₂³	1	16	yes	—
71	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
72	C₂×C₄⋊C₄×C₇₃	C₂³	1	8	yes	—
73	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
74	C₂×C₂²⋊C₄×C₇₃	—	2	16	no	—
75	C₂×C₂²⋊C₄×C₇₃	—	2	16	no	—
76	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
77	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
78	C₂×C₂²⋊C₄×C₇₃	C₂³	1	8	yes	—
79	C₂×C₂²⋊C₄×C₇₃	C₂³	1	8	yes	—
80	C₂×C₂²⋊C₄×C₇₃	C₂³	1	16	yes	—
81	C₂×C₂²⋊C₄×C₇₃	C₂³	1	16	yes	—
82	C₂×C₂²⋊C₄×C₇₃	C₂³	1	8	yes	—
83	C₂×C₄²×C₇₃	—	4	4	no	—
84	C₂×C₄²×C₇₃	D₄	1	8	yes	complemented
85	C₂×C₄²×C₇₃	C₂³	1	8	yes	—
86	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
87	#95×C₇₃	C₂³	1	8	yes	—
88	C₂⁴×C₇₃	—	2	4	no	—
89	C₂⁴×C₇₃	—	2	4	no	—
90	C₂⁴×C₇₃	—	2	4	no	—
91	C₂⁴×C₇₃	—	2	4	no	—
92	C₂⁴×C₇₃	—	2	4	no	—
93	C₂⁴×C₇₃	—	2	4	no	—
94	C₂⁴×C₇₃	—	2	4	no	—
95	C₂⁴×C₇₃	—	2	8	no	—
96	C₂⁴×C₇₃	—	2	8	no	—
97	C₂⁴×C₇₃	—	2	4	no	—
98	C₂⁴×C₇₃	—	2	4	no	—
99	C₂⁴×C₇₃	#41	1	8	yes	—
100	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
101	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
102	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
103	C₂×Q₈×C₇₃	—	2	16	no	—
104	C₂×Q₈×C₇₃	—	2	8	no	—
105	C₂×Q₈×C₇₃	—	4	16	no	—
106	C₂×D₄×C₇₃	—	2	32	no	—
107	C₂×D₄×C₇₃	—	2	16	no	—
108	C₂×D₄×C₇₃	—	2	32	no	—
109	C₂×D₄×C₇₃	—	2	8	no	—
110	C₂×D₄×C₇₃	—	2	32	no	—
111	C₂×D₄×C₇₃	—	2	16	no	—
112	C₂×D₄×C₇₃	—	2	8	no	—
113	C₂×D₄×C₇₃	—	4	16	no	—
114	C₂×D₄×C₇₃	—	4	64	no	—
115	C₂×D₄×C₇₃	—	4	16	no	—
116	C₂²×C₄×C₇₃	—	2	4	no	—
117	C₂²×C₄×C₇₃	—	2	8	no	—
118	C₂²×C₄×C₇₃	—	2	2	no	—
119	C₂²×C₄×C₇₃	—	2	8	no	—
120	C₂²×C₄×C₇₃	—	2	2	no	—
121	C₂²×C₄×C₇₃	—	2	4	no	—
122	C₂²×C₄×C₇₃	—	2	4	no	—
123	C₂²×C₄×C₇₃	—	2	4	no	—
124	C₂²×C₄×C₇₃	—	2	8	no	—
125	C₂²×C₄×C₇₃	—	2	4	no	—
126	C₂²×C₄×C₇₃	—	2	16	no	—
127	C₂²×C₄×C₇₃	—	2	16	no	—
128	C₂²×C₄×C₇₃	—	2	16	no	—
129	C₂²×C₄×C₇₃	—	4	32	no	—
130	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₇₃	C₂×D₄	1	16	yes	—
133	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₇₃	C₂×D₄	1	8	yes	—
135	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₇₃	C₂⁴	1	8	yes	—
139	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
141	C₄⋊C₄×C₇₃	—	2	8	no	—
142	C₄⋊C₄×C₇₃	—	2	32	no	—
143	C₄⋊C₄×C₇₃	C₂×D₄	1	32	yes	complemented
144	C₂²⋊C₄×C₇₃	—	2	16	no	—
145	C₂²⋊C₄×C₇₃	—	2	32	no	—
146	C₂²⋊C₄×C₇₃	—	2	32	no	—
147	C₂²⋊C₄×C₇₃	—	2	16	no	—
148	C₂²⋊C₄×C₇₃	—	2	16	no	—
149	C₄²×C₇₃	—	4	8	no	—
150	C₄²×C₇₃	C₂×D₄	1	16	yes	complemented
151	C₂³×C₇₃	—	2	16	no	—
152	C₂³×C₇₃	—	2	16	no	—
153	C₂³×C₇₃	—	2	16	no	—
154	C₂³×C₇₃	—	2	4	no	—
155	C₂³×C₇₃	—	2	4	no	—
156	C₂³×C₇₃	—	2	4	no	—
157	C₂³×C₇₃	—	2	4	no	—
158	C₂³×C₇₃	—	2	4	no	—
159	C₂³×C₇₃	—	2	4	no	—
160	C₂³×C₇₃	—	2	4	no	—
161	C₂³×C₇₃	—	2	8	no	—
162	C₂³×C₇₃	—	2	8	no	—
163	C₂³×C₇₃	—	2	4	no	—
164	C₂³×C₇₃	—	2	4	no	—
165	C₂³×C₇₃	—	4	8	no	—
166	C₂³×C₇₃	—	4	8	no	—
167	C₂³×C₇₃	—	4	8	no	—
168	C₂³×C₇₃	—	4	8	no	—
169	C₂³×C₇₃	—	4	8	no	—
170	C₂³×C₇₃	—	4	8	no	—
171	C₂³×C₇₃	—	4	8	no	—
172	C₂³×C₇₃	—	4	16	no	—
173	C₂³×C₇₃	—	4	16	no	—
174	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
175	C₂³×C₇₃	C₂²×D₄	1	4	yes	—
176	C₂³×C₇₃	C₂×#41	1	8	yes	—
177	C₂³×C₇₃	C₂×#41	1	4	yes	—
178	C₂³×C₇₃	H(5,𝔽₂)	1	2	yes	—
179	C₂³×C₇₃	2₋¹⁺⁴	1	2	yes	—
180	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
181	Q₈×C₇₃	—	4	16	no	—
182	D₄×C₇₃	—	2	32	no	—
183	D₄×C₇₃	—	4	64	no	—
184	D₄×C₇₃	—	4	16	no	—
185	C₂×C₄×C₇₃	—	2	8	no	—
186	C₂×C₄×C₇₃	—	2	8	no	—
187	C₂×C₄×C₇₃	—	2	32	no	—
188	C₂×C₄×C₇₃	—	2	4	no	—
189	C₂×C₄×C₇₃	—	2	8	no	—
190	C₂×C₄×C₇₃	—	2	2	no	—
191	C₂×C₄×C₇₃	—	2	8	no	—
192	C₂×C₄×C₇₃	—	2	2	no	—
193	C₂×C₄×C₇₃	—	2	4	no	—
194	C₂×C₄×C₇₃	—	2	4	no	—
195	C₂×C₄×C₇₃	—	2	4	no	—
196	C₂×C₄×C₇₃	—	2	8	no	—
197	C₂×C₄×C₇₃	—	2	4	no	—
198	C₂×C₄×C₇₃	—	4	8	no	—
199	C₂×C₄×C₇₃	—	4	8	no	—
200	C₂×C₄×C₇₃	—	4	32	no	—
201	C₂×C₄×C₇₃	#127	1	16	yes	—
202	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
203	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
204	C₂×C₄×C₇₃	C₂²×D₄	1	16	yes	—
205	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
206	C₂×C₄×C₇₃	C₂²×D₄	1	8	yes	—
207	C₂²×C₇₃	—	2	8	no	—
208	C₂²×C₇₃	—	2	8	no	—
209	C₂²×C₇₃	—	2	8	no	—
210	C₂²×C₇₃	—	4	4	no	—
211	C₂²×C₇₃	—	4	4	no	—
212	C₂²×C₇₃	—	4	4	no	—
213	C₂²×C₇₃	—	4	4	no	—
214	C₂²×C₇₃	—	4	32	no	—
215	C₂²×C₇₃	—	4	4	no	—
216	C₂²×C₇₃	—	4	4	no	—
217	C₂²×C₇₃	—	4	4	no	—
218	C₂²×C₇₃	—	4	8	no	—
219	C₂²×C₇₃	—	4	8	no	—
220	C₂²×C₇₃	—	8	16	no	—
221	C₂²×C₇₃	#525	1	4	yes	—
222	C₂²×C₇₃	C₂×#127	1	4	yes	—
223	C₂²×C₇₃	#537	1	4	yes	—
224	C₂²×C₇₃	#546	1	8	yes	—
225	C₂²×C₇₃	#548	1	8	yes	—
226	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
227	C₂²×C₇₃	C₂³×D₄	1	2	yes	—
228	C₂²×C₇₃	C₂²×#41	1	2	yes	—
229	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
230	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
231	C₄×C₇₃	—	2	4	no	—
232	C₄×C₇₃	—	2	4	no	—
233	C₄×C₇₃	—	2	16	no	—
234	C₄×C₇₃	—	4	4	no	—
235	C₄×C₇₃	—	4	4	no	—
236	C₄×C₇₃	C₂×#127	1	8	yes	—
237	C₂×#2540	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₂×C₇₃	—	4	8	no	—
239	C₂×C₇₃	—	8	4	no	—
240	C₂×C₇₃	#2540	1	8	yes	direct product factor
241	C₂×C₇₃	C₂×#525	1	1	yes	characteristic
242	C₂×C₇₃	C₂²×#127	1	1	yes	characteristic
243	C₂×C₇₃	C₂×#537	1	1	yes	characteristic
244	C₂×C₇₃	C₂×#546	1	2	yes	—
245	C₂×C₇₃	C₂×#548	1	2	yes	—
246	C₂²×#124	C₂×C₇₃	1	1	yes	characteristic, complemented
247	C₂²×C₂²⋊Q₈	C₂×C₇₃	1	2	yes	complemented
248	C₂²×#121	C₂×C₇₃	1	2	yes	complemented
249	C₂²×C₄×D₄	C₂×C₇₃	1	1	yes	characteristic, complemented
250	#2540	C₂×C₇₃	1	16	yes	direct product factor
251	C₂×#399	C₂×C₇₃	1	2	yes	complemented
252	C₂×#392	C₂×C₇₃	1	2	yes	complemented
253	C₂×#390	C₂×C₇₃	1	4	yes	complemented
254	C₂×C₄×C₄⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
255	C₇₃	C₂×#2540	1	1	yes	characteristic, direct product factor, Sylow
256	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
257	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
258	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
259	C₂³×D₄	C₂²×C₇₃	1	4	yes	—
260	C₂⁴×C₄	C₂²×C₇₃	1	2	yes	—
261	C₂×#124	—	2	8	no	—
262	C₂×#124	C₂²×C₇₃	1	8	yes	complemented
263	C₂×C₂²⋊Q₈	—	2	16	no	—
264	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	16	yes	complemented
265	C₂×#121	—	2	16	no	—
266	C₂×#121	C₂²×C₇₃	1	16	yes	complemented
267	C₂×C₄×D₄	—	2	8	no	—
268	C₂×C₄×D₄	C₂²×C₇₃	1	8	yes	complemented
269	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
270	C₂²×C₄⋊C₄	C₂²×C₇₃	1	4	yes	—
271	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
272	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
273	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	4	yes	—
274	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	4	yes	—
275	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
276	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
277	C₂²×C₄²	C₂²×C₇₃	1	2	yes	—
278	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
279	#399	C₂²×C₇₃	1	16	yes	complemented
280	#392	C₂²×C₇₃	1	16	yes	complemented
281	#390	C₂²×C₇₃	1	32	yes	complemented
282	C₄×C₄⋊C₄	C₂²×C₇₃	1	8	yes	complemented
283	C₂×#95	C₂²×C₇₃	1	2	yes	—
284	C₂⁵	C₂³×C₇₃	1	2	yes	—
285	C₂⁵	C₂³×C₇₃	1	2	yes	—
286	C₂²×Q₈	—	2	8	no	—
287	C₂²×Q₈	—	2	4	no	—
288	C₂²×Q₈	C₂³×C₇₃	1	4	yes	—
289	C₂²×D₄	—	2	8	no	—
290	C₂²×D₄	—	2	16	no	—
291	C₂²×D₄	—	2	4	no	—
292	C₂²×D₄	—	2	16	no	—
293	C₂²×D₄	—	2	8	no	—
294	C₂²×D₄	—	2	4	no	—
295	C₂²×D₄	—	4	8	no	—
296	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
297	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
298	C₂²×D₄	C₂³×C₇₃	1	16	yes	—
299	C₂³×C₄	—	2	8	no	—
300	C₂³×C₄	—	2	8	no	—
301	C₂³×C₄	—	2	8	no	—
302	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
303	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
304	C₂³×C₄	C₂³×C₇₃	1	8	yes	—
305	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
306	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
307	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
308	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
309	#124	—	2	32	no	—
310	C₂²⋊Q₈	—	2	64	no	—
311	#121	—	2	64	no	—
312	C₄×D₄	—	2	32	no	—
313	C₂×C₄⋊C₄	—	2	4	no	—
314	C₂×C₄⋊C₄	—	2	16	no	—
315	C₂×C₄⋊C₄	D₄×C₇₃	1	16	yes	complemented
316	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
317	C₂×C₄⋊C₄	C₂³×C₇₃	1	16	yes	—
318	C₂×C₄⋊C₄	C₂³×C₇₃	1	8	yes	—
319	C₂×C₂²⋊C₄	—	2	8	no	—
320	C₂×C₂²⋊C₄	—	2	16	no	—
321	C₂×C₂²⋊C₄	—	2	16	no	—
322	C₂×C₂²⋊C₄	—	2	8	no	—
323	C₂×C₂²⋊C₄	—	2	8	no	—
324	C₂×C₂²⋊C₄	C₂³×C₇₃	1	8	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₇₃	1	16	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₇₃	1	16	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₇₃	1	8	yes	—
328	C₂×C₂²⋊C₄	C₂³×C₇₃	1	8	yes	—
329	C₂×C₄²	—	4	4	no	—
330	C₂×C₄²	D₄×C₇₃	1	8	yes	complemented
331	C₂×C₄²	C₂³×C₇₃	1	8	yes	—
332	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
333	#95	C₂³×C₇₃	1	8	yes	—
334	C₂⁴	—	2	4	no	—
335	C₂⁴	—	2	4	no	—
336	C₂⁴	—	2	4	no	—
337	C₂⁴	—	2	4	no	—
338	C₂⁴	—	2	4	no	—
339	C₂⁴	—	2	4	no	—
340	C₂⁴	—	2	4	no	—
341	C₂⁴	—	2	8	no	—
342	C₂⁴	—	2	8	no	—
343	C₂⁴	—	2	4	no	—
344	C₂⁴	—	2	4	no	—
345	C₂⁴	#41×C₇₃	1	8	yes	—
346	C₂⁴	C₂⁴×C₇₃	1	4	yes	—
347	C₂⁴	C₂⁴×C₇₃	1	4	yes	—
348	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
349	C₂×Q₈	—	2	16	no	—
350	C₂×Q₈	—	2	8	no	—
351	C₂×Q₈	—	4	16	no	—
352	C₂×D₄	—	2	32	no	—
353	C₂×D₄	—	2	16	no	—
354	C₂×D₄	—	2	32	no	—
355	C₂×D₄	—	2	8	no	—
356	C₂×D₄	—	2	32	no	—
357	C₂×D₄	—	2	16	no	—
358	C₂×D₄	—	2	8	no	—
359	C₂×D₄	—	4	16	no	—
360	C₂×D₄	—	4	64	no	—
361	C₂×D₄	—	4	16	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	8	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	8	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	8	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	16	no	—
373	C₂²×C₄	—	2	16	no	—
374	C₂²×C₄	—	2	16	no	—
375	C₂²×C₄	—	4	32	no	—
376	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
377	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
378	C₂²×C₄	C₂×D₄×C₇₃	1	16	yes	—
379	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
380	C₂²×C₄	C₂×D₄×C₇₃	1	8	yes	—
381	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
382	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
383	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₇₃	1	8	yes	—
385	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
386	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	2	32	no	—
389	C₄⋊C₄	C₂×D₄×C₇₃	1	32	yes	complemented
390	C₂²⋊C₄	—	2	16	no	—
391	C₂²⋊C₄	—	2	32	no	—
392	C₂²⋊C₄	—	2	32	no	—
393	C₂²⋊C₄	—	2	16	no	—
394	C₂²⋊C₄	—	2	16	no	—
395	C₄²	—	4	8	no	—
396	C₄²	C₂×D₄×C₇₃	1	16	yes	complemented
397	C₂³	—	2	16	no	—
398	C₂³	—	2	16	no	—
399	C₂³	—	2	16	no	—
400	C₂³	—	2	4	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	2	4	no	—
405	C₂³	—	2	4	no	—
406	C₂³	—	2	4	no	—
407	C₂³	—	2	8	no	—
408	C₂³	—	2	8	no	—
409	C₂³	—	2	4	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	4	8	no	—
412	C₂³	—	4	8	no	—
413	C₂³	—	4	8	no	—
414	C₂³	—	4	8	no	—
415	C₂³	—	4	8	no	—
416	C₂³	—	4	8	no	—
417	C₂³	—	4	8	no	—
418	C₂³	—	4	16	no	—
419	C₂³	—	4	16	no	—
420	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
421	C₂³	C₂²×D₄×C₇₃	1	4	yes	—
422	C₂³	C₂×#41×C₇₃	1	8	yes	—
423	C₂³	C₂×#41×C₇₃	1	4	yes	—
424	C₂³	H(5,𝔽₂)×C₇₃	1	2	yes	—
425	C₂³	2₋¹⁺⁴×C₇₃	1	2	yes	—
426	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
427	Q₈	—	4	16	no	—
428	D₄	—	2	32	no	—
429	D₄	—	4	64	no	—
430	D₄	—	4	16	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	32	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	4	8	no	—
445	C₂×C₄	—	4	8	no	—
446	C₂×C₄	—	4	32	no	—
447	C₂×C₄	#127×C₇₃	1	16	yes	—
448	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
449	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
450	C₂×C₄	C₂²×D₄×C₇₃	1	16	yes	—
451	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
452	C₂×C₄	C₂²×D₄×C₇₃	1	8	yes	—
453	C₂²	—	2	8	no	—
454	C₂²	—	2	8	no	—
455	C₂²	—	2	8	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	32	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	4	8	no	—
462	C₂²	—	4	8	no	—
463	C₂²	—	4	4	no	—
464	C₂²	—	4	4	no	—
465	C₂²	—	4	4	no	—
466	C₂²	—	8	16	no	—
467	C₂²	#525×C₇₃	1	4	yes	—
468	C₂²	C₂×#127×C₇₃	1	4	yes	—
469	C₂²	#537×C₇₃	1	4	yes	—
470	C₂²	#546×C₇₃	1	8	yes	—
471	C₂²	#548×C₇₃	1	8	yes	—
472	C₂²	C₂³×D₄×C₇₃	1	2	yes	—
473	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
474	C₂²	C₂²×#41×C₇₃	1	2	yes	—
475	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
476	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
477	C₄	—	2	16	no	—
478	C₄	—	2	4	no	—
479	C₄	—	2	4	no	—
480	C₄	—	4	4	no	—
481	C₄	—	4	4	no	—
482	C₄	C₂×#127×C₇₃	1	8	yes	—
483	C₂	—	4	8	no	—
484	C₂	—	8	4	no	—
485	C₂	C₇₃×#2540	1	8	yes	direct product factor
486	C₂	C₂×#525×C₇₃	1	1	yes	characteristic
487	C₂	C₂²×#127×C₇₃	1	1	yes	characteristic
488	C₂	C₂×#537×C₇₃	1	1	yes	characteristic
489	C₂	C₂×#546×C₇₃	1	2	yes	—
490	C₂	C₂×#548×C₇₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₇₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#124×C₇₃	C₂	semidirect
2. C₂²×C₂²⋊Q₈×C₇₃	C₂	semidirect
3. C₂²×#121×C₇₃	C₂	semidirect
4. C₂²×C₄×D₄×C₇₃	C₂	semidirect
5. C₇₃×#2540	C₂	direct (N × H)
6. C₂×#399×C₇₃	C₂	semidirect
7. C₂×#392×C₇₃	C₂	semidirect
8. C₂×#390×C₇₃	C₂	semidirect
9. C₂×C₄×C₄⋊C₄×C₇₃	C₂	semidirect
16. C₂×#124×C₇₃	C₂²	semidirect
18. C₂×C₂²⋊Q₈×C₇₃	C₂²	semidirect
20. C₂×#121×C₇₃	C₂²	semidirect
22. C₂×C₄×D₄×C₇₃	C₂²	semidirect
33. #399×C₇₃	C₂²	semidirect
34. #392×C₇₃	C₂²	semidirect
35. #390×C₇₃	C₂²	semidirect
36. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
69. C₂×C₄⋊C₄×C₇₃	D₄	semidirect
84. C₂×C₄²×C₇₃	D₄	semidirect
143. C₄⋊C₄×C₇₃	C₂×D₄	semidirect
150. C₄²×C₇₃	C₂×D₄	semidirect
237. C₂×#2540	C₇₃	direct (N × H)
240. C₂×C₇₃	#2540	direct (N × H)
246. C₂²×#124	C₂×C₇₃	semidirect
247. C₂²×C₂²⋊Q₈	C₂×C₇₃	semidirect
248. C₂²×#121	C₂×C₇₃	semidirect
249. C₂²×C₄×D₄	C₂×C₇₃	semidirect
250. #2540	C₂×C₇₃	direct (N × H)
251. C₂×#399	C₂×C₇₃	semidirect
252. C₂×#392	C₂×C₇₃	semidirect
253. C₂×#390	C₂×C₇₃	semidirect
254. C₂×C₄×C₄⋊C₄	C₂×C₇₃	semidirect
255. C₇₃	C₂×#2540	direct (N × H)
262. C₂×#124	C₂²×C₇₃	semidirect
264. C₂×C₂²⋊Q₈	C₂²×C₇₃	semidirect
266. C₂×#121	C₂²×C₇₃	semidirect
268. C₂×C₄×D₄	C₂²×C₇₃	semidirect
279. #399	C₂²×C₇₃	semidirect
280. #392	C₂²×C₇₃	semidirect
281. #390	C₂²×C₇₃	semidirect
282. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
315. C₂×C₄⋊C₄	D₄×C₇₃	semidirect
330. C₂×C₄²	D₄×C₇₃	semidirect
389. C₄⋊C₄	C₂×D₄×C₇₃	semidirect
396. C₄²	C₂×D₄×C₇₃	semidirect
485. C₂	C₇₃×#2540	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#124×C₇₃	2
C₂²×C₂²⋊Q₈×C₇₃	2
C₂²×#121×C₇₃	2
C₂²×C₄×D₄×C₇₃	2
C₇₃×#2540	2
C₂×#399×C₇₃	2
C₂×#392×C₇₃	2
C₂×#390×C₇₃	2
C₂×C₄×C₄⋊C₄×C₇₃	2
C₂×#2540	73

Subgroups — C2×C73×#2540 #32944291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₃×#2540 #32944291