Subgroups — C₆₇×#61218 #30740469

Order 17152.

2166 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3319	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3318	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3307	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3306	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3135	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3099	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3062	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3008	C₂	1	2	yes	maximal, complemented
13	C₂×#442×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2897	C₂	1	2	yes	maximal, complemented
16	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
17	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
18	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
20	#559×C₆₇	—	2	2	no	—
21	#556×C₆₇	—	2	1	no	—
22	#555×C₆₇	C₂²	1	2	yes	complemented
23	#553×C₆₇	C₂²	1	4	yes	complemented
24	#550×C₆₇	—	2	1	no	—
25	#547×C₆₇	—	2	1	no	—
26	#547×C₆₇	C₂²	1	2	yes	complemented
27	#547×C₆₇	C₂²	1	2	yes	complemented
28	#546×C₆₇	—	2	2	no	—
29	#546×C₆₇	C₂²	1	4	yes	complemented
30	D₄²×C₆₇	—	2	1	no	—
31	D₄²×C₆₇	C₂²	1	2	yes	complemented
32	#538×C₆₇	—	2	2	no	—
33	#537×C₆₇	C₂²	1	2	yes	—
34	#535×C₆₇	C₂²	1	2	yes	complemented
35	#534×C₆₇	—	2	2	no	—
36	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	#532×C₆₇	C₂²	1	1	yes	characteristic
38	#532×C₆₇	C₂²	1	1	yes	characteristic
39	#525×C₆₇	—	2	2	no	—
40	C₂×#121×C₆₇	—	2	2	no	—
41	#520×C₆₇	C₂²	1	2	yes	complemented
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	#491×C₆₇	C₂²	1	2	yes	complemented
45	#490×C₆₇	C₂²	1	2	yes	complemented
46	#489×C₆₇	C₂²	1	2	yes	complemented
47	#489×C₆₇	C₂²	1	2	yes	complemented
48	#485×C₆₇	C₂²	1	4	yes	complemented
49	#483×C₆₇	C₂²	1	4	yes	complemented
50	#482×C₆₇	C₂²	1	4	yes	complemented
51	#481×C₆₇	C₂²	1	4	yes	complemented
52	#478×C₆₇	C₂²	1	4	yes	complemented
53	#476×C₆₇	C₂²	1	2	yes	complemented
54	#474×C₆₇	C₂²	1	2	yes	complemented
55	#469×C₆₇	C₂²	1	4	yes	complemented
56	#468×C₆₇	C₂²	1	4	yes	complemented
57	#466×C₆₇	C₂²	1	4	yes	complemented
58	#465×C₆₇	C₂²	1	4	yes	complemented
59	#463×C₆₇	C₂²	1	4	yes	complemented
60	#461×C₆₇	C₂²	1	2	yes	complemented
61	#459×C₆₇	C₂²	1	2	yes	complemented
62	#449×C₆₇	C₂²	1	4	yes	complemented
63	#449×C₆₇	C₂²	1	4	yes	complemented
64	#447×C₆₇	C₂²	1	4	yes	complemented
65	#447×C₆₇	C₂²	1	4	yes	complemented
66	#442×C₆₇	C₂²	1	4	yes	complemented
67	#442×C₆₇	C₂²	1	4	yes	complemented
68	#435×C₆₇	C₂²	1	4	yes	complemented
69	#435×C₆₇	C₂²	1	4	yes	complemented
70	#428×C₆₇	C₂²	1	2	yes	complemented
71	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	#418×C₆₇	C₂²	1	2	yes	—
74	#418×C₆₇	C₂²	1	4	yes	complemented
75	#417×C₆₇	C₂²	1	2	yes	complemented
76	#417×C₆₇	C₂²	1	4	yes	complemented
77	#416×C₆₇	C₂²	1	4	yes	complemented
78	#416×C₆₇	C₂²	1	2	yes	complemented
79	#416×C₆₇	C₂²	1	2	yes	complemented
80	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
81	C₂×#102×C₆₇	C₂²	1	4	yes	complemented
82	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	#408×C₆₇	C₂²	1	2	yes	complemented
84	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	H(5,𝔽₂)×C₆₇	—	2	8	no	—
86	H(5,𝔽₂)×C₆₇	—	4	4	no	—
87	C₂×#41×C₆₇	—	2	2	no	—
88	C₂×#41×C₆₇	—	2	2	no	—
89	C₂×#41×C₆₇	C₂³	1	2	yes	—
90	C₂×#41×C₆₇	C₂³	1	4	yes	—
91	C₂×#41×C₆₇	C₂³	1	2	yes	—
92	C₂²×D₄×C₆₇	—	2	4	no	—
93	C₂²×D₄×C₆₇	—	2	2	no	—
94	C₂²×D₄×C₆₇	—	2	2	no	—
95	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
97	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₆₇	—	2	1	no	—
99	C₂³×C₄×C₆₇	—	2	1	no	—
100	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
101	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
102	C₂×D₈×C₆₇	—	2	4	no	—
103	C₂×D₈×C₆₇	C₂³	1	4	yes	—
104	C₂×D₈×C₆₇	C₂³	1	4	yes	—
105	#131×C₆₇	—	4	4	no	—
106	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
107	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
108	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
111	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
115	#127×C₆₇	—	2	2	no	—
116	#127×C₆₇	D₄	1	1	yes	characteristic
117	#127×C₆₇	C₂³	1	1	yes	characteristic
118	#126×C₆₇	—	2	4	no	—
119	#125×C₆₇	C₂³	1	2	yes	—
120	#124×C₆₇	—	2	2	no	—
121	#124×C₆₇	—	2	4	no	—
122	#124×C₆₇	D₄	1	2	yes	—
123	#124×C₆₇	C₂³	1	2	yes	—
124	#123×C₆₇	—	2	4	no	—
125	#123×C₆₇	—	2	4	no	—
126	#123×C₆₇	—	2	4	no	—
127	#123×C₆₇	—	2	4	no	—
128	C₂²⋊Q₈×C₆₇	—	2	2	no	—
129	C₂²⋊Q₈×C₆₇	—	2	1	no	—
130	C₂²⋊Q₈×C₆₇	—	2	1	no	—
131	C₂²⋊Q₈×C₆₇	—	2	2	no	—
132	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
133	#121×C₆₇	—	2	4	no	—
134	#121×C₆₇	—	2	2	no	—
135	#121×C₆₇	—	2	2	no	—
136	#121×C₆₇	—	2	2	no	—
137	#121×C₆₇	—	2	4	no	—
138	#121×C₆₇	—	2	1	no	—
139	#121×C₆₇	—	2	1	no	—
140	#121×C₆₇	—	2	2	no	—
141	#121×C₆₇	—	2	4	no	—
142	#121×C₆₇	D₄	1	2	yes	—
143	#121×C₆₇	D₄	1	2	yes	—
144	#121×C₆₇	C₂³	1	4	yes	—
145	#121×C₆₇	C₂³	1	4	yes	—
146	#121×C₆₇	C₂³	1	4	yes	—
147	#120×C₆₇	—	2	4	no	—
148	#120×C₆₇	—	2	4	no	—
149	#120×C₆₇	—	2	4	no	—
150	C₄×Q₈×C₆₇	—	2	2	no	—
151	C₄×Q₈×C₆₇	—	2	1	no	—
152	C₄×Q₈×C₆₇	—	2	1	no	—
153	C₄×D₄×C₆₇	—	2	4	no	—
154	C₄×D₄×C₆₇	—	2	2	no	—
155	C₄×D₄×C₆₇	—	2	4	no	—
156	C₄×D₄×C₆₇	—	2	1	no	—
157	C₄×D₄×C₆₇	—	2	1	no	—
158	C₄×D₄×C₆₇	—	2	1	no	—
159	C₄×D₄×C₆₇	—	2	1	no	—
160	C₄×D₄×C₆₇	—	2	1	no	—
161	C₄×D₄×C₆₇	—	2	1	no	—
162	C₄×D₄×C₆₇	C₂³	1	2	yes	—
163	C₄×D₄×C₆₇	C₂³	1	2	yes	—
164	C₄×D₄×C₆₇	C₂³	1	2	yes	—
165	C₄×D₄×C₆₇	C₂³	1	2	yes	—
166	C₄×D₄×C₆₇	C₂³	1	2	yes	—
167	C₄×D₄×C₆₇	C₂³	1	2	yes	—
168	#117×C₆₇	—	2	2	no	—
169	#117×C₆₇	C₂³	1	4	yes	—
170	#117×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
177	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
178	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
179	#107×C₆₇	C₂³	1	4	yes	—
180	#106×C₆₇	C₂³	1	4	yes	—
181	#106×C₆₇	C₂³	1	4	yes	—
182	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
183	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
184	#103×C₆₇	C₂³	1	2	yes	—
185	#103×C₆₇	C₂³	1	2	yes	—
186	#103×C₆₇	C₂³	1	4	yes	—
187	#103×C₆₇	C₂³	1	2	yes	—
188	#103×C₆₇	C₂³	1	2	yes	—
189	#102×C₆₇	C₂³	1	4	yes	—
190	#102×C₆₇	C₂³	1	4	yes	—
191	#102×C₆₇	C₂³	1	4	yes	—
192	#102×C₆₇	C₂³	1	4	yes	—
193	#102×C₆₇	C₂³	1	2	yes	—
194	#102×C₆₇	C₂³	1	2	yes	—
195	#102×C₆₇	C₂³	1	2	yes	—
196	#102×C₆₇	C₂³	1	2	yes	—
197	#102×C₆₇	C₂³	1	4	yes	—
198	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
199	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
200	#97×C₆₇	C₂³	1	2	yes	—
201	#97×C₆₇	C₂³	1	2	yes	—
202	C₂⁴×C₆₇	—	2	1	no	—
203	C₂⁴×C₆₇	—	2	1	no	—
204	C₂⁴×C₆₇	—	2	4	no	—
205	#41×C₆₇	—	2	4	no	—
206	#41×C₆₇	—	2	4	no	—
207	#41×C₆₇	—	2	8	no	—
208	#41×C₆₇	—	2	4	no	—
209	#41×C₆₇	—	2	4	no	—
210	#41×C₆₇	—	4	4	no	—
211	#41×C₆₇	—	4	8	no	—
212	#41×C₆₇	—	8	4	no	—
213	C₂×Q₈×C₆₇	—	2	1	no	—
214	C₂×Q₈×C₆₇	—	2	1	no	—
215	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
216	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
217	C₂×D₄×C₆₇	—	2	8	no	—
218	C₂×D₄×C₆₇	—	2	4	no	—
219	C₂×D₄×C₆₇	—	2	2	no	—
220	C₂×D₄×C₆₇	—	2	4	no	—
221	C₂×D₄×C₆₇	—	2	4	no	—
222	C₂×D₄×C₆₇	—	2	4	no	—
223	C₂×D₄×C₆₇	—	2	1	no	—
224	C₂×D₄×C₆₇	—	2	1	no	—
225	C₂×D₄×C₆₇	—	2	1	no	—
226	C₂×D₄×C₆₇	—	2	4	no	—
227	C₂×D₄×C₆₇	—	2	1	no	—
228	C₂×D₄×C₆₇	—	2	2	no	—
229	C₂×D₄×C₆₇	—	2	2	no	—
230	C₂×D₄×C₆₇	—	2	2	no	—
231	C₂×D₄×C₆₇	—	4	4	no	—
232	C₂×D₄×C₆₇	—	4	8	no	—
233	C₂×D₄×C₆₇	—	4	16	no	—
234	C₂×D₄×C₆₇	—	8	4	no	—
235	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
236	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
237	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
239	C₂×D₄×C₆₇	#41	1	4	yes	complemented
240	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
241	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
242	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₆₇	—	2	1	no	—
244	C₂²×C₄×C₆₇	—	2	1	no	—
245	C₂²×C₄×C₆₇	—	2	4	no	—
246	C₂²×C₄×C₆₇	—	2	4	no	—
247	C₂²×C₄×C₆₇	—	2	2	no	—
248	C₂²×C₄×C₆₇	—	2	2	no	—
249	C₂²×C₄×C₆₇	—	2	2	no	—
250	C₂²×C₄×C₆₇	—	2	2	no	—
251	C₂²×C₄×C₆₇	—	2	2	no	—
252	C₂²×C₄×C₆₇	—	8	2	no	—
253	C₂²×C₄×C₆₇	—	8	2	no	—
254	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
257	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
258	SD₁₆×C₆₇	—	4	4	no	—
259	D₈×C₆₇	—	2	8	no	—
260	D₈×C₆₇	—	4	4	no	—
261	M₁₆×C₆₇	—	2	4	no	—
262	M₁₆×C₆₇	—	4	4	no	—
263	C₂×C₈×C₆₇	—	2	2	no	—
264	C₂×C₈×C₆₇	—	2	2	no	—
265	C₂×C₈×C₆₇	—	4	4	no	—
266	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
267	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
268	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
269	C₄⋊C₄×C₆₇	—	2	1	no	—
270	C₄⋊C₄×C₆₇	—	2	4	no	—
271	C₄⋊C₄×C₆₇	—	2	1	no	—
272	C₄⋊C₄×C₆₇	—	2	1	no	—
273	C₄⋊C₄×C₆₇	—	2	4	no	—
274	C₄⋊C₄×C₆₇	—	2	1	no	—
275	C₄⋊C₄×C₆₇	—	2	2	no	—
276	C₄⋊C₄×C₆₇	—	2	1	no	—
277	C₄⋊C₄×C₆₇	—	2	2	no	—
278	C₄⋊C₄×C₆₇	—	2	1	no	—
279	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
285	C₂²⋊C₄×C₆₇	—	2	4	no	—
286	C₂²⋊C₄×C₆₇	—	2	2	no	—
287	C₂²⋊C₄×C₆₇	—	2	4	no	—
288	C₂²⋊C₄×C₆₇	—	2	2	no	—
289	C₂²⋊C₄×C₆₇	—	2	2	no	—
290	C₂²⋊C₄×C₆₇	—	2	2	no	—
291	C₂²⋊C₄×C₆₇	—	2	2	no	—
292	C₂²⋊C₄×C₆₇	—	2	2	no	—
293	C₂²⋊C₄×C₆₇	—	2	4	no	—
294	C₂²⋊C₄×C₆₇	—	2	4	no	—
295	C₂²⋊C₄×C₆₇	—	2	2	no	—
296	C₂²⋊C₄×C₆₇	—	2	4	no	—
297	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
298	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
299	C₄²×C₆₇	—	2	4	no	—
300	C₄²×C₆₇	—	2	2	no	—
301	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
304	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
305	C₂³×C₆₇	—	2	2	no	—
306	C₂³×C₆₇	—	2	4	no	—
307	C₂³×C₆₇	—	2	2	no	—
308	C₂³×C₆₇	—	2	2	no	—
309	C₂³×C₆₇	—	4	8	no	—
310	C₂³×C₆₇	—	4	2	no	—
311	C₂³×C₆₇	—	8	1	no	—
312	C₂³×C₆₇	—	8	1	no	—
313	C₂³×C₆₇	—	8	1	no	—
314	C₂³×C₆₇	—	8	1	no	—
315	C₂³×C₆₇	—	8	4	no	—
316	C₂³×C₆₇	—	8	4	no	—
317	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
318	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
319	Q₈×C₆₇	—	2	4	no	—
320	Q₈×C₆₇	—	2	2	no	—
321	Q₈×C₆₇	—	2	2	no	—
322	Q₈×C₆₇	—	4	2	no	—
323	Q₈×C₆₇	—	8	1	no	—
324	D₄×C₆₇	—	2	8	no	—
325	D₄×C₆₇	—	2	4	no	—
326	D₄×C₆₇	—	2	4	no	—
327	D₄×C₆₇	—	2	2	no	—
328	D₄×C₆₇	—	2	2	no	—
329	D₄×C₆₇	—	2	2	no	—
330	D₄×C₆₇	—	2	2	no	—
331	D₄×C₆₇	—	2	2	no	—
332	D₄×C₆₇	—	4	2	no	—
333	D₄×C₆₇	—	4	2	no	—
334	D₄×C₆₇	—	4	8	no	—
335	D₄×C₆₇	—	4	2	no	—
336	D₄×C₆₇	—	4	8	no	—
337	D₄×C₆₇	—	4	4	no	—
338	D₄×C₆₇	—	4	2	no	—
339	D₄×C₆₇	—	8	1	no	—
340	D₄×C₆₇	—	8	4	no	—
341	D₄×C₆₇	—	8	4	no	—
342	D₄×C₆₇	—	8	4	no	—
343	D₄×C₆₇	C₂×#41	1	4	yes	—
344	C₂×C₄×C₆₇	—	2	4	no	—
345	C₂×C₄×C₆₇	—	2	4	no	—
346	C₂×C₄×C₆₇	—	2	2	no	—
347	C₂×C₄×C₆₇	—	2	2	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	2	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	4	1	no	—
352	C₂×C₄×C₆₇	—	4	1	no	—
353	C₂×C₄×C₆₇	—	4	8	no	—
354	C₂×C₄×C₆₇	—	4	4	no	—
355	C₂×C₄×C₆₇	—	4	4	no	—
356	C₂×C₄×C₆₇	—	4	4	no	—
357	C₂×C₄×C₆₇	—	8	2	no	—
358	C₂×C₄×C₆₇	—	8	2	no	—
359	C₂×C₄×C₆₇	—	8	1	no	—
360	C₂×C₄×C₆₇	—	8	1	no	—
361	C₂×C₄×C₆₇	—	8	4	no	—
362	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
363	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
369	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
370	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
371	C₈×C₆₇	—	2	2	no	—
372	C₈×C₆₇	—	2	2	no	—
373	C₈×C₆₇	—	2	4	no	—
374	C₂²×C₆₇	—	2	1	no	—
375	C₂²×C₆₇	—	2	1	no	—
376	C₂²×C₆₇	—	2	4	no	—
377	C₂²×C₆₇	—	2	4	no	—
378	C₂²×C₆₇	—	2	4	no	—
379	C₂²×C₆₇	—	2	4	no	—
380	C₂²×C₆₇	—	4	2	no	—
381	C₂²×C₆₇	—	4	2	no	—
382	C₂²×C₆₇	—	4	2	no	—
383	C₂²×C₆₇	—	4	2	no	—
384	C₂²×C₆₇	—	4	2	no	—
385	C₂²×C₆₇	—	4	2	no	—
386	C₂²×C₆₇	—	4	2	no	—
387	C₂²×C₆₇	—	4	2	no	—
388	C₂²×C₆₇	—	8	4	no	—
389	C₂²×C₆₇	—	8	4	no	—
390	C₂²×C₆₇	—	16	8	no	—
391	C₂²×C₆₇	#546	1	2	yes	—
392	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
393	C₄×C₆₇	—	2	1	no	—
394	C₄×C₆₇	—	2	1	no	—
395	C₄×C₆₇	—	2	1	no	—
396	C₄×C₆₇	—	2	1	no	—
397	C₄×C₆₇	—	2	4	no	—
398	C₄×C₆₇	—	4	2	no	—
399	C₄×C₆₇	—	4	2	no	—
400	C₄×C₆₇	—	4	2	no	—
401	C₄×C₆₇	—	4	2	no	—
402	C₄×C₆₇	—	4	2	no	—
403	C₄×C₆₇	#546	1	2	yes	—
404	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
405	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
406	#61218	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
407	C₂×C₆₇	—	2	2	no	—
408	C₂×C₆₇	—	4	4	no	—
409	C₂×C₆₇	—	4	4	no	—
410	C₂×C₆₇	—	8	2	no	—
411	C₂×C₆₇	—	8	2	no	—
412	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
413	C₂×C₆₇	#3585	1	1	yes	characteristic
414	C₂×C₆₇	#3585	1	1	yes	characteristic
415	#3506	C₂×C₆₇	1	1	yes	characteristic, complemented
416	#3496	C₂×C₆₇	1	1	yes	characteristic, complemented
417	#3319	C₂×C₆₇	1	4	yes	complemented
418	#3318	C₂×C₆₇	1	4	yes	complemented
419	#3307	C₂×C₆₇	1	4	yes	complemented
420	#3306	C₂×C₆₇	1	4	yes	complemented
421	#3135	C₂×C₆₇	1	1	yes	characteristic, complemented
422	#3099	C₂×C₆₇	1	2	yes	complemented
423	#3077	C₂×C₆₇	1	1	yes	characteristic, complemented
424	#3062	C₂×C₆₇	1	2	yes	complemented
425	#3036	C₂×C₆₇	1	1	yes	characteristic, complemented
426	#3008	C₂×C₆₇	1	2	yes	complemented
427	C₂×#442	C₂×C₆₇	1	1	yes	characteristic, complemented
428	#2932	C₂×C₆₇	1	1	yes	characteristic, complemented
429	#2897	C₂×C₆₇	1	2	yes	complemented
430	C₆₇	#61218	1	1	yes	characteristic, direct product factor, Sylow
431	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
432	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
433	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
434	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
435	#559	—	2	2	no	—
436	#556	—	2	1	no	—
437	#555	C₂²×C₆₇	1	2	yes	complemented
438	#553	C₂²×C₆₇	1	4	yes	complemented
439	#550	—	2	1	no	—
440	#547	—	2	1	no	—
441	#547	C₂²×C₆₇	1	2	yes	complemented
442	#547	C₂²×C₆₇	1	2	yes	complemented
443	#546	—	2	2	no	—
444	#546	C₂²×C₆₇	1	4	yes	complemented
445	D₄²	—	2	1	no	—
446	D₄²	C₂²×C₆₇	1	2	yes	complemented
447	#538	—	2	2	no	—
448	#537	C₂²×C₆₇	1	2	yes	—
449	#535	C₂²×C₆₇	1	2	yes	complemented
450	#534	—	2	2	no	—
451	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
452	#532	C₂²×C₆₇	1	1	yes	characteristic
453	#532	C₂²×C₆₇	1	1	yes	characteristic
454	#525	—	2	2	no	—
455	C₂×#121	—	2	2	no	—
456	#520	C₂²×C₆₇	1	2	yes	complemented
457	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
458	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
459	#491	C₂²×C₆₇	1	2	yes	complemented
460	#490	C₂²×C₆₇	1	2	yes	complemented
461	#489	C₂²×C₆₇	1	2	yes	complemented
462	#489	C₂²×C₆₇	1	2	yes	complemented
463	#485	C₂²×C₆₇	1	4	yes	complemented
464	#483	C₂²×C₆₇	1	4	yes	complemented
465	#482	C₂²×C₆₇	1	4	yes	complemented
466	#481	C₂²×C₆₇	1	4	yes	complemented
467	#478	C₂²×C₆₇	1	4	yes	complemented
468	#476	C₂²×C₆₇	1	2	yes	complemented
469	#474	C₂²×C₆₇	1	2	yes	complemented
470	#469	C₂²×C₆₇	1	4	yes	complemented
471	#468	C₂²×C₆₇	1	4	yes	complemented
472	#466	C₂²×C₆₇	1	4	yes	complemented
473	#465	C₂²×C₆₇	1	4	yes	complemented
474	#463	C₂²×C₆₇	1	4	yes	complemented
475	#461	C₂²×C₆₇	1	2	yes	complemented
476	#459	C₂²×C₆₇	1	2	yes	complemented
477	#449	C₂²×C₆₇	1	4	yes	complemented
478	#449	C₂²×C₆₇	1	4	yes	complemented
479	#447	C₂²×C₆₇	1	4	yes	complemented
480	#447	C₂²×C₆₇	1	4	yes	complemented
481	#442	C₂²×C₆₇	1	4	yes	complemented
482	#442	C₂²×C₆₇	1	4	yes	complemented
483	#435	C₂²×C₆₇	1	4	yes	complemented
484	#435	C₂²×C₆₇	1	4	yes	complemented
485	#428	C₂²×C₆₇	1	2	yes	complemented
486	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic, complemented
487	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
488	#418	C₂²×C₆₇	1	2	yes	—
489	#418	C₂²×C₆₇	1	4	yes	complemented
490	#417	C₂²×C₆₇	1	2	yes	complemented
491	#417	C₂²×C₆₇	1	4	yes	complemented
492	#416	C₂²×C₆₇	1	2	yes	complemented
493	#416	C₂²×C₆₇	1	2	yes	complemented
494	#416	C₂²×C₆₇	1	4	yes	complemented
495	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
496	C₂×#102	C₂²×C₆₇	1	4	yes	complemented
497	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
498	#408	C₂²×C₆₇	1	2	yes	complemented
499	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic, complemented
500	H(5,𝔽₂)	—	2	8	no	—
501	H(5,𝔽₂)	—	4	4	no	—
502	C₂×#41	—	2	2	no	—
503	C₂×#41	—	2	2	no	—
504	C₂×#41	C₂³×C₆₇	1	2	yes	—
505	C₂×#41	C₂³×C₆₇	1	4	yes	—
506	C₂×#41	C₂³×C₆₇	1	2	yes	—
507	C₂²×D₄	—	2	4	no	—
508	C₂²×D₄	—	2	2	no	—
509	C₂²×D₄	—	2	2	no	—
510	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
511	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
512	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
513	C₂³×C₄	—	2	1	no	—
514	C₂³×C₄	—	2	1	no	—
515	AGL(1,ℤ/8)	—	4	4	no	—
516	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
517	C₂×D₈	—	2	4	no	—
518	C₂×D₈	C₂³×C₆₇	1	4	yes	—
519	C₂×D₈	C₂³×C₆₇	1	4	yes	—
520	#131	—	4	4	no	—
521	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
522	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
523	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
524	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
525	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
526	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
527	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
528	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
529	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
530	#127	—	2	2	no	—
531	#127	D₄×C₆₇	1	1	yes	characteristic
532	#127	C₂³×C₆₇	1	1	yes	characteristic
533	#126	—	2	4	no	—
534	#125	C₂³×C₆₇	1	2	yes	—
535	#124	—	2	2	no	—
536	#124	—	2	4	no	—
537	#124	D₄×C₆₇	1	2	yes	—
538	#124	C₂³×C₆₇	1	2	yes	—
539	#123	—	2	4	no	—
540	#123	—	2	4	no	—
541	#123	—	2	4	no	—
542	#123	—	2	4	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	2	1	no	—
545	C₂²⋊Q₈	—	2	1	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
548	#121	—	2	4	no	—
549	#121	—	2	2	no	—
550	#121	—	2	2	no	—
551	#121	—	2	2	no	—
552	#121	—	2	4	no	—
553	#121	—	2	1	no	—
554	#121	—	2	1	no	—
555	#121	—	2	2	no	—
556	#121	—	2	4	no	—
557	#121	D₄×C₆₇	1	2	yes	—
558	#121	D₄×C₆₇	1	2	yes	—
559	#121	C₂³×C₆₇	1	4	yes	—
560	#121	C₂³×C₆₇	1	4	yes	—
561	#121	C₂³×C₆₇	1	4	yes	—
562	#120	—	2	4	no	—
563	#120	—	2	4	no	—
564	#120	—	2	4	no	—
565	C₄×Q₈	—	2	2	no	—
566	C₄×Q₈	—	2	1	no	—
567	C₄×Q₈	—	2	1	no	—
568	C₄×D₄	—	2	4	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	4	no	—
571	C₄×D₄	—	2	1	no	—
572	C₄×D₄	—	2	1	no	—
573	C₄×D₄	—	2	1	no	—
574	C₄×D₄	—	2	1	no	—
575	C₄×D₄	—	2	1	no	—
576	C₄×D₄	—	2	1	no	—
577	C₄×D₄	C₂³×C₆₇	1	2	yes	—
578	C₄×D₄	C₂³×C₆₇	1	2	yes	—
579	C₄×D₄	C₂³×C₆₇	1	2	yes	—
580	C₄×D₄	C₂³×C₆₇	1	2	yes	—
581	C₄×D₄	C₂³×C₆₇	1	2	yes	—
582	C₄×D₄	C₂³×C₆₇	1	2	yes	—
583	#117	—	2	2	no	—
584	#117	C₂³×C₆₇	1	2	yes	—
585	#117	C₂³×C₆₇	1	4	yes	—
586	C₂×C₄⋊C₄	—	2	2	no	—
587	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
590	C₂×C₂²⋊C₄	—	2	1	no	—
591	C₂×C₂²⋊C₄	—	2	1	no	—
592	C₂×C₂²⋊C₄	—	2	4	no	—
593	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
594	#107	C₂³×C₆₇	1	4	yes	—
595	#106	C₂³×C₆₇	1	4	yes	—
596	#106	C₂³×C₆₇	1	4	yes	—
597	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
598	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
599	#103	C₂³×C₆₇	1	2	yes	—
600	#103	C₂³×C₆₇	1	4	yes	—
601	#103	C₂³×C₆₇	1	2	yes	—
602	#103	C₂³×C₆₇	1	2	yes	—
603	#103	C₂³×C₆₇	1	2	yes	—
604	#102	C₂³×C₆₇	1	4	yes	—
605	#102	C₂³×C₆₇	1	2	yes	—
606	#102	C₂³×C₆₇	1	4	yes	—
607	#102	C₂³×C₆₇	1	4	yes	—
608	#102	C₂³×C₆₇	1	4	yes	—
609	#102	C₂³×C₆₇	1	4	yes	—
610	#102	C₂³×C₆₇	1	2	yes	—
611	#102	C₂³×C₆₇	1	2	yes	—
612	#102	C₂³×C₆₇	1	2	yes	—
613	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
614	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
615	#97	C₂³×C₆₇	1	2	yes	—
616	#97	C₂³×C₆₇	1	2	yes	—
617	C₂⁴	—	2	1	no	—
618	C₂⁴	—	2	1	no	—
619	C₂⁴	—	2	4	no	—
620	#41	—	2	4	no	—
621	#41	—	2	4	no	—
622	#41	—	2	8	no	—
623	#41	—	2	4	no	—
624	#41	—	2	4	no	—
625	#41	—	4	4	no	—
626	#41	—	4	8	no	—
627	#41	—	8	4	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
631	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
632	C₂×D₄	—	2	8	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	4	4	no	—
647	C₂×D₄	—	4	8	no	—
648	C₂×D₄	—	4	16	no	—
649	C₂×D₄	—	8	4	no	—
650	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
651	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
652	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
653	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
654	C₂×D₄	#41×C₆₇	1	4	yes	complemented
655	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
656	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
657	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	8	2	no	—
668	C₂²×C₄	—	8	2	no	—
669	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
670	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
672	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
673	SD₁₆	—	4	4	no	—
674	D₈	—	2	8	no	—
675	D₈	—	4	4	no	—
676	M₁₆	—	2	4	no	—
677	M₁₆	—	4	4	no	—
678	C₂×C₈	—	2	2	no	—
679	C₂×C₈	—	2	2	no	—
680	C₂×C₈	—	4	4	no	—
681	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
682	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
683	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
695	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
696	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
697	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
698	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
699	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
713	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
714	C₄²	—	2	4	no	—
715	C₄²	—	2	2	no	—
716	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
717	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
718	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
719	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
720	C₂³	—	2	2	no	—
721	C₂³	—	2	4	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	4	8	no	—
725	C₂³	—	4	2	no	—
726	C₂³	—	8	1	no	—
727	C₂³	—	8	1	no	—
728	C₂³	—	8	1	no	—
729	C₂³	—	8	1	no	—
730	C₂³	—	8	4	no	—
731	C₂³	—	8	4	no	—
732	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
733	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
734	Q₈	—	2	4	no	—
735	Q₈	—	2	2	no	—
736	Q₈	—	2	2	no	—
737	Q₈	—	4	2	no	—
738	Q₈	—	8	1	no	—
739	D₄	—	2	8	no	—
740	D₄	—	2	4	no	—
741	D₄	—	2	4	no	—
742	D₄	—	2	2	no	—
743	D₄	—	2	2	no	—
744	D₄	—	2	2	no	—
745	D₄	—	2	2	no	—
746	D₄	—	2	2	no	—
747	D₄	—	4	2	no	—
748	D₄	—	4	2	no	—
749	D₄	—	4	8	no	—
750	D₄	—	4	2	no	—
751	D₄	—	4	8	no	—
752	D₄	—	4	4	no	—
753	D₄	—	4	2	no	—
754	D₄	—	8	1	no	—
755	D₄	—	8	4	no	—
756	D₄	—	8	4	no	—
757	D₄	—	8	4	no	—
758	D₄	C₂×#41×C₆₇	1	4	yes	—
759	C₂×C₄	—	2	4	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	8	no	—
769	C₂×C₄	—	4	4	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	4	no	—
772	C₂×C₄	—	8	2	no	—
773	C₂×C₄	—	8	2	no	—
774	C₂×C₄	—	8	1	no	—
775	C₂×C₄	—	8	1	no	—
776	C₂×C₄	—	8	4	no	—
777	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
778	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
779	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
783	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
784	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
785	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
786	C₈	—	2	2	no	—
787	C₈	—	2	2	no	—
788	C₈	—	2	4	no	—
789	C₂²	—	2	1	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	4	no	—
792	C₂²	—	2	4	no	—
793	C₂²	—	2	4	no	—
794	C₂²	—	2	4	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	8	4	no	—
804	C₂²	—	8	4	no	—
805	C₂²	—	16	8	no	—
806	C₂²	#546×C₆₇	1	2	yes	—
807	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
808	C₄	—	2	1	no	—
809	C₄	—	2	1	no	—
810	C₄	—	2	1	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	4	no	—
813	C₄	—	4	2	no	—
814	C₄	—	4	2	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	2	no	—
818	C₄	#546×C₆₇	1	2	yes	—
819	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
820	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
821	C₂	—	2	2	no	—
822	C₂	—	4	4	no	—
823	C₂	—	4	4	no	—
824	C₂	—	8	2	no	—
825	C₂	—	8	2	no	—
826	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
827	C₂	C₆₇×#3585	1	1	yes	characteristic
828	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 ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3506	C₂	semidirect
2. C₆₇×#3496	C₂	semidirect
3. C₆₇×#3319	C₂	semidirect
4. C₆₇×#3318	C₂	semidirect
5. C₆₇×#3307	C₂	semidirect
6. C₆₇×#3306	C₂	semidirect
7. C₆₇×#3135	C₂	semidirect
8. C₆₇×#3099	C₂	semidirect
9. C₆₇×#3077	C₂	semidirect
10. C₆₇×#3062	C₂	semidirect
11. C₆₇×#3036	C₂	semidirect
12. C₆₇×#3008	C₂	semidirect
13. C₂×#442×C₆₇	C₂	semidirect
14. C₆₇×#2932	C₂	semidirect
15. C₆₇×#2897	C₂	semidirect
17. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
19. C₂×#131×C₆₇	C₂²	semidirect
22. #555×C₆₇	C₂²	semidirect
23. #553×C₆₇	C₂²	semidirect
26. #547×C₆₇	C₂²	semidirect
27. #547×C₆₇	C₂²	semidirect
29. #546×C₆₇	C₂²	semidirect
31. D₄²×C₆₇	C₂²	semidirect
34. #535×C₆₇	C₂²	semidirect
36. #533×C₆₇	C₂²	semidirect
41. #520×C₆₇	C₂²	semidirect
43. C₂×C₄×D₄×C₆₇	C₂²	semidirect
44. #491×C₆₇	C₂²	semidirect
45. #490×C₆₇	C₂²	semidirect
46. #489×C₆₇	C₂²	semidirect
47. #489×C₆₇	C₂²	semidirect
48. #485×C₆₇	C₂²	semidirect
49. #483×C₆₇	C₂²	semidirect
50. #482×C₆₇	C₂²	semidirect
51. #481×C₆₇	C₂²	semidirect
52. #478×C₆₇	C₂²	semidirect
53. #476×C₆₇	C₂²	semidirect
54. #474×C₆₇	C₂²	semidirect
55. #469×C₆₇	C₂²	semidirect
56. #468×C₆₇	C₂²	semidirect
57. #466×C₆₇	C₂²	semidirect
58. #465×C₆₇	C₂²	semidirect
59. #463×C₆₇	C₂²	semidirect
60. #461×C₆₇	C₂²	semidirect
61. #459×C₆₇	C₂²	semidirect
62. #449×C₆₇	C₂²	semidirect
63. #449×C₆₇	C₂²	semidirect
64. #447×C₆₇	C₂²	semidirect
65. #447×C₆₇	C₂²	semidirect
66. #442×C₆₇	C₂²	semidirect
67. #442×C₆₇	C₂²	semidirect
68. #435×C₆₇	C₂²	semidirect
69. #435×C₆₇	C₂²	semidirect
70. #428×C₆₇	C₂²	semidirect
71. C₂×#106×C₆₇	C₂²	semidirect
72. #423×C₆₇	C₂²	semidirect
74. #418×C₆₇	C₂²	semidirect
75. #417×C₆₇	C₂²	semidirect
76. #417×C₆₇	C₂²	semidirect
77. #416×C₆₇	C₂²	semidirect
78. #416×C₆₇	C₂²	semidirect
79. #416×C₆₇	C₂²	semidirect
81. C₂×#102×C₆₇	C₂²	semidirect
82. C₂×#102×C₆₇	C₂²	semidirect
83. #408×C₆₇	C₂²	semidirect
84. C₂×#97×C₆₇	C₂²	semidirect
239. C₂×D₄×C₆₇	#41	semidirect
406. #61218	C₆₇	direct (N × H)
415. #3506	C₂×C₆₇	semidirect
416. #3496	C₂×C₆₇	semidirect
417. #3319	C₂×C₆₇	semidirect
418. #3318	C₂×C₆₇	semidirect
419. #3307	C₂×C₆₇	semidirect
420. #3306	C₂×C₆₇	semidirect
421. #3135	C₂×C₆₇	semidirect
422. #3099	C₂×C₆₇	semidirect
423. #3077	C₂×C₆₇	semidirect
424. #3062	C₂×C₆₇	semidirect
425. #3036	C₂×C₆₇	semidirect
426. #3008	C₂×C₆₇	semidirect
427. C₂×#442	C₂×C₆₇	semidirect
428. #2932	C₂×C₆₇	semidirect
429. #2897	C₂×C₆₇	semidirect
430. C₆₇	#61218	direct (N × H)
432. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
434. C₂×#131	C₂²×C₆₇	semidirect
437. #555	C₂²×C₆₇	semidirect
438. #553	C₂²×C₆₇	semidirect
441. #547	C₂²×C₆₇	semidirect
442. #547	C₂²×C₆₇	semidirect
444. #546	C₂²×C₆₇	semidirect
446. D₄²	C₂²×C₆₇	semidirect
449. #535	C₂²×C₆₇	semidirect
451. #533	C₂²×C₆₇	semidirect
456. #520	C₂²×C₆₇	semidirect
458. C₂×C₄×D₄	C₂²×C₆₇	semidirect
459. #491	C₂²×C₆₇	semidirect
460. #490	C₂²×C₆₇	semidirect
461. #489	C₂²×C₆₇	semidirect
462. #489	C₂²×C₆₇	semidirect
463. #485	C₂²×C₆₇	semidirect
464. #483	C₂²×C₆₇	semidirect
465. #482	C₂²×C₆₇	semidirect
466. #481	C₂²×C₆₇	semidirect
467. #478	C₂²×C₆₇	semidirect
468. #476	C₂²×C₆₇	semidirect
469. #474	C₂²×C₆₇	semidirect
470. #469	C₂²×C₆₇	semidirect
471. #468	C₂²×C₆₇	semidirect
472. #466	C₂²×C₆₇	semidirect
473. #465	C₂²×C₆₇	semidirect
474. #463	C₂²×C₆₇	semidirect
475. #461	C₂²×C₆₇	semidirect
476. #459	C₂²×C₆₇	semidirect
477. #449	C₂²×C₆₇	semidirect
478. #449	C₂²×C₆₇	semidirect
479. #447	C₂²×C₆₇	semidirect
480. #447	C₂²×C₆₇	semidirect
481. #442	C₂²×C₆₇	semidirect
482. #442	C₂²×C₆₇	semidirect
483. #435	C₂²×C₆₇	semidirect
484. #435	C₂²×C₆₇	semidirect
485. #428	C₂²×C₆₇	semidirect
486. C₂×#106	C₂²×C₆₇	semidirect
487. #423	C₂²×C₆₇	semidirect
489. #418	C₂²×C₆₇	semidirect
490. #417	C₂²×C₆₇	semidirect
491. #417	C₂²×C₆₇	semidirect
492. #416	C₂²×C₆₇	semidirect
493. #416	C₂²×C₆₇	semidirect
494. #416	C₂²×C₆₇	semidirect
496. C₂×#102	C₂²×C₆₇	semidirect
497. C₂×#102	C₂²×C₆₇	semidirect
498. #408	C₂²×C₆₇	semidirect
499. C₂×#97	C₂²×C₆₇	semidirect
654. C₂×D₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3506	2
C₆₇×#3496	2
C₆₇×#3319	2
C₆₇×#3318	2
C₆₇×#3307	2
C₆₇×#3306	2
C₆₇×#3135	2
C₆₇×#3099	2
C₆₇×#3077	2
C₆₇×#3062	2
C₆₇×#3036	2
C₆₇×#3008	2
C₂×#442×C₆₇	2
C₆₇×#2932	2
C₆₇×#2897	2
#61218	67

Subgroups — C67×#61218 #30740469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61218 #30740469