Subgroups — C₆₇×#60376 #30739627

Order 17152.

4824 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#585×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#577×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#576×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3013	C₂	1	3	yes	maximal, complemented
6	C₆₇×#3012	C₂	1	3	yes	maximal, complemented
7	C₆₇×#3010	C₂	1	3	yes	maximal, complemented
8	C₆₇×#3008	C₂	1	3	yes	maximal, complemented
9	C₆₇×#3006	C₂	1	3	yes	maximal, complemented
10	C₆₇×#3005	C₂	1	3	yes	maximal, complemented
11	C₆₇×#3002	C₂	1	3	yes	maximal, complemented
12	C₂×#449×C₆₇	C₂	1	3	yes	maximal, complemented
13	C₆₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2897	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2880	C₂	1	1	yes	maximal, characteristic, complemented
16	#585×C₆₇	—	2	8	no	—
17	#585×C₆₇	—	2	8	no	—
18	C₂×2₋¹⁺⁴×C₆₇	—	2	1	no	—
19	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
20	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	3	yes	complemented
21	C₂×H(5,𝔽₂)×C₆₇	—	2	3	no	—
22	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	3	yes	complemented
24	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic, complemented
25	C₂²×#41×C₆₇	—	2	3	no	—
26	C₂²×#41×C₆₇	—	2	1	no	—
27	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×#41×C₆₇	C₂²	1	3	yes	complemented
29	C₂²×#41×C₆₇	C₂²	1	3	yes	complemented
30	#577×C₆₇	—	2	8	no	—
31	#576×C₆₇	—	2	8	no	—
32	C₂×#137×C₆₇	C₂²	1	3	yes	complemented
33	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	3	yes	complemented
34	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	3	yes	complemented
35	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	3	yes	complemented
36	C₂×#135×C₆₇	C₂²	1	3	yes	complemented
37	C₂×#135×C₆₇	C₂²	1	3	yes	complemented
38	C₂²×SD₁₆×C₆₇	C₂²	1	3	yes	complemented
39	C₂²×D₈×C₆₇	C₂²	1	3	yes	complemented
40	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#550×C₆₇	—	2	1	no	—
43	#548×C₆₇	—	2	1	no	—
44	#546×C₆₇	—	2	3	no	—
45	D₄²×C₆₇	—	2	3	no	—
46	#537×C₆₇	C₂²	1	3	yes	complemented
47	#535×C₆₇	C₂²	1	3	yes	complemented
48	#525×C₆₇	C₂²	1	3	yes	complemented
49	C₂×#121×C₆₇	C₂²	1	3	yes	complemented
50	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#452×C₆₇	C₂²	1	6	yes	complemented
52	#452×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	#452×C₆₇	C₂²	1	3	yes	complemented
54	#451×C₆₇	C₂²	1	3	yes	complemented
55	#450×C₆₇	C₂²	1	3	yes	complemented
56	#449×C₆₇	C₂²	1	6	yes	complemented
57	#449×C₆₇	C₂²	1	6	yes	complemented
58	#449×C₆₇	C₂²	1	6	yes	complemented
59	#449×C₆₇	C₂²	1	3	yes	complemented
60	#449×C₆₇	C₂²	1	6	yes	complemented
61	#449×C₆₇	C₂²	1	3	yes	complemented
62	#448×C₆₇	C₂²	1	3	yes	complemented
63	#448×C₆₇	C₂²	1	6	yes	complemented
64	#447×C₆₇	C₂²	1	6	yes	complemented
65	#447×C₆₇	C₂²	1	3	yes	complemented
66	#419×C₆₇	C₂²	1	3	yes	complemented
67	#418×C₆₇	C₂²	1	3	yes	complemented
68	#417×C₆₇	C₂²	1	3	yes	complemented
69	#417×C₆₇	C₂²	1	3	yes	complemented
70	#416×C₆₇	C₂²	1	3	yes	complemented
71	#416×C₆₇	C₂²	1	3	yes	complemented
72	C₂×#103×C₆₇	C₂²	1	3	yes	complemented
73	C₂×#102×C₆₇	C₂²	1	3	yes	complemented
74	#408×C₆₇	C₂²	1	3	yes	complemented
75	#408×C₆₇	C₂²	1	3	yes	complemented
76	#407×C₆₇	C₂²	1	3	yes	complemented
77	C₂×C₂²⋊C₈×C₆₇	C₂²	1	3	yes	complemented
78	2₋¹⁺⁴×C₆₇	—	2	16	no	—
79	2₋¹⁺⁴×C₆₇	—	2	4	no	—
80	2₋¹⁺⁴×C₆₇	—	2	12	no	—
81	2₋¹⁺⁴×C₆₇	—	2	12	no	—
82	2₋¹⁺⁴×C₆₇	D₄	1	8	yes	complemented
83	H(5,𝔽₂)×C₆₇	—	2	48	no	—
84	H(5,𝔽₂)×C₆₇	—	2	4	no	—
85	H(5,𝔽₂)×C₆₇	—	2	12	no	—
86	H(5,𝔽₂)×C₆₇	—	2	12	no	—
87	H(5,𝔽₂)×C₆₇	—	2	4	no	—
88	H(5,𝔽₂)×C₆₇	—	2	4	no	—
89	H(5,𝔽₂)×C₆₇	D₄	1	8	yes	complemented
90	C₂×#41×C₆₇	—	2	16	no	—
91	C₂×#41×C₆₇	—	2	48	no	—
92	C₂×#41×C₆₇	—	2	4	no	—
93	C₂×#41×C₆₇	—	2	4	no	—
94	C₂×#41×C₆₇	—	2	12	no	—
95	C₂×#41×C₆₇	—	2	12	no	—
96	C₂×#41×C₆₇	—	2	1	no	—
97	C₂×#41×C₆₇	—	2	3	no	—
98	C₂×#41×C₆₇	—	2	1	no	—
99	C₂×#41×C₆₇	—	2	12	no	—
100	C₂×#41×C₆₇	—	2	3	no	—
101	C₂×#41×C₆₇	—	2	6	no	—
102	C₂×#41×C₆₇	—	2	3	no	—
103	C₂×#41×C₆₇	—	2	12	no	—
104	C₂×#41×C₆₇	—	2	3	no	—
105	C₂×#41×C₆₇	—	2	3	no	—
106	C₂×#41×C₆₇	—	2	3	no	—
107	C₂×#41×C₆₇	—	2	3	no	—
108	C₂×#41×C₆₇	D₄	1	3	yes	—
109	C₂×#41×C₆₇	D₄	1	1	yes	characteristic
110	C₂×#41×C₆₇	C₂³	1	3	yes	—
111	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
112	C₂×#41×C₆₇	C₂³	1	6	yes	—
113	C₂×#41×C₆₇	C₂³	1	3	yes	—
114	C₂×#41×C₆₇	C₂³	1	3	yes	—
115	C₂×#41×C₆₇	C₂³	1	3	yes	—
116	C₂×#41×C₆₇	C₂³	1	3	yes	—
117	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
118	C₂²×Q₈×C₆₇	—	2	1	no	—
119	C₂²×Q₈×C₆₇	—	2	3	no	—
120	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
121	C₂²×Q₈×C₆₇	C₂³	1	3	yes	—
122	C₂²×Q₈×C₆₇	C₂³	1	3	yes	—
123	C₂²×D₄×C₆₇	—	2	3	no	—
124	C₂²×D₄×C₆₇	—	2	3	no	—
125	C₂²×D₄×C₆₇	—	2	3	no	—
126	C₂²×D₄×C₆₇	—	2	6	no	—
127	C₂²×D₄×C₆₇	—	2	3	no	—
128	C₂²×D₄×C₆₇	—	2	3	no	—
129	C₂²×D₄×C₆₇	—	2	3	no	—
130	C₂²×D₄×C₆₇	D₄	1	3	yes	—
131	C₂²×D₄×C₆₇	C₂³	1	3	yes	—
132	C₂²×D₄×C₆₇	C₂³	1	3	yes	—
133	C₂²×D₄×C₆₇	C₂³	1	3	yes	—
134	C₂³×C₄×C₆₇	—	2	3	no	—
135	C₂³×C₄×C₆₇	—	2	3	no	—
136	C₂³×C₄×C₆₇	C₂³	1	3	yes	—
137	#137×C₆₇	—	2	12	no	—
138	AGL(1,ℤ/8)×C₆₇	—	2	12	no	—
139	AGL(1,ℤ/8)×C₆₇	—	2	12	no	—
140	AGL(1,ℤ/8)×C₆₇	—	2	12	no	—
141	#135×C₆₇	—	2	12	no	—
142	#135×C₆₇	—	2	12	no	—
143	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×Q₁₆×C₆₇	C₂³	1	3	yes	—
145	C₂×SD₁₆×C₆₇	—	2	12	no	—
146	C₂×SD₁₆×C₆₇	C₂³	1	3	yes	—
147	C₂×SD₁₆×C₆₇	C₂³	1	3	yes	—
148	C₂×SD₁₆×C₆₇	C₂³	1	6	yes	—
149	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₆₇	C₂³	1	3	yes	—
151	C₂×D₈×C₆₇	—	2	12	no	—
152	C₂×D₈×C₆₇	C₂³	1	3	yes	—
153	C₂×D₈×C₆₇	C₂³	1	6	yes	—
154	C₂×D₈×C₆₇	C₂³	1	3	yes	—
155	#131×C₆₇	—	2	4	no	—
156	#131×C₆₇	—	2	4	no	—
157	C₂×M₁₆×C₆₇	C₂³	1	3	yes	—
158	C₂×M₁₆×C₆₇	C₂³	1	3	yes	—
159	C₂²×C₈×C₆₇	C₂³	1	3	yes	—
160	C₂²×C₈×C₆₇	C₂³	1	3	yes	—
161	#127×C₆₇	—	2	3	no	—
162	#124×C₆₇	—	2	3	no	—
163	#123×C₆₇	—	2	3	no	—
164	C₂²⋊Q₈×C₆₇	—	2	3	no	—
165	C₂²⋊Q₈×C₆₇	C₂³	1	3	yes	—
166	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
167	#121×C₆₇	—	2	6	no	—
168	#121×C₆₇	—	2	3	no	—
169	#121×C₆₇	—	2	3	no	—
170	#121×C₆₇	—	2	3	no	—
171	#121×C₆₇	C₂³	1	6	yes	—
172	#121×C₆₇	C₂³	1	3	yes	—
173	#121×C₆₇	C₂³	1	3	yes	—
174	#120×C₆₇	—	2	3	no	—
175	#120×C₆₇	—	2	6	no	—
176	C₄×Q₈×C₆₇	—	2	1	no	—
177	C₄×D₄×C₆₇	—	2	3	no	—
178	C₄×D₄×C₆₇	—	2	3	no	—
179	C₄×D₄×C₆₇	—	2	3	no	—
180	#117×C₆₇	C₂³	1	3	yes	—
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	3	yes	—
182	C₂×C₂²⋊C₄×C₆₇	—	2	3	no	—
183	#103×C₆₇	C₂³	1	1	yes	characteristic
184	#103×C₆₇	C₂³	1	3	yes	—
185	#103×C₆₇	C₂³	1	6	yes	—
186	#103×C₆₇	C₂³	1	3	yes	—
187	#103×C₆₇	C₂³	1	3	yes	—
188	#102×C₆₇	C₂³	1	3	yes	—
189	#102×C₆₇	C₂³	1	6	yes	—
190	#102×C₆₇	C₂³	1	3	yes	—
191	#102×C₆₇	C₂³	1	3	yes	—
192	#102×C₆₇	C₂³	1	1	yes	characteristic
193	C₂²⋊C₈×C₆₇	C₂³	1	3	yes	—
194	C₂²⋊C₈×C₆₇	C₂³	1	6	yes	—
195	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
196	C₂²⋊C₈×C₆₇	C₂³	1	3	yes	—
197	C₂²⋊C₈×C₆₇	C₂³	1	3	yes	—
198	C₂⁴×C₆₇	—	2	3	no	—
199	C₂⁴×C₆₇	—	2	3	no	—
200	C₂⁴×C₆₇	—	2	3	no	—
201	C₂⁴×C₆₇	C₂×D₄	1	3	yes	—
202	#41×C₆₇	—	2	24	no	—
203	#41×C₆₇	—	2	24	no	—
204	#41×C₆₇	—	2	48	no	—
205	#41×C₆₇	—	2	24	no	—
206	#41×C₆₇	—	2	24	no	—
207	#41×C₆₇	—	2	24	no	—
208	#41×C₆₇	—	2	24	no	—
209	#41×C₆₇	—	2	4	no	—
210	#41×C₆₇	—	2	8	no	—
211	#41×C₆₇	—	2	2	no	—
212	#41×C₆₇	—	2	6	no	—
213	#41×C₆₇	—	2	12	no	—
214	#41×C₆₇	—	2	12	no	—
215	#41×C₆₇	—	2	24	no	—
216	#41×C₆₇	—	2	2	no	—
217	#41×C₆₇	—	2	6	no	—
218	#41×C₆₇	—	2	12	no	—
219	#41×C₆₇	—	2	6	no	—
220	#41×C₆₇	—	2	6	no	—
221	#41×C₆₇	—	2	6	no	—
222	#41×C₆₇	—	2	6	no	—
223	#41×C₆₇	—	2	6	no	—
224	#41×C₆₇	—	2	6	no	—
225	#41×C₆₇	—	4	4	no	—
226	#41×C₆₇	C₂×D₄	1	4	yes	—
227	#41×C₆₇	C₂×D₄	1	4	yes	—
228	#41×C₆₇	C₂×D₄	1	12	yes	complemented
229	#41×C₆₇	C₂×D₄	1	12	yes	complemented
230	C₂×Q₈×C₆₇	—	2	24	no	—
231	C₂×Q₈×C₆₇	—	2	8	no	—
232	C₂×Q₈×C₆₇	—	2	4	no	—
233	C₂×Q₈×C₆₇	—	2	6	no	—
234	C₂×Q₈×C₆₇	—	2	6	no	—
235	C₂×Q₈×C₆₇	—	2	3	no	—
236	C₂×Q₈×C₆₇	—	2	3	no	—
237	C₂×Q₈×C₆₇	—	2	6	no	—
238	C₂×Q₈×C₆₇	C₂×D₄	1	3	yes	—
239	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₆₇	C₂×D₄	1	12	yes	complemented
241	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
242	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂×Q₈×C₆₇	C₂⁴	1	3	yes	—
244	C₂×D₄×C₆₇	—	2	24	no	—
245	C₂×D₄×C₆₇	—	2	48	no	—
246	C₂×D₄×C₆₇	—	2	24	no	—
247	C₂×D₄×C₆₇	—	2	24	no	—
248	C₂×D₄×C₆₇	—	2	6	no	—
249	C₂×D₄×C₆₇	—	2	3	no	—
250	C₂×D₄×C₆₇	—	2	1	no	—
251	C₂×D₄×C₆₇	—	2	3	no	—
252	C₂×D₄×C₆₇	—	2	3	no	—
253	C₂×D₄×C₆₇	—	2	24	no	—
254	C₂×D₄×C₆₇	—	2	12	no	—
255	C₂×D₄×C₆₇	—	2	6	no	—
256	C₂×D₄×C₆₇	—	2	6	no	—
257	C₂×D₄×C₆₇	—	2	3	no	—
258	C₂×D₄×C₆₇	—	2	3	no	—
259	C₂×D₄×C₆₇	—	2	3	no	—
260	C₂×D₄×C₆₇	—	2	6	no	—
261	C₂×D₄×C₆₇	—	2	3	no	—
262	C₂×D₄×C₆₇	—	2	3	no	—
263	C₂×D₄×C₆₇	—	2	6	no	—
264	C₂×D₄×C₆₇	—	2	6	no	—
265	C₂×D₄×C₆₇	—	2	6	no	—
266	C₂×D₄×C₆₇	—	2	3	no	—
267	C₂×D₄×C₆₇	—	4	12	no	—
268	C₂×D₄×C₆₇	—	8	6	no	—
269	C₂×D₄×C₆₇	C₂×D₄	1	6	yes	—
270	C₂×D₄×C₆₇	C₂×D₄	1	3	yes	—
271	C₂×D₄×C₆₇	C₂×D₄	1	3	yes	—
272	C₂×D₄×C₆₇	C₂×D₄	1	12	yes	complemented
273	C₂×D₄×C₆₇	C₂⁴	1	3	yes	—
274	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
275	C₂×D₄×C₆₇	C₂⁴	1	3	yes	—
276	C₂²×C₄×C₆₇	—	2	24	no	—
277	C₂²×C₄×C₆₇	—	2	24	no	—
278	C₂²×C₄×C₆₇	—	2	3	no	—
279	C₂²×C₄×C₆₇	—	2	3	no	—
280	C₂²×C₄×C₆₇	—	2	3	no	—
281	C₂²×C₄×C₆₇	—	2	1	no	—
282	C₂²×C₄×C₆₇	—	2	6	no	—
283	C₂²×C₄×C₆₇	—	2	3	no	—
284	C₂²×C₄×C₆₇	—	2	3	no	—
285	C₂²×C₄×C₆₇	—	2	6	no	—
286	C₂²×C₄×C₆₇	—	2	6	no	—
287	C₂²×C₄×C₆₇	—	2	3	no	—
288	C₂²×C₄×C₆₇	—	2	3	no	—
289	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
290	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
291	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
292	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
294	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
295	Q₁₆×C₆₇	—	2	2	no	—
296	Q₁₆×C₆₇	—	2	6	no	—
297	SD₁₆×C₆₇	—	2	6	no	—
298	SD₁₆×C₆₇	—	2	12	no	—
299	SD₁₆×C₆₇	—	2	6	no	—
300	SD₁₆×C₆₇	—	2	2	no	—
301	SD₁₆×C₆₇	—	2	6	no	—
302	D₈×C₆₇	—	2	6	no	—
303	D₈×C₆₇	—	2	12	no	—
304	D₈×C₆₇	—	2	6	no	—
305	M₁₆×C₆₇	—	2	6	no	—
306	M₁₆×C₆₇	—	2	6	no	—
307	C₂×C₈×C₆₇	—	2	6	no	—
308	C₂×C₈×C₆₇	—	2	6	no	—
309	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₂×C₈×C₆₇	C₂⁴	1	3	yes	—
311	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
312	C₂×C₈×C₆₇	C₂⁴	1	3	yes	—
313	C₄⋊C₄×C₆₇	—	2	3	no	—
314	C₄⋊C₄×C₆₇	—	2	1	no	—
315	C₄⋊C₄×C₆₇	—	2	3	no	—
316	C₄⋊C₄×C₆₇	C₂⁴	1	3	yes	—
317	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
318	C₂²⋊C₄×C₆₇	—	2	3	no	—
319	C₂²⋊C₄×C₆₇	—	2	1	no	—
320	C₂²⋊C₄×C₆₇	—	2	3	no	—
321	C₂²⋊C₄×C₆₇	—	2	3	no	—
322	C₂²⋊C₄×C₆₇	—	2	6	no	—
323	C₂²⋊C₄×C₆₇	—	2	3	no	—
324	C₄²×C₆₇	—	2	3	no	—
325	C₂³×C₆₇	—	2	12	no	—
326	C₂³×C₆₇	—	2	3	no	—
327	C₂³×C₆₇	—	2	1	no	—
328	C₂³×C₆₇	—	2	6	no	—
329	C₂³×C₆₇	—	2	12	no	—
330	C₂³×C₆₇	—	2	3	no	—
331	C₂³×C₆₇	—	4	3	no	—
332	C₂³×C₆₇	—	4	3	no	—
333	C₂³×C₆₇	—	4	6	no	—
334	C₂³×C₆₇	—	8	3	no	—
335	C₂³×C₆₇	—	8	3	no	—
336	C₂³×C₆₇	—	8	3	no	—
337	C₂³×C₆₇	—	8	3	no	—
338	C₂³×C₆₇	—	8	3	no	—
339	C₂³×C₆₇	—	8	3	no	—
340	C₂³×C₆₇	C₂²×D₄	1	3	yes	—
341	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
342	C₂³×C₆₇	C₂²×D₄	1	3	yes	—
343	Q₈×C₆₇	—	2	12	no	—
344	Q₈×C₆₇	—	2	6	no	—
345	Q₈×C₆₇	—	2	12	no	—
346	Q₈×C₆₇	—	2	1	no	—
347	Q₈×C₆₇	—	2	3	no	—
348	Q₈×C₆₇	—	2	1	no	—
349	Q₈×C₆₇	—	2	1	no	—
350	Q₈×C₆₇	#120	1	4	yes	—
351	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
352	Q₈×C₆₇	C₂²×D₄	1	6	yes	—
353	D₄×C₆₇	—	2	24	no	—
354	D₄×C₆₇	—	2	12	no	—
355	D₄×C₆₇	—	2	4	no	—
356	D₄×C₆₇	—	2	12	no	—
357	D₄×C₆₇	—	2	12	no	—
358	D₄×C₆₇	—	2	12	no	—
359	D₄×C₆₇	—	2	12	no	—
360	D₄×C₆₇	—	2	6	no	—
361	D₄×C₆₇	—	2	12	no	—
362	D₄×C₆₇	—	2	3	no	—
363	D₄×C₆₇	—	2	1	no	—
364	D₄×C₆₇	—	2	3	no	—
365	D₄×C₆₇	—	2	3	no	—
366	D₄×C₆₇	—	4	6	no	—
367	D₄×C₆₇	—	4	6	no	—
368	D₄×C₆₇	—	4	6	no	—
369	D₄×C₆₇	—	8	3	no	—
370	D₄×C₆₇	—	8	6	no	—
371	D₄×C₆₇	#120	1	12	yes	—
372	D₄×C₆₇	C₂²×D₄	1	2	yes	—
373	D₄×C₆₇	C₂²×D₄	1	6	yes	—
374	C₂×C₄×C₆₇	—	2	12	no	—
375	C₂×C₄×C₆₇	—	2	4	no	—
376	C₂×C₄×C₆₇	—	2	12	no	—
377	C₂×C₄×C₆₇	—	2	24	no	—
378	C₂×C₄×C₆₇	—	2	6	no	—
379	C₂×C₄×C₆₇	—	2	12	no	—
380	C₂×C₄×C₆₇	—	2	3	no	—
381	C₂×C₄×C₆₇	—	2	1	no	—
382	C₂×C₄×C₆₇	—	2	6	no	—
383	C₂×C₄×C₆₇	—	2	12	no	—
384	C₂×C₄×C₆₇	—	2	12	no	—
385	C₂×C₄×C₆₇	—	2	6	no	—
386	C₂×C₄×C₆₇	—	2	1	no	—
387	C₂×C₄×C₆₇	—	2	1	no	—
388	C₂×C₄×C₆₇	—	2	3	no	—
389	C₂×C₄×C₆₇	—	2	3	no	—
390	C₂×C₄×C₆₇	—	2	1	no	—
391	C₂×C₄×C₆₇	—	2	3	no	—
392	C₂×C₄×C₆₇	—	2	1	no	—
393	C₂×C₄×C₆₇	—	4	6	no	—
394	C₂×C₄×C₆₇	—	8	3	no	—
395	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
397	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
398	C₂×C₄×C₆₇	C₂²×D₄	1	6	yes	—
399	C₂×C₄×C₆₇	C₂²×D₄	1	6	yes	—
400	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
401	C₈×C₆₇	—	2	1	no	—
402	C₈×C₆₇	—	2	1	no	—
403	C₈×C₆₇	—	2	3	no	—
404	C₈×C₆₇	—	2	3	no	—
405	C₂²×C₆₇	—	2	3	no	—
406	C₂²×C₆₇	—	2	3	no	—
407	C₂²×C₆₇	—	2	3	no	—
408	C₂²×C₆₇	—	2	1	no	—
409	C₂²×C₆₇	—	2	1	no	—
410	C₂²×C₆₇	—	2	3	no	—
411	C₂²×C₆₇	—	2	3	no	—
412	C₂²×C₆₇	—	2	1	no	—
413	C₂²×C₆₇	—	2	6	no	—
414	C₂²×C₆₇	—	2	2	no	—
415	C₂²×C₆₇	—	4	3	no	—
416	C₂²×C₆₇	—	4	1	no	—
417	C₂²×C₆₇	—	4	3	no	—
418	C₂²×C₆₇	—	4	1	no	—
419	C₂²×C₆₇	—	4	3	no	—
420	C₂²×C₆₇	—	4	3	no	—
421	C₂²×C₆₇	—	4	3	no	—
422	C₂²×C₆₇	—	8	6	no	—
423	C₂²×C₆₇	—	8	12	no	—
424	C₂²×C₆₇	—	8	12	no	—
425	C₂²×C₆₇	—	16	6	no	—
426	C₂²×C₆₇	C₂×#120	1	6	yes	—
427	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
428	C₄×C₆₇	—	2	1	no	—
429	C₄×C₆₇	—	2	6	no	—
430	C₄×C₆₇	—	2	2	no	—
431	C₄×C₆₇	—	2	3	no	—
432	C₄×C₆₇	—	4	1	no	—
433	C₄×C₆₇	—	4	3	no	—
434	C₄×C₆₇	—	4	1	no	—
435	C₄×C₆₇	C₂×#120	1	6	yes	—
436	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
437	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
438	#60376	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
439	C₂×C₆₇	—	2	6	no	—
440	C₂×C₆₇	—	4	3	no	—
441	C₂×C₆₇	—	4	1	no	—
442	C₂×C₆₇	—	4	6	no	—
443	C₂×C₆₇	—	4	2	no	—
444	C₂×C₆₇	—	8	3	no	—
445	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
446	C₂×C₆₇	#3584	1	1	yes	characteristic
447	C₂×C₆₇	#3585	1	1	yes	characteristic
448	C₂×#585	C₂×C₆₇	1	1	yes	characteristic, complemented
449	C₂×#577	C₂×C₆₇	1	1	yes	characteristic, complemented
450	C₂×#576	C₂×C₆₇	1	1	yes	characteristic, complemented
451	#3488	C₂×C₆₇	1	1	yes	characteristic, complemented
452	#3013	C₂×C₆₇	1	3	yes	complemented
453	#3012	C₂×C₆₇	1	3	yes	complemented
454	#3010	C₂×C₆₇	1	3	yes	complemented
455	#3008	C₂×C₆₇	1	3	yes	complemented
456	#3006	C₂×C₆₇	1	3	yes	complemented
457	#3005	C₂×C₆₇	1	3	yes	complemented
458	#3002	C₂×C₆₇	1	3	yes	complemented
459	C₂×#449	C₂×C₆₇	1	3	yes	complemented
460	#2898	C₂×C₆₇	1	1	yes	characteristic, complemented
461	#2897	C₂×C₆₇	1	1	yes	characteristic, complemented
462	#2880	C₂×C₆₇	1	1	yes	characteristic, complemented
463	C₆₇	#60376	1	1	yes	characteristic, direct product factor, Sylow
464	#585	—	2	8	no	—
465	#585	—	2	8	no	—
466	C₂×2₋¹⁺⁴	—	2	1	no	—
467	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
468	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	3	yes	complemented
469	C₂×H(5,𝔽₂)	—	2	3	no	—
470	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
471	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	3	yes	complemented
472	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic, complemented
473	C₂²×#41	—	2	3	no	—
474	C₂²×#41	—	2	1	no	—
475	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
476	C₂²×#41	C₂²×C₆₇	1	3	yes	complemented
477	C₂²×#41	C₂²×C₆₇	1	3	yes	complemented
478	#577	—	2	8	no	—
479	#576	—	2	8	no	—
480	C₂×#137	C₂²×C₆₇	1	3	yes	complemented
481	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	3	yes	complemented
482	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	3	yes	complemented
483	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	3	yes	complemented
484	C₂×#135	C₂²×C₆₇	1	3	yes	complemented
485	C₂×#135	C₂²×C₆₇	1	3	yes	complemented
486	C₂²×SD₁₆	C₂²×C₆₇	1	3	yes	complemented
487	C₂²×D₈	C₂²×C₆₇	1	3	yes	complemented
488	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
489	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
490	#550	—	2	1	no	—
491	#548	—	2	1	no	—
492	#546	—	2	3	no	—
493	D₄²	—	2	3	no	—
494	#537	C₂²×C₆₇	1	3	yes	complemented
495	#535	C₂²×C₆₇	1	3	yes	complemented
496	#525	C₂²×C₆₇	1	3	yes	complemented
497	C₂×#121	C₂²×C₆₇	1	3	yes	complemented
498	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
499	#452	C₂²×C₆₇	1	1	yes	characteristic, complemented
500	#452	C₂²×C₆₇	1	3	yes	complemented
501	#452	C₂²×C₆₇	1	6	yes	complemented
502	#451	C₂²×C₆₇	1	3	yes	complemented
503	#450	C₂²×C₆₇	1	3	yes	complemented
504	#449	C₂²×C₆₇	1	3	yes	complemented
505	#449	C₂²×C₆₇	1	6	yes	complemented
506	#449	C₂²×C₆₇	1	6	yes	complemented
507	#449	C₂²×C₆₇	1	6	yes	complemented
508	#449	C₂²×C₆₇	1	3	yes	complemented
509	#449	C₂²×C₆₇	1	6	yes	complemented
510	#448	C₂²×C₆₇	1	3	yes	complemented
511	#448	C₂²×C₆₇	1	6	yes	complemented
512	#447	C₂²×C₆₇	1	3	yes	complemented
513	#447	C₂²×C₆₇	1	6	yes	complemented
514	#419	C₂²×C₆₇	1	3	yes	complemented
515	#418	C₂²×C₆₇	1	3	yes	complemented
516	#417	C₂²×C₆₇	1	3	yes	complemented
517	#417	C₂²×C₆₇	1	3	yes	complemented
518	#416	C₂²×C₆₇	1	3	yes	complemented
519	#416	C₂²×C₆₇	1	3	yes	complemented
520	C₂×#103	C₂²×C₆₇	1	3	yes	complemented
521	C₂×#102	C₂²×C₆₇	1	3	yes	complemented
522	#408	C₂²×C₆₇	1	3	yes	complemented
523	#408	C₂²×C₆₇	1	3	yes	complemented
524	#407	C₂²×C₆₇	1	3	yes	complemented
525	C₂×C₂²⋊C₈	C₂²×C₆₇	1	3	yes	complemented
526	2₋¹⁺⁴	—	2	16	no	—
527	2₋¹⁺⁴	—	2	4	no	—
528	2₋¹⁺⁴	—	2	12	no	—
529	2₋¹⁺⁴	—	2	12	no	—
530	2₋¹⁺⁴	D₄×C₆₇	1	8	yes	complemented
531	H(5,𝔽₂)	—	2	48	no	—
532	H(5,𝔽₂)	—	2	4	no	—
533	H(5,𝔽₂)	—	2	12	no	—
534	H(5,𝔽₂)	—	2	12	no	—
535	H(5,𝔽₂)	—	2	4	no	—
536	H(5,𝔽₂)	—	2	4	no	—
537	H(5,𝔽₂)	D₄×C₆₇	1	8	yes	complemented
538	C₂×#41	—	2	16	no	—
539	C₂×#41	—	2	48	no	—
540	C₂×#41	—	2	4	no	—
541	C₂×#41	—	2	4	no	—
542	C₂×#41	—	2	12	no	—
543	C₂×#41	—	2	12	no	—
544	C₂×#41	—	2	1	no	—
545	C₂×#41	—	2	3	no	—
546	C₂×#41	—	2	1	no	—
547	C₂×#41	—	2	12	no	—
548	C₂×#41	—	2	3	no	—
549	C₂×#41	—	2	6	no	—
550	C₂×#41	—	2	3	no	—
551	C₂×#41	—	2	12	no	—
552	C₂×#41	—	2	3	no	—
553	C₂×#41	—	2	3	no	—
554	C₂×#41	—	2	3	no	—
555	C₂×#41	—	2	3	no	—
556	C₂×#41	D₄×C₆₇	1	3	yes	—
557	C₂×#41	D₄×C₆₇	1	1	yes	characteristic
558	C₂×#41	C₂³×C₆₇	1	3	yes	—
559	C₂×#41	C₂³×C₆₇	1	3	yes	—
560	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
561	C₂×#41	C₂³×C₆₇	1	6	yes	—
562	C₂×#41	C₂³×C₆₇	1	3	yes	—
563	C₂×#41	C₂³×C₆₇	1	3	yes	—
564	C₂×#41	C₂³×C₆₇	1	3	yes	—
565	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
566	C₂²×Q₈	—	2	1	no	—
567	C₂²×Q₈	—	2	3	no	—
568	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
569	C₂²×Q₈	C₂³×C₆₇	1	3	yes	—
570	C₂²×Q₈	C₂³×C₆₇	1	3	yes	—
571	C₂²×D₄	—	2	3	no	—
572	C₂²×D₄	—	2	3	no	—
573	C₂²×D₄	—	2	3	no	—
574	C₂²×D₄	—	2	6	no	—
575	C₂²×D₄	—	2	3	no	—
576	C₂²×D₄	—	2	3	no	—
577	C₂²×D₄	—	2	3	no	—
578	C₂²×D₄	D₄×C₆₇	1	3	yes	—
579	C₂²×D₄	C₂³×C₆₇	1	3	yes	—
580	C₂²×D₄	C₂³×C₆₇	1	3	yes	—
581	C₂²×D₄	C₂³×C₆₇	1	3	yes	—
582	C₂³×C₄	—	2	3	no	—
583	C₂³×C₄	—	2	3	no	—
584	C₂³×C₄	C₂³×C₆₇	1	3	yes	—
585	#137	—	2	12	no	—
586	AGL(1,ℤ/8)	—	2	12	no	—
587	AGL(1,ℤ/8)	—	2	12	no	—
588	AGL(1,ℤ/8)	—	2	12	no	—
589	#135	—	2	12	no	—
590	#135	—	2	12	no	—
591	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
592	C₂×Q₁₆	C₂³×C₆₇	1	3	yes	—
593	C₂×SD₁₆	—	2	12	no	—
594	C₂×SD₁₆	C₂³×C₆₇	1	3	yes	—
595	C₂×SD₁₆	C₂³×C₆₇	1	6	yes	—
596	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
597	C₂×SD₁₆	C₂³×C₆₇	1	3	yes	—
598	C₂×SD₁₆	C₂³×C₆₇	1	3	yes	—
599	C₂×D₈	—	2	12	no	—
600	C₂×D₈	C₂³×C₆₇	1	3	yes	—
601	C₂×D₈	C₂³×C₆₇	1	6	yes	—
602	C₂×D₈	C₂³×C₆₇	1	3	yes	—
603	#131	—	2	4	no	—
604	#131	—	2	4	no	—
605	C₂×M₁₆	C₂³×C₆₇	1	3	yes	—
606	C₂×M₁₆	C₂³×C₆₇	1	3	yes	—
607	C₂²×C₈	C₂³×C₆₇	1	3	yes	—
608	C₂²×C₈	C₂³×C₆₇	1	3	yes	—
609	#127	—	2	3	no	—
610	#124	—	2	3	no	—
611	#123	—	2	3	no	—
612	C₂²⋊Q₈	—	2	3	no	—
613	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
614	C₂²⋊Q₈	C₂³×C₆₇	1	3	yes	—
615	#121	—	2	6	no	—
616	#121	—	2	3	no	—
617	#121	—	2	3	no	—
618	#121	—	2	3	no	—
619	#121	C₂³×C₆₇	1	3	yes	—
620	#121	C₂³×C₆₇	1	6	yes	—
621	#121	C₂³×C₆₇	1	3	yes	—
622	#120	—	2	3	no	—
623	#120	—	2	6	no	—
624	C₄×Q₈	—	2	1	no	—
625	C₄×D₄	—	2	3	no	—
626	C₄×D₄	—	2	3	no	—
627	C₄×D₄	—	2	3	no	—
628	#117	C₂³×C₆₇	1	3	yes	—
629	C₂×C₄⋊C₄	C₂³×C₆₇	1	3	yes	—
630	C₂×C₂²⋊C₄	—	2	3	no	—
631	#103	C₂³×C₆₇	1	3	yes	—
632	#103	C₂³×C₆₇	1	6	yes	—
633	#103	C₂³×C₆₇	1	1	yes	characteristic
634	#103	C₂³×C₆₇	1	3	yes	—
635	#103	C₂³×C₆₇	1	3	yes	—
636	#102	C₂³×C₆₇	1	3	yes	—
637	#102	C₂³×C₆₇	1	6	yes	—
638	#102	C₂³×C₆₇	1	1	yes	characteristic
639	#102	C₂³×C₆₇	1	3	yes	—
640	#102	C₂³×C₆₇	1	3	yes	—
641	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
642	C₂²⋊C₈	C₂³×C₆₇	1	3	yes	—
643	C₂²⋊C₈	C₂³×C₆₇	1	3	yes	—
644	C₂²⋊C₈	C₂³×C₆₇	1	3	yes	—
645	C₂²⋊C₈	C₂³×C₆₇	1	6	yes	—
646	C₂⁴	—	2	3	no	—
647	C₂⁴	—	2	3	no	—
648	C₂⁴	—	2	3	no	—
649	C₂⁴	C₂×D₄×C₆₇	1	3	yes	—
650	#41	—	2	24	no	—
651	#41	—	2	24	no	—
652	#41	—	2	48	no	—
653	#41	—	2	24	no	—
654	#41	—	2	24	no	—
655	#41	—	2	24	no	—
656	#41	—	2	24	no	—
657	#41	—	2	4	no	—
658	#41	—	2	8	no	—
659	#41	—	2	2	no	—
660	#41	—	2	6	no	—
661	#41	—	2	12	no	—
662	#41	—	2	12	no	—
663	#41	—	2	24	no	—
664	#41	—	2	2	no	—
665	#41	—	2	6	no	—
666	#41	—	2	12	no	—
667	#41	—	2	6	no	—
668	#41	—	2	6	no	—
669	#41	—	2	6	no	—
670	#41	—	2	6	no	—
671	#41	—	2	6	no	—
672	#41	—	2	6	no	—
673	#41	—	4	4	no	—
674	#41	C₂×D₄×C₆₇	1	4	yes	—
675	#41	C₂×D₄×C₆₇	1	4	yes	—
676	#41	C₂×D₄×C₆₇	1	12	yes	complemented
677	#41	C₂×D₄×C₆₇	1	12	yes	complemented
678	C₂×Q₈	—	2	24	no	—
679	C₂×Q₈	—	2	8	no	—
680	C₂×Q₈	—	2	4	no	—
681	C₂×Q₈	—	2	6	no	—
682	C₂×Q₈	—	2	6	no	—
683	C₂×Q₈	—	2	3	no	—
684	C₂×Q₈	—	2	3	no	—
685	C₂×Q₈	—	2	6	no	—
686	C₂×Q₈	C₂×D₄×C₆₇	1	3	yes	—
687	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
688	C₂×Q₈	C₂×D₄×C₆₇	1	12	yes	complemented
689	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
690	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
691	C₂×Q₈	C₂⁴×C₆₇	1	3	yes	—
692	C₂×D₄	—	2	24	no	—
693	C₂×D₄	—	2	48	no	—
694	C₂×D₄	—	2	24	no	—
695	C₂×D₄	—	2	24	no	—
696	C₂×D₄	—	2	6	no	—
697	C₂×D₄	—	2	3	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	3	no	—
700	C₂×D₄	—	2	3	no	—
701	C₂×D₄	—	2	24	no	—
702	C₂×D₄	—	2	12	no	—
703	C₂×D₄	—	2	6	no	—
704	C₂×D₄	—	2	6	no	—
705	C₂×D₄	—	2	3	no	—
706	C₂×D₄	—	2	3	no	—
707	C₂×D₄	—	2	3	no	—
708	C₂×D₄	—	2	6	no	—
709	C₂×D₄	—	2	3	no	—
710	C₂×D₄	—	2	3	no	—
711	C₂×D₄	—	2	6	no	—
712	C₂×D₄	—	2	6	no	—
713	C₂×D₄	—	2	6	no	—
714	C₂×D₄	—	2	3	no	—
715	C₂×D₄	—	4	12	no	—
716	C₂×D₄	—	8	6	no	—
717	C₂×D₄	C₂×D₄×C₆₇	1	6	yes	—
718	C₂×D₄	C₂×D₄×C₆₇	1	3	yes	—
719	C₂×D₄	C₂×D₄×C₆₇	1	3	yes	—
720	C₂×D₄	C₂×D₄×C₆₇	1	12	yes	complemented
721	C₂×D₄	C₂⁴×C₆₇	1	3	yes	—
722	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
723	C₂×D₄	C₂⁴×C₆₇	1	3	yes	—
724	C₂²×C₄	—	2	24	no	—
725	C₂²×C₄	—	2	24	no	—
726	C₂²×C₄	—	2	3	no	—
727	C₂²×C₄	—	2	3	no	—
728	C₂²×C₄	—	2	3	no	—
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	6	no	—
731	C₂²×C₄	—	2	3	no	—
732	C₂²×C₄	—	2	3	no	—
733	C₂²×C₄	—	2	6	no	—
734	C₂²×C₄	—	2	6	no	—
735	C₂²×C₄	—	2	3	no	—
736	C₂²×C₄	—	2	3	no	—
737	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
738	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
739	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
740	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₆₇	1	3	yes	—
742	C₂²×C₄	C₂⁴×C₆₇	1	3	yes	—
743	Q₁₆	—	2	2	no	—
744	Q₁₆	—	2	6	no	—
745	SD₁₆	—	2	6	no	—
746	SD₁₆	—	2	12	no	—
747	SD₁₆	—	2	6	no	—
748	SD₁₆	—	2	2	no	—
749	SD₁₆	—	2	6	no	—
750	D₈	—	2	6	no	—
751	D₈	—	2	12	no	—
752	D₈	—	2	6	no	—
753	M₁₆	—	2	6	no	—
754	M₁₆	—	2	6	no	—
755	C₂×C₈	—	2	6	no	—
756	C₂×C₈	—	2	6	no	—
757	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
758	C₂×C₈	C₂⁴×C₆₇	1	3	yes	—
759	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
760	C₂×C₈	C₂⁴×C₆₇	1	3	yes	—
761	C₄⋊C₄	—	2	3	no	—
762	C₄⋊C₄	—	2	1	no	—
763	C₄⋊C₄	—	2	3	no	—
764	C₄⋊C₄	C₂⁴×C₆₇	1	3	yes	—
765	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
766	C₂²⋊C₄	—	2	3	no	—
767	C₂²⋊C₄	—	2	1	no	—
768	C₂²⋊C₄	—	2	3	no	—
769	C₂²⋊C₄	—	2	3	no	—
770	C₂²⋊C₄	—	2	6	no	—
771	C₂²⋊C₄	—	2	3	no	—
772	C₄²	—	2	3	no	—
773	C₂³	—	2	12	no	—
774	C₂³	—	2	3	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	6	no	—
777	C₂³	—	2	12	no	—
778	C₂³	—	2	3	no	—
779	C₂³	—	4	3	no	—
780	C₂³	—	4	3	no	—
781	C₂³	—	4	6	no	—
782	C₂³	—	8	3	no	—
783	C₂³	—	8	3	no	—
784	C₂³	—	8	3	no	—
785	C₂³	—	8	3	no	—
786	C₂³	—	8	3	no	—
787	C₂³	—	8	3	no	—
788	C₂³	C₂²×D₄×C₆₇	1	3	yes	—
789	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
790	C₂³	C₂²×D₄×C₆₇	1	3	yes	—
791	Q₈	—	2	12	no	—
792	Q₈	—	2	6	no	—
793	Q₈	—	2	12	no	—
794	Q₈	—	2	1	no	—
795	Q₈	—	2	3	no	—
796	Q₈	—	2	1	no	—
797	Q₈	—	2	1	no	—
798	Q₈	#120×C₆₇	1	4	yes	—
799	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
800	Q₈	C₂²×D₄×C₆₇	1	6	yes	—
801	D₄	—	2	24	no	—
802	D₄	—	2	12	no	—
803	D₄	—	2	4	no	—
804	D₄	—	2	12	no	—
805	D₄	—	2	12	no	—
806	D₄	—	2	12	no	—
807	D₄	—	2	12	no	—
808	D₄	—	2	6	no	—
809	D₄	—	2	12	no	—
810	D₄	—	2	3	no	—
811	D₄	—	2	1	no	—
812	D₄	—	2	3	no	—
813	D₄	—	2	3	no	—
814	D₄	—	4	6	no	—
815	D₄	—	4	6	no	—
816	D₄	—	4	6	no	—
817	D₄	—	8	6	no	—
818	D₄	—	8	3	no	—
819	D₄	#120×C₆₇	1	12	yes	—
820	D₄	C₂²×D₄×C₆₇	1	2	yes	—
821	D₄	C₂²×D₄×C₆₇	1	6	yes	—
822	C₂×C₄	—	2	12	no	—
823	C₂×C₄	—	2	4	no	—
824	C₂×C₄	—	2	12	no	—
825	C₂×C₄	—	2	24	no	—
826	C₂×C₄	—	2	6	no	—
827	C₂×C₄	—	2	12	no	—
828	C₂×C₄	—	2	3	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	6	no	—
831	C₂×C₄	—	2	12	no	—
832	C₂×C₄	—	2	12	no	—
833	C₂×C₄	—	2	6	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	3	no	—
837	C₂×C₄	—	2	3	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	3	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	4	6	no	—
842	C₂×C₄	—	8	3	no	—
843	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
845	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
846	C₂×C₄	C₂²×D₄×C₆₇	1	6	yes	—
847	C₂×C₄	C₂²×D₄×C₆₇	1	6	yes	—
848	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
849	C₈	—	2	1	no	—
850	C₈	—	2	1	no	—
851	C₈	—	2	3	no	—
852	C₈	—	2	3	no	—
853	C₂²	—	2	3	no	—
854	C₂²	—	2	3	no	—
855	C₂²	—	2	3	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	3	no	—
859	C₂²	—	2	3	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	6	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	4	3	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	3	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	3	no	—
868	C₂²	—	4	3	no	—
869	C₂²	—	4	3	no	—
870	C₂²	—	8	6	no	—
871	C₂²	—	8	12	no	—
872	C₂²	—	8	12	no	—
873	C₂²	—	16	6	no	—
874	C₂²	C₂×#120×C₆₇	1	6	yes	—
875	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
876	C₄	—	2	1	no	—
877	C₄	—	2	6	no	—
878	C₄	—	2	2	no	—
879	C₄	—	2	3	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	3	no	—
882	C₄	—	4	1	no	—
883	C₄	C₂×#120×C₆₇	1	6	yes	—
884	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
885	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
886	C₂	—	2	6	no	—
887	C₂	—	4	3	no	—
888	C₂	—	4	1	no	—
889	C₂	—	4	6	no	—
890	C₂	—	4	2	no	—
891	C₂	—	8	3	no	—
892	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic
893	C₂	C₆₇×#3584	1	1	yes	characteristic
894	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂²×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#585×C₆₇	C₂	semidirect
2. C₂×#577×C₆₇	C₂	semidirect
3. C₂×#576×C₆₇	C₂	semidirect
4. C₆₇×#3488	C₂	semidirect
5. C₆₇×#3013	C₂	semidirect
6. C₆₇×#3012	C₂	semidirect
7. C₆₇×#3010	C₂	semidirect
8. C₆₇×#3008	C₂	semidirect
9. C₆₇×#3006	C₂	semidirect
10. C₆₇×#3005	C₂	semidirect
11. C₆₇×#3002	C₂	semidirect
12. C₂×#449×C₆₇	C₂	semidirect
13. C₆₇×#2898	C₂	semidirect
14. C₆₇×#2897	C₂	semidirect
15. C₆₇×#2880	C₂	semidirect
20. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
23. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
24. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
28. C₂²×#41×C₆₇	C₂²	semidirect
29. C₂²×#41×C₆₇	C₂²	semidirect
32. C₂×#137×C₆₇	C₂²	semidirect
33. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
34. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
35. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
36. C₂×#135×C₆₇	C₂²	semidirect
37. C₂×#135×C₆₇	C₂²	semidirect
38. C₂²×SD₁₆×C₆₇	C₂²	semidirect
39. C₂²×D₈×C₆₇	C₂²	semidirect
40. C₂×#131×C₆₇	C₂²	semidirect
41. C₂×#131×C₆₇	C₂²	semidirect
46. #537×C₆₇	C₂²	semidirect
47. #535×C₆₇	C₂²	semidirect
48. #525×C₆₇	C₂²	semidirect
49. C₂×#121×C₆₇	C₂²	semidirect
50. #520×C₆₇	C₂²	semidirect
51. #452×C₆₇	C₂²	semidirect
52. #452×C₆₇	C₂²	semidirect
53. #452×C₆₇	C₂²	semidirect
54. #451×C₆₇	C₂²	semidirect
55. #450×C₆₇	C₂²	semidirect
56. #449×C₆₇	C₂²	semidirect
57. #449×C₆₇	C₂²	semidirect
58. #449×C₆₇	C₂²	semidirect
59. #449×C₆₇	C₂²	semidirect
60. #449×C₆₇	C₂²	semidirect
61. #449×C₆₇	C₂²	semidirect
62. #448×C₆₇	C₂²	semidirect
63. #448×C₆₇	C₂²	semidirect
64. #447×C₆₇	C₂²	semidirect
65. #447×C₆₇	C₂²	semidirect
66. #419×C₆₇	C₂²	semidirect
67. #418×C₆₇	C₂²	semidirect
68. #417×C₆₇	C₂²	semidirect
69. #417×C₆₇	C₂²	semidirect
70. #416×C₆₇	C₂²	semidirect
71. #416×C₆₇	C₂²	semidirect
72. C₂×#103×C₆₇	C₂²	semidirect
73. C₂×#102×C₆₇	C₂²	semidirect
74. #408×C₆₇	C₂²	semidirect
75. #408×C₆₇	C₂²	semidirect
76. #407×C₆₇	C₂²	semidirect
77. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
82. 2₋¹⁺⁴×C₆₇	D₄	semidirect
89. H(5,𝔽₂)×C₆₇	D₄	semidirect
228. #41×C₆₇	C₂×D₄	semidirect
229. #41×C₆₇	C₂×D₄	semidirect
240. C₂×Q₈×C₆₇	C₂×D₄	semidirect
272. C₂×D₄×C₆₇	C₂×D₄	semidirect
438. #60376	C₆₇	direct (N × H)
448. C₂×#585	C₂×C₆₇	semidirect
449. C₂×#577	C₂×C₆₇	semidirect
450. C₂×#576	C₂×C₆₇	semidirect
451. #3488	C₂×C₆₇	semidirect
452. #3013	C₂×C₆₇	semidirect
453. #3012	C₂×C₆₇	semidirect
454. #3010	C₂×C₆₇	semidirect
455. #3008	C₂×C₆₇	semidirect
456. #3006	C₂×C₆₇	semidirect
457. #3005	C₂×C₆₇	semidirect
458. #3002	C₂×C₆₇	semidirect
459. C₂×#449	C₂×C₆₇	semidirect
460. #2898	C₂×C₆₇	semidirect
461. #2897	C₂×C₆₇	semidirect
462. #2880	C₂×C₆₇	semidirect
463. C₆₇	#60376	direct (N × H)
468. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
471. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
472. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
476. C₂²×#41	C₂²×C₆₇	semidirect
477. C₂²×#41	C₂²×C₆₇	semidirect
480. C₂×#137	C₂²×C₆₇	semidirect
481. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
482. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
483. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
484. C₂×#135	C₂²×C₆₇	semidirect
485. C₂×#135	C₂²×C₆₇	semidirect
486. C₂²×SD₁₆	C₂²×C₆₇	semidirect
487. C₂²×D₈	C₂²×C₆₇	semidirect
488. C₂×#131	C₂²×C₆₇	semidirect
489. C₂×#131	C₂²×C₆₇	semidirect
494. #537	C₂²×C₆₇	semidirect
495. #535	C₂²×C₆₇	semidirect
496. #525	C₂²×C₆₇	semidirect
497. C₂×#121	C₂²×C₆₇	semidirect
498. #520	C₂²×C₆₇	semidirect
499. #452	C₂²×C₆₇	semidirect
500. #452	C₂²×C₆₇	semidirect
501. #452	C₂²×C₆₇	semidirect
502. #451	C₂²×C₆₇	semidirect
503. #450	C₂²×C₆₇	semidirect
504. #449	C₂²×C₆₇	semidirect
505. #449	C₂²×C₆₇	semidirect
506. #449	C₂²×C₆₇	semidirect
507. #449	C₂²×C₆₇	semidirect
508. #449	C₂²×C₆₇	semidirect
509. #449	C₂²×C₆₇	semidirect
510. #448	C₂²×C₆₇	semidirect
511. #448	C₂²×C₆₇	semidirect
512. #447	C₂²×C₆₇	semidirect
513. #447	C₂²×C₆₇	semidirect
514. #419	C₂²×C₆₇	semidirect
515. #418	C₂²×C₆₇	semidirect
516. #417	C₂²×C₆₇	semidirect
517. #417	C₂²×C₆₇	semidirect
518. #416	C₂²×C₆₇	semidirect
519. #416	C₂²×C₆₇	semidirect
520. C₂×#103	C₂²×C₆₇	semidirect
521. C₂×#102	C₂²×C₆₇	semidirect
522. #408	C₂²×C₆₇	semidirect
523. #408	C₂²×C₆₇	semidirect
524. #407	C₂²×C₆₇	semidirect
525. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
530. 2₋¹⁺⁴	D₄×C₆₇	semidirect
537. H(5,𝔽₂)	D₄×C₆₇	semidirect
676. #41	C₂×D₄×C₆₇	semidirect
677. #41	C₂×D₄×C₆₇	semidirect
688. C₂×Q₈	C₂×D₄×C₆₇	semidirect
720. C₂×D₄	C₂×D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#585×C₆₇	2
C₂×#577×C₆₇	2
C₂×#576×C₆₇	2
C₆₇×#3488	2
C₆₇×#3013	2
C₆₇×#3012	2
C₆₇×#3010	2
C₆₇×#3008	2
C₆₇×#3006	2
C₆₇×#3005	2
C₆₇×#3002	2
C₂×#449×C₆₇	2
C₆₇×#2898	2
C₆₇×#2897	2
C₆₇×#2880	2
#60376	67

Subgroups — C67×#60376 #30739627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60376 #30739627